Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects [1 ed.] 9781624170645, 9781624170638

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Electromagnetic Fields: Principles, Engineering

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Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

PHYSICS RESEARCH AND TECHNOLOGY

ELECTROMAGNETIC FIELDS

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PRINCIPLES, ENGINEERING APPLICATIONS AND BIOPHYSICAL EFFECTS

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Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

PHYSICS RESEARCH AND TECHNOLOGY

ELECTROMAGNETIC FIELDS PRINCIPLES, ENGINEERING APPLICATIONS AND BIOPHYSICAL EFFECTS

Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

MYUNG-HEE KWANG AND

SANG-OOK YOON EDITORS

New York

Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

Copyright © 2013 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Electromagnetic fields : principles, engineering applications, and biophysical effects / [edited by] Myung-Hee Kwang and Sang-Ook Yoon. pages cm Includes bibliographical references and index. ISBN 978-1-62417-063-8 (hardcover) ,6%1H%RRN 1. Electromagnetic fields. I. Kwang, Myung-Hee, editor of compilation. II. Yoon, Sang-Ook, editor of compilation. QC665.E4E555 2013 530.14'1--dc23 2012037318

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CONTENTS Preface Chapter 1

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Chapter 2

vii Earth’s Natural Electromagnetic Noises in a Very-Low Frequency Band: Their Deep-Seated Origin, Effect on People, Recording and Application In Geophysics Yury P. Malyshkov, Sergey Yu. Malyshkov, Vasily F. Gordeev, Sergey G. Shtalin, Vitaly I. Polivach, Vladimir A. Krutikov and Michail M. Zaderigolova Electromagnetic Interaction between Environmental Fields and Living Systems Determines Health and Well-Being Dimitris J. Panagopoulos

1

87

Chapter 3

Thermodynamics of Surface Electromagnetic Waves Illarion Dorofeyev

131

Chapter 4

Magnetic Field Originated by Power Lines J. A. Brandão Faria and M. E. Almeida Pedro

169

Chapter 5

Microwave Heating for Metallurgical Engineering Jingjing Yang, Ming Huang and Jinhui Peng

203

Chapter 6

Extremely Low Frequency Electromagnetic Field and Cytokines Production M. Reale and P. Amerio

239

High Frequency Induction Heating for High Quality Injection Molding Keun Park

255

Chapter 7

Chapter 8

Electromagnetic Characterization of Electrically Small Piezoelectric Antennas and Waveguiding Devices for Detection of Cancer-Related Anomalies in Biological Tissues Diego Caratelli and Alessandro Massaro

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283

vi Chapter 9

Chapter 10

Chapter 11

Chapter 12

Contents Electro-magnetic Field Induced Entropy Production in a Cell: Its Difference between Cancerous and Normal Cells Liaofu Luo and Changjiang Ding

309

An Evaluation of Neurotoxicity Markers in Rat Brains, Using a Pre-Convulsive Model and Exposure to 900 MHz Modulated GSM Radio Frequency María Elena López-Martín and Francisco José Ares-Pena

331

The Effect of Settlement Reoccupation on Electromagnetic Induction Data Sets in Archaeology Daniel P. Bigman

349

New Cooperative Effects in Single- and Two-Photon Interactions of Radiators with Electromagnetic Bath Nicolae A. Enaki

363

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Index

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421

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PREFACE In this book, the authors gather and present current research in the study of the principles, engineering applications and biophysical effects of electromagnetic fields. Topics discussed include the thermodynamics of surface electromagnetic waves; exposure to magnetic fields produced by power lines; microwave heating for metallurgical engineering; the effect of electromagnetic fields exposure on cytokines production; high frequency induction heating for high quality injection molding; electromagnetic techniques for non-invasive detection of malignancies in biological tissue; the entropy production rate in a cell under electromagnetic field; studies of cerebral activity in humans and in animal models after exposure to modulated radio frequency of mobile phones; electromagnetic induction data sets in archaeology; and single and two-photon interactions of radiators with electromagnetic bath. Chapter 1 – Earlier the Earth’s electromagnetic noise was attributed to atmospheric thunderstorms, but the concept that EM noise is of atmospheric origin has been proved to be inconsistent. There has been shown that most pulses are generated not in the atmosphere but in the Earth’s crust due to its continuous, highly-stable and strictly periodic movement. Such a movement, in the authors’ opinion, is caused by the eccentric rotation of the Earth’s core and shell. This paper is further development of the hypothesis. Many-year observations and review of the Earth’s EM noises in various regions of Eurasia have proved that principal regularities of noises’ spatial and temporal variations can be explained in full by deformation waves generated by the eccentric motion of the Earth’s core and crust. This paper also covers principles of designing the measuring tools to record and to monitor the EM noises’ spatial and temporal variations, as well as the research and methodological approaches to methods of recording the Earth’s EM noises in order to detect geodynamically active areas in the Earth’s crust. Here one can find examples of assessing the stress and strain state of rock massifs, monitoring the land sliding conditions of river banks and slopes, revealing geodynamically active areas along existing gas and oil pipelines in Russia including the Ural and Kuzbass regions. If deep-seated lithospheric waves detected by us really exist and manifest themselves in many geophysical processes on the Earth’s surface, therefore, their effect might be observed in human biorhythms as well. Each human being during his life span and the human race as a whole during its entire evolution have obviously been affected by lithospheric processes or, at least, by continuous and universal EM noise of the Earth. If so, one can expect its footprint to be seen in human life activity. The authors have analyzed data on 2,000,000 case of ambulance calls-out in Tomsk (Russia) over a period of 2000-2011 and many-year

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viii

Myung-Hee Kwang and Sang-Ook Yoon

observations on the child delivery rate in Tomsk and in Pribaikalye region that have resulted in revealing clear signals of effect of lithospheric processes to human life activity and wellbeing. The results obtained not only prove the existence of deep-seated waves generated by the Earth’s core but also convince us that constantly circulating waves affect the human wellbeing, birth and death and even “orchestrate” suicides. Chapter 2 – In the present chapter the authors present data showing the electric nature of both our natural environment and the living organisms and how the inevitable interaction between the two, determines health and well-being. The authors first give a brief theoretical background of electromagnetic fields (EMFs) and waves and delineate the differences between natural and man-made electromagnetic radiation. Apart from other differences, while man-made radiation produced by oscillation circuits is polarized, natural radiation produced by atomic events is not. The authors describe the electromagnetic nature of our natural environment on Earth, i.e. the terrestrial electric and magnetic fields, the natural radiation from the sun and the stars, the cosmic microwaves and the natural radioactivity. The authors note that all living organisms on Earth live in harmony with these natural fields and types of radiation as long as these fields are within normal levels and are not disturbed by changes, usually in solar activity. The authors then describe the electrical nature of all living organisms as this is determined by the electrical properties of the cell membranes, the circadian biological clock, the endogenous electric currents within cells and tissues, and the intracellular ionic oscillations. The authors explain how the periodicity of our natural environment mainly determined by the periodical movement of the earth around its axis and around the sun, implies the periodical function of the suprahiasmatic nuclei (SCN) - a group of neurons located above the optic chiasm - which constitute the central circadian biological clock in mammals. The authors discuss the probable connection between the central biological clock with the endogenous electric oscillations within cells and organs constituting the “peripheral clocks”, and how the central clock controls the function of peripheral ones in the heart, the brain, and all parts of the living body by electrical and chemical signals. The authors explain how cellular/tissue functions are initiated and controlled by endogenous (intracellular/trans-cellular) weak electric currents consisting of directed free ion flows through the cytoplasm and the plasma membrane, and the connection of these currents with the function of the circadian biological clock. The authors present experimental data showing that the endogenous electric currents and the corresponding functions they control can be easily varied by externally applied electric or magnetic fields of similar or even significantly smaller intensities than those generating the endogenous currents. The authors present two possible ways by which external EMFs like those produced by human technology can distort the physiological endogenous electric currents and the corresponding biological/physiological functions: a) By direct interference between the external and the endogenous fields and, b) By alteration of the intracellular ionic concentrations (i.e. by changing the number of electric current carriers within the cells) after irregular gating of electrosensitive ion-channels on the cell membranes. Finally, the authors discuss how maintenance of this delicate electromagnetic equilibrium between living organisms and their natural environment, determines health and well-being, and how its disturbance will inevitably lead sooner or later to health effects. Chapter 3 – The chapter is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, the

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Preface

ix

authors used dielectric and metal samples characterized by local and nonlocal optical properties. Thermodynamic properties of surface eigenmodes of plane interfaces are discussed. Various thermodynamic functions, different definitions of density of states and spectral characteristics of surface polaritons in equilibrium at the interface formed by vacuum and lossy medium are described and discussed. The generalized density of states is calculated based on the Barash-Ginzburg theory and dispersion relations for the surface states in different approaches. All formulas for thermodynamic functions are represented in terms of density of states. It is exemplified that different definitions of the density of states are identical in the case of dissipationless materials. The spectral functions and integrated over all frequencies thermodynamic characteristics and their temperature dependences are demonstrated. Chapter 4 – Danger to human health from living near to high-voltage power lines has been a matter of concern and controversy over the past years; exposure to magnetic fields produced by power lines has been suspected of increasing the risk of cancer. Guidelines, put forward by the International Commission of Non Ionizing Radiation Protection, have been established for safe public exposure to power-frequency magnetic fields. This chapter starts with electromagnetic field equations to explain how magnetic fields can be deleterious for human health, and how the operating frequency plays a decisive role for that matter. Next, an analysis of the magnetic field originated by the current-carrying conductors of a high-voltage single-circuit three-phase overhead power line is thoroughly developed. The analysis takes into account the effect of protective ground wires, the effect of earth return currents and, furthermore, incorporates the non-uniform character of the power line structure arising from conductor sagging between towers. For magnetic field evaluation purposes, matrix techniques are made use in order to implement multi-conductor transmission line theory –a key tool for this subject. Mitigation techniques usually employed to decrease magnetic field levels are also addressed, namely, mitigation loops with or without compensation capacitors. Graphical and numerical computation results concerning magnetic field evaluation are presented and discussed, not only for the fundamental power frequency of 50 Hz, but also for higher order harmonics, up to 800 Hz. In the latter case, balanced and unbalanced line loads are considered. Underground power cables do not have as a visual impact as overhead power lines. Nonetheless, they also originate a magnetic field above the ground surface. This aspect is also paid attention. Chapter 5 – As a sort of electromagnetic waves ranging from 300MHz to 3000GHz, microwaves have been widely used in wireless communication, radar, heating and sensing. Microwave heating is best known for heating food in the kitchen, and in the last two decades it has emerged as a ubiquitous tool in chemistry. Despite its broad technological importance, microwave heating remains an unpredictable tool because the detailed physics of the interaction between microwave and substance is poorly known. In this Chapter, the authors revisit the reflection and transmission of microwave by conducting medium. The authors show that when a large piece of metal is milled into particles and flours, it becomes a good microwave absorber. To reveal the mechanism behind this phenomenon, firstly, three models based on effective media theory, i.e., qusi-static model, equivalent parameter model and RC network models are studied. Then, a new equation is introduced to characterize the Debye and

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Myung-Hee Kwang and Sang-Ook Yoon

non-Debye relaxations under microwave irradiation. Some new physical phenomena including local field enhancement and temperature dependent relaxation time, etc., which exist in non-Debye materials can be explained by this equation. Finally, the authors show that the local field enhancement is a ubiquitous and nonlinear phenomenon in granular materials, which is relative to microwave power, boundary condition, constituent and micro-structure of the materials, etc., and this is the main reason that microwave assisted chemical reactions can take place at a much lower average temperature compared with conventional heating. Examples about the application of microwave heating in metallurgy engineering are given. These works lay a solid foundation for the development of microwave metallurgical engineering. Chapter 6 – Cytokines are proteins that interact with cells of the immune system in order to regulate the body's response to disease, infection, inflammation, and trauma. Once induced, cytokines help determine how the immune system should respond and to what degree, and their overproduction or inappropriate production can affect the immune response. Some cytokines act to make disease worse (proinflammatory), whereas others serve to reduce inflammation and promote healing (anti-inflammatory). The effects of Extremely Low Frequency (ELF) 50/60 Hz EMF, produced by many sources, e.g., transmission lines and all devices containing current-carrying wires, including equipment and appliances in industries and in homes, on human health remain unclear. There are many reports that ELF-EMF may modulate the immune response affecting human health. Studies of the possible health effects of EMF has been particularly complex and did not provide straightforward answers. Although the mechanism of this interaction is still obscure it has been shown that ELF-EMF can cause changes in cell proliferation, cell differentiation, cell cycle, apoptosis, DNA replication and expression. The effects of EMF may be useful and harmful depending on the intensity and frequency of the field, the period of exposure and the organism itself. A complete understanding of electromagnetic field effects on organisms helps in curing numerous illnesses as well as protecting from dangerous effects of electromagnetic fields. This review summarizes the effect of EMF exposure on cytokines production, although further studies are required to shed light on the mechanism by EMF regulate immune response influencing cytokines production. Chapter 7 – High-frequency induction heating is an efficient way to rapidly heat metal surface by utilizing a high frequency skin effect. Because the procedure allows for the rapid heating and cooling of mold surfaces, it has been recently applied to the injection molding in various purposes. This article introduces basic theory of the high-frequency induction heating, multiphysics simulation techniques of the induction heating and injection molding, and various industrial applications of high-frequency induction heating to high quality injection molding. Chapter 8 – The development of innovative and efficient electromagnetic techniques for non-invasive detection of malignancies in biological tissues is an important research topic for both the academic and industrial communities. In this paper, an extensive study on the electromagnetic characterization of electrically small antennas for detection of cancer-related anomalies is presented. In particular, after a thorough overview on the currently available medical approaches used to tackle the mentioned problem, non-invasive and minimally invasive sensing approaches based on the use of electrically small antenna sensors are discussed. The radiation properties of the considered micrometer antennas are accurately investigated by using dedicated locally conformal finite-difference time-domain (FDTD) and

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finite element method (FEM) modeling tools. The developed locally conformal FDTD procedure is based on the definition of effective material parameters accounting for the local electrical and geometrical properties of the structure under analysis. In this way, an enhanced numerical accuracy can be achieved over the conventional stair-case modeling approach. On the other hand, the adopted FEM tool is suitable for the accurate near- and far-field analysis of micrometer devices such as photonic crystals. The proposed study is aimed at the evaluation of cancer-risk levels and definition of detection criteria by means of theoretical approaches. Some examples of tailored wireless telemetry systems based on electrically small antennas are presented in the paper, and the relevant technology, manufacturing and circuital aspects discussed in detail. Chapter 9 – Entropy production is a thermodynamic quantity of fundamental importance for a living system. The general relations between entropy production，entropy flow and information flow are discussed. The entropy production rate in a cell under electro-magnetic field is calculated. The special efforts are focused on the comparison of two kinds of cells, healthy cell and cancerous cell. It is demonstrated that the ratio of the field-induced entropy production between cancerous and normal cells depends on a function of dielectric permittivity and specific electro-conductivity of two kinds of cells. In a wide range of dielectric parameter choice the field-induced entropy production for a healthy cell is higher than that for cancerous. Then, based on the comparative measurement of entropy production rates in a pair of normal cell (human breast epithelial cell MCF10A or hepatoma cell line HL7702) and cancerous cell (human breast cancer cell MDA-MB-231 or hepatic cell line SMMC-7721) under alternating electric field the authors proved that for both two cell lines the field-induced entropy production for normal cells is obviously higher than cancerous in a large range of field strength from 5 to 25V/cm which gives direct experimental support to above theoretical estimates. It means that the applied field may reverse the direction of entropy-information flow between two kinds of cells and therefore have some therapeutic effect for organisms. Chapter 10 – Studies of cerebral activity in humans and in animal models after exposure to the modulated radio frequency (RF) of mobile phones have often indicated alterations of normal physiology and signs of toxicity in the nervous system. In recent years, the authors’ laboratory has carried out consecutive experiments to investigate how exposure to radiation similar to that of mobile phones affects the cerebral activity of rats previously exposed to a state of pre-excitability in their neuronal activity. An experimental radiation system was designed, involving a standing wave chamber built to maintain constant electromagnetic parameters and provide stress-free exposure to nonthermal levels of radiation. Rats were given an intraperitoneal injection of a sub-convulsive dose of picrotoxin to create a pre-convulsive experimental model and then the animals were exposed to 900MHz GSM radio frequency in the radiation chamber for two hours. Afterwards, they suffered convulsions and showed marked increases in neuronal activity in the neocortex, paleocortex, hippocampus and thalamus. Clinical differences were also found in the electroencephalographic (EEG) signals and in c-Fos expression in the brains of rats exposed to modulated and unmodulated GSM radiation. The most marked effects of GSM radiation on c-Fos expression in picrotoxin-treated rats were in the limbic structures, olfactory cortex and subcortical areas, the Dentate Gyrus and the centro-lateral nucleus of the intralaminar nuclear group of the thalamus. Animals not

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treated with picrotoxin and exposed to unmodulated radiation presented higher levels of neuronal activation in cortical areas. Morphological examination revealed that most rat brain areas except the limbic cortex have shown an important increase in neuronal activation 24 hours after picrotoxin and radiation. Three days later, radiation effects were still evident in the neocortex, Dentate Gyrus and CA3, but had diminished in the limbic cortex (entorhinal and pyriform). During this period, glial activity increased, with convulsions observed in radiated rats treated with picrotoxin. The authors’ findings of neurotoxicity markers in a sub-convulsive model of rat brains exposed to radiation indicates how exposure to mobile phone radiofrequency fields may induce changes in brain tissue that is physiologically susceptible to electrical instability. These results suggest that the effects of mobile phones on at-risk populations should be thoroughly studied. Chapter 11 – This chapter compares results of electromagnetic induction surveys from two archaeological contexts, Drake’s Field and Southeast Plateau, located at Ocmulgee National Monument in Macon, GA. One is a single component area and the other a multicomponent area. This survey was conducted to understand large, landscape scale, human settlement patterns in an efficient, cost effective manner without disturbing the archaeological record. I carried out field tests using a soil conductivity meter in continuous data collection mode at a frequency of 12150 Hz. I collected 6 to 9 measurements per meter and spaced transects 1 m apart. The conductivity meter recorded more variation in apparent conductivity values (mS/m) for the reoccupied site (Southeast Plateau). The two data sets differed in interpretability of horizontal grey scale plots and single traces of apparent conductivity values. Drake’s Field resembled similar surveys of single occupation sites. I could interpret anomalies as specific features and patterned clusters of anomalies as buildings. However, 4,000 years of human reoccupation on the Southeast Plateau left a high density of archaeological remains including postholes, hearths, burials, storage pits, and garbage pits. The density of features results in overlapping electromagnetic signatures and anomalies cannot be attributed to specific feature types nor can the location of a specific anomaly be accurately determined. Despite the difficulty in interpreting electromagnetic data sets from reoccupied sites, an important recognition came from this comparison: archaeological sites containing multiple reoccupations yield a specific and recognizable electromagnetic signature. This signature reflects the complicated subsurface modifications made by humans throughout history and can be distinguished from contexts of single occupancy and presumably from unoccupied zones. Archaeologists could potentially use this method for rapid assessment of occupational intensity or length. Chapter 12 – Two types of resonances between the spontaneous and induced emissions by two- and single photon transitions of three inverted radiators from the ensemble are proposed to accelerate the collective decay rate of the entangled photon pairs generated by the system relative the dipole-forbidden transition. The influence of the bath temperature to such processes is studied. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipole-forbidden transitions of third atom. Second effect corresponds to the scattering situation, when the difference of the excited energies of two dipole-active radiators are in the resonance with the dipole-forbidden transitions of third atom. These effects are accompanied

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with the interferences between single- and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions.

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 © 2013 Nova Science Publishers, Inc.

Chapter 1

EARTH’S NATURAL ELECTROMAGNETIC NOISES: THEIR DEEP-SEATED ORIGIN, EFFECT ON PEOPLE, RECORDING AND APPLICATION IN GEOPHYSICS Yury P. Malyshkov1, 2, Sergey Yu. Malyshkov1, 2, Vasily F. Gordeev1, 2, Sergey G. Shtalin1, 2, Vitaly I. Polivach1, 2, Vladimir A. Krutikov 1 and Michail M. Zaderigolova 3 1

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Institute of Monitoring of Climate and Ecosystems, Siberian Branch of the Russian Academy of Science, Russia 2 OOO Emission, Tomsk, Russia 3 OOO Geotech, Moscow, Russia

ABSTRACT Earlier the Earth’s electromagnetic noise was attributed to atmospheric thunderstorms, but the concept that EM noise is of atmospheric origin has been proved to be inconsistent. There has been shown that most pulses are generated not in the atmosphere but in the Earth’s crust due to its continuous, highly-stable and strictly periodic movement. Such a movement, in the authors’ opinion, is caused by the eccentric rotation of the Earth’s core and shell. This paper is further development of the hypothesis. Many-year observations and review of the Earth’s EM noises in various regions of Eurasia have proved that principal regularities of noises’ spatial and temporal variations can be explained in full by deformation waves generated by the eccentric motion of the Earth’s core and crust. This paper also covers principles of designing the measuring tools to record and to monitor the EM noises’ spatial and temporal variations, as well as the research and methodological approaches to methods of recording the Earth’s EM noises in order to detect geodynamically active areas in the Earth’s crust. Here one can find examples of assessing the stress and strain state of rock massifs, monitoring the land sliding conditions of river banks and slopes, revealing geodynamically active areas along existing gas and oil pipelines in Russia including the Ural and Kuzbass regions. If deep-seated lithospheric waves detected by us really exist and manifest themselves in many geophysical processes on the Earth’s surface, therefore, their effect might be observed in human biorhythms as well. Each human being during his life span and the human race as a whole during its entire evolution have obviously been affected by

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2

Yury Malyshkov, Sergey Yu. Malyshkov, Vasily Gordeev et al. lithospheric processes or, at least, by continuous and universal EM noise of the Earth. If so, one can expect its footprint to be seen in human life activity. We have analyzed data on 2,000,000 case of ambulance calls-out in Tomsk (Russia) over a period of 2000-2011 and many-year observations on the child delivery rate in Tomsk and in Pribaikalye region that have resulted in revealing clear signals of effect of lithospheric processes to human life activity and well-being. The results obtained not only prove the existence of deepseated waves generated by the Earth’s core but also convince us that constantly circulating waves affect the human well-being, birth and death and even “orchestrate” suicides.

INTRODUCTION There is some immeasurable might in the Earth’s heart which is sometimes felt on the surface, and its traces appear everywhere…

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Mikhail Lomonosov, 1750

Pulse electromagnetic interferences were first discovered by an English pilot during the World War II. He heard whistling sounds in his earphones. Investigations started after this made researchers come to a conclusion that such interference relate to thunderstorms occurring in the atmosphere. Currently there still exists an established opinion that pulse radio noises in a very-lowfrequency band (VLF) are attributed to thunderstorm activities occurring in the Earth’s atmosphere, mainly in tropic latitudes, world’s thunderstorm centers [Alexandrov et al., 1972; Raspopov and Kleymenova, 1977; Remizov, 1985; Bashkuev et al., 1989]. Field pulses, socalled “atmospherics”, are considered to appear in the moment of the lightning discharge and to travel from the discharge point to the observation point via an earth-ionosphere waveguide. One can record two Earth’s natural pulse electromagnetic field (ENPEMF) components, i.e. a noise and a pulse component, at any point of the Earth’s surface. A noise component is attributed to weak lightning discharges and pulses having traveled around the globe many times, whereas a pulse component is attributed to stronger lightning discharges. The intensity of both signals, a noise and pulse ones, is constant neither in time nor in space. One can clearly see two peaks, a night and an afternoon one, in diurnal variations of ENPEMF. The night peak is explained by tropical thunderstorms and better conditions for radio waves propagation along the Earth-Ionosphere waveguide during a dark part of a day. The afternoon peak observed in summer time is attributed to local and equatorial thunderstorms getting stronger in hottest afternoons. In autumn and in winter the thunderstorm centers shift to the tropics for up to 2000 km that explains the ENPEMF intensity reduction in the Northern hemisphere and its increase in the Southern hemisphere in winter time. [Bashkuev et al., 1989]. This ENPEMF origin would seem to be reliably proved, rather reasoned and to be an undisputable fact. In the late 60-ties of the last century a professor A.A. Vorob’yov, Tomsk Polytechnic University, now deceased, introduced a term “Earth’s natural pulse electromagnetic field” (ENPEMF) to define this phenomenon. We will use more often the term «electromagnetic noise of Earth» or «EM noise». It was him who expressed a hypothesis that pulses can arise not only in the atmosphere but also in the Earth’s crust due to the transformation of tectonic

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Earth’s Natural Electromagnetic Noises in a Very-Low Frequency Band

3

energy into electrical energy [Vorob’yov, 1970; Vorob’yov, 1979]. According to the hypothesis named “Thunderstorm inside the Earth” an increased intensity of the pulse flux is expected to appear on the eve and at the moment of strong earthquakes. In the beginning of 1970-ties A.A. Vorob’yov created a research team that still exists and currently keeps working in Tomsk. The authors of this paper (Malyshkov, Yu.P., Malyshkov, S.Yu., Gordeev, V.F., Shtalin, S.G., Polivach, V.I.) are the team members. An idea that mechanic-to-electric energy transformation is activated a day before earthquakes was being developed in the end of the last century. [Sadovskii, 1982; Gokhberg et al., 1985; Gokhberg et al., 1988; Surkov 2000]. At present the number of publications has reduced because expectations for high efficiency of using the ENPEMF to predict earthquakes were not met. First doubts in the ENPEMF atmospheric origin appeared in the beginning of 1980-ties [Malyshkov and Dzhumabaev, 1987]. That time we put a question mark if it is particularly atmoshperics that determine diurnal and annual variations of the electromagnetic noises of the Earth because, on the eve of many earthquakes, we observed field intensity decrease instead of increase. Depending on a forthcoming event magnitude there was observed a decreased counting of pulses lasting from a few hours up to several days both at night and in the afternoon and in any season, during the summer and winter months. If the field intensity increased, one would think about additional pulse sources occurring in the epicenter of rock destruction. But reduction of the pulse flux generated perplexity. How could processes of “local” earthquakes preparation influence the regional and, moreover, world-wide thunderstorm activity? The more we kept our observations, the more we made sure that most pulses are continuously, not only a day before the event, generated inside the Earth’s crust (in the lithosphere) but not in the atmosphere. A mistake seemed to be made in the middle of the last century when the ENPEMF was being actively studied. That time research and direct finding of high intensity pulses made it possible to deduce an inference about thunderstorm origin of such pulses because the pulses actually came from world thunderstorm centers and were related to strong lightning discharge. But it was impossible to measure a pulses’ noise component because their amplitude was hardly higher than equipment sensitivity. Therefore the inference that powerful pulses are of the thunderstorm origin has been transferred, without reasonable justification, to a noise component as well that lead to a fatal error. We use the word “fatal error” not in vain because, to our mind, it is particularly a field’s noise component that contains most valuable data on earthquake preparation and other deep-seated processes occurring inside the Earth’s crust, and information about the Earth’s core motion. When defending the lithospheric origin of pulses one needs to explain their diurnal and yearly variations in a new light. Causes for such variations could be, inter alia, periodic changes in Earth’s crust motion. One can also observe periodicity in variations of tidal forces and the atmosphere pressure. However neither tidal forces nor the atmospheric pressure have strict diurnal and yearly variations and, thus, their variations cannot explain highly-stable diurnal and yearly periodicity inherent to the ENPEMF. Many references [Korovyakov and Nikitin, 1998; Avsyuk et al., 2001; Sidorenkov, 2002] consider a topic of possible shift of the Earth’s core relative to the geometric center of the planet. If the core really shifts, the Earth’s rotation, from our viewpoint, must inevitably result in pressure traveling from the center of the shifted core to the Earth’s shell. A zone of pressure starts shifting due to the diurnal rotation of the Earth and, when such a disturbance

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zone is traveling, it makes points on the Earth’s surface move together with it that generates diurnal variations in the Earth’s crust. Yearly shift of the crust generates yearly variations. We started considering such a mechanism of generation of diurnal and yearly variations of ENPEMF and seismicity in our preceding publications [Malyshkov et al., 2000; 2004; 2009]. The mechanism of appearing clear diurnal, semi-diurnal and yearly rhythms of the Earth’s crust movements attributed to the eccentric rotation of the Earth’s core and the shell is most thoroughly overviewed in our following publications [Malyshkov, Malyshkov, 2009, 2012]. This manuscript continues developing the hypothesis. It starts with a brief overview of data proving the inconsistency of the idea that an ENPEMF’s noise component has an atmospheric origin and then it lists principal arguments in favor of our hypothesis of the shifted core and its influence on many Earth’s spheres. The paper covers main regularities of generation of deep-seated deformation waves and their impact on geophysical processes occurring inside the crust. Then the paper gives description of specialized equipment (recording units) designed by our team to record the Earth’s natural pulse electromagnetic noises. Various modifications of recording units have been used and keep being widely used to monitor the ENPEMF 24 hours a day throughout Russia. They are designed to continuously record the ENPEMF parameters and to monitor geodynamic processes in the Earth’s crust, as well as to measure EM fields while carrying out geophysical prospecting. When being used to monitor EM fields on-line the recording units can be operated unattended applying the remote control of measurement modes and data exchange via radio, satellite and cellular communications. Their design and operational functions are described in publications that can hardly be accessed by wide audience and exist only in Russian. Therefore, one chapter of this paper is devoted to the units description to close the gap. In our earlier publication [Malyshkov, Malyshkov, 2012] we drew the attention to the probability of strong impact of Earth’s crust variations to human life, activity and well-being. Each human being, in the course of his/her life, as well as the human race as a whole, has obviously been experiencing a continuous action of lithospheric processes, at least, an action of any-time and any-place EM noise of the Earth. Rhythms of human life and activity must have a certain footprint of such an action. Search for evidences of the impact of the core and lithospheric processes on a human body is one of the main tasks of this paper. We have reviewed 2,000,000 cases of medical emergencies in Tomsk over 2000-2011and many-year data on a birth rate in the Baikal region and in Tomsk; the review corroborates our inferences. In addition to the fact that the review outcomes confirm the existence of deep waves generated by the Earth’s core, they also have convinced us that such constantly circulating waves affect the human well-being, birth and death and even “orchestrate” suicides. In its end the paper covers issues of application of Earth’s EM noises to reveal geodynamically active areas. It gives example cases of assessment of the rocks’ strain-stress state, monitoring of landsliding activity of mountainsides and shorefaces, and detection of geodynamically dangerous area along existing oil and gas pipelines in Russia including the Ural and Kuzbass regions. The methods proposed can be quite useful in solving many practical engineering geology tasks. The main goal we set for this paper is to get high-quality observational material and provide most trustworthy outcomes of observational data processing. Readers may blame us on presenting the excessive number of various graphs and figures, especially figures

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illustrating research data on human biological rhythms. We did it purposely thinking that someone from probable followers or opponents of our ideas can explain the data presented in the paper in a more logic and detailed way and, using graphs and figures in it, to find new arguments to support or counter our hypothesis. A probability that someone will be able to find new information on the Earth’s core motion in the human biological rhythms cannot either be excluded. It should be emphasized that up to now we keep explaining the variations we have identified in ENPEMF, Earth’s seismicity and human biological rhythms by mechanical processes related to the eccentric motion of the Earths’s core and shell, and by deformation waves generated in the lower mantle and traveling upwards to the daylight surface. To our opinion, such a mechanical model of processes pretty well explains observational results we got. However the lack of direct experimental measurements of mechanical waves makes us disquiet. Why has such a strong impact of mechanical waves on many geophysical processes been revealed not directly in the motion of the Earth’s crust? Has nobody noticed it? Maybe, has one been looking for badly? Perhaps, it might be the reason. But this is possible also in case if the Earth’s core generates not mechanical waves (or not only mechanical ones) but waves of other kinds as well. Such other kind waves of known or unknown origin can also have effects on various Earth’s spheres similar to that one that mechanical waves do. We keep the topic of origin of strictly periodic lithospheric and biospheric variations, that we identified, still open. However the fact itself, that wave processes directly related to the Earth’s rotation and playing an extremely important role in Earth’s spheres dynamics exist, is to our opinion obvious.

ECCENTRIC SHIFT OF THE EARTH’S CORE – IS A MAIN CAUSE OF DEEP-SEATED RHYTHMS OF THE EARTH’S CRUST MOTION, DIURNAL AND YEARLY VARIATIONS OF PROCESSES OCCURRING IN VARIOUS SPHERES OF THE EARTH Let us consider the facts that made us put a question mark on reliability and consistency of common notions about the atmospheric origin of Earth’s EM noises and then completely give up on this viewpoint.

1. Inconformity of ENPEMF Variations to the Atmospheric Mechanisms of their Generation Diurnal variations occurred in the VLF (very low frequency) band are commonly attributed to two reasons: better propagation of atmospherics during darkness hours and the afternoon increase in thunderstorm activity during the hottest hours in summer. VLF flashes and VLF spikes are also considered to be generated by lightning discharges in the band of very-low-frequency waves. A main argument for such an assumption refers to the fact that the diurnal variation exists. A model of the magnitude-constant world thunderstorm center located at the equator at a point corresponding to 17-18 hours of local time is used as a

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phenomenon model. In the course of the day this center, following the Sun, travels around the Earth along its equator [Bliokh et al., 1977]. Let us list the fact that contravene such an explanation of diurnal and yearly variations of Earth’s EM noises. 1) Both in winter and in summer single EM pulses recorded by different channels (N-S and W-E receiving channels) of the same recording unit do not come to the unit at the same, concurrent moments. Therefore such asynchronous pulses are generated by different independent sources and cannot be generated by the world thunderstorm center located to the South from the recording units. At the same time when reviewing long-term series of observations one can see that diurnal, monthly and yearly variations rather highly correlate with temporal variations of EM fields at both receiving channels. This situation is possible when there is a process that simultaneously involves big areas and activates many independent pulse sources and when the pulse sources are of a local origin, are at a few-tens-kilometer distance from a recording unit and the “work” of these pulse sources is synchronized by a disturbance zone traveling along particularly this area of the Earth’s crust. 2) There is a bigger number of stable peaks but not only two ones being a night and an afternoon peak. In addition to the peaks at 2 and 16 hours of local solar time there appear other peaks at 20, from 6 till 8, at 22 and 4 hours of local solar time. The position of peaks and valleys do not follow the shift of sunrise and sunset and is not subjected to the duration of the darkness and lightness hours of the day. 3) The afternoon peak attributed to local thunderstorms begins to appear in the Nearthe-Baikal area and in other regions in Siberia already in the second decade of March, long before the local thunderstorms occur and disappears in the second decade of December irrespective of the fact that the thunderstorm period in Siberia is over in the end of August. Moreover, the afternoon peak of ENPEMF does not just disappear as it can be expected according to the atmospheric hypothesis but, starting from September, is transformed and becomes the deepest valley that completely concurs with the afternoon peak. The obvious fact of the peak-to-valley transformation cannot be explained from the perspective of the atmospheric origin of Earth’s EM noises. 4) Patterns of EM noises’ diurnal variations for different months are repeated from year to year with an amazing stability. Not only main peaks and valleys in the diurnal variations of the ENPEMF exactly concur with accuracy to the minute but even small details in curves constructed for the same months but for different years coincide. Diurnal variations respond neither dry or rainy years nor thunderstormy or nonthunderstormy periods. That fact says that there exists a mechanism being much more stable than processes occurring in the atmosphere. The review of many-year observations of EM noises in various regions in Russia has convinced of occurrence of the common mechanism of ENPEMF generation but not of the two independent from each other causes as propagation conditions and periods of higher thunderstorm activity. 5) Correlation of readings taken from recording units spread at a distance of thousand kilometers proves the occurrence of a mechanism that manages the “work” of natural sources of EM fields in huge territories. The occurrence of such a global mechanism

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being the same for the whole Earth and running around the Earth as it rotates is obvious.

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2. Matching of the ENPEMF Spectral Distribution and Seismicity with Solar Tidal Waves and Suppression of Lunar Components Most important arguments for the hypothesis on the Earth’s core shift and its role in generation of periodic lithospheric waves have been obtained when we studied diurnal variations and the spectral distribution of ENPEMF and seismicity [Malyshkov, Malyshkov, 2009, 2012]. If diurnal fluctuations are assumed to exist, they have to induce earthquakes with a different probability in different hours of day. Variations of Earth’s natural EM noises and seismicity must correlate with each other due to being affected be one and the same process – diurnal motion of the Earth’s crust. Such a correlation has been identified basing on the review of 300,000 earthquakes occurred in the Baikal region over a period of 1962-1996. Time when the events occurred was converted from GMT to local solar time with regards to geographical coordinates of the event epicenter. Night and afternoon peaks appear to reveal themselves not only in each event occurred in the Baikal region but for all the events having the magnitude of higher and lower than 7. And the time when the peaks appeared matched pretty much with relevant peaks in ENPEMF variations. Earlier the publication [Malyshkov et al., 1998] presented facts of the occurrence of night and afternoon peaks for both the ENPEMF and events occurred in the North Tien Shan. Such a phenomenon is possible only if a common mechanism managing physical processes inside the Earth’s crust is at work. The occurrence of the common mechanism that manages ENPEMF variations and earthquakes can also be seen in spectral characteristics of long-term time series of these processes [Malyshkov, Malyshkov, 2009, 2012]. ENPEMF periodograms and seismicity periodograms have been constructed using minute values of EM field intensity over a period of September 12, 1997 till September 15, 2002 and hourly values of the number of events for 1971-1990, respectively. We have identified the exact match of main spectral bands of ENPEMF and seismicity. Diurnal, semi-diurnal, 8-hour and 6-hour frequency bands of EM fields match with each other up to six numbers including up to the fourth decimal place. Less reliable yearly components match up to the fourth decimal place as well. All the periodicities of ENPEMF and seismicity we identified are also observed in known spectra of tidal waves [Mel’ckior, 1983] спектрах The variations we observed match with variations of solar tidal waves up to the third, fourth decimal places. What surprises us mostly is that in our spectra no frequencies generated by the lunar gravity are observed. Neither ENPEMF spectra nor earthquakes spectra have even a show of frequencies related to the Moon’s revolution; and that is irrespective of the fact that the Moon’s gravitational effect (tidal influence of the Moon) is at least twice stronger than that of the Sun. In our spectra none of the seventeen main lunar tidal waves has a lunar component. Moreover, a thorough analysis has proved that lunar components are not just missed but they are suppressed by process acting in opposition to the gravitational effect of the Moon. Such a situation is possible only in case if:

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Yury Malyshkov, Sergey Yu. Malyshkov, Vasily Gordeev et al. 1) There exists a common, not discovered before, mechanism that manages ENPEMF variations and induces earthquakes. 2) All periodicities we identified in ENPEMF and seismicity variations in the Baikal region are not of tidal origin. 3) The mechanism generating geophysical rhythms relates to the daily and yearly rotation of the Earth and a one-way effect to the Earth (acting either outwards or inwards) created by an additional object which counteracts the Earth’s attraction to the Moon and the Sun.

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These regularities can be successfully explained by the assumption that such a counteracting object can be the Earth’s inner solid core shifted relatively to the geometrical center of the planet. The shift of the core can be caused both by the core’s stronger inertia than that of the less dense Earth’s shell (lithosphere) and by the screening effect of the Earth’s shell that reduces the gravitational attraction of the core by the Moon and the Sun. Following such an interpretation it would be more correct to say that it is the lithosphere that is shifted relative to the inertial core. Stronger attraction of the lithosphere in comparison to that of the core may perturb the symmetry of the Earth’s inner structure. A “clearance” between the lithosphere and inner core filled up with a molten liquid core becomes less on the side opposite to the direction of the Earth’s shell shift. The geometrical center of the inner core appears to be farther from the Moon and the Sun than the geometrical center за the planet.

Figure 1. Perturbation produced by eccentric motion of core and lithosphere. See text for explanation.

Now let us make this system move and rotate following the daily rotation of the Earth. Ahead of the Earth’s solid core and ahead of narrower clearance between the shell and the core, the melt starts being compressed and bulged in the direction opposite to the daily rotation of the Earth, resembling the work of a rotor pump. A higher pressure zone in the melt acts outwards to the mantle and deforms the mantle near the shifted core that creates a wave of mechanical strains traveling up to the surface and, when reaching it, will travel in strict accordance with the Earth’s revolution and in the direction opposite to the Earth’s daily rotation (Figure 1). Big arrows illustrate the direction of the Earth’s daily rotation and a small arrow shows the direction of motion of an observation station (Station Talaya) relatively to a higher pressure zone in the melt inside the Earth. Melt high pressure zone is shown in Fig. 1 by a convex spot.

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A strain wave traveling around the globe exactly within 24 hours will be like zones of compression and tension of the Earth’s crust changing each other in turn. Due to the shift the core appears to be farther from the Moon and the Sun than the Earth’s geometric center. And it produces forces that counteract the Moon’s and the Sun’s gravitational attraction and effects that suppress tidal forces in spectral ENPEMF and seismicity bands. When looking at results from the spectral bands review [Malyshkov, Malyshkov, 2012] one can hardly reject the fact of suppressing the gravitational effect, at least, the gravitational effect of the Moon.

3. Yearly Path of the Core Shift Relatively to the Earth’s Center and its Characteristics

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Thus, diurnal variations of EM noises of the Earth may be considered as a respond of the near-surface layers of the crust to traveling of a wave of strains produced by rotation of the Earth and motion of the shifted core. This strain wave looks as zones of compression and tension of the Earth’s crust changing each other alternatively during a day. Depending on a zone, a compression or a tension one, it will amplify or suppress processes of mechanic-toelectric conversion occurred in rocks or increase or reduce the amplitude of an EM pulse flux recorded by units. In polar coordinates the ENPEMF diurnal variations represent a distribution diagram of strains produced by the shifted core. A review of diurnal variations of mechanical stresses inside the crust makes it possible to determine a daily location of the Earth’s core and a value of its shift. Figure 2 illustrates a yearly path of core motion relatively to the planet’s geometrical center; the path has been constructed basing on a review of manyyear measurements of EM noises in the Baikal region [Malyshkov, Malyshkov, 2009, 2012]. One can see in Figure 2 that the inner core is never in the center of the planet, coming closest to it in April and September.

Figure 2. Yearlong path of motion of core inside Earth (pole view).

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It should be noted that Figure 2 is a two-dimensional pole view of core motion during a year. The core moves most likely along an elliptic orbit or along a more complicated close orbit, being similar to the analemma of the Sun, near the ecliptic plane. In Figure 2 one can see just a project of the orbit on equator plane, therefore, it should be taken into account when speaking about the remoteness of the core from the planet’s center. The plane of core motion is perpendicular to the equator plane and is at 45 to the direction to the Sun and yearly orbital motion of the Earth. The path along which the core moves during a year is asymmetric relatively to the Earth’s geometrical center. Most significant displacements of the core relatively to the center are observed in July-August and in February, and the shift in summer time is more significant than that in February. The Moon must also greatly affect the yearly path of the Earth’s inner core. Therefore the plane of the core shift orbit will not coincide exactly with a solid line (Figure 2) going through 16 and 2 hours. Being opposite in phase to the Moon, the core is moving along this line following a certain spiral, the occurrence of which particularly proves and explains the scattering of points in Figure 2. Judging by the scattering, turns of such a spiral have rather big diameter and the duration of each turn is equal to a lunar month. Following this logics one can assume that the core is shifted following the displacement of the Sun in the ecliptic plane. Therefore the core has to move to the Northern hemisphere during afternoon hours in summer time. Then in spring and autumn it, probably, shifts for a short time to the Southern hemisphere and winter it returns back to the Northern hemisphere but to the dark part of the Earth. The core must reduce the gravitational action of the Sun like that of the Moon, and like the Moon’s, the Sun’s gravitational effect is compensated by the core displacement. In our spectra we observe not the impact of the Moon’s and Sun’s gravitational effects to geophysical and biophysical processes, but the effect of combined action of the shifted core and the Earth’s rotation. The diurnal rotation and yearly revolution of the Earth take part in producing both tidal waves and waves we identified. That is particularly why, at the same time, one observes the exact match of frequencies related to the Earth’s diurnal rotation and the obvious mismatch of amplitudes of different components of “our” waves and relevant components of solar tidal waves. There appear many higher amplitudes frequencies. Spectral characteristics of geophysical fields we have reviewed contain many 6-, 8- and 21-hour bands and other frequencies which are not important for tidal waves because they are related to other generation mechanism. Unfortunately our records and calculations do not allow reconstructing a 3-D picture of yearly displacement of the core. The intuition suggests that the core should alternatively shift both to the Northern and Southern hemispheres during a year. Such a core shift is proved by significant increase and decrease of EM noises intensity in summer and winter, respectively. Most of the spectra we estimated and analyzed contain the 364.08 days band, not a band of expected duration of year of 365.25 days, showing off a high probability that the angular velocity of the core is higher the angular velocity of the Earth’s rotation by 1.1 degree per year. The core most likely moves intermittently along its yearly orbit; now it displaces relatively to the center when some forces are imbalanced, then it slows down its motion in the viscous melt when such forces become balanced again. The review of long-term series of ENPEMF variations allows us to make an inference about the intermittent motion of the core. Few days of EM noises higher intensity values usually alternate with few days of lower values. But in case of both higher and lower intensity values the shape of diurnal patterns and

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the shape of diurnal intensity variations remain the same. A period of such a low-frequency modulation of EM noise intensity can last from a few days up to a moth and is easily seen in ENPEMF records for any month. The ENPEMА spectra include processes of such periods as well. However, the periodicity of these processes do not coincide with main lunar tides (13.65 and 27.55 days), thus, they may hardly be attributed to the Moon’s gravitational effect. It should be noted that, as a rule, the diurnal pattern is disturbed only on the eve of forthcoming event [Malyshkov, Malyshkov, 2012]. According to our idea, it is caused by interlocking arrangement of adjacent blocks of the Earth’s crust that creates a massive non-mobile consolidated system consisting of few blocks. Because of its being bulky, the system is not able to respond wave processes produced by the eccentric motion of the Earth’s core and lithosphere. One could see it with half an eye that the shape of diurnal patterns resembles sea waves. Particularly this similarity has urged us to seeking for latitude effects which should reveal themselves while the core is moving in the melt. A characteristic feature of waves produced by a ship moving across sea is a distinctive arrangement of wave crests. When looking at them from the top one can see two lines of waves diverging from the snout of ship like “moustaches”. The “moustaches” are diverging at a certain angle (19.5°) to the direction of ship movement (a diverging wave). The wavetrain of diverging waves and ship movement direction creates an angle, a so-called Kelvin cone. This angle value is constant, is a ratio of phase velocity and group velocity of waves and is function of neither the ship speed nor the ship form. And one can see a system of transverse waves and a turbulent wake behind the ship. If the core is assumed to be next to the ecliptic plane in any season of the year, the occurrence of similar wave processes traveling from the core center can be expected. Disturbances have to decay as they are moving northwards and southwards away from the line of intersection of the ecliptic plane and the Earth’s surface. It also causes gradual delay of processes because any disturbance travels in a medium with a certain finite velocity. Thus the “swing” of diurnal ENPEMF variations is expected to become less and exposure of distinctive parts of the diurnal pattern is expected to be delayed as an observation point is moving away northwards. The core motion in a spherical space can hardly be compared to a ship moving across sea and to producing moustaches-like ship waves diverging from the core. However the occurrence of latitude effects and delay of diurnal waves when moving northwards were discovered during testing for our previous work [Malyshkov, Malyshkov, 2012]. In any case this fact can be considered to be established for summer time and midlatitudes of the Northern hemisphere. Moreover, an angle determined by using the delay time within the accepted accuracy appears to be equal to the Kelvin angle (19.5°). However, the logics suggests that the delay time of diurnal variations when moving away northwards or southwards should not remain constant yearlong, at least, for southern latitudes. So, when determining the delay time by two recording units located at different latitudes, we will most probably find out a complicated change of the delay time. If one of the recording units is placed, say, in a latitude between the equator and the tropic of Cancer, then, during the summer, the core moving to the Northern hemisphere will intersect this latitude. This recording unit and the unit located in more northern latitudes will happen to be on different sides from the core latitude, on different parts of the “moustaches” of ship waves, if they exist. Then, further displacement of the core to the Northern hemisphere will result in gradual reduction of the delay time down to certain minimum values. In the beginning of August the

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core starts moving back from the Northern to the Southern hemisphere. And the delay period starts getting longer and achieving certain maximum values, and then will remain constant for some time. However, for the time being all these are just assumptions to verify which a network of recording units placed in different latitudes of the globe is required. The paper authors hope that there are some people among the paper readers who are able to support such a research.

MULTI-CHANNEL GEOPHYSICAL UNITS FOR RECORDING THE NATURAL PULSE EM FIELD OF THE EARTH

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We used multi-channel geophysical recording units of various modification to get data on EM noises of the Earth presented in this paper. The units have been designed by the paper authors in the Institute of Monitoring of the Climatic and Ecologic Systems, Siberian branch of the Russian Academy of Science. The recording unit MGR-01 shown in Figure 3. is certified (Certificate № 24184), entered in the State Register of Measuring Tools under the reference number № 31892-06 and is allowed to be used in the Russian Federation.

Figure 3. Multi-channel geophysical recording unit MGR-01.

1. Pulse EM Field Recording Unit MGR-01 Since the spatial-temporal field of mechanical stresses in the crust there is complex, then, in order to receive signals from maximally possible number of natural sources of EM pulses, we used several field receivers in units of all modifications. Fig 4 illustrates a block schematic diagram of the multi-channel geophysical recording unit MGR-01. In its basic design the MGR-01 unit has 2 Channels to record a magnetic component H (2, 4) and one Channel to record an electric component (6) of the EM field. The channels are equipped with Antennae 1, 3, 5 and connected to the Control Unit 11, which, it its turn, can

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be connected to a personal computer via a COM port 12. Depending on tasks solved the MGR-01 unit can be fitted out with extra Channel (8) with Sensor (7) and GSM-modem combined with Power Unit Control (10). External antenna (9) is connected to the GSMmodem. The modem is designed to transfer data to a server via a GPRS channel. The power unit control powers off the MGR-01 unit when the external power supply reduces down to 10 V to protect a battery from being overdischarged. The Unit can be powered with an 12Vdirect-voltage external power supply or a battery of the same voltage. Antennae to receive a magnetic component of ENPEMF at the N-S (1) and W-E (3) receiving directions are magnetic ferrite antennae receiving a signal in a very-low-frequency band. The right-angle arrangement of the antennae allows getting a directional diagram similar to a round one. A differential capacitive sensor operating in a near-zone reception mode within a 500Hz – 100kHz band is used as Antenna (5) to receive an electrical component of ENPEMF.

1

2

3

4

5

6

7

8

9

10

11

12

27

Figure 4. Multi-channel recording unit MGR -01. Block schematic diagram: 1- antenna to receive a magnetic component H in North-South (N-S) direction; 2 – measuring channel (N-S); 3- antenna to receive a magnetic component H in West-East (W-E) direction; 4 – measuring channel (W-E); 5 – antenna to receive an electric component E; 6 – measuring channel E; 7 – sensor of extra channel; 8 – extra measuring channel; 9 – external antenna GSM; 10 – GSM/GPRS modem and power unit control; 11 – MGR-01 Unit control bock; 12 – buffer of COM port; 27 –devices not included into the basic design set and supllied on order.

The MGR-01 unit records ENPEMF parameters as it is described below. ENPEMF pulses generated by rock matrix at an observation point are received by Antennae 1, 3 and 5 and travel to the inlets of relevant Channels 2, 4, 6 where the pulses are amplified and filtered through a certain frequency band. Then pulses exceeding a reference voltage limit prescribed are summed up during a certain period of time. The amplitude of the first pulse that exceeds the reference voltage is recorded within the same period of time. When the time period prescribed is over, data are transferred from channels to the Control unit (11). All the recording unit channels are designed according to the same scheme but differ in amplitude-frequency response characteristics and filter tuning. The arrangement of a channel is shown in Figure 5. The analog signal goes from Antenna (1) to Pre-amplifier (13) where the output impedance of the antenna agrees with the input impedance of the first-cascade amplifier consisting of Attenuator (14) and Amplifier (15). The attenuator 14 attenuates the

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signal and then the amplifier 15 amplifies it by a fixed factor. The attenuation factor can be gradually adjusted (there are 266 attenuation steps) when tuning the recording unit. This is a way how a signal received by the first cascade is amplified.

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Figure 5. Block scheme of channel of field magnetic component: 1 – antenna; 13 – pre-amplifier of signal; 14 – first-cascade attenuator; 15 – first-cascade amplifier; 16 – band-pass filter; 17 – secondcascade attenuator; 18 – second-cascade amplifier; 19 – repeating amplifier; 20 –comparator unit; 21 – channel microcontroller.

In the second cascade the signal is amplified similarly to as in the first cascade, but here Attenuator (17) and Amplifier (18) are used. When leaving the first-cascade amplifier (15) the analog signal travels to the input of the band-pass filter (16) that passes the signal through a frequency band pre-set. Then the analog signal of a frequency band required goes to the input of second-cascade attenuation consisting of Attenuator (17) and Amplifier (18). And, after that, the signal amplified and filtered travels to inputs of Repeating amplifier (18) and Comparator unit (20). The comparator unit compares the amplitude of signals arrived to the reference voltage and, if the amplitude exceeds the reference voltage value, it forms rectangular pulses at its output. When the recording unit is being tuned, the microcontroller (21), following an operator’s command sent from a personal computer, sets up the value of comparator unit’s reference voltage and a signal attenuation step via the control block (11). Adjusting the reference voltage value allows deleting lower-amplitude pulses being, as a rule, tools and apparatus noises, anthropogenic interferences and low-informative natural background noises. From the comparator unit, rectangular pulses go to the built-in counter of the channel microcontroller (21) where they are summed up for a time increment set. The repeating amplifier (19) is designed to align the output of the amplifier (18) with the input of an analog-to-digital converter integrated into the channel microcontroller (21). The analog-to-digital converter is used to digitize an analog signal of the ENPEMF parameter measured. Such a signal digitized is used to determine and store data on the maximum pulse amplitude at the magnetic component channel and to store pulse shape at the electrical component channel. Thus the microcontroller (21) records the number of pulses arrived, the maximum amplitude of the first pulse or its shape for a given period of time and transfers this information to the control block (11) (see Figure 4). The control block (11), the block diagram of which is presented in Figure 6, controls the recording unit operation with a help of specialized software.

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Figure 6. Block diagram of recording unit’s control block: 12 – buffer of COM; 22 – controlling microcontroller; 23 – static random access memory (RAM); 24 – runtime clock and non-volatile memory; 25 – interface of external-timing reference to start measuring; 26 – read-only memory (ROM).

This software is stored in an electrically reprogrammable ROM (26). The software helps synchronize the operation of channels using a runtime у clock (24), program parameters of amplification paths of the channels mentioned above, take digital data out of the channels and store them in the RAM (23). The RAM size in its standard design is 1Mbyte but it can be enhanced up to 4 MBytes. The control block can be connected to the personal computer via the buffer of the COM port (12) that is supported by two standard interfaces – RS-232 and RS-485. The COM port is also used to transfer measurement data from a recording unit to the personal computer, to update the unit’s software and to set a measurement mode when tuning the recording unit before measurements. In the output of the ENPEMF recording unit the computer memory creates a file containing information including a calendar date and current time, channel number, the number of pulses arrived at this channel within a time period set and the amplitude or shape of the first pulse arrived at a given channel within a time period set. A time period (1 sec, 10 sec, 1 min, etc.) is programmed by an operator before measurements start. The control block and each measuring channel have their own software installed in the built-in electrically reprogrammable RAM of microcontrollers. This makes it possible to change the algorithm of data collection and pre-processing. To record ENPEMF characteristics, the recording unit is programmed for a mode of either continuous monitoring or field measurements to seek for structural and lithological heterogeneities in the Earth’s crust. Operating under a field measurement mode the recording unit initiates its measurement by a signal that has come from the interface of external-timing reference (25) to start measuring (Figure 6). One can connect a synchrosignal coming from a blasting machine or from a button on a control panel of the recording unit to this interface. A synchrosignal generated by a blasting machine is usually used to record the EM response to dynamic (impact) excitation of the Earth’s surface and to investigate short-term fast processes. First the command “fire” is initiated to set off a charge or start a shock hammer. After a while (a delay time) or immediately upon the command “fire”, the analog signals of rocks’ EM response to dynamic impact start being digitized at the E-component, as well as the number and the amplitude of pulses start being recorded at two H-channels. The delay time is set either by an operator or automatically by the moment when a signal exceeds the

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trigger level set by an operator during first trial actions to the object under observation. Here the EM response can be digitized with timing frequency of 2 Hz; 4 Hz; 8 Hz; 16 Hz; 32 Hz; 64 Hz; 128 Hz; 256 Hz; 512 Hz; and 1024 Hz. The digitizing frequency is set by an operator using a PC keyboard. Under this mode the recording unit can be fitted out with an extra acoustic channel to record vertical movements of the ground produced by the blast. A standard geophone СВ-5 or its compatible can be used for the purpose as a displacement sensor. Readings of the displacement sensor are also digitized during recording an EM response of rocks to the dynamic impact that makes it possible to correlate timing of arrivals of acoustic and EM signals and to explain and validate data better. When triggering the unit with a start button the EM field characteristics are recorded for a pre-programmed period of time. EM pulses the intensity of which is higher than the operation threshold preset by operator are recorded at two independent H-component channels and an E-component channel; the pulse amplitude is measured at the H-component channels. Pulses recorded at the E-component are also digitized that makes it possible to investigate the shape and spectral characteristics of the signal received by this channel. Thus ENPEMF characteristics are recorded and on-line monitored until the memory of the recording unit is completely full. The natural rhythmic motion of the crust is clearly observed when recording stations are tuned on a certain optimal sensitivity. Therefore, before starting measurements, one has to tune recording units programmatically on an optimal sensitivity according to a speciallydeveloped calibration worksheet depending on season and local solar time [Malyshkov et al., 2011].

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SIGNS OF THE EARTH’S CORE EFFECT ON HUMAN ACTIVITY AND WELL-BEING People have been aware that biological rhythms exist since ancient times. A rhythmic character of life on the Earth is so obvious and everyday that nobody notices it. Biorhythms started being studied in 1729 when a French astronomer Jean-Jacques d'Ortous de Mairan discovered that plant leaves kept their movement periodical even in full darkness. Later it has been discovered that biorhythms of living functions are so exact that they are often called a “biological clock”. A pioneer researcher of the impact of geomagnetism and solar activity rhythms on living organism conditions is a well-known Russian doctor and biophysicist A.L. Chizhevsky. He was the first who, basing on statistical data collected, demonstrated a close link of collective response of living organisms on oversubtle solar-induced alterations in the environment. A.L. Chihzevsky emphasized that the Sun’s periodical activity regulates when and how strong epidemic diseases would occur. His publications [Chizhevsky, 1924, 1930, 1968, 1976] considered epidemic processes, death variations and tree growth in details. He revealed that the solar activity affects the birth rate, marriage rate, the weight of new-born babies and the crime rate; it aggravates diseases especially cardio-vascular and nervous illnesses and disturbances of mind. Over the latest decades the world has shown a higher interest to studies of rhythmical processes occurring in the human body both in normal and pathological conditions. There has

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been collected a lot of data proving that diurnal and seasonal periodicity is typical of most physiological functions for both plants and animals. This keeps being true for many processes even if there is no obvious action of external sensor of time. One may assume that each molecule of any living organism including DNA molecules that store the genetic information has a mechanism of time keeping. The living body itself is considered to produce biorhythms. The interest to chronobiology issues is quite natural and understandable. Biological rhythms dominate in the nature and cover all life displays from subcellular structures and single cells up to sophisticated forms of behavior of a living organism, and even populations and ecological systems. They reveal themselves at each level starting from simplest biological reactions occurring in a cell and ending with complex behavioral response of a human being. Periodicity is an integral feature of a substance and a rhytmicity phenomenon is a universal one. Biological rhythms cover a wide range of time periods from milliseconds up to few years. Currently in a human body there occur many hundreds of physiological processes rhythmically altering in the course of time. Such processes have already been investigated but mainly the attention of researchers is attracted by and focused on studying diurnal and seasonal rhythms. And this is not by accident. In a complex hierarchy of variations, these rhythms, especially diurnal variations, act like a conductor of all rhythmical processes. The diurnal rotation and yearly revolution of the Earth, cyclic activity of the Sun, and revolution of the Moon cause the rhythmical alteration of the environment factors including temperature, sun lighting, relative air humidity, barometric pressure, electric and EM processes occurring in the atmosphere and lithosphere, space radiation and gravity. In the course of evolution the human being and other living organisms (plants and animals) have adopted a certain rhythm of life caused by rhythmical alterations of geophysical characteristics of the environment. The evolution has fixed human biorhythms genetically. The diurnal rotation of the Earth causes diurnal rhythms in living creatures. The Earth’s yearly revolution around the Sun alters seasons and causes yearly rhythms of biological objects. Thus any living creature is a complex of many rhythms with various characteristics. The duration of many biorhythms including diurnal, seasonal, yearly, lunar and tidal variations in bioobjects’ life activities is equal to the duration of relevant geophysical cycles. Due to such rhythms the periods of the living organism’s hyper metabolism and highest activity match with most favorable external conditions, and time of day, month and seasons. According to the degree of their response to external conditions, biorhythms are divided into exogenous (external) and endogenous (internal). Exogenous rhythms, being biochemical processes, completely depend on environmental variations. Endogenous rhythms are slightly dependent on the environment and mostly caused by processes occurring inside the living body such as heat beating, breathing, blood pressure, mental activity and sleep intensity and other. Circadian rhythms hold a central position in rhythmical processes occurring in living organisms. Such circadian rhythms are congenial and endogenous, i.e. caused by features and qualities of the body. A period of circadian rhythms lasts for 23-28 hours and 23-25 hours for plants and animals, respectively. Because living bodies usually live in environments that cyclically vary their properties and characteristics, the bodies’ rhythms are caught by such environment cyclic variations and become diurnal. Diurnal rhythms cover the human body that is a uniform system of interaction of organs, tissues and cells. The integration of the

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environment and the body reveals itself in the fact that peaks and declines of physiological processes coincide with certain hours in day. Due to getting adapting to rhythmical variations in environment properties, a human body is physiologically preparing itself to being awaken and active even when the body is sleeping. And vice versa, the human body gets ready for sleeping long before falling asleep. Circumannual rhythms having a period of 10-13 months are seasonal or yearly rhythms and considered to be caused by the Earth’s revolution around the Sun and be produced by seasonal variations in the environment like length of light hours, air temperature and amount of precipitations, etc. These rhythms are often observed in laboratory conditions and their period is not stable. The difference between circumannual and environmental rhythms bears off the evidence of their endogenic origin. This type of rhythms is supposed to form in progress of natural selection and to be firmly adapted in the body. Yearly rhythms are typical of all physiological and psychological functions. Psychical and muscular irritability of people is much higher in spring and in the beginning of summer than in winter. Metabolism, blood pressure and the heart rate change during a year. The heart rate is lower in spring and autumn, and becomes higher in winter and summer. The human being’s fitness to work also follows the circumannual rhythm, being highest in autumn. Seasonal rhythms are observed in any living body in any area from polar to tropical ones. Yearly rhythms are also seen in migrations and movements of birds and animals, winter and summer hibernations, nesting and hole digging. To the researchers’ opinion, lunar, lunar-diurnal, lunar-monthly and tidal rhythms correspond to the monthly lunar phase, lunar-diurnal and lunar-monthly rhythms lasting for 24.8 and 29.5 days, respectively. Such rhythms examples can be the periodicity of an insect coming out of its pupa-case and menstrual cycles and etc. Tides depend on the motion of the Moon and, in turn, life of onshore plants and animals depends on tides. Tidal rhythms reveal themselves in periodicity of mobility of animals, opening of shellfish’s valves and vertical distribution of plankton in a water column. Even animals living in aquariums preserve the tidal rhythms that indicates the internal nature of biorhythms. Weekly and monthly rhythms last for 7 and 30 calendar days, respectively. They reveal themselves in variations of motor activity and fluctuations of mood and general state. One assumes that biorhythms do not match with periodic natural processes but are produced by the human being himself in the course of the evolution and historical development. Thus a social (exogenous) component – alteration of work and rest, following which human body’s functional features and characteristics vary - is clearly seen in weekly rhythms. There are few-year rhythms, for example, a periodicity of biological processes related to eleven-year solar cycles. Such 11-year cycles are considered to have an impact on the illness and death rate, functional state of the human nervous system, bursts of injurious insects and the crop yield. As state-of-art researches have proved that human biorhythms keep varying through the age cycle entirely. So, a biorhythmical cycle of new-borns and babies is very short, an active and a relaxation phases alters each 3-4 hours. Moreover, it is almost impossible to determine a chronotype (being a “skylark”, “pigeon” or “owl”) of children at the age of 6-8 years. As a child gets older, cycles of biorhythms gradually become longer and gain a character of diurnal biorhythms by his/her sexual maturation. At the same time he/she obtains his/her chronotype that determines his/her biorhythms during his/her life entirely. The human biorhythms are most stable at the age of 20 till 50. When a human being is 50 and older the biorhythm

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structure becomes less frank. A night “owls” get features of early “skylarks”. One of the most obvious and unpleasant display of unstable biorhythms of elderly people is insomnia. The activity phase becomes shorter and a relaxation phase becomes longer that is shown up as hypersomnia. Most rhythms are formed at very early stages of an individual development. So diurnal variations of a baby’s various functions activity are observed long before his/her birth, they can be recorded already in the second half of pregnancy. It should be mentioned that the nature of periodicities of biological systems is not completely clear. Inferences about mechanisms of generating and sustaining the rhythmicity of functional activities of living organisms are often speculative and theoretical. Questions about causes of occurrence and disturbance of human biorhythms are far from being answered and need to be thoroughly investigated. When investigating the periodicity of geophysical processes and having found evidences of occurrence of deep-seated lithospheric waves, we thought that these waves can also affect biological processes like any other external environmental factor. Reading through publications made us be amazed that they contain just light hints on lithosphere and biosphere interactions. Most attention is paid to investigating the apparent fact of periodic effect of the Sun and the Moon. Not less significant, sometimes even more powerful energy processes occurring just under man’s feet are not considered and not analyzed at all, moreover, they are ignored as factors being able to affect the rhythmicity of living bodies including a human being. The lack of methodologies and ways of monitoring lithospheric processes can explain such “unfairness” to deep-seated processes. There are no data on processes occurring in the Earth interior except for tidal waves showing off mainly the Moon’s impact and earthquakes and volcanic eruptions already occurred. But earthquakes and eruptions are quite rare events and they disturb the rhythmicity of life. Impacts they make on living bodies is still discussed but inferences resemble more exotic hypothesis than scientific facts. If our hypothesis about a possible link of EM noises with the eccentric motion of the Earth’s core and shell is right, then the noise intensity can be a unique and natural indicator of Earth’s interior movement. Maybe the clue is in periodicity and stability of main rhythms of nature and their alignment with the environment? Investigating the rhythms of EM noises and seismicity we have found diurnal, seasonal and yearly rhythms being main ones in life on the Earth. Perhaps it is particularly this “immeasurable power being hidden in the Earth’s heart” that orchestrate life and death on the Earth? One can probably find answers to such questions by correlating spectral characteristics of lithospheric processes with references for biorhythms. A good overview of available published evidence and various manifestations of rhythms in living and nonliving nature is given, for instance, in [Beri, 2010; Boyarsky and Desccherevsky, 2010; Sidorin, 2010]. However the first meet with rhythmology, being a new subject for us, depressed us. References suggest so big number of all kinds of periodicities, the trustworthy and relevance of which give rise to doubts, that we give up this intention. Moreover, just match of these or those frequencies with characteristics of lithospheric processes we found is not enough. In case of a link between biorhythms and deep-seated processes, there not only frequencies of main periods, but also amplitudes of different frequencies, should match in spectral characteristics. Therefore we decided to carry out a comparative analysis by reviewing man’s

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life activity characteristics we are interested in. By that time we had already had software required to do this. In order to solve the task set we used objective and available statistical data on human activity assessment, particularly data on the birth rate and the rate of ambulance calls-out. The ambulance calls-out were sorted out for ones done for children, men and women, as well as because of cases of death, suicides and pregnancy abnormality. These data are usually recorded by relevant departments and they actually reflect the psychological state and health status of a human being. Such criteria seemed to be interesting and catching because they, compared to other criteria, are least defined by human life schedule and happen regardless of his/her will or wish. A social (exogenous) component, a weekly rhythm of work and rest, is naturally observed in man’s biorhythm. Yearly and seasonal variations of human life activity can also be greatly affected by public holidays, changing hours for winter and summer time. In case where it was important we used time series of those years during which the hours for winter and summer time were not changed. Before 1980 the legal time used in the territory of Russia (the former Soviet Union) was 1 hour ahead of the solar time. All the data on the birth rate and ambulance call-out rate, both in case of switching the hours for summer and winter time and not switching, were recalculated according to the solar time with regards to the geographical coordinates of communities. When reviewing the data we did not confine ourselves with just correlation of frequencies and amplitudes of different periodicities, but tried to find evidences of a wave character of lithospheric and biospheric processes and explain what caused waves to change their directions of movement; we correlated the shape of waves that determines the rhythmicity of the phenomena investigated and possible direction of such waves movement, etc. We published our first outcomes of the analysis of biospheric-lithospheric interactions in 2002-2003 [Malyshkov et al., 2002; Malyshkov, Malyshkov, 2003]. More details of that can be found in the publication [Malyshkov, Malyshkov, 2012]. This paper mostly presents new data that have not been published yet. Periodicities of EM noises of the Earth are calculated as per minute values of EM field intensity for a time series of June 12, 1997 till September 15, 2002. It should be mentioned that there were some interruptions in operation of ENPEMF recording units. The lack of records was covered with data recorded at the same time of the nearest day. In case of longer periods of data lack we used the arithmetical mean value for the same calendar dates from preceding or next following years. Total lack of data is 20% and less. Seismicity periodograms were calculated using hourly data of about 3,000 events occurred in the Baikal region over a period of 1971 - 1990. [Earthquake bulletin ..., 19701975; Seismicity materials…,1976-1991]. Time when the event occurred was converted from MGT into local solar time with regards to geographical coordinates of the event epicenter. In order to review the birth rate we used data form a birth log book of a maternity hospital in the city of Angarsk (Russia) over a period of 1974 - 1980. These rather “old” data were selected consciously in order to minimize data distortion due to medicines used for augmentation of labor. That time deliveries were registered each 5 minutes. Therefore diurnal series missed 288 values, but not 1440 values (number of minutes in day). Before 1981 the time was not switched for summer or winter in Russia (in the former Soviet Union) that highly enhanced the trustworthiness of the human life activity analysis.

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The review of totally 1,998,000 cases of ambulance calls-out in Tomsk over a period of August 21, 2000 till September 30, 2011 (minute values) has resulted in spectral bands of ambulance calls-out and diurnal and yearly variations. This number includes:       

794,228 cases of ambulance calls-out for women (November 1, 2004 - September 30, 2011); 558,150 cases of ambulance calls-out for men (November 1, 2004 - September 30, 2011); 702,365 cases of ambulance calls-out followed by taking sick people to hospital; 31,838 cases of ambulance calls-out for children; 26,470 cases with the death diagnosis; 18,600 cases of pregnancy abnomalies that could be determined as abortions; 10,170 cases of suicides including parasuicides and pseudo suicides.

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1. Diurnal and Seasonal Variations of EM Noises of the Earth Let us start seeking for signs of lithospheric-biospheric interactions with considering the diurnal variations. First of all one should consider most characteristic features of diurnal variations of EM noises revealed by many-year observations on the Talaya station in the Baikal region. Figure 7 illustrates diurnal variations of ENPEMF for January as an example. Figure 7 а shows mean minute values of EM noise intensity for each day in January for a 4year period, totally being plotted 1440 mean values for 124 January days for the years specified in the figure. Let us repeat the curve in Figure 7 а three times to visualize the shape of a diurnal wave (Figure 7 b). Just a first glance at EM diurnal variations is enough to notice the wave nature of them. We see that the curve resembles a profile of a moving wave. If such a wave is assumed to have a steep wave front and a sloping tail edge, then one may propose that the waves moves from the left to right relatively to an observer. The maximum intensity is recorded from 2 till 4 a.m. of local solar time. Thus, particularly during this period of time, a recording unit located in the Baikal region gets into the zone of tension of the Earth’s crust and is at a minimal distance from the shifted core. A zone of maximum compression of the Earth’s crust (consequently, being at a maximum distance from the core) is at 4 p.m. of local solar time. One can see two characteristic points more in Figure 7, being at 8 a.m and 8 p.m. Particularly during these hours the compression zone alters the tension zone. Let us do similar conversion of EM noise diurnal variations for other month of year (Figure 8). One can see that a disturbance wave changes the direction of its motion twice. From November till March it moves from left to right and from May till September – from right to left. Judging by Figure 8 the wave changes its motion direction in April and in October. Both diurnal variation patterns and intensity of EM noises in April almost exactly match with those in October. In these two months, the wave seems to move in turn away from and toward the observer.

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Figure 7. Diurnal variations pattern of EM noises of the Earth in January (а) and the wave shape repeated three times to make it more visual (b).

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We see almost the same characteristic points on the time scale for each month of year where processes are significantly changed (at about 2, 16 and 6, 18 hours). Having a closer look at diurnal variations makes you think that they have been produced by a common mechanism which is at work all the year around. In Figures 7 and 8 one can notice several axes of symmetry for a diurnal pattern. So, rotating single parts of the diurnal pattern around vertical and horizontal axes makes us sure that they are mirror reflexions of the other pattern parts. For example, a mirror rotation matches a tension zone with a compression zone. A January diurnal pattern is nothing else but a smaller mirror reflexion of the diurnal pattern recorded in July, like diurnal patterns of April and October. This fact validates our assumptions that the processes considered occur in a spherically closed space that has several axes of symmetry. Let us list characteristic features of EM noises of the Earth which are easily seen when looking at Figure 8:      

It is apparent that disturbances producing the EM noise variations are of the wave nature; There exists a certain direction of traveling of the disturbance, altering in April and October; There are characteristic hours (at 2; 6, 16 and 18 h of local solar time) in a day during which the processes dynamics apparently changes; There are vertical and horizontal axes of symmetry for some parts of the diurnal pattern; The difference in the waveforms of daily variations is the greatest between winter and summer days and the smallest between April and October. The highest sub-diurnal EM noise peaks are times the minimum values in any month of the year.

Let us try to understand these peculiarities of diurnal variations of the Earth’s EM noises according to the mechanism of eccentric rotation of the Earth’s core and crust and the occurrence of deep-seated deformation waves we assumed. Figure 9 shows the yearly orbit of the Earth relatively to the Sun and the direction of the Earth’s rotation.

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Figure 8. EM noises diurnal pattern, averaged per years given in parentheses, for different months.

021282.

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During a winter half-year period, since November to March, the maximum intensity in EM noises is recorded at night hours with its maximum intensity at approximately 2 a.m. (Figure 8). So, at this time of the year the Earth’s core is in the unlit side of the Earth where the zone of tension stress is produced. Such zones are shown on the Earth’s contour with bold curves in Figure 9. Arrows near the curves show the direction of the Earth’s surface “running up” onto the disturbed zone due to diurnal rotation of the Earth’s shell. In April and October this zone moves to the midnight period, and then it goes to the sunlit side of the Earth and is recorded at approximately 16.00 hours of the local solar time. Let us locate the observer at a certain point of the space, for example, in the center of the picture, in the point of the Sun location. Let us review how the diurnal variation pattern will change for such an observer in different seasons of the year. In winter andsummer months the processes will look diametrically opposite for the observer who looks at the Earth from the side of the Sun. In winter months the tension area will stay in the Earth’s unlit side not seen by the observer. The Earth’s shell will be rolling onto the tension zone, as if moving from the right to the left. Thus, the wave produced by the compression zone in front of the core will have the opposite direction of propagation. It will be moving from the left to the right, just as we see it in Figure 7. In summer the observer looking at the Earth from the side of the Sun will see the tension zone in the part of the Earth staying in the day-light. Earth’s shell in the area where the electromagnetic noise registration point is located will be moving to the maximum tension zone at 16.00, moving from the left to the right. Thus, in summer and winter the diurnal variation must not only turn from its maximum to its minimum, but also the direction of disturbance wave propagation should change for the opposite one. In April and October the core is still in the unlit side of the Earth, and moving up the annual path crosses line 0-12 hours of solar time (ref. Figure 2). That is why the maximum disturbance during these months is registered sharply at midnight. A more demonstrative picture of the Earth rotation versus the slowly-moving displaced core and the Earth’s crust tension zone is shown in Figure 10. Arrows in Figure 10 indicate the direction of the Earth rotation and relocation of the observation point versus the disturbed zone. Naturally, the disturbance zone itself is also moving within a year, in accordance with the annual motion path of the Earth’s core, but in shorter time periods these displacements are small relatively to the speed of the diurnal rotation of the point where the noises are recorded. Let us note that if the Moon did not have any impact on the Earth’s core, the date of the core displacement through the line of 0-12 h, 6-18 h in the yearly variation (Figure 2) and changes in the direction of the core movement in early August and early February would fall on one and the same calendar days. However, non coincidence in the lunar and solar calendar brings about certain dispersion of these dates in different years. This is one of the reasons for dispersion of points in Figure 2, blooming of schedules of diurnal and annual variations in electromagnetic noises received via the averaging of many-year observations.

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Figure 9. Yearly orbit of the Earth and direction of Earth’s core displacement in different seasons. Clarifications are given in the text.

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The figures also explain the non coincidence which we observed in the changes of diurnal variations with dates of solstices, equinoxes, aphelion point and perihelion point of the Earth. This is linked with the fact that the identified route of annual core movement (Ref. Figure 2) is displaced versus the geometric center of the planet and is located angle-wise to the direction towards the Sun. The displacement and the angle change the dates of main changes in annual variations of diurnal rate for the later periods, while the bend-over points are shifted to the postmeridian and post-midnight time.

Figure 10. Location of Earth’s core and tension zone in summer and winter. The time scale shows the observation point (station Talaya) relatively to slowly-moving tension zone of Earth’s core at various hours of day.

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If the core moved not following the path which we found but always stayed at the line 012 h of solar time, then in the diurnal variations there would always be specific points - just at 0, 12, 6 and 18 h of the local solar time. In this case in winter (Figure 10) our observation point would stay in the zone on the maximum tension of the Earth’s crust (maximum intensity) at 0 h of local solar time. Then, from 0 to 6 h the observation point would move away from the Earth’s crust tension zone, while from 6 to 12 h it will move closer to the compression zone, to the minimum of EM noises intensity. After 12 h it would move away from the compression zone and again enter the tension zone reaching the maximum of noise intensity by 0 h. As we see in Figure 8, practically full match of the points characteristics in the diurnal variations from 0, 12, 6 and 18 h is observed in April and October, when according to our data the core, in its annual displacement versus the planet center, crosses the 0-12 h line. However, at the same months the core moves from the shadow to the sunlit side of the Earth. Such transition, most probably, happens not instantaneously but takes some days in spring and autumn. Under the influence of the Moon the core, during these transition days, can come back to the unlit part of Earth. That is why the diurnal variations contain the characteristic elements typical of both winter and summer diurnal variations. Occurrence of two peaks and two valleys in EM noise diurnal variations during these days apparently relate to drastic changes in flowing the liquid melt around the core. If during winter and summer months the liquid melt flows outside the core, then during spring and autumn months the core can probably be inside the flowing stream of the liquid melt. Under such flowing of the melt stream around the core the high-pressure zone will appear both ahead and behind the obstacle (the core). Therefore there appear two tension zones and, consequently, two maximums and two minimums of EM noises. It cannot be excluded that particularly during these days the Earth’s core moves away from the Northern to the Southern hemi-sphere. Then in the beginning of summer, adhering to the ecliptic plane, the core moves back to the Northern hemi-sphere but to the lit side of the Earth. The core is closest to the geometric center of the planet in the end of January – beginning of February. Minimal values of the EM noise intensity are recorded particularly during this period, and the distribution diagram of mechanical stresses in the Earth’s crust plotted by EM noise diurnal variations is similar to a circular diagram (Figure 11). If it is so, the solid core is shifted to the Northern hemi-sphere during most time of year, coming closest to the planet’s geometrical center in the end of January from the unlit side of the globe. The core is at the greatest distance from the Earth’s center in the end of July. This time the core is displaced to the meridian corresponding to 16 h of local solar time. We understand that our description of the processes occurring inside the Earth is approximate. It is based rather on intuition and indirect facts then on research and testing data. We hope that our naïve and possibly mistaken ideas will cause more thorough and theoretical investigation of the mechanism of generating the wave processes in the Earth’s lithosphere and biosphere.

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Figure 11. Polar diagrams of averaged (over 1997-2004) and smoothed diurnal ENPEMF variations [Малышков, Малышков, 2009, 2012].

2. Diurnal and Seasonal Variations of Ambulance Calls-Out Thus, we have considered main regularities of formation of wave processes in the Earth’s lithosphere on the example of EM noises of the Earth. Let us see if such regularities reveal themselves in rhythms of human health and life activity. Now we will perform a similar analysis of available statistic data on ambulance calls-out in Tomsk (Russia). Figure 12 illustrates daily variations in ambulance calls-out intensity (average number of calls per one minute) in Tomsk based on the analysis of 1,998,000 calls to the ambulance service over the period from August 21, 2000 to September 30, 2011. Figure 12a shows how daily variations in number of calls vary yearly from month to month. For each month of the stated period from 310 days minimum (February) to 359 days

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maximum (September) were accounted. For each curved line 1440 readings conforming to the number of minutes per day were examined. Then the curved lines roughness was reduced by smoothing the curves with a movable slot by 60 points. In Figure 12 b the daily variations are given three times to make the presentation of ambulance calls “wave” more illustrative. As the pictures show, the ambulance calls wave shape remains unchanged during a year; it hardly depends on the seasons both in the wave shape and in the calls intensity. A considerable wave amplitude in number of calls is noted. The same as in the case of daily variations in electromagnetic noise, the maximum numbers of ambulance calls within 24 hours in any month of a year are several times greater than the minimum values. The same as with the electromagnetic noise, the greatest difference is noted between winter and summer months (Figure 12 c). Contrary to electromagnetic noise, a social context of switch to daylight-saving time and of revert to winter time is apparent in ambulance calls though it is possible that a shift in time can partially be associated with seasonal variations in number of calls, too. For example, a maximum shift in time is noted for April. It is attributed to the switch to daylight-saving time in the last Sunday of March. Then, during a few months, a gradual reduction of time shift magnitude takes place and daily variations in time approximate winter values. Revert to winter time was on the last Sunday of October. Unfortunately, it is impossible to make a distinction between the share of social factors in the seasonal time shift and that of purely seasonal factors. Please note: some of the curved lines in this and in the subsequent pictures are shown by points. In this case points are used purely to symbolize a curve. In actual fact 1440 points were quantified for each curved line. In 2012 a switch to daylight saving time was cancelled in Russia and in a few years, after accumulation of sufficient amount of statistical data, more accurate data about seasonal changes in daily variations will be possible. In our analysis of daily variations in electromagnetic noise of the Earth an effect was noted that in our opinion can be attributed to a turn of disturbance wave movement direction in winter and in summer months. Let us see if a similar effect appears in ambulance calls. We shall study ambulance calls in night hours (Figure 12d). As you can see, call number maximums are closer to each other than minimums on curves of winter and summer day variations. Let us normalize the curves for maximum values of call numbers and let us shift the “summer” curve to the right by one hour in order to eliminate the effects contributed to clock hands setting forward or back (Figure 12 e). As you can see, summer maximum of ambulance calls takes place at a later time than winter minimum. Consequently, an effect is also noted in the ambulance calls - though maybe slight but still exceeding the computational errors - which resembles a turn of disturbance wave movement direction. In electromagnetic noise of the Earth we noted transformation of noise maximums into noise minimums as well as maximums transit from afternoon to night hours. Similar effects are also present in daily variations in ambulance calls (Figure 12f). To prove it, we shall normalize the curves of Figure 12 f for area under the curves (Figure 13 a). It will eliminate the difference in the number of calls and make the number of calls per day seemingly identical for all the seasons (Figure 13 b, c). Scale of ordinates in Fig 13 is multiplied by 1000. Summer diurnal course is shifted one hour to the right. It is apparent that as compared to winter time (Figure 13 b), in the summer time part of ambulance calls are “pumped” from morning over to evening. A slight effect due to a disturbance wave direction turn is also apparent.

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Figure 12. Daily variations in ambulance calls in Tomsk averaged for 2000-2011 (summer diurnal course in Figure 13 e was shifted one hour to the right).

Similarly to electromagnetic noise, diurnal courses of April and October 9 (Figure 13 c) in some cases fully coincide. We did not make any time shift in this case as both in April and in October summer time was functioning. You can see that during summer (from April to October) a certain return of diurnal course (in April shifted one hour to the left) to winter time takes place. Consequently in daily variations in ambulance calls we can also see - maybe slight but still distinguishable - features of seasonal changes in daily variations similar to seasonal changes in electromagnetic noise of the Earth. It would be dupable to think that in the case when lithospheric and biospheric processes are interrelated, the daily variations in electromagnetic noise, seismic activity and ambulance calls must be identically shaped with maximums and minimums occurring at the same time. If, for example, lithospheric and biospheric processes are “controlled” by a mechanical wave of strains in the Earth crust, then electromagnetic noise may be maximal during maximal stretching of Earth crust and minimal during maximal compression. Seismic activity can probably rise both in the case of

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compression and stretching of the Earth crust. A man in his turn can hardly react to a magnitude or signal of mechanical strains somewhere deep down, in the Earth crust. It is more probable that biorhythms may be synchronized by a pulsed electromagnetic flow or waves of some other origin. In this case not only the magnitude of some disturbance, but also its modulation rate or acceleration can be decisive. Therefore lack of coincidence in maximum and minimum points and bends in daily variations in lithospheric and biospheric processes does not denote an absence of direct or indirect relationship between those two factors or some third factor (associated with an eccentric rotation of the Earth core and crust). Let us group all ambulance calls into groups of calls to male and female patients, calls to children under 18, calls due to death, calls followed by patients’ admission to hospital, calls due to attempted suicide. Let us see if the trend we detected in day and seasonal variations persists in the above variants of ambulance calls.

Figure 13. Seasonal changes of daily variations in ambulance calls in Tomsk (summer diurnal curve in Figure 13 b is shifted one hour to the right).

Figure 14 presents daily variations in various types of ambulance calls in winter and summer months. In the winter months all days of December, January and February were averaged and in the summer months those of June, July and August were averaged. For each curve the mean values of number of calls at this minute of the day were estimated (1440 values on every curve). Curves estimated for April and October (Figure 15) were first normalized for area

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under the curves, ordinate values were increased by 1000. For better illustration all curves of Figure 14, Figure 15 were smoothed after averaging with the use of a movable plot by 60 points.

Figure 14. Difference between winter and summer daily variations in different types of ambulance calls.

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Figure 15. Daily variations in various types of ambulance calls in April and in October. The curves are normalized for area, ordinate values are multiplied by 1000.

Practically the regularities we discovered in electromagnetic noise of the Earth can be observed in all variations in ambulance calls. We can see that all the daily variations have the same shape as a disturbance wave and the wave front is inclined differently in winter and in summer. It is equivalent to the wave direction turn effect we discovered for electromagnetic noise of the Earth. For ambulance calls, the same as for lithospheric processes, there exist

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some characteristic points (hours within a 24 hour period) where radical changes of process dynamics take place. Practically they are the same points (4, 9, 14, 20 hours) - only mirrorreversed hours - as in the electromagnetic noise variations (2, 6, 16, 18). These “special” hours are preserved throughout a year. Practically for all the types of ambulance calls as well as for electromagnetic noise of the Earth the greatest difference in daily variations is observed between winter and summer months. For April and October the curves are practically identical. “Pumping” of a certain share of ambulance calls from morning to evening hours is also evident at the transition time from winter to summer. The pumping is identical to transformation of winter night intensity maximum of Natural Pulsed Electromagnetic Field of the Earth into summer afternoon maximum. Now we shall look into annual variations in lithospheric and biospheric processes.

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3. Annual Variations in Lithospheric Processes and in Man Morbidity Rates Within-year variations in lithospheric processes are presented in Figure 16. Annual electromagnetic noise variations are plotted using our measurement data measured in 1998 to 2004 in the Baikal region. Annual variations in seismic activity in the Baikal region are based on about 50 thousand earthquakes that happened for 17 years and were entered in Siberia earthquake bulletin between 1971 and 1991. Years of 1975, 1979, 1986, 1989 were excluded from the calculations. A number of strong earthquakes happened during these years which were accompanied by swarms of forshock events that appreciably distorted typical annual variations. After the calculations the plotted curves were smoothed by a movable slot. Smoothing slot width is shown in the figures. Annual variations in ambulance calls are presented in Figures 17 to 19. Calculations are based on analysis of 11 years of ambulance service functioning in Tomsk (2000 - 2011). In leap years the data for February 29 were extracted for alignment of all the lines by calendar dates. It had to be done for identifying the social factor linked with holidays’ reflection on the people’s health and the morbidity rate. Annual variations in the number of calls well indicate the “consequences” of holidays extensively celebrated in the USSR before (and in Russia nowadays): the New Year (January 1), International Women’s Day (March 8), International Day of Working People’s Solidarity (May 1), Victory Day (May 9), Great October Socialist Revolution (November 7). If we disregard the social effects linked with holidays, then both for the litospheric processes and for ambulance call-out cases there are similar characteristic points in annual variations. Just at these points we notice the main changes in the processes development dynamics. These specific points are noted the end of June – beginning of August and the end of January – beginning of February. Just at this period the minimum population morbidity rate is registered in Tomsk. Minimum values of ambulance call-outs at the end of July beginning of August is observed for practically all the ambulance call-out cases (Figure 1719). Here we see the break-over point of all the curves, transition from gradual reduction in the number of patient who fell ill to the gradual increase in the morbidity rate. This period fully coincides with the minimum of seismic activity in the Baikal region (Figure 16). Just in this very interval of the year we observe similar changes in the process dynamics. Seismic activity changes its trend from the reduction to the growth pattern.

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The intensity in the electromagnetic noises of the Earth in July – early August shows an inverse correlation (Figure 16). At this period of the year after the sharp jump in the electromagnetic noises intensity there follows a reduction in the level of electromagnetic noises. Unfortunately, insufficient statistics and, presumably, Lunar influence do not let us see a more accurate picture of these changes or more precisely identify the moments of changes in the processes dynamics. Under the Lunar influence such bends in curves can be found for different years and at different calendar dates which misrepresents the observed picture.

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Figure 17. Annual variations in all types of ambulance call-outs, calls with subsequent patients’ admission to hospital and call-outs to sick children.

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Figure 18. Annual variations in ambulance call-outs to male and female patients and calls due to pregnancy abnormalities.

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Figure 19. Annual variations in ambulance call-outs to patients with diagnosis “death” and “suicide.”

Significant changes in the dynamics of the lithospheric and biospheric processes come also at the end of January – beginning of February. Since October to mid-January the seismic activity in the Baikal region gets stabilized at one and the same level (Figure 16). At this period the minimum level of electromagnetic noises of the Earth is registered. Noises intensity gradually decreases. At the end of January the dynamics of lithospheric processes changes. A jump is seismic activity is observed. Seismic activity reaches its maximum at the beginning of February, then it starts to decrease. Similar, but inverse correlation is noticed also for the electromagnetic noises. Noise intensity reaches its minimum at the beginning of February, and then it starts to grow. Generally, the winter stretch of seismic activity more resembles the summer period in the electromagnetic noises of the Earth. This fact, in our view, again proves presence of a number of symmetry axes typical for the spherical systems. Similar process dynamics is traced in the changing numbers of ambulance call-outs. If we exclude the social factor of morbidity rate growth during holidays clearly traceable in all the ambulance call-out cases, the dynamics in the ambulance call-out number looks as follows. Intensity in all ambulance call-outs gets stabilized at the end of October. Stable morbidity remains unchanged by the end of January. At the end of January such stability is violated. Both general Tomsk population morbidity rate and the intensity rate of different diseases start to grow. So, in the annual rhythm of lithospheric and biospheric processes, too, we observe powerful influence of some third factor that governs these processes all over the year. It is

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hard to imagine that during these couple of days (end of January – beginning of February and end of July – beginning of August) some profound changes happen in the duration of the daylight hours, air temperature, amount of precipitation, atmospheric pressure drop, or other changes occur in the human environment. But biorhythms are usually considered to be linked just to these changes in the environment around us. Everything becomes explainable if you proceed from our assumption that the decisive role in the lithospheric and biospheric rhythms formation is that of the core of the Earth. According to our knowledge, just at the end of January – beginning of February the core of the Earth comes closer to the geometric center of the Earth and changes the direction of its annual movement. It starts to move from the shadow side of the Earth towards its lightened side. Just at the end of July – beginning of August the core of the Earth moves away from the center. The reverse process of the Earth’s core movement now from the lightened half of the planet towards its unlighted part. We would like to underline one more peculiar feature of the annual rhythms typical both for the seismic processes and for the human morbidity rate. We mentioned high amplitude of diurnal waves in lithospheric and biospheric processes. Maximum values of the above processes inside one day-and-night is a number of times higher (usually 5-6 times higher) than the minimum values. Diurnal waves in lithospheric and biospheric processes looked alike both considering their appearance and their amplitude. Annual waves in seismic activity and waves in human morbidity rate also looked the same (Figure 20). However, the maximum values of these processes within a year (unlike the daily ones) are insignificantly higher than the minimum values. Difference between the maximum and minimum in annual variations in seismic activity and ambulance call-out cases was not more than 30%. Presence of some global process that governs both lithospheric and biospheric processes on the Earth is especially noticeable when we compare the diurnal variations in lithospheric processes and ambulance call. For example, let us compare diurnal variations in electromagnetic noises of the Earth and the “wave” in suicide rate. They are shown in Figure 21. The curves represent the minute values of correspondent parameters averaged by many years of observations (1440 points a day). The curves are smoothed by 60 minutes (60 points). On the top schedules the original curves are given. For electromagnetic noises (Figure 21, а) we show a typical situation in July. Variations in the suicide cases (Figure 21, b) insignificantly depend on the time of the year. That is why we show the average annual variations in the picture. For more apparent comparison of these processes let us make some preliminary transformations. Looking at the upper pictures we feel that the diurnal variations in the suicide rate are a mirror reflection of the electromagnetic noises registered by the stations in July. Let us norm out both curves for their maximum values. . Let us rotate the diurnal variations in electromagnetic noises from the right to the left and shift it by 12 hours. As we can see, (Figure 21, с и d), after such changes the diurnal variations in electromagnetic noises coincided with the diurnal variations in suicide rate, both in their form and the amplitude. The same can be said about Figure 21, e and f, where such changes are introduced for diurnal variation in electromagnetic noises in January. In this case even no time shift became necessary.

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Figure 20. Annual variations in seismic activity (a) and ambulance call-out cases (в).

As another example, let us consider the diurnal variations in seismic activity and death of people (Figure 22). In order to see daily variations in human death rate (Figure 22, a) we analyzed 26 thousand 470 ambulance call-outs over the period of 2000 - 2011. Figures on the axial of ordinates show average values of the calls number at this very minute of the day. When we calculated daily variations in seismic activity (Figure 22, b), we considered all the earth quakes in the Baikal region entered in the catalogues over the period from 1962 to 1996 (approximately 300 thousand earthquakes). Time of the event occurrence was recalculated from Greenwich time to local solar time in accordance with coordinates of earthquake focus. Figures at the axis of ordinates shows the cumulative number of earthquakes that took place at this very minute of the day in the specified years. The curve is smoothed by 60 points.

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Figure 21. Intra-diurnal variations in electromagnetic noises of the Earth in July and January and ambulance call-outs with the diagnosis “Suicide.”

It is seen that the maximum number of death cases falls on the period of minimum seismic activity of the Earth (at least, of its Northern hemisphere). Let us turn the seismic activity curve in the way that the minimums will be converted into maximums. In order to do it let us, for example, deduct the number of earthquakes that took place at this very minute of the day from the total 80 (Figure 22, b). The curve of death cases will be smoothed by 60 points, as we did with the seismic activity. Let us compare the interdependencies provided in Figure 22, c and in Figure 22, d. The difference in position of maximums and minimums in the curves does not exceed one or two hours. The shape of the curves indicates that in both processes there is some third force that reflects an impact on lithospheric and biospheric diurnal rhythms. If we consider that the movement means life while absolute rest means death than the seismic inactivity can be figuratively compared with the death of the Earth (Earth's crust). Let the readers forgive us for such free and easy application of the human criteria to the processes

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in the Earth. We compared the inverted curve of seismic activity with the “death” of the Earth. (An arrow in Figure 22 c is drawn in memory of my friend Zelentsov V.I. Just a few days ago we were sitting together at a fire on a riverside and discussed the existence of a “death wave” which made its daily tours over the surface following the Earth rotation. Next morning we were standing by when my friend suddenly fell dead. The arrow marks the time of his death, which thus became a full stop in our discussion on the waves of life and death. Note by Malyshkov Yu.P.). So, these examples confirm existence of some universal mechanism that governs the dynamics of lithospheric and biospheric processes within the whole year. They prove similarity in winter and summer processes, existence of many symmetry axes, typical for spherical systems.

Figure 22. Intra-diurnal variations in seismic activity and ambulance call-outs to patients with diagnosis “Death.”

If the reality is such as it is. If there is a certain universal mechanism that governs the dynamics of electromagnetic noises of the Earth and its seismic activity, birth and death of people and their health, then the spectral-response characteristics of a third factor, such a powerful one, must become part of the spectral structure of all the above-mentioned processes. In this case they must not only become their components, but also ensure close interrelation between amplitudes of different frequencies. Let us try to make sure that the situation is really such based on the spectral analysis in the timing series of the investigated lithospheric and biospheric processes.

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4. Solar Cycles in Spectra of Some Lithospheric and Biospheric Processes In the beginning it is pertinent to discuss long-period components of some lithospheric and biospheric processes. See, for instance, spectra of EM noise and seismicity compared with morbidity, death, and birth rates, etc. in humans (Figure 23). The EM noise spectra are based on Earth’s natural PEMF records in the N—S channel from 1997 through 2002 (hourly means). The true signal amplitudes (the ordinates) are 109 times reduced in all panels of Figure 23 and the figures below. The frequency of earthquakes from the Baikal area is according to catalogs for Siberia from 1971 to 1999 (hourly means). The amplitudes of signals (the ordinates) in all seismicity curves are 103 times reduced. The spectra of ambulance calls are from Tomsk city, a time series from 21 August 2000 through 30 September 2011 (number of calls per minute). The ordinate values are likewise 103 times reduced (except the calls for pregnancy problems, deaths, and suicide cases). The birth rates areestimated as number of births per 5 minutes from 1974 through 1980 according to data from Angarsk (Irkutsk region). Note that the estimates of years-long components are of quite a low accuracy for the limited lengths of the time series (several years in all spectra except seismicity in the Baikal area). Therefore, it is impossible to prove or disprove with confidence whether the solar 11 yr cycles exist in the sampled lithospheric and biospheric processes. The existence of 11-yr periodicity is not very likely in the EM noise and seismicity spectra. A periodicity about 11 years appears traceable in some series of ambulance calls, but any definite conclusions on solar activity as a control of human morbidity and other life and death events require analysis of longer times series. series. The annual and seasonal cycles in the series we analyzed (Figures 24 and 25) are more reliable. The annual rhythms of many processes (six out of twelve curves in the figures) bear a cycle of 364.09 days. This cycle is shorter than the Earth orbital cycle of 365.25 days. Solid arrows under the abscissas mark solar tide components borrowed from [Melchior, 1983]. The annual periodicity in the analyzed spectra never exactly matches the astronomic year (except that for death ambulance calls with 364.09-day and 412-day cycles) and may rather have some other shorter-period terrestrial control. We attribute the lead to the faster rotation rate of the core relative to that of the whole planet orbiting [Malyshkov and Malyshkov, 2012]. Although being within the uncertainty range, the difference hardly may be due calculation errors: the same period appears too often. Hardly it can be purely fortuitous, more so that the picked spectral components are present in different times series and in diverse processes. Above we mentioned the importance of post-holiday social factors in human life rhythms, and now we check the significance of weekly cycles of working days and weekends. The weekly and subweekly variations in the same lithospheric and biospheric time series (Figures 26 and 27) show quite expected patterns. Namely, the EM noise and seismicity spectra lack week- and half-week cycles: of course, social factors cannot influence processes in the crust. However, the 7.00 and 3.500 day periods are prominent in almost all series of ambulance calls and exactly fit the expected values, except the birth cases (neither males nor females). The latter is likewise quite a natural result since babies, who actually command the births, are yet independent of social factors, while mothers’ rhythms matter much less in this case.

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Figure 23. Long-period components in spectra of lithospheric (EM noise and seismicity) and biospheric (human death and life events) processes.

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Figure 24. Annual and subannual components in spectra of lithospheric (EM noise and seismicity) and biospheric (human morbidity) processes.

The annual and seasonal cycles in the series we analyzed (Figures 24 and 25) are more reliable. The annual rhythms of many processes (six out of twelve curves in the figures) bear a cycle of 364.09 days. This cycle is shorter than the Earth orbital cycle of 365.25 days. Solid arrows under the abscissas mark solar tide components borrowed from [Melchior, 1983]. The annual periodicity in the analyzed spectra never exactly matches the astronomic year (except that for death ambulance calls with 364.09-day and 412-day cycles) and may rather have some other shorter-period terrestrial control. We attribute the lead to the faster rotation rate of

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the core relative to that of the whole planet orbiting [Malyshkov and Malyshkov, 2012]. Although being within the uncertainty range, the difference hardly may be due calculation errors: the same period appears too often. Hardly it can be purely fortuitous, more so that the picked spectral components are present in different times series and in diverse processes.

Figure 25. Annual and subannual components in morbidity (Tomsk) and birth (Angarsk) rates.

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Figure 26. Weekly and subweekly components in spectra of lithospheric and biospheric processes.

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Figure 27. Spectra of ambulance calls and births in the vicinity of weekly periods.

Above we mentioned the importance of post-holiday social factors in human life rhythms, and now we check the significance of weekly cycles of working days and weekends. The weekly and subweekly variations in the same lithospheric and biospheric time series (Figs. 26 and 27) show quite expected patterns. Namely, the EM noise and seismicity spectra

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Figure 28. Daily and hourly components in spectra of lithospheric processes and ambulance calls.

lack week- and half-week cycles: of course, social factors cannot influence processes in the crust. However, the 7.00 and 3.500 day periods are prominent in almost all series of ambulance calls and exactly fit the expected values, except the birth cases (neither males nor females). The latter is likewise quite a natural result since babies, who actually command the births, are yet independent of social factors, while mothers’ rhythms matter much less in this case.

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49

Figure 29. Daily and hourly components in spectra of ambulance calls and births.

The spectra of ambulance calls (for male and female patients and children) and hospitalization cases show well pronounced 56.0 hr (2.33 days), 42.0 hr, 33.6 hr, and 28.0 hr variations, which appear neither in the spectra of death and birth cases nor in lithospheric events. We withhold any comments on this matter.

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The similarity is the closest for daily and hourly periodicities in the lithospheric and biospheric spectra (Figures 28 and 29): the rhythms of PEMF, earthquakes, and births bear the same set of characteristic daily and hourly components. All time series contain periods of 24 hr (most prominent) and 12 hr (second most prominent), as well as 8 hr, 6 hr, and 4 hr. The two latter cycles are either more or less significant in the spectra of different processes. The rhythms of ambulance calls likewise show several significant variations (cycles of 21, 28 hr, etc.) that are absent from the spectra of EM noise, earthquakes, and births. See a fragment of enlarged hourly components in the spectra of all ambulance calls in Figure 30.

Figure 30. Daily and hourly components in spectra of all ambulance calls. An enlarged fragment.

Consider more closely the periods that are the most prominent in all spectra and are present in both lithospheric and biospheric time series. These are the ranges where to pick signatures of some global-scale mechanism responsible for synchronicity of diverse terrestrial processes. The daily components in the spectra of lithospheric and biopsheric time series are shown in Figures 31 and 32, likewise with solar tide components (arrows) from [Melchior, 1983]. The numerals at peaks are the respective periods we calculated. The diurnal wave in all spectra splits in at least six bands which are present in the EM noise, seismicity, ambulance calls, and birth patterns (Figure 31, 32). The perfect match of periods (to fourth or fifth decimal digits) in all the bands is evidence that there must be some universal control of biotic and abiotic processes. The coincidence of the subannual periodicities, with one another as well as with solar tide variations, would indicate the solar gravitation to be a likely candidate for the global govern mechanism. However, the lack of the bands corresponding to still stronger lunar tidal action in the spectra (see above and below) prompts rather the existence of some other one-way action on the Earth. Our hypothesis is that the eccentricity of the Earth’s inner core may exert such a

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unilateral action similar to that of tides. If this is the case, the Earth rotation (irrespective of the core eccentricity direction) must maintain perfect match of periodicities between the analyzed processes and tidal strain, including the 24 hr and all other cycles related with subtle variations in the Earth rotation about its axis and about the Sun.

Figure 31. 24 hr components in spectra of lithospheric processes and ambulance calls. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Figure 32. 24 hr components in spectra of ambulance calls and births.

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Figure 33. 12 hr components in spectra of lithospheric and biospheric processes.

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Figure 34. 12 hr components in spectra of ambulance calls and births.

The results are similar for other hour-scale lithospheric and biospheric variations. The 12 hr periodicity (Figures 33, 34) provides still more spectacular evidence of some mechanism that must govern biotic and abiotic rhythms, other than gravitation or tides.

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Figure 35. 8 hr components in spectra of lithospheric processes and ambulance calls.

Thinking whether tidal strain can influence anyhow the human life, note that the effect of Moon tides in middle latitudes is as small as 10-7 of the average human weight, and it changes very slowly during 24 hours; the solar tides can cause still a weaker effect. It is hard to even imagine that an action commensurate with a breath of air would cause any notable influence on the birth, death, or health of a man. The shorter-period 8-, 6-, and 4-hr variations support this doubt ever more (Figures 35-39). The action of some other mechanism related with the Earth rotation but independent of the tides shows up also as the same set of periods and similar respective spectral patterns, in both biotic and abiotic time series.

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Figure 36. 8 hr components in spectra of ambulance calls and births.

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Figure 37. 6 hr components in spectra of lithospheric processes and ambulance calls.

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Figure 38. 6 hr components in spectra of ambulance calls and births.

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Figure 39. 4 hr components in spectra of lithospheric and biospheric processes.

The spectra of ambulance calls contain some periodicities that are missing from EM noise and seismicity series (21, 28 hr and others), as well as from the patterns of abortion, birth, death, and suicide cases (Figure 28-30). These periods more likely have social (working days and days off) or biological (sleep and wake rhythms) controls. See, for example, the 21 hr cycles (Figures 40, 41) which are present in some groups of ambulance calls but are absent

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from both lithospheric spectra (EM noise and earthquakes) and those of weaker social controls (abortions, births, and deaths).

Figure 40. 21 hr components in spectra of EM noise, seismicity, and ambulance calls.

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Figure 41. 21 hr components in spectra of ambulance calls and births.

At this point we finish the analysis of diurnal and annual variations related with the Earth rotation and check whether the gravitation action of the Sun and the Moon can be directly responsible for the periodicities we discovered in lithospheric and biospehric spectra. For this we look more closely into their lunar tide components. The Moon’s tidal wave being twice as great as that of the Sun, its rotation cycles would be especially prominent as gravitation effects, in the same way in all curves. On the other hand, the Moon-related components should be strongly dissimilar if the biotic and abiotic rhythms we sampled are due to agents inside rather than outside the Earth.

5. “Lunar” Cycles in Spectra of Some Lithospheric and Biospheric Processes In this section we discuss details of “lunar” periodicity in the spectra of the processes we study. The attribute lunar is used in quotes because we expect the Moon-related components to be suppressed instead of being prominent.

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The model we suggest [Malyshkov and Malyshkov, 2009, 2012] predicts that the solid core moving in the Earth’s interior does track the position of the Moon in the space, but not because the Moon would be responsible directly for the core eccentricity. It is rather the Earth’s outer shells (the lithosphere) that shift toward the Moon by gravitation while the inner core itself remains fixed being inert or, possibly, being shielded by the lithosphere. As the outer shells displace toward the Moon, the core becomes farther from it than the Earth’s geometrical center, and there arises apparent eccentricity and disbalance of the system. Thus the solid inner core moves inside the liquid outer core in counter-phase with the Moon and acts against the Moon’s action. This compensation effect reasonably should leave its imprint in the lithospheric (PEMF and seismicity) and biospheric (human life and death rhythms)

Figure 42. Lunar tide components (27.55 and 13.66 day cycles) in spectra of EM noise, seismicity, and ambulance calls. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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spectra, namely, the counter-phase motion of the Moon and the core is expected to suppress the lunar components. Now we check whether these expectations prove valid in long-term time series. Indeed, the bands corresponding to lunar periodicities are absent from the analyzed spectra (See the lunar month (27.55 days) and half-month (13.66 days) periods in the lithospheric and biospheric spectra of Figures 42 and 43; the Moon tide data (dash-line arrows) are borrowed from [Melchior, 1983]). Furthermore, these components are damped to below the average values. The damping effect indicates the existence of some action in counter-phase with that of the Moon. The same inference is possible for other variations as well (Figure 44-49), arrows mark solar (solid line) and lunar (dash line) components). Namely, the lunar-scale periodicity in the EM noise, seismicity, ambulance calls, and birth spectra looks suppressed instead of giving peaks.

Figure 43. Lunar tide components (27.55 and 13.66 day cycles) in spectra of ambulance calls and births.

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Figure 44. Lunar tide components (24 hr cycles) in spectra of EM noise, seismicity, and ambulance calls.

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Figure 45. Lunar tide components (24 hr cycles) in spectra of ambulance calls and births.

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Figure 46. Lunar tide components (12 hr cycles) in spectra of EM noise, seismicity, and ambulance calls.

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Figure 47. Lunar tide components (12 hr cycles) in spectra of ambulance calls and births.

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Figure 48. Lunar tide components (8 hr cycles) in spectra of EM noise, seismicity, and ambulance calls.

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Figure 49. Lunar tide components (8 hr cycles) in spectra of ambulance calls and births.

DETECTING SURFACE ACTIVE GEODYNAMIC ZONES FROM ELECTROMAGNETIC NOISE PATTERNS Natural pulsed electromagnetic fields are mostly produced by shallow crustal discontinuities, cracks and microcracks. Electromagnetic noise patterns have been employed for mapping faults, monitoring stress and strain in the ground, and for predicting geodynamic movements since the beginning of PEMF studies, though they remain of almost no use in

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geophysical prospecting applications. The lithospheric component of pulsed EM responses becomes prominent only if the instruments are sensitive enough [Malyshkov and Malyshkov, 2009, 2012] but records of very sensitive acquisition systems are very noisy and abound in atmospheric signals. On the other hand, low sensitive systems record only the heaviest thunderstorms and miss lithospheric responses. Thus, the data acquisition units have to be adjusted to a certain optimum sensitivity range depending on local ground properties. It is convenient to tune instruments against empirical calibration relationships (look, for example, Figure 8), based on years-long measurements of the Earth's natural pulsed electromagnetic field in different parts of Eurasia. In this it is important that the behavior of the recorded time series were proximal to diurnal ENPEMF rhythms typical of a given season [Malyshkov and Malyshkov, 2012]. The precision of ENPEMF measurements is about 10 nT. One has to take into account that about 90 % of responses come from sources outside the target objects and cannot represent their geology. The way of picking spatial ENPEMF anomalies from the flow of recorded signals has been patented (RF Patent No. 2414726) [Malyshkov et al., 2011].

1. Separating Space and Time Variations in a Flow of EM Signals In the suggested approach, atmospherics and remote responses from objects outside the area of interest are removed from the flow of recorded signals. Filtering from irrelevant components is provided at the stage of data acquisition and processing by:  

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

using a network of synchronously operated largely spaced fixed and mobile EM stations; tuning the stations to the optimum sensitivity and checking their consistency in terms of sensitivity and precision; discriminating between remote and local responses.

PEMF signals vary both in space and time. The fixed stations in ENPEMF systems record only variations in time and serve for reference, while the others are mobile and sample both temporal and spatial field patterns along profiles that cross the target areas. The systems include at least two receivers, the greater their number the better the resolution. Local and remote responses can be discriminated according to their amplitude and time of arrival at distantly spaced stations. Remote responses (e.g., atmospherics) propagate along the Earth-ionosphere waveguide to arrive at proximal stations almost simultaneously, and have the same amplitudes. Responses of large lithospheric objects reach the surface and travel further as ground rays at about the light speed and decay very slowly, which provides their synchronous recording at all stations with similar amplitudes. Unlike the remote signals, local responses travel mostly through rocks in the vicinity of stations. Signals immediately over the source and those from more distant points have markedly different amplitudes because of rapid decay. In threshold acquisition systems that cut off low signals, more distant receivers can record fewer responses than those located near the anomaly. However, prominent local responses recorded by all distantly spaced stations have different amplitudes depending on the source-receiver distance, which is employed in the instruments and techniques we suggest.

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For instance, profile PEMF data of Figure 50 are spatial and temporal variations of Earth’s electromagnetic noise recorded at every 15 m, with the sampling time 5 min at each point. The curves represent pulsed EM field averaged over the sampling time, in two channels: one in the N—S direction (pr3N-S) and the other in the W—E direction (pr3E-W). ENPEMF is higher in the W—E channel at points 109-119.

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Figure 50. PEMF variations in space and time along a profile.

In Figure 51, these curves are compared with EM noise patterns recorded at the same time by the fixed reference station, which are no more than 10 % above the background. Thus, at least 90 % of responses have no immediate relation to the study area and bear no message of its stress and strain. They come from outside the area and are recorded by all stations simultaneously. To remove the unwanted responses, the field parameters at the reference station are divided by those at the given mobile station. The picked spatial ENPEMF variations are shown in Figure 51, b.

Figure 51. ENPEMF variations. a: Profile PEMF variations in space and time and temporal variations recorded by the reference station; b: Profile PEMF variations in space after removing temporal variations. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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The patterns change dramatically after the temporal variations have been removed: especially prominent PEMF peaks appear at points 91, 100-105, and 109 instead of being restricted to the end of the profile as one may expect from the curves of Figure 50. These points coincide with places of extension associated with an active landslide.

2. Mapping Stress and Strain of Rocks and Faulting Patterns

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As it was mentioned above, natural Earth’s EM noise results from crustal discontinuities, domains of high stress and strain, cracks and microcracks. Mechanic-to-electric energy conversion under the effect of strain waves from the mantle, tides, microseisms, winds, and technological loads produces pulsed EM fields which make up the natural lithospheric EM background. According to long-term measurements in different areas, lithospheric ENPEMF responses have well-defined diurnal and seasonal rhythms because crustal strain waves are associated with Earth’s rotation about its axis and about the Sun. The diurnal cycles depend on the calendar dates, geographic coordinates, and geophysical properties. Typical diurnal variations respond to changes in crustal rhythms, for instance, when a consolidated domain of several interlocked fault blocks forms during earthquake nucleation or when stress and strain change rapidly. Thus, ENPEMF measurements can provide a universal tool for geophysical surveys and geodynamic monitoring or for any other application in geosciences. We applied ENPEMF surveys to assess slope stability in the Kama River right bank in central Russia (Figure 52) where the Urengoi – Pomary – Uzhgorod gas pipeline crosses the river. There is a cascade of landslides in the slope, which pose serious hazard to the line.

Figure 52. Area of ENPEMF surveys for slope stability monitoring.

During 1D profile surveys, one reference station was fixed and sampled ENPEMF temporal variations. It was placed ~150 m away from the slope, on a flat surface outside the landslide zone, and the slope stability and stress-strain patterns in the landslide were estimated against its data. Before the acquisition, the stations were synchronized with clocks built into MGR recorders, to fractions of a second. This allowed removing the responses that arrive simultaneously at all stations and thus come from outside the landslide. Information was inferred from the profile-to-reference station ratios of the measured parameters. Sampling at all stations was every 1 s (i.e., at least 300 counts at each point). Statistical processing included filtering the data from diurnal cycles and remote responses. Measurements were run along eleven profiles, both along and across the slope. In addition to measuring stress and strain in the southern part of the landslide, surveys along profile 1, upslope from the river,

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between pipelines one and two, aimed at estimating whether the detected anomalies remained stable with time. Each point was sampled twice by two different stations, 20 minutes one after another, which allowed testing the measurement quality and checking the anomalies in a while after the first sampling. Repeated measurements at station 2 were taken 20 min after sampling at station 4; the EM noise patterns used to infer stress and strain in the southern part of the pipeline are shown in Figure 53.

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Figure 53. Variations of Earth’s EM noise. a: N—S channel; b: W—E channel

The results from different stations obviously remain consistent after filtering out the time component of ENPEMF. The highest landslide activity is recorded in the steepest part of the slope. Spatial variations are quite stable and hold with time. The spatial ENPEMF pattern remains almost invariable at least for 20 min and persists within some region of scatter. However, this stability may be upset either by interior processes inside the landslide or by exterior triggers, such as seasonal changes in ground moisture, snow melting, long rainfalls, technological loads, etc. Images in Figure 54 are processed 2D data of different years. Alternating zones of extension and compression are restricted mainly to the northern and central parts of the landslide slope. They appear as peaks and troughs in the 3D model above, with their heights and depths proportional to the stress magnitude, and as red or blue zones, respectively, in the map below. Later surveys in July 2008 confirmed that main active sliding zones remained in the same places though the ENPEMF spatial pattern changed slightly in the course of the landslide life. Zones of extension, as well as their sharp borders with compression zones, are especially hazardous for pipelines. The most active landslide zones are located on the right, both in the 3D model and in the map (Figure 54), where exactly the compression and extension stresses are the highest and where most of pipeline accidents occurred for the past years. Thus, the ENPEMF method, being cheap and straightforward, turns out to be no less informative than geomorphological analysis, seismic survey, or drilling. The data from the landslide slope of the Kama right bank demonstrate the applicability of PEMF surveys to estimating stress and strain of rocks. According to evidence of multiple tests, with repeated surveys, synchronous sampling at several stations, and checks against the classical methods, the appropriate use of the ENPEMF techniques ensures precise, well reproducible, and reliable records of slope activity.

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Figure 54. Patterns of stress and strain in landslide slope based on radiowave measurements of different years.

Thus records of the Earth’s natural pulsed EM field can highlight zones of high and low sliding activity in unstable slopes, as well as zones of extension and relative compression and stress directions.

3. Monitoring of Sliding Activity in Unstable Slopes, Assessment of the Degree of their Danger In the end of 2007 an automatic system for slope stability monitoring was launched within the Urengoi – Pomary - Uzhgorod pipeline in the area where it crosses the Kama. The system currently comprises twelve multichannel stations MGR-01 deployed at sites of prominent stress-strain anomalies chosen proceeding from geophysical data. The stations consist of a recorder, a receiving antenna, and a battery, all placed in a tight container transparent for radiowaves (Figure 55). The containers are buried under the ground to avoid damage from vandalism while the transmitter GPS antennas emerge on the ground surface and are naturally camouflaged. The reference station (T4rep) is set up on the flat surface about 80 m away from the slope (Figure 56).

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Figure 55. A PEMF station at a landslide site.

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Data from the other stations are processed with regard to temporal variations of ENPEMF parameters from the reference station. In addition to the MGR stations, there are four boreholes on the slope in which downhole cable recorders sample horizontal ground motions at different depths, concurrently with measurements of groundwater level and chemistry. Furthermore, special smart devices (UB) pick up strain of metal in all nine pipes of the line on the slope top and at its base (Figure 56, b).

Figure 56. Locations of MGR-01 stations, UB smart devices, and drill holes on the landslide slope.

The EM noise data are saved in the recorder’s memory and are available for reading on a PC or for sharing via a password-protected FTP web server. The recorded field parameters are collected, processed, and visualized at a specially designed web portal [Kapustin] equipped with all necessary tools. In the database created at the portal, the processed data are available in a graphic form or in a mode of hazard monitoring, which allows automatic assessment of slope stability at certain sites according to analysis of data in a data page. Figure 57 shows a window a portal user sees. The ENPEMF data are visualized as curves two radiowave channels (N—S channel H1 and W—E channel H2). Stress and strain data at the monitored landslide sites are available as color-coded curves and provide information on sliding hazard. The greater the curve departure from zero (green line) the more rapidly stress and strain change at the respective PEMF measurement point.

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Figure 57. The view of a window at the web portal.

The algorithm of slope stability monitoring from PEMF parameters employs two criteria: one shows the field recorded on the slope relative to that at the reference station and the other estimates the similarity of data from different stations. The excess flow of ENPEMF signals at each station (Т1, Т2, Т3, Т5, Т6, Т7, Т8, Т9, Т10, Т11, Т12) relative to the reference field at Т4 rep is found as

К (С  Ю ) 

К(ЗВ) 

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



( N1T ( i )  N1T ( r ) ) N1T ( r )

,

( N 2T (i )  N 2T ( r ) )

where N 2T ( i )

N 2T ( r ) N1T ( i )

is the flow of ENPEMF signals in the N—S direction at the i-th station;

is the flow of ENPEMF signals in the W—E direction at the i-th station;; N1T ( r ) , N 2T ( r ) are the flows of ENPEMF signals in the N—S and W—E directions at the reference station.

The coefficients K0 correspond to extension, the higher the K value the greater the stress. This parameter is a main diagnostic criterion of the geodynamic state of ground. The second parameter accounts for correlation between ENPEMF diurnal variations at the reference and i-th stations, with Spearman’s rank correlation coefficient between the two statistical samples found as

r 1

n 6 ( xi  yi ) 2  3 n  n i 1 ,

where

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xi is the rank of the i-th element of the first sample in the sample itself (e.g., for the x sample {5, 8, 4, 6} x1 = 2, x2 = 4, 3 = 1, x4 = 3); yi is the rank of the i-th element of the second sample in the sample. Then the integral slope stability coefficient is found as

Rоб 

K  (1  r ) 2 ,

where

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Rоб is the integrate parameter of empirically estimated residual stability. An excess stability coefficient holding above 150% for three days or more indicates sliding hazard dangerous for the pipeline operation. The suggested approach to ENPEMF data acquisition and processing provides precise and reliable assessment of slope stability (sliding activity, extension and compression, and stress directions) in real time. Monitoring with our ENPEMF system in the course of several years has shown that different parts of the river side are dynamically developing structures and the slope stability within the landslide area can change locally even over 24 hours. ENPEMF anomalies were recorded more than ten times over the period of operation at different sites of the landslide and appeared as upset diurnal rhythms persisting for several days. On these days, data from different slope stations differed markedly. Two panels of Figure 58 are the cases when records from the reference station and another station at a landslide site are concordant (normal pattern, Figure 58, a) and discordant (anomalous pattern, Figure 58, b). The records were taken on 6 and 8 June 2008, respectively, and the field held high as long as a few days.

Figure 58. Typical (a) and anomalous (b) landslide responses.

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Once such field peaks appeared, gas transport from the hazardous line was moved to a standby line. Most often the Earth’s EM noise records alerted before other monitoring devices became triggered. The ENPEMF curve in Figure 59 is recorded near the gas line with pipe strain pickup (by a smart device). The common diurnal rhythm of EM pulses became upset on March 9, before ground motion showed up as a strain peak on March 13; the ENPEMF diurnal rhythm recovered in the end of the record. The monitored pipeline segment ran smoothly, without any accident, for over four years of the ENPEMF system operation. Of course, it was largely due to preventive engineering measures undertaken in cases of alert. Currently, monitoring systems of this kind are being deployed elsewhere at sites of Gazprom pipelines.

Intensity PEMF, pulse/min

120 100 80 60 40 20

Data of smart devices

0 -66,0 -66,5 -67,0 -67,5

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-68,0

9 00 .2 3 .0 03

9 00 .2 3 .0 05

9 00 .2 3 .0 07

9 00 .2 3 .0 09

9 00 .2 3 .0 11

9 00 .2 3 .0 13

9 00 .2 3 .0 15

Date

Figure 59. Upset diurnal PEMF rhythms (above) and pipe strain gage data (below).

In addition to landslide monitoring, the Earth’s natural EM noise data were used for mapping faults and estimating their activity. Namely, ENPEMF measurements in the Krasnoyarsk region allowed constraints on the amount and geometry of slip on an active fault which was revealed from aerial and satellite imagery. The ENPEMF stations were spaced at 50 meters and sampling was taken for 5 minutes at every 1 s at each point, i.e., at least 300 measurements in total in each N-S and W-E channel (Figure 60). The peaks were the most prominent, both in the N-S and W-E channels, between points 65 and 95. It was exactly the place where the profile traversed the axis of the fault boundary between neotectonic blocks. One more ENPEMF profile collected near another gas line, in an area of known geology, traversed three Late Paleozoic and Mesozoic-Cenozoic faults of different geometries (normal, reverse, and strike slip). The profile ran also across linear anomalies presumably corresponding to steeply dipping water-saturated zones of fractures, faults, and folds (kinks of monoclinal layers).

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Figure 60. Profile ENPEMF variations across a fault.

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The pulsed EM field was sampled between the points 150.0 and 172.0 km, at every 25 m, in 2 min sessions. Additionally, repeated surveys were applied as a check at sites where anomalous PEMF responses were recorded during the first survey. Figure 61 shows ENPEMF data collected between 151.5 and 153.2 km along profile 1 which traversed the anomaly attributed to the steep fractured zone according to classical geophysical surveys (151.8 to 152.0 km). The reference ENPEMF station within the heavily faulted site of the highest lineament field (from 152.5 to 153.2 km) was deployed in a fault near the point 152 km. For better reliability of the results, the profile was acquired twice, in forward and back directions. Both curves show statistically confident ENPEMF peaks exactly at sites of deformed crust.

Figure 61. PEMF pattern along profile 1, forward (curve 1) and back (curve 2) directions.

PEMF profile 2 (Figure 62), from 155 to 159.5 km, ran across a fault at 155.5 to 157.0 km and a fault and a fold at 158.7 km. The fault walls and the lineaments revealed in the gravity field show up clearly as ENPEMF peaks.

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Figure 62. PEMF pattern along profile 2.

Profile 3 (Figure 63), from 162 to 172.5 km, crossed two faults, an anomaly corresponding to a fractured zone, and a gravity lineament, which likewise appear as prominent ENPEMF peaks. Surveys between 167.5 and 172.5 km were run twice, in July and in August, and the PEMF anomalies were quite well reproducible, with a minor difference caused by stress and strain changes. In conclusion it is pertinent to highlight the key feature of the suggested approach which makes it advantageous over other geophysical techniques. ENPEMF signals are generated by lithological and structural heterogeneities as a result of micro-scale motions of rocks associated with natural processes in the crust. This makes the method environment-friendly and selectively sensitive to various geological boundaries. The new approach joins the advantages of the resistivity and seismic surveys and, moreover, saves much labor, money, and time as it requires neither special preparation work nor shooting.

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The PEMF parameters are highly sensitive to structural and lithological boundaries in the crust, which is important in stress-strain applications. We developed techniques of picking up global, regional, and local ENPEMF variations. Detecting variations of different scales allows predicting the possible time, energy, and locations of pending earthquakes [Malyshkov and Malyshkov, 2012, Malyshkov et al., 2004], as well as landslide and ground failure hazard in places of abandoned mines. The new method has been successfully tested in engineering geological practice (assessment of slope stability and ground stress and strain; detection of active faults; engineering geological mapping) as well as in mineral and petroleum exploration.

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COMMENTS AND CONCLUSION Thus, we have gained more evidence of a universal global control over many natural processes in the lithosphere and in biological systems. The mechanic model suggested to explain this forcing implies differential motion of the eccentric Earth’s solid inner core and the lithosphere. The solid core rotating eccentrically with respect to the mantle pumps the liquid material and thus gives rise to high- and low-pressure zones. Rotation of the latter at a diurnal periodicity produces strain waves in the crust and causes daily variations in the Earth’s EM noise and seismicity. The core changes its position in the extraterrestrial space during the year, and this motion is responsible for annual periodicity in various processes on the Earth and for annual and subannual modulation of daily rhythms. The Earth’s natural pulsed electromagnetic field may, in its turn, maintain daily and seasonal physiological cycles in plants and animals, because fluxes of EM pulses can reach any point in the space, in shallow ground, or inside buildings, as well as babies in mother’s wombs, and act without any evident exterior “clock”. When relating the daily and annual periodicity with strain waves, we admitted a contribution of other known or yet unknown waves from the core which likewise may produce seismic activity, EM noise, birth, death, and despair (suicide) cycles. The question about the mechanism of periodic lithospheric and biospheric variations remains so far open. However, the very existence of some universal forcing and its relation with the Earth rotation appears obvious. The existence of this mechanism has been proved on the basis of a whole collection of data rather than mere similarity of curves or bandwidths. Specifically, we took into account the waveforms and frequency bands of signals, as well as the match of periods and amplitude ratios at different frequencies. Additionally, we compared the waveforms and possible directions of waves corresponding to lithospheric and biospheric rhythms trying to find proofs for the periodicity and to explain the causes of changes in wave direction, etc. As a summary of the results, here is a list of main features shared by both lithospheric and biospheric processes we studied in their daily and yearly variations.  

Wave-like source patterns (perturbations) that produce daily variations; Propagation of the waves in a certain direction and their switch to the opposite direction in April and October;

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

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

Abrupt changes in lithospheric and biospheric processes in late January-early February and in late July-early August; Characteristic hours of the day (2 and 6-8 a.m, 4 and 6-8 p.m.) when the behavior of the monitored parameters obviously changes; Vertical and horizontal symmetry of some segments of diurnal cycles one relative to another indicating that the processes are confined within a closed space; The greatest dissimilarity of daily variation waveforms between winter and summer days and their greatest similarity in April and October; Marked changes in intensity of the processes at different hours of the day, the highest intensity being times the minimum level; Translation of events to other time spans, most often spaced at 10 hours rather than 12 hours, and switch from maximums to minimums; Exact coincidence (to fourth or fifth decimal digits) of periods in 24, 12, 8, 6, and 4 hour bands in the spectra of both lithospheric and biospheric processes we sampled; similarity of amplitude ratios of the respective bands; Exact coincidence of many bands with solar tide waves, though the wave amplitudes being different; Suppression of all bands where lunar tide waves may be expected in lithospheric and biospheric spectra.

Some sceptics may argue that all above features would be explainable in terms of the common daily Earth rotation without invoking exotic hypotheses. Wave processes, however, cannot arise from mere rotation but rather require a unilateral action from an object inside or outside the planet. There are tens of agents that may exert such an action: heat and light from the sun, solar wind pressure, electromagnetic effects, or finally the solar and lunar gravitation, but none can account for all listed features in the spectra taken together. For instance, the action changes its polarity in summer and in winter, but none action from the Sun or the Moon ever does: all are directed either from or to the Sun (the Moon) all year round. Neither they can ever change within short time spans in the end of January (July) and beginning of February (August). It is unlikely that the duration of daylight hours would become shorter or longer, or the temperature and pressure of air and precipitation would change dramatically every year on the same few days. Note that these very environment changes are believed to be responsible for biological rhythms. Meanwhile, the seasonal and daily variations we observed receive a logical explanation if their control is assumed to come from the Earth’s interior. The interior processes are slightly asymmetrical about the Earth’s geometrical center. Indeed, in the end of January-beginning of February the core approaches the closest to the geometrical center (minimum eccentricity) and then changes direction in its annual path to move from the night to the day part of the globe. On the contrary, in late July-early August, the eccentricity is maximum and the core turns back to the night side. Thus, the lithosphere shifted toward the Sun and the inertial eccentric core follow an annual path corresponding to counter-phase gravitational shifts of the core with respect to the Sun and the Moon. Therefore, one may expect that the solar annual path of the core would be superposed by the lunar spiral, with its one turn equal to the duration of a lunar month [Malyshkov and Malyshkov, 2012]. The inner core motion along its annual orbit, under the joint action of the Sun and the Moon, is apparently pulse-like. It

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either moves rapidly off the Earth’s geometrical center or slows down this motion in the viscous melt. Unfortunately there are no quantitative estimates of the core shift as yet. And the available theoretical estimates are very controversial varying from vanishing values to hundreds of meters (Antonov and Kondrat’ev, 2004). Unfortunately, our data are insufficient to provide a 3D image of the annual core motion. We expect intuitively that in its oscillative motion about the Earth’s center, the core should move forth and back between the northern and southern hemispheres, along an elliptic or a more complex closed orbit near the ecliptic. See Figure 64 for the intuitively imagined path of the inner core in the plane А-А which runs parallel to the rotation axis (slightly off it), across the points 2 a.m. and 4 p.m. of local solar time. We hypothesize that the core arrives at the extremes of its annual path, both in the vertical plane А-А and in the equatorial plane (see Figure 2), in end January-beginning February and end July-beginning August, being the least eccentric in winter and the most eccentric in summer. In March and September, the core leaves the Northern hemisphere for the Southern one to return, respectively, in April and October, and stays in the Northern hemisphere for the greatest part of the year. The reader may notice some discrepancy between the earlier core path in the equatorial plane (Figure 2) and the path in the plane A-A in Figure 64. Here we note that Figure 64 is not to any scale, and the curve is purely intuitive. On the other hand, when drawing Figure 2, we normalized the curves for estimating the core shift [Malyshkov and Malyshkov, 2009, 2012]. Perhaps, that normalizing was rather a wrong choice because it could give a winter core shift considerably overestimated relative to the true value.

Figure 64. Inferred annual path of the solid core in the plane A-A (without Moon’s action).

We are aware that the suggested core motion model is very tentative or even sometimes controversial. It is largely based on intuition, implicit evidence, and quite a modest amount of experimental work. Hopefully, the ideas we wish to share will inspire larger-scale investigations, including theoretical ones, for the mechanisms that maintain periodicity in lithospheric and biospheric processes. The question arises whether the reported data and inferences have substantial theoretical and practical implications. Of course, they do. If our model is true, the core must be a critical agent in the Earth’s orbital motion, either pushing it forward or pulling it back. The core

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balances the distance from the Sun moving either to or from it about the Earth’s geometrical center. In its interaction with the mantle, the core imparts additional periodical spin to the Earth maintaining its diurnal rotation rate. It might be the core moving alternately to the Northern or Southern hemispheres that holds the axial tilt at 23°27'. The departure of the core from its “standard” path may be a cause of many disastrous events. Furthermore, the compensation effect the core exerts on tidal strain waves has to be taken into account in the theory of tides. That is why it is important to set up core motion monitoring, with a global network of stations like the MGR instruments we designed, deployed systematically from north to south. The scope of practical applications may be expected to grow increasingly. EM noise measurements have been used successfully for earthquake prediction, as we reported in [Malyshkov and Malyshkov, 2012], and promising results were also obtained in geophysical surveys for petroleum exploration. In this study, we have discussed the application of the method to hazard mitigation (mapping stress and strain in shallow crust, detecting fault activity, and slope stability monitoring). In late 2007 we put into operation an automatic system to monitor slope stability in the area where the Urengoi – Pomary - Uzhgorod pipeline crosses the Kama River. Currently, the system consists of twelve MGR-01 stations and ensures trouble-free operation of the respective pipeline segment due to timely preventive engineering measures. So far we have only detected some traces of the core effect on people’s life and health. If this linkage is proved valid, many views of biological rhythms in humans will need a revision, namely, the rhythms in medical therapy, in school education, and in working schedules. People have to be aware of possible “death and despair” cycles and be cautious at the most dangerous hours of the day, as in the case of the Earth’s EM noise anomalies. Another point to analyze is the effect of man-caused PEMF changes on rhythms in biological systems. The fact that the ENPEMF daily variations become upset before large earthquakes made us expecting similar influence (possibly, on the subconscious level) on the life rhythms of people who live near the epicenter of the pending event. As a preliminary study of a few years ago demonstrated, such a research may have good prospects. In the case of success, there will appear another tool for earthquake prediction in densely populated areas, which is very cheap and requires no sophisticated technologies. Yet, we have to postpone this research for an uncertain time for the lack of funding. We are open to collaboration and ready to discuss any proposals for development of our ideas. Please, feel free to contact us at [email protected]. Translation from Russian made by Bocharova T.V. and Perepelova T.I.

REFERENCES Aleksandrov, M.S., Baklenova, Z.M., Gladshtein, N.D., Ozerov, V.P., Potapov,A.V., Remizov, L.T., 1972. VLF Variations of the Earth’s Electromagnetic Field [in Russian]. Nauka, Moscow. Antonov, V.A., Kondrat’ev, B.P., 2004. On the magnitude of the inner core eccentricity. Izv. RAN, Fizika Zemli, No. 4, p. 63–66.

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Avsyuk, Yu.N., Adushkin, V.V, Ovchinnikov, V.M., 2001. Integrate studies of inner core motion. Izv. RAN, Fizika Zemli, No. 8, p. 64–75. Bashkuev, Yu.B., Khaptanov, V.B., Tsydypov, Ch.Ts., Buyanova, D.G., 1989. Earth’s Electromagnetic Field in Transbaikalia [in Russian]. Nauka, Moscow. Berry B.L. (Berri) 2010 Heliogeophysical and other natural processes, periods of their oscillations and predictions. Journal «Geophysical processes and biosphere».. v. 9, № 4, p. 21-66. Bliokh, P.V., Nikolaenko, A.P., Filippov, Yu.F., 1977. Global Electromagnetic Resonance in the Earth-Ionosphere System [in Russian]. Naukova Dumka, Kiev. Boyarsky E.A. , Desherevsky A.V. 2010. Music of geospheres and practicality of statistical criteria. Comment on «Heliogeophysical and other natural processes, periods of their oscillations and predictions» by B.L. Berry. Journal «Geophysical processes and biosphere». v. 9, № 4, p. 67-99. Chizhevsky A. L. 1924. Physical Factors of the Historic Process. Kaluga, 72 pp. Chizhevsky A.L. 1930. Epidemic Catastrophes and Periodic Solar Activity. Gosizdat, Moscow, 176 pp. Chizhevsky A. L. 1968. Physicochemical reactions as indicators of extraterrestrial events, in: The Earth in the Universe, Mysl, Moscow, pp. Chizhevsky A.L. 1976. A terrestrial echo of solar storms. Mysl, Moscow. 376 pp. Earthquakes Catalog in Siberia. 1970-1975 [in Russian]. IZK SO RAN, Irkutsk. Vorobiev, A.A., 1970. On probability of electric discharges in the Earth’s interior. Geologiya i Geophysika, No.12, p. 3-13. Vorobiev A.A., 1979. Tectonoelectric phenomena and origin of the earth’s natural pulse electromagnetic field – ENPEMF [in Russian]. Tomsk, Presented by Tomsk Polytechnic University, Kept on deposit in VINITI, Part 1 - No. 4296-79; Part 2 - No. 4297 - 79; Part 3 - No. 380-80. Gokhberg, M.B., Morgunov, V.A., Gerasimovich, E.A., Matveev, E.A., 1985. Electromagnetic Earthquake Precursors [in Russian]. Nauka, Moscow. Gokhberg, M.B., Morgunov, V.A., Pokhotelov, O.A., 1988. Seismic and Electromagnetic Phenomena [in Russian]. Nauka, Moscow. Kabanov M. M., Kapustin S. N., Koltun P. N., Milovantsev P. B. 2011. A web portal for monitoring geodynamic processes, in Proc. VII International Congress GEO-SIBIR' 2011, 19-21 April 2011, Novosibirsk. SGGA, Novosibirsk, Book 1, Part 1, pp. 138-142 Korovyakov, N.I., Nikitin, A.N., 1998. Diurnal and annual periodicity of eccentric rotation of Earth’s core and lithosphere. Soznanie i Fizicheskaya Realnost’ 3 (2), p. 23–30. Malyshkov, Yu.P., Dzhumabaev, K.B., 1987. Earthquake prediction from parameters of Earth’s pulse EM field. Vulkanologiya i Seismologiya, No. 1, p. 97–103. Malyshkov Yu.P., Dzhumabaev K.B., Omurkulov T.A. and Gordeev V.F. 1998. Influence of Lithospheric Processes on the Behavior of the Earth’s Electromagnetic Field: Implications for Earthquake Prediction. // Volc. Seis., v. 20, p. 107-122. Malyshkov, Yu.P., Dzhumabaev, K.B., Malyshkov, S.Yu., Gordeev, V.F., Shtalin, S.G., Masalskii, O.K., 2004. A Method of Earthquake Prediction [in Russian]. Patent RF No. 2238575, 20.10.2004, Bull. No.29. Malyshkov Yu.P., Malyshkov S.Yu. 2003. Lithospheric-biospheric interaction and its dynamics, in: Self-organization and Dynamics of Geomorphic Systems. Proc. XXVVII Plenum of the Geomorphological Commission, Tomsk, pp. 178-184

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Malyshkov, Yu.P., Malyshkov, S.Yu., 2009. Periodicity of Geophysical fields and Seismicity: possible link with core motion. Russian Geology and Geophysics, 50, p.115-130. Malyshkov Yu. P., Malyshkov S. Yu. 2012. Eccentric Motion of the Earth’s Core and Lithosphere: Origin of Deformation Waves and their Practical Application. In hardcover: The Earth's Core: Structure, Properties and Dynamics, Editors: Jon M. Phillips, Nova Science Publishers, Inc. ISBN: 978-1-61324-584-2, p. 115-212. Malyshkov Yu.P., Malyshkov S.Yu., Chernenko R.A., Sergeeva L.S. 2002. Diurnal rhythms in the lithosphere and in the biosphere, in: Кабанов М.В., Солдаткин Н.П. (EDs.), Monitoring and Rehabilitation of the Environment. Proc. III International Symposium. Spektr, Institute of Atmosphere Optics, Tomsk, pp. 108-110. Malyshkov, Yu.P., Malyshkov, S.Yu., Gordeev, V.F., 2000. Pulse Fields: Possible Link with Crustal Motion. Proc. Second International Symposium “Environmental Monitoring and Rehabilitation” [in Russian], Izd. “Spectr”, Tomsk, p.169-171. Malyshkov, Yu.P., Malyshkov, S.Yu., Shtalin, S.G., Gordee, V.F., Polivach, V.I., 2009. A Method for determination of attitude position and parameters of the Earth’s inner core motion [in Russian]. Patent RF No. 2352961, 20.04.2009, IB 11. Malyshkov, Yu.P., Malyshkov, S.Yu., Shtalin, S.G., Gordee, V.F., Polivach, V.I., 2011. A method of Geophysical Survey [in Russian]. Patent RF No. 2414726, 20.03.2011, IB 8. (filed under Patent Cooperation Treaty No. PCT/RU2010/000007) Melchior, P., 1983. Earth Tides. Pergamon Press, Oxford. Raspopov, O.M., Kleimenova, N.G., 1977. Perturbation of Earth’s EM Field. Part 3. VLF Radiation [in Russian]. Leningrad University, Leningrad. Remizov, L.T., 1985. Natural Radiowave Noise [in Russian]. Nauka, Moscow. Seismicity in Siberia from 1976 through 1991, Institute of the Earth’s Crust, Irkutsk. Sidorenkov, N.S., 2002. Physics of Earth Rotation Instability [in Russian]. Nauka, Moscow. Sidorin A.Ya. 2010. A new harmonic model of the world: discovery or delusion? Journal «Geophysical processes and biosphere». v. 9, № 4, p. 5-20. Surkov, V.V., 2000. Electromagnetic effects in case of earthquakes and blasts [in Russian]. Izd. MIFI, Moscow. Sadovskii, M.A. (Ed.), 1982. Electromagnetic Earthquake Precursors [in Russian]. Nauka, Moscow.

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Chapter 2

ELECTROMAGNETIC INTERACTION BETWEEN ENVIRONMENTAL FIELDS AND LIVING SYSTEMS DETERMINES HEALTH AND WELL-BEING Dimitris J. Panagopoulos University of Athens, Department of Biology, Athens, Greece Radiation and Environmental Biophysics Research Centre, Athens, Greece

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ABSTRACT In the present chapter we present data showing the electric nature of both our natural environment and the living organisms and how the inevitable interaction between the two, determines health and well-being. We first give a brief theoretical background of electromagnetic fields (EMFs) and waves and delineate the differences between natural and man-made electromagnetic radiation. Apart from other differences, while man-made radiation produced by oscillation circuits is polarized, natural radiation produced by atomic events is not. We describe the electromagnetic nature of our natural environment on Earth, i.e. the terrestrial electric and magnetic fields, the natural radiation from the sun and the stars, the cosmic microwaves and the natural radioactivity. We note that all living organisms on Earth live in harmony with these natural fields and types of radiation as long as these fields are within normal levels and are not disturbed by changes, usually in solar activity. We then describe the electrical nature of all living organisms as this is determined by the electrical properties of the cell membranes, the circadian biological clock, the endogenous electric currents within cells and tissues, and the intracellular ionic oscillations. We explain how the periodicity of our natural environment mainly determined by the periodical movement of the earth around its axis and around the sun, implies the periodical function of the suprahiasmatic nuclei (SCN) - a group of neurons located above the optic chiasm - which constitute the central circadian biological clock in mammals. We discuss the probable connection between the central biological clock with the endogenous electric oscillations within 

Correspondence: 1) Dr. Dimitris Panagopoulos, Department of Biology, University of Athens, Panepistimiopolis, 15784, Athens, Greece. Fax: +30210 7274742, Phone: +30210 7274273. E-mail: [email protected], 2) Dr. Dimitris Panagopoulos, Radiation and Environmental Biophysics Research Centre, 79 Ch. Trikoupi str., 10681 Athens, Greece., E-mail: [email protected]

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Dimitris J. Panagopoulos cells and organs constituting the “peripheral clocks”, and how the central clock controls the function of peripheral ones in the heart, the brain, and all parts of the living body by electrical and chemical signals. We explain how cellular/tissue functions are initiated and controlled by endogenous (intracellular/trans-cellular) weak electric currents consisting of directed free ion flows through the cytoplasm and the plasma membrane, and the connection of these currents with the function of the circadian biological clock. We present experimental data showing that the endogenous electric currents and the corresponding functions they control can be easily varied by externally applied electric or magnetic fields of similar or even significantly smaller intensities than those generating the endogenous currents. We present two possible ways by which external EMFs like those produced by human technology can distort the physiological endogenous electric currents and the corresponding biological/physiological functions: a) By direct interference between the external and the endogenous fields and, b) By alteration of the intracellular ionic concentrations (i.e. by changing the number of electric current carriers within the cells) after irregular gating of electrosensitive ionchannels on the cell membranes. Finally, we discuss how maintenance of this delicate electromagnetic equilibrium between living organisms and their natural environment, determines health and well-being, and how its disturbance will inevitably lead sooner or later to health effects.

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1. INTRODUCTION For millions of years since the beginning of their existence, all living organisms live within a natural electromagnetic environment determined by the earth’s electric and magnetic fields, the sun’s electromagnetic activity, cosmic ionizing and non-ionizing radiation (including the “cosmic microwaves”), and terrestrial radioactivity consisting of γ radiation and charged particles. These natural electromagnetic field/radiation sources generate a continuous flow of electromagnetic energy within which all living creatures exist. This natural electromagnetic environment with frequencies ranging from infrared to gamma rays (with the exception of the static terrestrial fields and the cosmic microwaves) has more or less a constant intensity level most of the time and living organisms have adapted to this stable electromagnetic environment for millions of years. Nevertheless, during “magnetic storms” arising from increased sun activity, variations on the order of 20% in the normal levels of natural fields take place. During these variations that usually last a few days a considerable increase in health problems takes place in humans and all living organisms on earth. During the last century and especially during the last decades, man-made EMFs (like those associated with power lines) and wireless communications radiation at frequencies below the low limit of infrared have appeared with constantly increasing levels at very high rates. These unnatural (artificial) EMFs are quiet different from the natural ones basically due to the fact that they are polarized, varying, usually modulated, and generated in a continuous mode by electric/electronic oscillation circuits. These artificial EMFs add to the natural environmental ones increasing the exposure of living creatures to EMFs and constituting what is called “electromagnetic pollution”. The technological evolution connected with the production and use of these artificial polarized electromagnetic fields is tremendous and can be used either for the benefit or the destruction of humankind and the environment. An increasing number of biological and

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consequent health effects are being reported to be connected with these artificial fields. These effects range from simple changes in the normal cellular rates, to reproductive collapses and DNA damage with following consequences (cancer, cell death, degenerative neural deceases, heritable mutations etc) (Goodman et al. 1995; Phillips et al. 2009; Johansson 2009; Panagopoulos 2011). Epidemiological studies show a connection between exposure to manmade electromagnetic fields of different frequencies and different types of cancer in human population (Wertheimer and Leeper 1979; Savitz et al. 1988; Feychting and Ahlbom 1993; 1994; 1995; Coleman et al. 1989; Draper et al. 2005; Carlo and Jenrow 2000; Hallberg and Johansson 2002; Hardell et al. 2007; 2009; Hardell and Carlberg 2009; Khurana et al. 2009). Some still insist that they see nothing of these, that environmental man-made electromagnetic fields cannot cause any biological/health effects as long as they don’t cause tissue heating, and that the reported effects simply do not exist. Could that ever be possible? All living organisms consist of cells and have a precise and delicate electromagnetic nature. All functions at cellular, tissue, and organ level are controlled by physiological endogenous electric fields like the trans-membrane electric fields, and corresponding weak transient endogenous electric currents, like the intracellular electric currents originating from cytoplasmic voltage differences due to corresponding differences in the concentrations of mobile ions within cells. Intracellular electric currents are found to control cell growth, proliferation, differentiation, etc, while corresponding electric currents within tissues involving hundreds/thousands of cells, control embryonic development, wound healing, or tissue regeneration. Electromagnetic oscillations generated in the brain of all mammals by the SCN specialized neurons constituting their central circadian biological clock - seem to control physiological functions, health and vitality. Moreover, “spontaneous” intracellular ionic oscillations in the extremely low frequency (ELF: 0-300 Hz) range within every part of the body seem to constitute the peripheral clocks controlled by the central biological clock. Similar biological clocks and intracellular oscillations exist within all living organisms. This internal subtle electromagnetic network within all living bodies will inevitably interact with any other electromagnetic field - natural or manmade - in their environment. This interaction will cause changes (distortion) in the form, intensity, frequency and direction of the subtle natural endogenous electromagnetic fields/currents, and this in turn will distort the corresponding cellular/biological functions controlled by the specific endogenous fields. If the external fields are of a constant form (like the terrestrial static electric and magnetic fields) the cells adapt to them more easily. But if they change constantly and unexpectedly (as during magnetic storms or as with most types of man-made fields) the cells cannot adapt. This is when alterations in cellular functions leading to biological changes and health effects originate. Therefore it is obvious that under normal conditions an electromagnetic equilibrium occurs between living organisms and natural environment. If this equilibrium is disturbed, physiological functions will be disrupted also. In the present chapter we explain how the electromagnetic nature of all living organisms interacts with the electromagnetic natural environment to maintain health and well-being and how unnatural electromagnetic radiation/fields can disrupt this equilibrium.

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2. ELECTROMAGNETIC FIELDS AND WAVES 2.1. Maxwell Equations Classical electromagnetic theory is synopsized in the following four Maxwell’s equations: 1. Electric field flow through a closed surface (S) is proportional to the net electric charge (q) included within this surface:

 

 E u

N

dS 

S

q

(1)

o

2. Magnetic field flow through a closed surface (S) is zero:

  B   uN dS  0

(2)

S

3. Electric field circulation along a closed line (l) (in other words, the magnetically induced electromotive force - voltage - V along a closed conductor l ), equals the temporal variation rate of the magnetic field flow through the surface (S) included within that closed line:

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  d   E  d l   B  uN dS l dt S

(3)

4. Magnetic field circulation along a closed line (l) (in other words, the induced magnetic field along a closed line l) is proportional to the total electric current (the transport current I, plus the displacement current) through the surface (S) included within that closed line:





 B  dl   I    o

l

o

o

d   E  uN dS dt S

 

(4)



where: E , B are the intensities of the electric and magnetic field respectively, u N is the unit



vector vertically to the surface S, dl is an incremental length along the closed conductor l, o = 8.85410-12 C2/Nm2 = 1/4e is the electric permittivity (dielectric constant) of vacuum, and ο=410-7 Vsec/Am =4 m is the magnetic permeability of vacuum. The above form of Maxwell’s equations is valid for the vacuum or the air. Equations (3) and (4) will be more useful to us in a differential form, which is correspondingly:

     E = t

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Electromagnetic Interaction between Environmental Fields ...

    E and   B = o j   o o t

(6)



where, j is the electric current surface density. The first equation, also known as Gauss’ law for the electric field, declares that the electric field is proportional to the net electric charge that generates it. The second equation, also known as Gauss’ law for the magnetic field, declares that there can be no single magnetic poles but any magnetic pole is always in pair with an equal opposite one. Thereby, the amount of magnetic flow leaving a closed surface containing a magnet (with two opposite poles) will always equal the amount entering the same closed surface. According to the third equation, also known as Faraday-Henry law, a temporally varying magnetic field induces an electric field, the intensity of which is proportional to the variation rate of the magnetic field intensity. According to the fourth equation, also known as Ampere-Maxwell law, an electric current I, or/and a temporally varying electric field induce a magnetic field, the intensity of which is linearly dependant to the electric current intensity plus the variation rate of the electric field intensity.

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2.2. Plane Electromagnetic Waves The generation of an electromagnetic wave, presumes time-varying electric and magnetic fields connected to each other in a way that the one induces the other in a degree proportional to the rate of temporal variation, according to Maxwell’s third and fourth laws. If we consider an oscillating electric field parallel to Υ axis and an oscillating magnetic field parallel to Ζ axis in a rectangular coordinate system (X, Y, Z), then from equations (3) and (4) [or better from (5) and (6) correspondingly] after operations, it comes that:

 2E 1  2E  t 2  o  o x 2 and:

 2B 1  2B  t 2  o o x 2

(7)

(8)

Comparing eq. (7), (8), with the Wave Equation: 2  2 2   u t 2 x 2

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Dimitris J. Panagopoulos





(where  is a disturbance, transmitted in the x direction with a velocity u ), it follows that the oscillating electric and magnetic fields in Eqs. (7), (8), are transmitted in the direction of Χ axis (vertically to both the electric and the magnetic fields) with a velocity:

c=

1

(10)

 o o

The magnitude of this velocity (which is also the velocity of light since light is also electromagnetic radiation) in the vacuum or in the air, was found experimentally by Heinrich R. Hertz, in 1888 and it is the transmission velocity, of every time-varying electromagnetic field, in the vacuum or in the air:

c=

1

 o o

= 2.9979108 m/sec  3108 m/sec.

Then the value of the constant ο (magnetic permeability of the vacuum), was arbitrarily defined: ο=410-7 Vsec/Am = 4m and according to this, the value of ο , (dielectric constant or electric permittivity of the vacuum), was calculated by Eq. (10):

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ο = 8.85410-12 C2/Nm2 = 1/4e The described electromagnetic waves are called plane or linearly polarized electromagnetic waves, since both the electric and the magnetic components oscillate on certain planes vertical to each other. The plane of the E-component is considered as the plane of the electromagnetic wave. If, in addition, the electric and the magnetic fields vary harmonically with a frequency   = /2 , then they produce harmonic waves (in the x direction) with a wavelength:  = 2/kw. In this case:

 = o sin kw(x-ct) = o sin (kw x- t)

(11)

and  = ο sin kw(x-ct) = o sin (kw x- t)

(12)

where:  = 2πν =kwc, is the circular frequency and kw (=2/) is called the wavenumber. [The product of the frequency times the wavelength is the velocity of the electromagnetic wave (and of any wave): c = λ ν ] From equations (10), (11), (12) and because

E B , [deriving from eq. (5)], we  x t

finally get:

 = c

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Electromagnetic Interaction between Environmental Fields ...





Equation (13), refers to the magnitudes of the vectors E , B , declaring that the two fields/components of the electromagnetic wave, are at every moment, in phase with eachother (in the case of harmonic plane waves). A combination of linearly polarized electromagnetic waves with equal amplitudes for each field and with certain phase difference, gives circularly polarized electromagnetic waves, or elliptically polarized, if the corresponding amplitudes are different. [Circularly polarized, are the three-phase Power Transmission Line Fields away from the lines. Near and under the lines these fields are elliptically polarized]. 2.3. Energy of Electromagnetic Waves The Energy Density of an electric field (in the vacuum or in the air), is given by the equation:

We =

1 2 o 2

(14)

Eq. (14), also gives the energy density related to the electric component of an electromagnetic wave (not necessarily plane one). Correspondingly, the energy density for magnetic field, (or for the magnetic component of an electromagnetic wave), is:

Wm =

1 2 o

2

(15)

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From equations (10), (13), (14), (15), we get (for a plane, harmonic wave):

Wm = We =

1 2  o 2

(16)

Thus, the total energy density (in J/m3) of a plane, harmonic electromagnetic wave (in the vacuum or in the air), is: W = We + Wm = o2

(17)

2.4. Intensity of Electromagnetic Waves, (Power Density) The Intensity of the electromagnetic wave, (power per unit surface area), is equal to the  energy density times the wave velocity c :

  J = cW It has the same direction as the velocity of the wave, and is called “Poynting vector”.

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Dimitris J. Panagopoulos For a plane, harmonic wave in the vacuum or in the air,

  J = c o2

(19)

From eq. (13), (19), it comes that:

   J = c2 o E  B 1   or = EB o

(20) (21)

If we know the intensity J of a plane, harmonic wave, then according to Eqs. (21) and (13), the magnitude of its electric component in the vacuum or in the air, is calculated by the equation:

2 = J

where

(22)

o = 376.87   377 , is called the “wave impedance”. Hence: o

2  J 377

(23)

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( in V/m, J in W/m2) Correspondingly, the magnitude of the magnetic component in the vacuum or in the air, satisfies the equation:

2 =

o c

J

(24)

or 2  J 4.210-15

(25)

( in T, J in W/m2) The vector, represents the intensity of the magnetic field within a certain medium and is usually called also, Magnetic Induction, or Magnetic Flux Density.



Frequently in textbooks we also see the H vector, which represents the intensity of the magnetic field regardless of the medium. The two vectors are connected by the relation:

  B = ο H (Η, in A/m in SI)

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Electromagnetic Interaction between Environmental Fields ...

where:  is the relative magnetic permeability of the medium. [In the vacuum or in the air,  = 1. Within biological matter it is similarly   1]. From Eqs. (13), (26) we get for the plane, harmonic wave in the vacuum or in the air:

E/H =

o  377  o

(27)



The relation between the different units of and B , (in the vacuum or in the air), is:









1G ( B ) = 1 Oe ( H ) = 10-4 T ( B ) = 79.58 A/m ( H )

3. NATURAL AND MAN-MADE ELECTROMAGNETIC FIELDS IN THE TERRESTRIAL ENVIRONMENT

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3.1. Natural EMFs on Earth For millions of years throughout the course of evolution, all living organisms in the terrestrial environment have been constantly exposed to terrestrial static electric and magnetic fields of average intensities 130 V/m and 0.5 G respectively. Variations in the intensity of the terrestrial magnetic field on the order of 0.1 G during “magnetic storms” or “geomagnetic pulsations” mainly due to changes in solar activity are connected with increased rates of animal (and human) health incidents, including nervous and psychic diseases, hypertensive crises, heart attacks, cerebral accidents, and (consequently) mortality (Dubrov 1978; Presman 1977). Increase in solar activity leads to corresponding increases in the intensity of visible, ultraviolet, gamma, and meson solar radiation, increase in ionization of the earth’s atmosphere, intensity of atmospheric discharges, and increases in the earth’s magnetic and electric fields (Presman 1977). It is interesting to note that even human female fertility periodic variations seem to follow variations in the earth’s magnetic field due to lunar periodic variations determined by the lunar month (28 days). Terrestrial Electric Field: On the earth’s surface there is a natural electric field of constant polarity (static) with an average intensity 130 V/m, and vertical direction from the atmosphere towards the earth. Its intensity varies with latitude. It is minimum at the equator and at the poles and becomes maximum at intermediate latitudes. Moreover, its intensity diminishes exponentially with height from the sea surface (at 9 km above sea its intensity is 5 V/m). This terrestrial electric field displays annual and diurnal periodicity in its intensity following the corresponding variation in atmospheric conductance which in turn depends on storm periodicity. That means that during winter, the intensity of terrestrial electric field at a certain place is larger than during summer. Intensity variations between different places follow the variations of storm frequency (Pressman 1977). Terrestrial Magnetic Field: This is also of constant polarity. Magnetic poles are close but opposite to the corresponding geographical poles. In every place the terrestrial magnetic field has a vertical and a horizontal component. At the magnetic poles the horizontal component becomes almost zero while at the magnetic equator the vertical component becomes almost

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zero. The average resultant intensity of the terrestrial magnetic field is 0.5 G. In every place there are periodic variations as well as non-periodic disturbances (changes) in its intensity on the order of ±0.1 G, called “magnetic storms” which result from variations in solar activity (variation in the number of solar “spots” and “flares”) (Dubrov 1978). Cosmic Microwave Radiation: More than five decades ago it was discovered that microwave radiation of a broad spectrum (10 MHz – 10GHz) and of cosmic origin, reaches the earth’s surface and can be detected (Presman 1977). Its intensity is very low (10-17 mW/cm2/MHz), and probably represents radiation of higher frequencies above the low limit of infrared (31011 Hz ) which reaches on Earth with decreased frequency because of the universal expansion. Other types of Natural Electromagnetic Radiation on Earth: Within the different types of natural electromagnetic radiation on Earth we should also refer to the infrared, visible and ultraviolet radiation from the sun and the stars, and the natural gamma radiation of cosmic origin and radioactive minerals on Earth (uranium, radium, strontium, etc). Nevertheless, in the present chapter we shall refer mainly to the natural and artificial EMFs with frequencies below the low limit of infrared.

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3.2. Artificial EMFs on Earth At the same time, modern man is constantly exposed to artificial (man-made) EMFs with frequencies ranging from ELF to radio-frequencies (RF)/microwaves which reach closer and closer to the low limit of infrared. One of the most common EMF-exposures in modern human environment since the beginning of the twentieth century and even earlier, is the exposure to the fields associated with electric power generation, transport, and consumption. Electric energy is produced in the form of 50-60 Hz alternating three-phase electric current and transported to residential areas by high-voltage power lines of usually hundreds of kV in order to minimize thermal looses. Within residential areas the high voltage is transformed to 220-230 V prior to distribution for residential usage. Close to transformer substations or under power lines the magnetic field intensity may reach values between 0.5 and 1 G, while the electric field may reach values up to 10 kV/m. A large number of biological effects due to magnetic field exposure have been reported (Goodman et al. 1995). In addition, several epidemiological studies during the last thirty years have shown a connection between exposure to power line or transformer magnetic fields and cancer (Wertheimer and Leeper 1979; Savitz et al. 1988; Feychting and Ahlbom 1993; 1994; 1995; Coleman et al. 1989; Draper et al. 2005). This connection has been shown for magnetic field intensities down to 2 mG (Feychting and Ahlbom 1994), or distances from power lines up to 600 m (Draper et al. 2005). Another epidemiological study points to the electric and not to the magnetic component of the power line fields as having a connection with child leukemia for intensities down to 10 V/m, (Coghill et al. 1996). The current Exposure Limits for 50 Hz Magnetic Fields, (for rms magnetic field intensities), are 1G (24h exposure) for the general population and 10 G (exposure of a few hours during the working day) for occupational exposure. The corresponding 50 Hz Electric Field Exposure Limits are 5 kV/m and 10 kV/m (ICNIRP 1998; IRPA 1990). These values are even higher than those found under power lines or close to transformers.

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In addition to the 50-60 Hz EMFs, modern man as well as animals and plants are exposed since the early decades of the twentieth century to constantly increasing levels of manmade RF/microwave radiation from radio/television station antennas and radars. In addition, and especially during the last twenty years, modern man is exposed to a “sea” of microwave radiation from wireless telecommunications, wireless internet connections (Wi-Fi), satellites etc. The type of radiation emitted by these technological applications is of varying intensity, polarized, including simultaneously two or more different, usually varying, frequencies (a carrier frequency plus a modulation frequency, and recently several different carrier and modulation frequencies and a pulse repetition frequency which is also usually variable). The strongest and most commonly used microwave emitters in human proximate daily environment are the GSM (Global System for Mobile Telecommunications) mobile phones (also called “cell phones”) with a maximum output power 1-2 W, usually carried and used with no precaution in contact with the human body/head even by small children. These devices emit complicated, constantly and unpredictably changing signals which include a more and more complicated modulation in order to carry more and more information i.e. not only voice (GSM), but also video, music, internet , etc (3G, 4G, Tetra). Still, while the use of mobile phones is voluntary, human exposure to similar radiation emitted by the mobile telephony base station antennas which are installed everywhere within residential and working areas, although of usually smaller intensity (at a distance of several tenths or hundreds of meters) than that of a mobile phone in contact, is continuous (24 h daily) and involuntary. If additionally we take into account exposures from cordless domestic phones (DECT), wireless internet (Wi-Fi) which tends to be installed everywhere in schools, public places, stores, coffee places, homes, etc., which all emit similar types of microwave radiation, it follows that exposure to microwave radiation of modern wireless communications is another main type of human/environmental EMF-exposure. Therefore modern man and his environment are constantly and increasingly exposed to artificial types of EMFs/radiation constantly and unpredictably varying, polarized, and unknown to living organisms throughout development. A large and constantly increasing number of biological/health effects are attributed in our day to human and animal exposure to these artificial EMFs. Among them, the most serious is genotoxicity (DNA damage) which may lead to cell death, reproductive declines, functional disorders, cancer induction, heritable mutations, etc. (Phillips et al. 2009; Johansson 2009; Panagopoulos 2011). Since all living organisms on Earth live in harmony with the natural terrestrial EMFs for millions of years, but increased health problems appear whenever these natural fields vary mainly due to variations in solar activity as explained before, it seems that living organisms have the natural ability to adapt to constant values of natural static electric and magnetic fields, while variations in these fields generate health problems. Living organisms seem to perceive EMFs as environmental stress factors (Panagopoulos 2011) and they can adapt more easily to them when their parameters are kept constant or vary slightly. In addition, living organisms do not seem to have defense mechanisms against large variations of natural EMFs, and moreover do not have defense against unnatural (man-made) EMFs which are mostly not static but varying. This is probably the reason why cells in response to manmade EMF-exposure activate heat shock genes much more rapidly and at a much higher rate than for heat itself (Weisbrot 2003).

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3.3. Differences between Natural and Artificial Electromagnetic Radiation All time-varying EMFs produce electromagnetic waves propagating with the velocity of light and with the frequencies of the EMFs which generate them. Natural electromagnetic radiation is generated (and absorbed) by matter discontinuously by single atomic/molecular events and in particular, excitation and de-excitation of molecules (infrared), atomic electrons (visible, ultraviolet, x-rays), and atomic nuclei (gamma rays). Therefore, it is transmitted also discontinuously in the form of discrete wave-packets called “quanta” or “photons” and the energy of each photon, is given by Planck’s equation:

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Wphoton = h

(28)

where: h = 6.62510-34 Jsec, is the Planck’s constant and  the photon’s frequency. Artificial (manmade) electromagnetic waves are generated in electrical/electronic oscillation circuits by induced (forced) oscillations of electric charge (free electrons) and transmitted by antennas connected to the oscillation circuits. Thus they are (usually linearly) polarized with the plane of polarization determined by the geometry of the oscillation circuit. Moreover, artificial electromagnetic waves, have frequencies below the low limit of infrared, (  31011 Hz), and they can be emitted continuously, (in the form of continuous waves), by the oscillation circuits. In contrast, electromagnetic waves emitted by natural sources, (and by some artificial ones, like the electric light), are not polarized, since every source of radiation/light, consists of many elementary sources, i.e. radiating atoms or molecules, randomly polarized, so that actually there is no polarization. In addition, natural electromagnetic waves, have frequencies ranging from the low limit of infrared up to gamma rays, (31011 Hz    31022 Hz). [Cosmic microwave radiation which seemingly constitutes an exception to this rule, probably is, as already explained, radiation of higher frequencies (most likely above the low limit of infrared) which reaches the earth with decreased frequency because of the universal expansion]. Polarized waves can produce interference effects and induce coherent forced-vibrations on charged/polar molecules within a medium, whereas non-polarized, cannot. This is probably the reason why polarized waves, (like manmade EMFs), seem to be in many cases more bioactive than non-polarized radiation of equal or even higher frequency and intensity (as is natural light).

4. INTERACTION BETWEEN MAN-MADE EMFS/RADIATION AND LIVING MATTER 4.1. A General Hypothesis for the Type of Interaction The interaction mechanisms of (natural) infrared, visible, ultraviolet and ionizing electromagnetic radiation with matter (biological and inanimate) are more or less known since the early decades of the 20th century. Here we are mostly concerned with the interaction of manmade EMFs - frequencies below infrared - and of natural static electric and magnetic fields with biological matter. The mechanisms of this interaction are still under investigation.

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Electromagnetic Interaction between Environmental Fields ...

As already explained, natural terrestrial electric and magnetic fields are mainly of static nature and thus exert constant forces on charged/polar bio-molecules resulting to a slight polarization of the biological matter towards the direction of the terrestrial electric field (towards the centre of the earth) and vertically to the level determined by the terrestrial magnetic field and the velocity of these charged bio-molecules which are free to move as are the mobile ions (Laplace/Lorenz forces). Within normal intensity values of the terrestrial static fields, living organisms can tolerate these natural electric and magnetic forces. [Polarization of biological tissue by external fields is discussed more extensively in section 6.1.]. Natural electromagnetic radiation, in the form of photons of different polarization and with frequencies ranging from infrared to gamma rays, is generated and absorbed by matter through excitation/de-excitation phenomena as already mentioned. Artificial oscillating EMFs with frequencies ranging from a few Hz to 1010 Hz reaching more and more closely to the low limit of infrared (31011 Hz), produce polarized electromagnetic waves which cannot induce molecular or atomic excitation or ionization but are able to induce forced-vibrations in the charged/polar molecules of living matter. Let us examine what happens when a polarized, non-ionizing electromagnetic oscillation - wave - passes through a mass of polar and charged molecules such as those composing biological tissue. The electromagnetic wave will induce a forced-oscillation on each of these particles that it meets and will transfer to each of them a tiny part of its energy. This induced oscillation will be most intense on the free particles which carry a net electric charge such as the free (mobile) ions that exist in large concentrations in all types of cells or extracellular biological tissue determining practically all cellular/biological functions (Alberts et al. 1994; Panagopoulos and Margaritis 2003). The induced oscillation will be much weaker or even totally negligible on the polar biological macromolecules and the water molecules that do not have a net charge and additionally are usually bound chemically to other molecules. After each such event of interaction between the wave and a charged or polar particle, the remaining wave continues on its way through the tissue possibly scattered by a tiny angle and reduced by a tiny amount in its amplitude/intensity. After large numbers of such events, depending on the tissue’s mass, density, and the number of polar/charged molecules, the remaining wave, if any, leaves the tissue as a scattered wave of reduced amplitude/intensity (Panagopoulos et al. 2013). The density of energy We (energy per unit volume) of an electric field E within a medium with relative permittivity , is given - in respect to Eq. (14) - by the equation:

We =

1 o 2 2

(29)

The total energy density Wem of a plane, harmonic electromagnetic wave (as those usually produced by “Thomson” circuits) accounting also for the magnetic component, is in respect to Eq (17): Wem = o 2 (30)

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Thus according to Eq. (29) and (30), when the amplitude/intensity E of the oscillating field or wave is decreasing after interaction with the charged/polar molecules of a medium, its energy density decreases as well. That means that a part of its energy per unit volume is transferred to the charged/polar molecules of the medium. In general, the amount of energy absorbed by a certain amount of matter determines the degree of interaction between exposed matter and exposing radiation. But in the case of biological matter this is not as simple. Biological tissue is a much more complicated and organized form of matter compared to inanimate. The degree of interaction does not necessarily determine the biological effect. Even if we could accurately estimate the amount of absorbed energy by a whole organ (e.g. by measuring an increase in temperature if any), the biological effect depends on which specific bio-molecule(s) will absorb a certain amount of energy and this is impossible to discern. Some bio-molecules may get damaged while others may not by the same amount of radiation energy. Thus, in the case of biological matter, the amount of absorbed energy alone is not enough to determine the biological effect (Panagopoulos et al. 2013). For example, when radiation is absorbed by lipids the damage will most likely be less than when the same amount of energy is absorbed by enzymes and potentially even smaller than when absorbed by nucleic acids - especially DNA. The situation becomes even more complicated in case that the biological effects are indirect as they are in most cases. For example, damage in the DNA may be due not to the energy absorbed directly by the DNA molecule but due to a conformational change in a membrane protein leading to irregular alteration of intracellular ionic concentrations (as described in section 6.2) and this in turn giving a signal for a cascade of intracellular events causing irregular release of free radicals or DNases which finally damage DNA (indirect effect). In conclusion, in regard to the interaction between radiation and living matter (especially man-made electromagnetic but not only), the amount of absorbed radiation energy alone, does not determine the biological effect. For this, dosimetry based on the Specific Absorption Rate (SAR) (defined as the amount of radiation power absorbed by the unit mass of biological tissue) might not be a credible measure to determine the biological activity of EMFs (Panagopoulos et al. 2013).

4.2. The Energy Absorbed by Biological Molecules during Exposure to Man-Made EMFs Is Normally Well Below the Thermal Level Electromagnetic radiation absorbed by matter does not always cause measurable temperature increases. Heating naturally occurs when the absorbed radiation has a frequency above the lower limit of infrared (31011 Hz) (Panagopoulos and Margaritis 2003). Manmade microwave radiation used in modern telecommunications and other applications with frequencies 108-1010 Hz cannot directly cause measurable temperature increases in biological tissue unless it is of large enough intensity (well above 1 mW/cm2) as for example in the case of a microwave oven that operates at about 103 W. Radiation of even lower frequency would need to be of even larger power/intensity to produce thermal effects. Usual microwave intensities in modern human environment (mainly due to mobile telephony handsets and base

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station antennas, Wi-Fi, and radio-television station antennas) are between 0.01 μW/cm2 and 100 μW/cm2 (Panagopoulos et al. 2013). Man-made radiation that has neither the frequency nor the intensity to cause tissue heating (thermal effects), is absorbed - as explained above - in much smaller quantities by inducing forced-oscillations on polar molecules and free charges such as the free ions within all living cells. These forced-oscillations are superimposed on the thermal vibration of the same particles increasing - theoretically - their thermal energy. But as we shall demonstrate, the energy of the oscillations induced by external EMFs at environmental exposure levels (intensities) is normally millions of times smaller than the average thermal energy kT of the molecules within biological tissue, and thus it does not produce measurable temperature increases (Panagopoulos et al. 2013). Although these induced oscillations (with kinetic energy usually thousands/millions of times lower than the average thermal energy) normally do not add to tissue temperature, they can still cause severe biological alterations (such as DNA damage) without heating the tissue (Panagopoulos 2011). These are called “non-thermal effects” and if not properly equilibrated by the organism’s immune and other compensatory systems, they may very well result in health effects (Goodman 1995; Johansson 2009; Carlo 1998; Carlo and Jenrow 2000; Carlo and Thibodeaux 2001). Let us estimate the amount of energy lost by a plane harmonic electromagnetic wave after an interaction with a single free ion within biological tissue. The total energy acquired by the charged free particle due to the forced-oscillation induced by the wave is the total energy of the harmonic oscillation:

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i =

1 mi uo2 2

(31)

where, mi is the ion mass which in the case of a Na+ ion, is mi  3.810-26 kg. uo is the particle’s maximum velocity of the forced-oscillation assumed to be equal to  0.25 m/s, which is the drift velocity of Na+ ions along an open trans-membrane sodium channel, as calculated from patch-clamp ionic current measurements through open channels (Neher and Sakmann 1992; Stryer 1996; Panagopoulos et al. 2000). From Eq. (31) after substituting the values of the parameters, we get that the energy absorbed by a single ion due to the interaction with the electromagnetic wave, is on the order of: i ≈ 10-27 J. Considering that the concentration of free ions within cells is on the order of 1 ion per nm (Alberts et al. 1994) and a typical cell volume up to 103 μm3, a single cell contains about 1012 free ions and thus it will absorb about 101210-27 J = 10-15 J. A human body of average size consisting of ~1014 cells, will absorb about 101410-15 = 10-1 J. For waves emitted by a supposed unidirectional antenna operating with 1 W (= 1 J/sec) output power, (thereby transmitting energy 1 J per sec) it takes about 10 human bodies in sequence in order to be totally absorbed, according to the above mechanism, which seems a reasonable result. Certainly, except for the energy absorbed by mobile ions within biological tissue, there will be additional energy absorption by the water dipoles and the charged or polar macromolecules like proteins, lipids, or nucleic acids, which will also be forced to oscillate by the applied field. While we can have a rough estimation as shown above for the energy 3

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Dimitris J. Panagopoulos

absorbed by mobile ions, we are unable to estimate much smaller amounts of energy absorbed by water or charged/polar biological macromolecules. These smaller amounts of energy may be of decisive importance for the biological effect (Panagopoulos et al. 2013). Let us compare the velocity and kinetic energy acquired by a free ion within biological tissue, due to an external EMF, with the thermal velocity and energy of such a particle: The maximum velocity of the ion’s induced vibration is assumed to be, uo  0.25 m/s as explained already, and the corresponding maximum kinetic energy given by Eq (31), is calculated to have a value: i ≈ 10-27 J. This ion possesses also an additional average velocity ukT, due to its thermal energy, given by the equation:

3kT mi

ukT =

(32)

where T=310 oK (the temperature of the human body at 37oC), k = 1.38110-23 JK-1 the Boltzmann’s constant, and mi the ion’s mass (mi  3.810-26 kg for Na+ ions) (Panagopoulos et al. 2000; 2002; 2013). Eq. (32) derives from the equation for the average kinetic energy of a single-atom molecule/free ion due to thermal motion (Mandl 1988):

kT =

1 3 mi ukT 2 = kT 2 2

(33)

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From Eqs. (32) and (33) respectively we get: ukT  0.58103 m/s, and kT  6.410-21 J. Comparing the values of the above two different velocities/energies we find that, the velocity acquired by a free ion within biological tissue due to an environmental EMF is normally about 2.3103 (

ukT ) times smaller than its thermal velocity, and its kinetic uo

1 mi uo2 induced by the environmental EMF is about 5.3106 times smaller than 2 3 the average thermal energy kT of such a particle. 2 energy i =

Thereby, we have shown that oscillations induced on biological molecules by environmental EMFs do not usually contribute to the tissue temperature, except if these fields were millions of times more powerful, as for example the fields within a microwave oven operating at about 1000 W and focusing all of its radiating power within its cavity, in contrast to a mobile phone ( 0.1-1 W) or even a mobile telephony base station antenna ( 10-100 W) radiating (and distributing their energy) in all directions within wide angles. This is the reason why initially it was believed by scientists and authorities that environmental EMFs could not induce any biological effect (Adair 1991a). Even though some scientists still express skepticism regarding the existence of non-thermal effects (Verschaeve et al. 2010), there is already a large and constantly increasing number of studies indicating that environmental

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man-made EMFs can produce severe biological alterations such as DNA damage without heating the biological tissue (Panagopoulos and Margaritis 2008; Panagopoulos 2011; 2012; Johansson 2009; Goodman et al. 1995; Carpenter and Livstone 1968; Kwee et al. 1998; Velizarov et al. 1999). This can take place through non-thermal mechanisms that involve direct changes in intracellular ionic concentrations or changes in enzymatic activity (Panagopoulos et al. 2000; 2002; Liboff and McLeod 1988; Lednev 1991).

5. PHYSIOLOGICAL ENDOGENOUS ELECTRIC FIELDS IN CELLS AND TISSUES PRACTICALLY CONTROL ALL CELLULAR/BIOLOGICAL FUNCTIONS

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5.1. Trans-Membrane Electric Field All membranes in living cells have a voltage difference between their external and internal surfaces called “resting membrane potential” with resultant strong electric field on the order of 107 V/m across the membrane, with the internal always negative in regard to the external. The membrane potential is mainly generated by unequal distributions of free ions between the internal and the external sides of the membrane aqueous solutions. This refers both to the plasma membranes surrounding the whole cell and the membranes of intracellular organelles like the mitochondria, endoplasmic reticulum, etc. When stimulated, some types of cells respond with short potential changes on their plasma membrane resting potential and revert to normal value again. These transient potential changes are called “action potentials” and are mostly found in nerve, muscle, and sensory cells. In this way (by generation of action potentials) information is transmitted between different parts of a living body through electrical signals in the form of transmitted changes in membrane potentials, which convert into chemical signals to pass from the one adjacent cell to the next, reconvert into electrical ones, and so on. All cell membranes are lipid bilayers with polar external and internal surfaces and hydrophobic interior, forming a mosaic structure with membrane proteins. Some of these proteins called “trans-membrane proteins” penetrate completely the lipid bilayer forming channels through which polar/charged molecules can pass. On both sides of every cell membrane, there are free ions, (mainly K  , Na  , Cl  , Ca 2 etc.), which: a) control the cell volume, by generating osmotic forces which are responsible for the entrance or exit of water, b) play an important role in a plethora of metabolic cell processes/signal transduction processes, c) create the strong electric field between the two sides of the cell membrane. Actually, these ions are not really “free” but they are weakly and transiently bound to water dipoles. Nevertheless it is known that when they pass through the pores of the membrane channels they are dehydrated (Leuchtag 1992; 1994; Miller 2000) meaning that these ions have the ability to jump or flow between different water dipoles. These ions are also called, “mobile ions”. Mobile (“free”) ions play a particularly important role in cell function. They move in and out of the cell membranes through trans-membrane protein channels of specific diameter, different for each type of ion. The channel walls are constructed from several trans-membrane parallel a-helices forming the channel’s pore between them when the channel is in its open

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state. A specific type of channels are the “voltage-gated” or “electro-sensitive” ones, which are cation channels. These channels change between open and closed state when their “voltage-sensors” receive an electrostatic force after a change in the membrane potential of about 30mV (Bezanilla et al. 1982; Liman et al. 1991). Similarly there exist “ligand-gated” channels responding to chemical signals in the form of specific molecules (ligands) that bind to specific sites of the channel to induce gating, and “mechanically-gated” channels changing between open and closed state by mechanical pressure depending on the concentration of ions at the channel site. The voltage sensors of the electro-sensitive channels, are four symmetrically arranged, transmembrane, positively charged a-helices, each one designated S4, (Noda et al. 1986; Stuhmer et al. 1989). Membrane potentials were originally studied in the giant axons of the squid and other types of nerve and muscle fiber cells (Hodgkin and Huxley 1952). A more recent method is based on measuring equilibrium concentrations of ions between the external and internal sides of the membrane using charged dyes that bind to specific ions and performing fluorescence or absorption measurements (Neumcke 1983). After determining the concentrations of ions on both sides of the membrane, the trans-membrane voltage (membrane potential) is calculated by the Nernst Equation (34). This gives the potential difference across the plasma membrane, under equilibrium conditions, due to a particular type of ion:

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o -  i = -

RT Co ln zFc Ci

(34)

where: o, i are the electrical potential on the external and internal surface of the membrane respectively, R is the gas constant, T is the Absolute Temperature (in K), z is the ion’s electric charge in electrons (the ion’s valence), Fc is the Faraday constant, and Co, Ci are the concentrations of a certain type of ion on the external and internal side of the membrane respectively at equilibrium, in other words, when the net flux of this ion, is zero. The total electrical potential difference across the membrane, is the sum of the contributions from all the existing types of ions, restoring the final balance between osmotic and electrical forces. Ion flux through cell membranes is caused by forces due to concentration and voltage gradients, between the two sides of the membrane. Under equilibrium conditions, the net ion flux through the membrane is zero and the membrane has a voltage difference (“resting membrane potential”) Δ =  o -  i between its external and internal surface, varying between 20 and 200 mV in animal cells, with the internal always negative in relation to the external (Baker et al. 1962; Hille 1992; Hodgkin and Huxley 1952; Alberts et al. 1994). The intensity m = Δ / s of the transmembrane electric field, assuming an average membrane width s  100 A = 10 8 m and Δ  100 mV = 0.1 V, has a value on the order of 10 7 V/m as already mentioned. The membrane electric field is, as also stated already, mainly generated by the unequal distribution of mobile ions in the external and internal sides of the membranes, with the majority of positive ions at the external side. The “leak” channels of Κ  and Na+ ions, play a crucial role, in cooperation with the Κ  - Να  pump (Κ  - Να  ATPase), while other

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electrogenic pumps contribute to a smaller degree, (Hille 1992; Stryer 1996). It is also the majority of negative charged lipids, on the inner surface of the lipid bilayer, in all membranes, and the majority of fixed anions in this side that contribute to the generation of the transmembrane potential (Honig et al. 1986; Neumke 1983; Alberts et al. 1994). In any case, the existence of the trans-membrane electric field is maintained by active transport of ions, since without the contribution of the electrogenic ion pumps, only a passive diffusion of ions through the membrane would not be enough to maintain the potential difference. The Κ  Να  ATPase transports by energy (ATP) consumption more Na+ ions outside of a cell than K+ ions inside at a ratio of 3/2, contributing in this way to a more negative cell interior.

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5.2. The Circadian Biological Clock The daily rotation of the earth around its axis and its yearly rotation around the sun, impose on living organisms adaptation to diurnal and seasonal periodicity. In addition, the moon’s monthly rotation around the earth (27.32 days orbital period or 29.53 days for an observer on Earth) seems to determine in a still unknown way the periodicity in human female fertility. Thus, all living organisms on Earth have adapted for millions of years to certain types of natural periodicity and have in this way become natural oscillators. This natural environmental periodicity has imposed on all living organisms a corresponding functional periodicity in accordance with its frequencies. In this way, all living organisms on Earth have developed endogenous molecular circadian and seasonal clocks to synchronize their behavioural, biological, and metabolic rhythms to natural environmental periodicity in order to perform at their best over a daily, monthly and yearly span. This is a form of resonance between the periodicity of our environment seen as an “exciter” and living organisms seen as individual oscillators who perform at their maximum when the frequencies of the exciter coincide with their self-frequencies. Since all living organisms’ “self-frequencies” are developed and stabilized by the periodicity of the natural environment during millions of years, if the periodicity of the environment changes artificially e.g. by exposure to light during normally dark periods of the 24-h cycle, the “exciter” changes its frequency and thus resonance is abolished. In particular, the natural diurnal periodicity of light and dark is of apparent importance and the coordinated circadian regulation of sleep/wake, rest/activity, fasting/feeding, and catabolic/anabolic cycles is crucial for optimal health and well-being. Throughout the course of evolution, all animals and plants are exposed to regularly alternating periods of light and darkness during each day. This allowed species to adjust their physiology and synchronize it with the natural light/dark environment. In order to achieve such a synchronization/resonance with the natural environment, vertebrates (including mammals) evolved a group of neurons to monitor the photoperiodic environment and to adjust accordingly the function of each single cell, organ, and their whole organism. It is a paired group of light-responsive neurons located in the mediobasal preoptic area at the diencephalic-telencephalic junction just anterior to the hypothalamus. Since these neurons lie immediately above the decussating axons of the optic nerve, i.e., the optic chiasm, they are named the suprachiasmatic nuclei (SCN). The fact that the SCN in the anterior hypothalamus of the brain constitute the central biological clock in mammals has been known

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since 1972. The SCN consists of two regions of several clusters of small and densely packed paired neurons in which various peptidergic transmitters are expressed (Weaver 1998; Reiter et al. 2011; Schwartz 2009). The SCN clock is composed of multiple, single-cell circadian oscillators firing rhythmic nerve (electrical/chemical) impulses, which, when synchronized, generate co-ordinated circadian outputs that regulate the biological rhythms of the whole organism. The daily periodicity in the alternating intervals of light and darkness seems to be the most potent synchronizer for the SCN. Light from the environment is perceived in the eyes by specialized intrinsically photosensitive retinal ganglion cells (ipRGC) containing the specialized photopigment, melanopsin, sensitive to blue wavelengths of about 460-480 μm (Kawasaki and Kardon 2007). The axons of these neurons travel in the optic nerve to the level of the optic chiasm where they then diverge to penetrate the SCN where they make synaptic contact with clock neurons. It is via this neural pathway, referred to as the retinohypothalamic tract, that the light/dark cycle adjusts continuously the function of the biological clock. Thus, the SCN clock receives photic information via the retinohypothalamic tract. Retinal signals, mediated by glutamate, induce calcium release and activate a number of intracellular cascades involved in photic gating and phase shifting. Cell membrane events are directly involved in rhythmic expression. Calcium and potassium currents influence the electrical output of pacemaker neurons by altering shape and intervals of impulse prepotentials, afterhyperpolarization periods, and interspike intervals, as well as altering membrane potentials and thereby shaping the spontaneous rhythmic spiking patterns. As with the involvement of neuronal membrane events that play a crucial role, postsynaptic events and transmembrane ion fluxes are also essential elements in circadian rhythm generation and entrainment (Lundkvist and Block 2005). The biological clock of the circadian timing system, composed of master molecular oscillators within the SCN, paces self-sustained and cell-autonomous molecular oscillators in peripheral tissues through electrical and chemical signals. In turn, circadian rhythms in gene expression synchronize biochemical processes and metabolic fluxes with the external environment, allowing the organism to function effectively in response to predictable physiological changes (Mazzoccoli et al. 2012). Each neuron in the SCN central clock has the necessary molecular machinery for generating circadian rhythmicity. The electric oscillations in the central clock neurons are electrically/chemically communicated to all molecular clocks in peripheral tissues cells. In this way the SCN regulate circadian rhythmicity in all peripheral tissues. In cases where the peripheral oscillators cease to be in tune with the central clock, circadian disruption (chronodisruption) results. To keep cellular rhythms in synchrony with the central clock, the system requires regular input from the ipRGC. We may speculate that the peripheral clocks in each individual cell of the organism are intimately related to the so called “spontaneous” intracellular ionic oscillations discovered in all types of cells (described in section 5.3 of the present chapter). Clock oscillators have been found in many peripheral tissues, such as the liver, adipose tissue, intestine, heart and retina. All aspects of physiology and behaviour, including sleep/wake cycles, brain and cardiovascular activity, endocrine system, physiology of the gastrointestinal tract, hepatic metabolism, etc, are controlled by the circadian clock. The SCN clock not only sends signals to synchronize the molecular oscillators in peripheral tissues, but

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also to prevent the dampening of the circadian rhythms in these tissues. The SCN accomplish this task via neuronal connections or by triggering the circulation of humoral factors (Froy 2011). The interplay between the central and the peripheral tissue clocks is not yet fully understood and remains a major challenge in determining how neurological and metabolic homeostasis is achieved across the sleep-wake cycle. Disturbances in the communication between the different individual body clocks can desynchronize the circadian system, which in turn may lead to unwell ness, chronic fatigue, decreased performance, obesity, neuropsychiatric disorders, and the development of different diseases (Albrecht 2012). The hierarchical organization of the circadian system, through which the SCN central clock controls the peripheral circadian clocks in the cortex, the pineal gland, the liver, the kidney, the heart, and in every part of the body, ensures the proper timing of all physiological processes. In each SCN neuron, interconnected transcriptional and translational feedback loops enable the circadian expression of the clock genes. Although all the neurons have the same genotype, the oscillations of individual cells are highly heterogeneous in dispersed cell culture: many cells present damped oscillations and the period of the oscillations varies from cell to cell. These heterogeneous oscillations of individual cells are continuously adjusted and synchronized by the central SCN clock. In addition, the neurotransmitters that ensure the intercellular coupling, and thereby the synchronization of the cellular rhythms, differ between the two main regions of the SCN. Interestingly it seems that this cellular heterogeneity between the two regions is not detrimental to synchronization performances, but on the contrary helps resynchronization after jet lag. It seems that the heterogeneous architecture of the SCN decreases the sensitivity of the network to short entrainment perturbations while, at the same time, improving its adaptation abilities to long term changes (Hafner et al. 2012). Nutritional status is sensed by nuclear receptors and co-receptors, transcriptional regulatory proteins, and protein kinases, which synchronize metabolic gene expression and epigenetic modification, as well as energy production and expenditure, with behavioural and light-dark alternation. Physiological rhythmicity characterizes these biological processes and body functions, and multiple rhythms coexist presenting different phases, which may determine different ways of coordination among the circadian patterns, at both the cellular and whole-body levels. A complete loss of rhythmicity or a change of phase may alter the physiological array of rhythms, with the onset of chronodisruption or internal desynchronization, leading to metabolic derangement and disease, i.e., chronopathology (Mazzoccoli et al. 2012). The cycle of electrical activity of the SCN is not precisely 24 hours in duration, but it is, in fact, closer to 25 hours. Thus, the neural clock “runs slow”. Perhaps this is due to some form of natural dampening. If this rhythm would not be continuously adjusted closer to a 24hour cycle, the physiology of the organism would run out of phase with the appropriate environmental time, in other words the organism would be desynchronized or chronodisrupted (Reiter et al. 2011). The SCN neuronal populations are mostly electrically silent during the night, start to fire action potentials near dawn and then continue to generate action potentials with a slow and steady pace all day long. Sets of currents of different ions like Na+, K+, and Ca2+ currents are responsible for keeping these daily rhythms. These rhythms in electrical activity which are crucial for the operation of the circadian timing system, including the expression of clock genes, are found to decline with ageing and disease (Colwell 2011).

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One significant circadian element that transfers daily time information to the organism is the melatonin hormone cycle. Melatonin is mainly produced in the pineal gland (epiphysis) of the brain in mammals. It is a key hormone for the regulation of the whole body’s biological cycle and has an oncostatic action preventing the development of different types of cancer. It is synthesized by the neurotransmitter serotonin which contains the amino acid tryptophan. Its concentration in the blood is always at low levels during the day and at high levels during darkness. Melatonin is also produced in the gastrointestinal tract by the entero-endocrine cells of the gut following ingestion of tryptophan-containing meal. The consequences of an altered melatonin cycle with chronodisruption have been linked to a variety of pathologies, including those of the gastrointestinal tract. When the photoperiodic environment is artificially perturbed, e.g., with light exposure during the normal dark period, the central circadian pacemaker receives irregular information for that time, resulting in melatonin suppression and circadian disruption (Reiter et al. 2011). We may also speculate that the same phenomenon may take place with exposure during the night to manmade radiation/EMFs. It is found that exposure to EMFs of different frequencies inhibits the synthesis of melatonin and reduces its oncostatic action (Cos et al. 1991; Liburdy et al. 1993). SCN outputs control the daily rhythm in melatonin release from the pineal gland. In addition, many other hormones involved in metabolism, such as insulin, glucagon, adiponectin and corticosterone, exhibit circadian periodicity in their synthesis and action. Compelling evidence that the circadian clock controls metabolism and that circadian disruption is associated with multiple negative metabolic manifestations, is demonstrated by clock gene mutant mouse models. Thus, it seems that the synthesis of metabolic hormones is ultimately controlled by the SCN (Kalsbeek et al. 2011; Froy 2011). In the heart, ion channels on the plasma membrane of sinoatrial nodal pacemaker cells (SANCs) are the proximal cause of action potentials. Each individual channel type has been thoroughly characterized under voltage clamp recordings, and the ensemble of the ion channel currents generate rhythmic action potentials. Thus, this ensemble can be envisioned as a surface "membrane clock" (M clock). Localized subsarcolemmal Ca2+ releases are generated by the sarcoplasmic reticulum via ryanodine receptors during late diastolic depolarization and are referred to as an intracellular "Ca2+ clock," because their spontaneous occurrence is periodic during voltage clamp or in detergent-permeabilized SANCs. In spontaneously firing SANCs, the M and Ca2+ clocks do not operate independently but work together via numerous interactions modulated by membrane voltage, subsarcolemmal Ca2+, protein kinase A, and calmodulin-dependent protein kinase II phosphorylation. Through these interactions, the two subsystem clocks become mutually entrained to form a robust, stable, coupled-clock system that drives normal cardiac pacemaker cell automaticity (Lakatta et al. 2010). Finally, this coupled-clock system of the heart is controlled by nerve impulses from the SCN to be in tune with the central circadian biological clock. Thus, the rhythmic operation of the heart is also driven by the SCN. Moreover, harmonic analysis of the alpha rhythm of brain bio-potentials has revealed that the brain contains several electromagnetic oscillators generating frequencies close to 10 Hz (Wiener 1963; Presman 1977). These brain oscillators probably result from combination of coherent ionic oscillations between a large number of brain cells which are also electrically/chemically tuned to the circadian clock. The prominent influence of the circadian clock on human physiology is demonstrated by the temporal activity of a plethora of systems, such as sleep–wake cycles, feeding behaviour,

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metabolism, physiological and endocrine activity, and even the rhythmic function of the heart, the brain, and every single cell of a living body. Disrupted circadian rhythms will lead to attenuated feeding rhythms, unwellness, disrupted metabolism, and eventually to disrupted health. Probably it is not just the photic diurnal and annual periodicity that determine the function of the central biological clock (SCN) but also the diurnal and annual periodicity in the intensity of the terrestrial electric and magnetic fields. Yet such an influence is not investigated so far.

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5.3. The Intracellular Electric Oscillations In all kinds of cells investigated, spontaneous intracellular ionic oscillations in the ELF range (0.01-0.2 Hz) have been detected. These are rhythmic changes in the intracellular ionic concentrations, accompanied by corresponding oscillations in the plasma membrane potential. These harmonic oscillations of different types of free ions within cells like calcium (Ca2+), potassium (K+), sodium (Na+), etc, and in particular calcium, seem to play a vital role in cellular and physiological functions as well as in embryonic development. Some of these oscillations result from periodic release of certain types of ions from intracellular reservoirs. In particular calcium oscillations seem to be initiated by periodic release of these ions by the endoplasmic reticulum (ER) (Berridge and Galione 1998). These intracellular ionic oscillations are accompanied by oscillations in the potential difference across the membrane of the ER as well as the plasma membrane. It is not known whether membrane voltage oscillations precede ionic concentration oscillations or vice versa, but it seems to us that rather the opposite occurs: Ionic concentration oscillations are translated to electric charge fluctuations and this in turn is translated to voltage corresponding fluctuations between the external and the internal sides of a cell membrane. The intracellular ionic oscillations span the entire day and have been discovered in both animal and plant cells. In particular, the fluctuations in the cytosolic concentration of free calcium ions seem to encode circadian clock signaling information as well as signaling information about diverse physiological and developmental events (Imaizumi et al. 2007). These periodical fluctuations in the concentration of free cytosolic calcium ion are found to promote cell phase transitions in early embryonic division and persist even if these transitions are blocked. These observations suggest that intracellular ionic oscillations and especially Ca2+ oscillations are essential timing elements of the early embryonic "master clock". This was observed in both sea urchin and Xenopus embryos (Craig et al. 1997). An ATP-dependent uptake of Ca2+ from the cytosol into the ER, the Ca2+ release from the ER through channels following a calcium-induced calcium release mechanism, and a potential-dependent Ca2+ leak flux out of the ER seem to occur. The binding of calcium to specific proteins such as calmodulin seems to be related to the fact that calcium oscillations in the cytoplasm can arise without a permanent influx of calcium into the cell (Marhl 1997). Although the origin of the “spontaneous” ionic oscillations remains unknown, we may speculate that they are intimately connected with the circadian biological clock and thus possibly generated through a yet unknown way by rhythmic signals from the SCN, the periodicity of which is - as explained - imposed by the periodicity of our natural environment. They seem to constitute the peripheral clocks driven by the central (SCN) biological clock.

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In addition, as we have suggested before (Panagopoulos et al. 2000; 2002) the ELF frequencies of the intracellular ionic oscillations may represent the “self-frequencies” of individual cells and consequently of the whole living organism.

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5.4. The Endogenous Electric Fields/Currents It has been well documented that in all living organisms there are endogenous physiological, static electric fields within single cells or within whole tissues, with intensities 0.1-1 V/cm (10-100 V/m), controlling cell growth, division, differentiation, migration, wound healing, tissue regeneration after amputations or bone fractures, etc (McGaig and Zhao 1997; McGaig and Dover 1989; Nuccitelli 1988; 2000). These fields give rise to corresponding endogenous weak electric currents in certain directions, controlling cellular/tissue functions in these directions. These endogenous electric currents consist of directed flows of certain types of ions through the plasma membrane and the cytoplasm of the corresponding cells. It was found that these endogenous electric currents are preceding cell growth and differentiation events and have always the same conventional direction with the growing part of the cell. These endogenous currents have been detected in all kinds of animal and plant cells studied so far in regard to these phenomena. These currents have a duration that usually ranges from a few hours to a few days ( 104 - 106 sec) and display current densities between 1 and 100 μA/cm2. No cellular or tissue growth has been observed so far without the existence of endogenous electric currents. Distortion, suppression, or nullification of these endogenous fields/currents with pharmacological agents or externally applied electric fields of opposite polarity, results in distortion or cessation of the corresponding cellular/tissue function (development, proliferation, differentiation, wound healing, regeneration, etc), while enhancement with externally applied fields of similar polarity increases the rate of this function (Weisenseel 1983; Lee et al. 1993; Nuccitelli 2000). Moreover, in all animals there is a potential difference across the epithelium called the trans-epithelial potential (TEP). TEP in the intact epithelium around a wound acts like a battery, giving rise to significant ion flux and electric current at the wound. These circulating endogenous currents generate an electric field oriented towards the wound, with the wound as the cathode (Reid et al. 2011). Similar endogenous electric currents control not only cell growth, proliferation, differentiation, and wound healing but all other cellular functions as well, such as signal transduction, synthesis and release of enzymes, etc (Lee et al. 1993; Messerli and Graham 2011). Physiological direct current (DC) electric fields with intensities 10-100 V/m have been measured in developing chicken and amphibian embryos as well as in adult tissues near skin wounds. This is in agreement with the above observations that endogenous electric fields play a crucial role in development, regeneration and wound healing. Endogenous fields of 20-30 V/m have been measured just beneath the epidermis of chick and frog embryos and the distortion of these physiological fields results in abnormal development. Endogenous electric fields of 60-100 V/m have been measured in regenerating epidermal wounds in all animals and in regenerating amphibian limbs (Nuccitelli 2000).

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Electric fields are applied clinically to humans in order to provide stronger signal for the enhancement of healing of chronic wounds. Although clinical trials during the last decades have shown that applied electric fields enhance healing of chronic wounds, the mechanisms by which cells sense and respond to external EMFs remain under investigation. Nevertheless, it is understood that plasma membrane voltage-gated ion channels play a major role, and that the cell membrane is the site of perception and transduction of information that generates the endogenous electric currents (Messerli and Graham 2011). An early hypothesis made by Jaffe (1979) assumes that the triggering of exogenous or endogenous factor(s) to initiate spatial growth and differentiation of a cell is perceived asymmetrically around the cell by specific receptors on the plasma membrane, causing a slight and transient asymmetry in the arrangement of ion pumps and channels on its surface. This in turn generates an electric current consisting of mobile ions entering the cell at one site and pumped out at another. [In section 6.2 of the present chapter we describe a mechanism by which weak externally applied electric or magnetic fields may affect cell function by changing intracellular ionic concentrations through irregular gating of voltage-gated channels on cell membranes (Panagopoulos et al. 2000; 2002)]. Externally applied static electric fields of similar intensities with the endogenous fields are found to direct cell migration, cell proliferation, stimulate mammalian and amphibian nerve regeneration, and nerve sprouting at wounds, wound healing, or spinal cord injury healing (Borgens 1988; Borgens et al. 1986a; 1986b; Wang and Zhao 2010). Accordingly, pulsed ELF magnetic fields (having the ability to induce corresponding electric ones) are found to accelerate bone regeneration and bone fracture healing in mammals (Brighton et al. 1979; 1989; Brighton and McClusky 1987; Brighton and Townsend 1988; Bassett et al. 1964). In the alga Vaucheria, visible electromagnetic radiation (blue light) induces changes in the plasma membrane that cause ionic currents to pass through the membrane. The zygotes of brown algae Fucus and Pelvetia, when illuminated by linearly polarized light, germinate parallel to the electric vector. The same brown algae are found to germinate toward the side of the zygote with higher K+, Ca+, or H+ concentrations. An electric current with density 1-2 μA/cm-2 starts to enter the shaded side of unilateral irradiated cells, about 2-3 h after fertilization. It is also found that pollen grains of Lilium and spores of Equisetum germinate toward the positive electrode in a DC externally applied electric field or parallel to an externally applied strong magnetic field (Weisenseel 1983). Such orientation effects induced by external EMFs may be controlled by endogenous electric currents after depolarization of the cell membrane or alterations in intracellular ionic concentrations, especially Ca2+. Irradiation with red light causes a Ca2+ -dependent depolarization of the cell membrane by about 60 mV in the green alga Nitella, and increased uptake of Ca2+ in the cells of the filamentous alga Mougeotia. Activation of fish eggs or sea urchin eggs by the entry of sperm, induces a large increase in cytosolic free Ca2+ concentration as well as an elevation in the internal pH-value (Weisenseel 1983). In a recent study, it was shown that directed neuronal migration depends on the establishment of cell polarity, and cells are polarized dynamically in response to extracellular electromagnetic signals. In particular, it was shown that cell division of cultured hippocampal cells is oriented by an applied electric field, which also directs neuronal migration. Directed migration involved polarization of the leading neurite, of the microtubule-associated protein

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MAP-2, the Golgi apparatus, and the centrosome, all of which repositioned asymmetrically to face the cathode of the applied field (Yao et al. 2009). Thus, it seems that externally applied electric fields of similar (or even smaller) intensity and similar polarity with the corresponding physiological endogenous ones can be used as a novel type of therapy regarding tissue repair and regeneration. Combination of the electric stimulation and other well understood biochemical regulatory mechanisms may offer powerful and effective therapies for tissue repair and regeneration (Wang and Zhao 2010). Cells are found to respond in vitro to external DC electric fields (aligning, migrating, or growing along a direction with respect to the applied electric field), at a threshold between 3 and 7 V/m (Nishimura et al. 1996; Huang et al. 2009; McKasson et al. 2008; Messerli and Graham 2011). Moreover, soft tissue preparations like bovine fibroblasts, chicken tendons, etc, are found to respond to externally applied electric fields (by changes in protein synthesis, proliferation, alignment with respect to the field direction, etc), at very low thresholds  4 mV/m (McLeod et al. 1987; Cleary et al. 1988; Lee et al. 1993). These intensities are significantly smaller that those of endogenous physiological electric fields described in the previous paragraphs. Since cells are found to respond to external EMFs at intensities of the order of 10-3 V/m, it follows that externally applied EMFs of much larger intensities like those accounted in modern human residential and working environment may interact (directly or indirectly) with the endogenous physiological fields. Such an interaction would cause an alteration in the parameters of these fields (intensity, direction, etc) and a consequent alteration in their corresponding functions. Perhaps this should be the focus for the explanation of the biological action of natural and man-made environmental EMFs. In the following paragraphs we shall describe two plausible ways for this interaction.

6. DISTORTION OF ENDOGENOUS ELECTRIC FIELDS BY EXTERNAL EMFS 6.1. Distortion of Endogenous Electric Fields by Direct Electromagnetic Interference with External Fields An intracellular (endogeneous) electric field originating from ion concentration difference across two different cell sites and controlling specific cellular/physiological functions, will interact with any external electric field by simple vector addition giving a resultant field which will be of different magnitude, frequency, and direction than the original intracellular field. Apart from the interaction with the endogenous fields, the external field will cause a polarization of the biological tissue containing the specific cell(s). More specifically:



Polarization of Biological Tissue: Any externally applied electric field Eex will, theoretically, induce a polarization of biological matter by rearranging the electric charges in the extracellular aqueous solution and even on the cell membrane and the intracellular solutions as well. This re-localization of electric charge will be most evident in the “free” (mobile) ions which are loosely bound to water molecules and carry a net electric charge. In

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other words, the induced polarization will - theoretically - alter free ion distribution and bind a number of charge carriers (free ions) to certain positions, decreasing their mobility and their availability to be used for keeping the correct ionic concentrations and the cells’ electrochemical equilibrium. This condition represents anyway a stress for the organism. The cells will then be forced to keep their electrochemical balance (correct ionic concentrations in every site of the cytoplasm and of the external surface of the cell membrane) by active ion transport (i.e. by activating pumps like for example the K+-Na+ ATPase, or other protein pumps). Activation of pumps will in turn increase the energy consumption by the cells by decreasing ATP which is the main energy storage molecule. In other words, the organism overcomes the stress by energy consumption. The induced polarization/rearrangement of electric charges within the biological tissue





generates a polarization field E p in opposite direction of the externally applied field Eex . The intensity of the polarization field varies in different sites of the biological tissue and between different sites of each cell depending on local permittivity and charge availability. The magnitude of the polarization field is given by application of Eq (1) (Gauss law for the electric field) within the tissue:

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Ep =

1

o



qp S

(35)

where qp is the polarization charge, ε the local tissue permittivity, and S a surface area vertical to the polarization field containing the charge qp. The polarization field will never be larger in magnitude than the external field: Ep  Eex . [In metals Ep  Eex, resulting to nullification of the field within their interior. In biological tissue the polarization field is in any case smaller than the external field: Ep  Eex ]. The remaining - resultant field induced within e.g. a cell by the externally applied field,



will be called internal or induced electric field Ein and it will be the difference between the external field and the polarization field:

   Ein = Eex - E p

(36)

For example, in case that the external field is of a sinusoidal alternating magnitude (as those associated with power lines) with a circular frequency ω, Eex=osint, then from Eqs. (35), (36), the vector of the internally induced electric field each moment is given by:

 q  Ein = (o sin t - 1  p ) uex o S   (where uex is the unit vector parallel to the external field Eex ).

(37)

Although these equations show that there is always a change in the magnitude of the externally applied field within the tissue due to polarization, the calculation of the polarization field is not an easy task, mainly due to the difficulty in the calculation of the

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polarization charge. Since according to experimental evidence (section 5.4), cellular processes associated with specific endogenous fields are found to be altered (enhanced, diminished and even nullified) by externally applied fields of similar or even significantly smaller intensities than the endogenous ones (Borgens 1988; Borgens et al. 1986a; 1986b; Brighton et al. 1979; 1989; Brighton and McClusky 1987; Brighton and Townsend 1988; Bassett et al. 1964; Lee et al. 1993; Wang and Zhao 2010; Messerli and Graham 2011), it comes that the polarization of biological tissue induced by external fields must either be very small and it does not reduce significantly the external fields (as would happen e.g. with a Faraday cage where the polarization field is equal and opposite to the external field and thus the field is zero within a metal conductor placed within an external field as mentioned already), or the external electric fields interact by indirect ways with the endogenous ones (as described in section 6.2). In any case, biological matter is not metal to shield the externally applied fields as supported by others (Adair 1991b). Instead of the free electrons in metals, biological tissue’s carriers are mainly the mobile ions (transiently bound to water molecules) the mobility of which is much less than that of free electrons. Interaction with Endogenous Fields: The remaining/resultant internally induced electric



field Ein whatever it is, will be in the same direction as the external field and it will interact



directly with any endogenous physiological electric field Eend by simple vector addition, resulting in distortion of the endogenous physiological field to some degree significant or insignificant depending on polarization as explained. The distorted endogenous field, which

'

we shall name E end , will be the sum vector of the physiological endogenous field plus the internally induced field:

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   E 'end = Eend + Ein

(38)

This final/distorted endogenous field will have a significantly or insignificantly altered magnitude, direction and even frequency than the original physiological endogenous field. In the case of an alternating external field, according to Eqs (37), (38) the vector of the final distorted endogenous field will theoretically be given by:

  q  E 'end = Eend + (o sin t - 1  p ) uex o S

(39)

Any distortion of the physiological endogenous field, if not properly corrected by cell’s homeostasis (e.g. by enforcing the original endogenous field by active ion transport/pump activation and consequent ATP consumption), will result in a corresponding distortion of the cellular/physiological functions controlled by the original physiological endogenous field. Even if the polarization field is large enough to significantly attenuate the induced field within the biological tissue, the polarization itself represents an altered condition for the living organism (as already explained), decreasing the availability of carriers (mobile ions) to participate in the physiological endogenous functions, and this will also require ATP consumption in order to be corrected e.g. by active ion transport.

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Thus, eventually, the interaction of external EMFs with biological tissue will result in either energy (ATP) consumption, or distortion of cellular/physiological functions, or both. Thus, even if the external field will not cause alteration in physiological functions, it will cause additional energy consumption by the organism. Again, we should emphasize that, since cellular/physiological functions controlled by endogenous fields are found to be nullified by application of external fields of similar intensities and polarities opposite to the endogenous ones, the polarization field must either be of very small importance, or the external fields interact with the endogenous ones in indirect ways as shown below. We consider that this second option might be more probable.

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6.2. Distortion of Endogenous Electric Fields by Alteration of Intracellular Ionic Concentrations Endogenous electric fields originate from ionic concentration differences between different sites of the cytoplasm. The resulting endogenous currents are positive ion flows towards lower electrical potential and/or negative ion flows towards higher potentials. It is therefore obvious that alteration of intracellular ionic concentrations by any external factor (e.g. an external EMF), if not corrected by cell’s homeostasis e.g. by active ion transport and consequent ATP consumption as already mentioned, may result in distortion of physiological intracellular electric fields and currents. It has been shown that intracellular ionic concentrations may be altered by interaction of external oscillating EMFs with voltage-gated channels on cell membranes and irregular gating of these channels, according to the Ion Forced-Vibration Theory that we have proposed (Panagopoulos et al. 2000; 2002). This irregular gating of ion channels may lead, nonthermally, to disruption of the cell’s electrochemical balance and function, as we describe below. According to this theory which is considered so far the most valid one of all the proposed theories, (Creasey and Goldberg, 2001; Halgamuge and Abeyrathne 2011), even very weak ELF electric fields on the order of 10-4 V/m, are theoretically able to change the intracellular ionic concentrations and thus, disrupt cell function. Since all types of RF-microwave radiation and especially those used in modern mobile telecommunications are always transmitted in ELF pulses, or include ELF modulating signals of intensities usually thousands of times higher than 10-4 V/m, this theory can be applied for the explanation of their bioeffects. The basic idea is based on the fact that any external oscillating electric or magnetic field, induces a forced-vibration on the mobile ions inside and outside of all living cells in the exposed biological tissue. When the amplitude of this forced-oscillation exceeds some critical value, the electrostatic force exerted by the oscillating ions’ charge on the electric sensors of the voltage-gated membrane ion channels, can irregularly gate these channels, resulting in alteration of the intracellular ionic concentrations. As already explained, mobile ions play a key role in all cellular functions, and alterations in their intracellular concentrations initiate or accompany all cellular biochemical/biophysical processes.

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Consider an external oscillating electric field (or the electric component of an electromagnetic wave) inducing an internal field of intensity E within the biological tissue,  and acting in the x direction on a free ion in the vicinity of a cell membrane. The forced-oscillation of each free ion due to the external oscillating field is described by the equation:

mi

d 2x dx + + mi o2 x = o z q e sin t 2 dt dt

(40)

in the case of an external harmonically oscillating electric field, inducing a corresponding internal field  = o sin t, with circular frequency  =2, (, the frequency in Hz), where: z is the ion’s valence, q e =1.610 19 C the elementary charge, F1 =o z q e sin t is the force exerted on the ion by the field, F2 = -mi ωο2 x is a restoration force proportional to the displacement x of the free ion, mi the ion’s mass and  o =2o, with o the ion’s oscillation self-frequency if the ion was left free after its displacement x . In our case, this restoration force is found to be very small compared to the other forces and thus it does not play an important role. F3 = - u is a damping force, where u =

dx is the ion’s velocity due to the dt

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forced-oscillation and  is the attenuation coefficient for the ion’s oscillation, which for the cytoplasm or the extracellular medium is calculated to be   10-12 Kg/sec, while for ions moving inside channel proteins, is calculated to have a value:   6.410 12 Kg/sec, (in the case of Νa+ ions, moving through open Νa+ channels) (Panagopoulos et al. 2000). Assuming that the ions’ self-frequencies coincide with the frequencies of the cytosolic free ions’ spontaneous oscillations (described in section 5.3) observed as membrane potential spontaneous oscillations in many different types of cells with values smaller than 1 Hz and assuming that the ion’s maximum oscillation velocity has a value of 0.25 m/s, as calculated for the movement of sodium ions through open sodium channels using patch-clamp conductivity data (Panagopoulos et al. 2000), it comes after operations that the general solution of equation (40), is:

x =

Eo zqe



cos  t -

Eo zqe



(41)

Since the second term of the second part of equation (41) is constant, the oscillating movement is described by the first term:

x =

Eo zqe



cos  t

(42)

Eq. (42) shows that the free ion’s forced-oscillation is in phase with the external force. The amplitude of the forced-oscillation is:

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A=

Eo zqe

(43)



Thus, the amplitude is proportional to the intensity and inversely proportional to the frequency of the oscillating field. Equation (41) declares that, at the moment when the external field is applied and at the moment when it is interrupted, the displacement of the ion becomes twice the amplitude of the forced vibration, because of the constant term which adds to the amplitude. For pulsed EMFs, this takes place continuously with every repeated pulse. This explains why pulsed EMFs are reported to be more bioactive than continuous ones of the same other characteristics (Goodman et al. 1995). The coherently oscillating ions due to the action of the external EMF represent a periodical displacement of electric charge, able to exert coherent forces on every fixed charge of the membrane, such as the charges on the voltage sensors of voltage-gated ion channels. Once the amplitude of the ion’s forced-oscillation exceeds some critical value, the coherent forces that the ions exert on the voltage sensors of the voltage-gated membrane channels can trigger the irregular opening or closing of these channels, disrupting in this way the cell’s electrochemical balance and function, by altering the intracellular ionic concentrations. Voltage-gated channels are leak cation channels. The state of these channels, (open/closed), is determined by electrostatic interaction between the transmembrane voltage and the channels’ voltage sensors. They interconvert between open and closed state, when the electrostatic force, exerted by transmembrane voltage changes on the electric charges of their voltage sensors, transcends some critical value. The voltage sensors of these channels, as already mentioned, are four symmetrically arranged, transmembrane, positively charged a-helices, each one designated S4, (Noda et al. 1986; Stuhmer et al. 1989). It is known that changes of about 30 mV in the transmembrane voltage, are able to gate these electrosensitive channels by exerting the necessary electrostatic force on the fixed charges of the S4 helices (Bezanilla et al. 1982; Liman et al. 1991; Lecar et al. 2003). It has been shown that a single ion’s displacement  r, of 10-12 m, in the vicinity of S4, can exert an electrostatic force on each S4, equal to that exerted by a change of 30 mV, in the transmembrane voltage, (Balcavage et al. 1996; Panagopoulos et al. 2000): The intensity of the transmembrane electric field is:

m =

 s

(44)

where, ΔΨ is the transmembrane voltage and s the membrane’s width. In addition, m = where

F q

(45)

F in this case is the force acting on an S4 domain and q is the effective charge on

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Dimitris J. Panagopoulos

q  1.7 q e

(46)

From equations (44), (45) we obtain:

F=

 q q   F = Δ s s

(47)

(where ΔΨ is the change in the transmembrane voltage, necessary to gate the channel). For Δ=30 mV, s=10 8 m and substituting q from (46), equation (47) gives:  F = 8.16 10-13 N. This is the force, on the voltage sensor of a voltage-gated channel, required normally, to interconvert the channel between closed and open state. The force acting on the effective charge of an S4 domain, via an oscillating, free zvalence cation, is:  F = -2

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r=

F=

1 4 o



1 4 o



q  zqe  r2

q  zqe  r  (ignoring the minus sign), r3

2o F  r 3 q  zq e

(48)

This is the minimum displacement of a single, z-valence cation, in the vicinity of S4, able to generate the necessary force  F to gate the channel. Where: r is the distance between the free ion with charge zqe and the effective charge q on each S4 domain, which can be conservatively taken as 1 nm (Panagopoulos et al. 2000), since the concentration of free ions on both sides of mammalian cell membranes, is about 1 ion per nm3 (Alberts et al. 1994). The relative dielectric constant  can have a value 80 for a water-like medium, (cytoplasm or extracellular space), or a value as low as 4 for channel-proteins, (Honig et al. 1986; Leuchag 1994). Let us calculate  r for one single-valence cation, interacting with an S4 domain. If two or more single-valence cations interact (in phase) with an S4 domain from 1nm distance,  r decreases proportionally. For ions moving inside channel-proteins, we assume that they move in single file (Palmer 1986; Panagopoulos et al. 2000). From equation (48) and for  F = 8.16 10-13 N, we get:

 r  0.810-10 m, (for  = 80) and:  r  410-12 m, (for  = 4)

(49)

Thus, only one single-valence cation’s displacement of only a few picometers from its initial position, is able to interconvert voltage-gated channels, between open and closed states, (for cations moving or bound within channels).

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Therefore, any external field, which can induce a forced-oscillation on mobile ions, with an amplitude A  4 10-12 m, is able to irregularly gate electrosensitive channels and disrupt the cell’s function. Substituting A from Eq. (43) in the last condition, it comes that, a bioactive external oscillating electric field of internal intensity amplitude o and circular frequency  inducing a forced-oscillation on every single-valence ion (z=1), satisfies the condition:

E o qe



 4 10-12 m

(50)

Since we adopted a value for  r (  410-12 m) valid for cations within channels (where  = 4), we shall use the corresponding value for , calculated also for cations moving within channels (Panagopoulos et al. 2000):   6.410 12 Kg/s. Thereby, the last condition becomes:

o   1.6 10-4

(51)

or o   10-3

(52)

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( in Hz, o in V/m) If two or more cations interact (in phase) with an S4 domain from 1nm distance,  r in (49) decreases proportionally. The concentration of free ions on both sides of mammalian cell membranes is about 1 ion per nm3, as mentioned, and for this we have initially calculated  r for one cation interacting with an S4 domain, although it is very likely that several ions interact simultaneously each moment with an S4 domain from a distance of about 1nm. This applies also for ions moving already within channels, since it is known that although they pass through the narrowest part of the channel in single file (Miller 2000; Palmer 1986; Panagopoulos et al. 2002), several ions fill the pore each moment as they pass sequentially and several ion-binding sites (three in potassium channels) lie in single file through the pore, close enough that the ions electrostatically repel each other (Miller 2000). Thus, if two single-valence (z =1) cations interact with the channel’s sensor, the first part of cond. (50) is multiplied by 2. Moreover, if they are double valence cations (z =2), the first part is multiplied by 4 while at the same time the second part is divided by 2, according to Eq. (48). Moreover, for pulsed fields, the first part is again multiplied by 2 as explained. Therefore, in the case of pulsed fields and for only two double-valence cations (i.e. Ca+2) interacting simultaneously with the S4 channel sensor, the first part of the cond. (50) is multiplied by 8 and the second part divided by 2. Thus finally, the second part is divided by 16 and the condition for irregular gating of the channel becomes:

o    0.625  10-4 ( in Hz, o in V/m).

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(53)

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Whenever condition (53) is satisfied for the induced internal field amplitude Eo, the external field can irregularly gate the ion channel. Condition (53) declares that ELF electric fields with induced internal intensities even smaller than 0.1 mV/m (= 10-4 V/m) are theoretically able to disrupt cell function by irregular gating of ion channels. In the cases of cells of surface tissues, like skin cells, nerve cells reaching the skin, eyes, etc, condition (53) is also satisfied for the intensity of the external field. For inner cells and tissues, the externally applied field will - theoretically - be diminished to a varying degree, due to polarization (as explained in section 6.1). Since external electric fields are found to have a biological action at thresholds 10-3 V/m, it follows that any polarization effects do not reduce significantly the action of external electric fields as probably takes place due to the described mechanism. Respectively, an externally applied alternating magnetic field B=Bosint will also induce a forced oscillation on the mobile ions. The ion displacement due to the magnetic field after substituting the electric force by a corresponding magnetic one F΄1 = Bou z q e sin t

(54)

will be described by an equation similar to Eq (40):

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mi

d 2x dx + + mi o2 x = Bou z q e sin t 2 dt dt

(55)

The ion’s maximum displacement, (amplitude of the corresponding forced-oscillation) due to a magnetic field as described by Eq (55), is calculated to be normally much smaller than the corresponding displacement due to an electric field of the same frequency (given by Eq 43). The corresponding bioactivity condition to (53) for the magnetic field B in G (which is the unit for environmentally encountered magnetic field intensities) is: Bo  2.5

(56)

( in Hz, Bo in G) Comparing the conditions (53) and (56) for the biological activity of oscillating electric and magnetic fields respectively, it looks as magnetic fields are less bioactive than electric ones of the same frequency. Nevertheless, a large number of experimental and epidemiological data suggest intense biological activity of manmade ELF magnetic fields (Goodman et al. 1995; Wertheimer and Leeper 1979; Savitz et al. 1988; Feychting and Ahlbom 1993; 1994; 1995; Coleman et al. 1989; Draper et al. 2005). A possible explanation is that the magnetically induced electric field is rather the bioactive component than the magnetic field itself. This conclusion arising from our presented theory is in agreement with several experimental/epidemiological observations indicating that the magnetically induced

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electric field is probably the actual bioactive component instead of the magnetic field itself (Koana et al. 2001; Liburdy 1992; Greene et al. 1991; Coghill et al. 1996). It is important to note that the magnetically induced electric field given by Maxwell’s third equation (3), is always naturally produced and co-existing with any time-varying magnetic field and, especially in the case of ELF fields, there is no way to totally eliminate it or insulate it by shielding. [Metal grids can reduce ELF electric fields to a certain degree but not totally eliminate them. For a significant decrease, a closed metal box is necessary]. The magnetically induced electric field has the same waveform and the same frequency as the magnetic one that generates it. The two fields have a phase difference of π/2 between them. Thus, in reality there is never any pure exposure to a time-varying magnetic field without a simultaneous exposure to a corresponding induced electric one. The reverse does not occur: In the case of a time-varying electric field, the corresponding induced magnetic one, given by the second term of the second part of Maxwell’s fourth equation (4), is usually of negligible intensity due to the small value of the constant product o ο included in this term. For any biological effect produced by a combination of the two co-existing fields (in case of time-varying magnetic field exposures), it is unknown whether it is due to the magnetic or to the corresponding induced electric field or due to the combination of both. Yet, the majority of the studies seem to ignore the induced electric field and concentrate only on the magnetic component. According to the described mechanism, lower frequency fields are more bioactive than higher frequency ones as indicated by Eq (43). Thereby, ELF fields are especially bioactive according to this mechanism. This applies not only to purely ELF fields as those associated with electric power production (50-60 Hz), but also to the ELF pulses or modulation signals associated with microwave radiation. Microwave radiation is always pulsed or modulated by ELF frequencies in order to be able to carry and transmit information as already stated. In addition, pulsed fields are shown to be more bioactive than continuous (uninterrupted) ones because of the constant term in the second part of Eq. (41) which doubles the displacement of the oscillating ions at the onset and at the end of every pulse (Panagopoulos et al., 2002). The ELF pulses of the mobile telephony signals as well as of any other type of modern microwave radiation are certainly of adequate intensity to produce biological/health effects on living organisms according to this mechanism. The threshold ELF intensities predicted by the present mechanism to be able to alter biological function (~10-4 V/m), being in agreement with the experimentally observed thresholds (~10-3 V/m) (section 5.4), are millions of times smaller than the current ELF exposure limits (~104 V/m) (ICNIRP 1998).

6.3. EMF-Induced Displacement of Mobile Ions Cannot be Masked by Thermal Motion Certainly, free ions move anyway because of thermal activity, with kinetic energies much larger normally (millions of times as already shown), than the ones acquired due to the action of an external electromagnetic field at intensities encountered in the human

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environment. For this, it has been claimed (Adair 1991a) that thermal motion masks the motion induced by the external field, making this motion unable to produce any biological effect. But as we have explained (Panagopoulos et al. 2000; 2002), thermal motion is a random motion, in every possible direction, different for every single ion, causing no displacement of the ionic “cloud” and for this it does not play any particular role in the gating of channels, or in the passing of the ions through them. On the contrary, forced-vibration is a coherent (in phase) motion of billions of ions together in the same direction. The thermal motion of each ion and moreover the thermal motion of many different ions, results in mutually extinguishing forces on the voltage sensor of an electrosensitive ion channel, while the coherent - parallel motion of the forced-oscillation results in additive forces on the voltage sensor. Even if we consider only one single-valence ion interacting with an S4 domain, this ion moving with a drift velocity u = 0.25 m/s due to the forced-oscillation, it needs a time interval ∂t =

r  1.610-11 s, in order to be displaced at the necessary distance  r = 410-12 m u

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[according to Eq (49)]. The ions’ mean free path in the aqueous solutions around the membrane is about 10-10 m, (Chianbrera et al. 1994), and it is certainly smaller within the channels, (the diameter of a potassium ion is about 2.6610-10 m and the diameter of the narrowest part of a potassium channel is about 310-10 m, thereby the mean free path of a potassium ion within the channel has to be on the order of 10-11 m), (Panagopoulos et al. 2002; Miller 2000). During the same time interval ∂t, this ion will also be displaced by its thermal motion, at a total distance ∂rkT = ukT  ∂t which, according to Eq (32) gives: ∂rkT =

3kT ∂t  930  10-11 m mi

Therefore the ion within the above time interval δt, will run because of its thermal activity, 930 (in other words hundreds/thousands) mean free paths, each one in a different direction, exerting mutually extinguishing opposing forces on the channel’s sensors, while at the same time the ion’s displacement because of the external field is in a certain direction, exerting on each S4 domain a force of constant direction. If in addition we consider several ions interacting simultaneously with the S4 domain, then the effect of the external field is multiplied by the number of ions, whereas the effect of their random thermal motions becomes even more negligible. Thus thermal motion, although normally thousands of times larger (corresponding to millions of times larger kinetic energies), is unlikely to mask the displacement of the mobile ions caused by external EMFs, according to this analysis.

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7. ENDOGENOUS ELECTRICAL BALANCE IN LIVING ORGANISMS DETERMINES HEALTH AND WELL-BEING The presented data in section 5 of this chapter show the electric nature of all living organisms. The endogenous electric currents, the intracellular electric oscillations, the cell membrane electrical potential, and the function of the circadian biological clock are characteristic manifestations of this subtle and unique electric nature. The oscillating (timevarying) kind of this electric nature makes it electromagnetic. The present study is probably the first attempt to present these individually observed bio-electromagnetic manifestations in living organisms as mutually connected. The described electromagnetic nature of living organisms is supposed to be in tune (resonance/harmony) with the electromagnetic natural environment. It is clear that weak endogenous periodically varying physiological electric fields in living organisms play a fundamental role in all their physiological functions. Since distortion in the physical parameters of these fields results to the cessation or alteration of the corresponding biological/physiological functions, it comes that these endogenous physiological fields should not be distorted by external fields. Moreover, since endogenous physiological fields can be altered by external ones of significantly smaller intensities according to both experimental and theoretical evidence, it follows that the electrical balance of living organisms is a very delicate one, and can be very easily disrupted by external EMFs. In other words, endogenous electrical balance in living organisms cannot occur in the presence of unnatural – manmade – electromagnetic pollution in the environment. Since this pollution is inevitably connected with human technological evolution, we must find the maximum exposure levels from artificial EMFs that can be tolerated by living organisms without adverse health consequences. These actual maximum permissible exposure levels that would be tolerated by the living organisms and would not disturb their physiological function, seem to be thousands of times below the current exposure limits according to both experimental/epidemiological evidence and theoretical calculations. For example, GSM mobile phone radiation is found to cause DNA damage on insect reproductive cells (gametes) and adversely affect reproduction for intensities down to 1 μW/cm2 after only a few minutes daily exposure (Panagopoulos et al. 2010). This intensity value is between 450 and 950 times smaller than the corresponding limits for 900 and 1900 MHz microwave radiation emitted by these devices (ICNIRP 1998). Moreover, the presented mechanism in section 6.2 shows that ELF electric fields of only  10-4 V/m intensity can disrupt physiological cell function. This intensity is about 108 times (a hundred million times) lower than the 50-60 Hz current electric field exposure limit (5-10 kV/m) (ICNIRP 1998). According to Liboff (2009), wellness can be described in physical terms as a state that is a function of the organism's electric polarization by environmental EMFs. Any application of manmade EMFs is combined in any case with the continuous exposure to the natural (terrestrial) fields. Living organisms have adapted throughout evolution to the subtle polarization caused by the “steady” natural fields. One can alter tissue polarization by application of external EMFs in different combinations with the natural ones. Even when exposure to manmade EMFs does not result to an alteration of the endogenous physiological fields, the additional polarization that generates within the biological tissue represents a stress

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for the organism as explained. A healthy organism overcomes the additional stress by additional energy (ATP) consumption, but it might not be the same for young organisms during development, old organisms, or even healthy organisms during combined stress (costress) conditions, during sickness, etc. The strikingly low EMF intensities which are found to alter biological function (described in section 5.4) is a fact intimately connected with the existence of physically equivalent endogenous weak electric fields as explained in the present study. These very low intensities found experimentally to affect biological function are in agreement with the intensities predicted by at least one of the mechanisms presented in the present study (section 6.2). These facts make claims related to electromagnetic pollution more credible and also provide a basis for future electromagnetic applications in medicine. They also reinforce the notion that physical factors acting to influence the electrical condition of living organisms play a key role in biology (Liboff 2009). Based on the presented data, we could define “well-being” as a condition where a living organism is not just healthy, but moreover, is at an equilibrium state with the natural environment. Since both the natural environment and living organisms are of electric/electromagnetic nature, “wellness” is a condition of subtle electromagnetic equilibrium. If this equilibrium is disrupted by exposure to unnatural EMFs, wellness will be disrupted as well, and if this situation persists health will be impacted sooner or later.

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CONCLUSION In the present study we attempted to elucidate the fact that the nature of life itself is electromagnetic. Electric oscillations imposed on living organisms by the environmental periodicity due to the terrestrial and lunar motion (circadian, monthly, annual, etc) through the operation of the central circadian biological clock (the SCN in the mammalian brain), play a fundamental role in keeping organisms in resonance with their natural environment. These electrical oscillations manifesting as cell membrane voltage oscillations, or intracellular ionic oscillations, seem to control the operation of the heart, brain, and the rest of bodily organs, and of every single cell. We tried to show the connection these electrical oscillations described previously as intracellular “spontaneous” ionic oscillations, have with the function of the circadian biological clock, and consequently with the periodicity of our natural environment. External EMFs interact with endogenous physiological ones and can be either beneficial or detrimental for living organisms. External EMFs that generate endogenous currents coherent with physiological ones e.g. during wound healing or bone fracture healing, can be beneficial. These are usually static fields of intensities similar to (or even smaller than) the endogenous physiological ones. On the contrary, external EMFs of varying/alternating nature, modulated and pulsed fields such as those associated with modern wireless telecommunications or produced by power lines, would not be expected to have beneficial action. Rather as demonstrated in the present chapter, these can be expected to be detrimental even at intensities thousands or even millions of times smaller than those of the current exposure limits. Ways of direct and indirect electromagnetic interaction between environmental fields and living systems are described in the present chapter. Perhaps, indirect ways (section 6.2) seem to be more plausible.

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Electricity and magnetism are natural powers discovered and used by our civilization. They can be used either for the benefit or to the detriment of life. It is obvious that we cannot use these natural powers without cost. We should then rather use them safely and gently, always being mindful of biological/health consequences for all living creatures and of the integrity of our natural environment. Without this, our technology is useless and meaningless.

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Chapter 3

THERMODYNAMICS OF SURFACE ELECTROMAGNETIC WAVES Illarion Dorofeyev * Institute for Physics of Microstructures, Nizhny Novgorod, Russia

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ABSTRACT The chapter is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, we used dielectric and metal samples characterized by local and nonlocal optical properties. Thermodynamic properties of surface eigenmodes of plane interfaces are discussed. Various thermodynamic functions, different definitions of density of states and spectral characteristics of surface polaritons in equilibrium at the interface formed by vacuum and lossy medium are described and discussed. The generalized density of states is calculated based on the Barash-Ginzburg theory and dispersion relations for the surface states in different approaches. All formulas for thermodynamic functions are represented in terms of density of states. It is exemplified that different definitions of the density of states are identical in the case of dissipationless materials. The spectral functions and integrated over all frequencies thermodynamic characteristics and their temperature dependences are demonstrated.

INTRODUCTION Coupled surface excitations of optically active vibrations of solids and photons are called surface polaritons (SP) by analogy with bulk excitations. The surface electromagnetic waves or surface polaritons are proper modes of solid surfaces that exist due to an interface [1-5]. Surface polaritons propagate only along the surface and have a non-radiative nature. The nonradiative or evanescent character of the surface electromagnetic waves means that it cannot propagate away from the ideally smooth surface without adjusting devices because of the *

E-mail address: [email protected] ; [email protected].

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pure imaginary normal component of the wave vector of this surface mode. Surface electromagnetic states have an important role in different physical processes including those in the van der Waals interaction of bodies, in the heat transfer between the bodies, in the continuous growth of crystals, in the Raman-scattering characteristics, in the capture of atoms, molecules, and coherent material states, in photochemistry, in surface phenomena such as the adsorption and desorption phenomena, the heterogeneous chemical catalysis, and etc. Surface polaritons can be excited by external sources (that is, sources placed outside the sample), including laser radiation and a beam of particles, or by internal thermal fluctuations inside a body [6-17]. Thermally excited electromagnetic fields within a body due to charge and currents fluctuations can be conditionally divided into propagating and evanescent waves. The waves partially reflect on the vacuum-sample interface return back to the body, and in part the waves penetrate into a vacuum region outside the body, where the penetrating waves form the electromagnetic background in the near- and far-field regimes. Properties of the propagating and evanescent electromagnetic fluctuating fields are crucially different. In the near field the energy density can be much larger in magnitude than in the far field. The matter is that the optical properties and sample geometry have a strong influence on the characteristics of thermally excited near fields. As a result, the noise spectra in the near field regime differ essentially from the noise spectra in the far field regime. Moreover, the coherence properties of thermal electromagnetic fluctuations in a near field regime are extremely different from those of the propagating waves [18-21]. Theory of fluctuating electromagnetic fields of solids was developed on the basis of the Maxwell's equations [9-12]. The Green’s tensor together with the fluctuation-dissipation theorem (FDT) are key points for calculating the spectral properties of thermally stimulating electromagnetic fields. The fluctuation-dissipation theorem as applied to thermal fields in equilibrium with a medium gives known relations between the cross-spectral density of the fields components and the Green’s tensor of the system under study. In its turn, these cross-spectral densities determine the spatial and temporal coherence properties of fields. It should be emphasized that the developed theoretical formalism allows computing the properties of absorptive and nonlocal systems. The spatial-temporal tensor and thermodynamic characteristics of thermal fields can be calculated in a vacuum space outside and within of heated dispersive and absorptive bodies. In this connection it should be noted that a problem of defining and calculating an electromagnetic energy in dispersive inhomogeneous and absorbing media in equilibrium can be defined well, see for instance [22-24]. The subtle point is concerned to the energy balance relation following from the Poynting’s theorem. Being a direct consequence of Maxwell’s equations, the energy balance relation is valid under arbitrary thermodynamical conditions, so it can be used to describe different systems including out-of-equilibrium systems. However, in general it is impossible to separate the electromagnetic energy coupled with the dissipated heat in the balance equation in an unambiguous way. Fortunately, in the systems where a thermal equilibrium is established, the dissipated heat vanishes in average. That is why; it is possible to define the electromagnetic energy within dispersive and absorbing medium [22-24]. A system in thermodynamic equilibrium is a very fruitful model for the simplest physical conditions in which the system under study is fully characterized by its thermodynamic functions [25]. Thermodynamic functions specifiy all properties of a system in equilibrium. In its turn all the thermodynamic functions can be expressed in different ways; in terms of the partition function, by using the density of states (DOS) for uniform systems or local density

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Thermodynamics of Surface Electromagnetic Waves

133

of states (LDOS) for nonuniform systems, by using the method of the Green’s function, or by using some auxiliary functions, which directly associated with the DOS and Green’s functions [26]. It must be stressed that in general, in a characterization procedure of systems, the density of states (DOS) is a fundamental quantity which allows obtaining many of macroscopic quantities. For example, along with the thermodynamic and spectral properties of a system, the scattering amplitudes, transition and transmission probabilities, cross-sections of elastic and inelastic processes, etc., depend on the DOS of final and initial states. In its turn, the Green's function determines the spectral properties of observables of a dynamical system [7, 8, 27-29]. For instance, the poles of the Green's function determine the spectrum of excitations and their dampings, the Green's function allows calculating various kinetic and thermodynamic coefficients, also the knowledge of the electronic Green's function permits the calculation of the total electron density in a system and one also to obtain other useful information such as wave functions, density of states, and currents. The DOS is usually obtained by taking the imaginary part of the Green function of the system. Traditionally, thermodynamic quantities are well-known for bulk or infinite systems. The related example that we want to mention here is the energy, free energy, entropy and thermal capacity of the blackbody radiation in a cavity. But in general, natural and manufactured compound structures consist of volume and surface parts separated by transition layers that connect them. Calculating the DOS near interfaces separating two subsystems are necessary steps in many physical problems. In problems of calculating the spectral characteristics of random electromagnetic fields there are various ways to introduce the DOS and local DOS to take into account the effect of interfaces between media [17, 30-33]. As we have already mentioned the phenomenological physics of the fluctuating electromagnetic fields is well developed, but a problem of calculation of the fields within compound structures is quite laborious, even for the case of lossless materials. In this chapter we consider a system of normal surface electromagnetic fields of plane interfaces of adjoined materials based on the papers [34, 35]. In these papers the spectral energy densities of surface plasmon and phonon polaritons in case of thermodynamic equilibrium are calculated using general definition of the DOS accepted in theory of solids [36, 37]. It is demonstrated that the spectral distribution of surface polaritons in equilibrium, depending on the optical properties of the material, is quite differ from the Planck’s law for photons. Temperature dependence of the surface density of energy for two dimensional thermal fluctuations is differ from the temperature dependence of volume density of energy for photons in equilibrium is also shown. Three dimensional fluctuations of thermally excited fields in vacuum near a plane interface and two dimensional thermal fluctuations of surface polaritons mainly occur at the frequency of the quasistatic surface polariton. But, a manifestation of the resonance in the spectral energy density of thermal three- and two dimensional fluctuations depends on the exponential factor in the mean energy of an oscillator and on the resonance spectral terms. Based on the Barash-Ginzburg general formulae for free energy of the electromagnetic fields within inhomogeneous and lossy materials, thermodynamic functions of the interface modes using dispersion equations in various local and nonlocal approaches are calculated. In particular, the energy and free energy of thermally stimulated electromagnetic fields corresponding to the surface eigenmodes of a plane interface and of a plane parallel film are considered. Our attention is devoted on a description of thermodynamic properties of the fields in near-interface region because it can be considered as the transition layer between two bulk subsystems and ipso facto this

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134

Illarion Dorofeyev

question is directly related to the mesoscopicity of a complex system. A correspondence between the Barash-Ginzburg approach in calculations of thermodynamic properties of the fluctuating electromagnetic fields within spatially nonuniform dispersive and dissipative systems and the traditional textbook definition of energy via the density of states of eigenmodes of spatially nonuniform dissipationless systems is established. It is shown that the Barash-Ginzburg basic definition of free energy of the surface electromagnetic fields within inhomogeneous lossy materials is identical to the related expression as derived from the wellknown definition of density of states usually accepted in theory of solids in the case of dissipationless materials. Dispersion relations for the surface states in different approaches are considered and showed that negative values of the function  ( ) in the general theory can be concerned to the bounded states of fields within a material. The longitudinal bulk waves are the bounded states manifesting in the negative sign of the function  ( ) in whole frequency range despite of dissipation. In its turn, the transverse fields inside bulk or surface systems contain only in part the coupled waves with a matter via some dissipative mechanism. It is follows that the Barash-Ginzburg theory gives qualitatively the same spectral distribution of surface plasmon polaritons as in the Planck law for bulk photons in a vacuum. In its turn, other considered approaches yield in a shift of the spectral power density maximum towards lower frequencies with respect to the Planck law. Moreover, along with the quantitative difference in the spectral distribution, these spectral power densities are qualitatively different as it clearly seen from demonstrated figures. This spectral shift exists despite of the dissipation factors in model dielectric functions that is why corresponding experiments would be very important.

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DISPERSION OF SURFACE POLARITONS AT A PLANE BOUNDARY A theory of surface electromagnetic waves is known from many textbooks and reviews, see for instance [1-5]. Surface polaritons at a vacuum–matter plane interface are characterized by the specific dispersion relation and validity condition as follows

 2  ( ) k  2 , c  ( )  1 2 SP

Re{ ( )}  1 ,

(1)

where  ( )   ( )  i ( ) is an isotropic, frequency-dependent, complex dielectric function. Following to [1] we consider two cases: of the complex wavenumber of the surface polariton and a pure real frequency and of the complex frequency and a pure real wavenumber. To illustrate the characteristic features of surface polaritons supported by a plane boundary between a vacuum and a medium, we use two different models of the dielectric function for description of the material optical properties. Namely, for the Drude and for the oscillatory model we have correspondingly

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135

Thermodynamics of Surface Electromagnetic Waves

 ( )  1 

P2 ,  (  i )

(2)

and 2 2  (LO  TO )   ( )    1  2 , 2  TO    i 

(3)

P is the plasma frequency,  is the electron relaxation frequency,  0 ,   are the respective dielectric constants at low and high frequencies, TO is the frequency of the where

transverse optical phonon, and  is the anharmonic decay constant. In case of a pure real frequency we separate the real and imaginary parts of the complex wavenumber in Eq.(1)

 ( )  ikSP  ( )  p( )  i ( ) , kSP ( )  kSP

(4)

which are equal to

 2  (    2   2 )  (    2   2 ) 2   2  p ( )  2  , 2c  (   1)2   2 

(5)

 2  (    2   2 ) 2   2  (    2   2 )   ( )  2  , 2c  (   1)2   2 

(6)

2

  ( / c ) () /( ()  1) where we selected the roots displaying correct results for kSP 2

  0 in case of transition to the transparent medium and kSP

2

2

 ( )  0 .

By definition, the real and the imaginary parts in Eqs.(5) and (6) of a wavenumber are expressed via the wavelength  ( ) and the propagation length L( ) of surface polaritons

kSP ( )  in

2 1 i  p( )  i ( ) ,  ( ) L( )

order

to

obtain

an

appropriate

(7)

solution

in

the

form



exp{i[kSP ()r  t ]}  exp{i[ p()r  t ]} exp[ ()r ] , where r is the lateral 

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2

coordinate. Eqs.(5) and (6) yield two equations, namely, the dispersion relation

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(8)

136

Illarion Dorofeyev

Figure 1. The surface phonon polariton dispersion relation Re{kSP }  frequency



p( ) in case of the pure real

in accordance with Eq.(5) for GaAs at two different anharmonicity factors 

 0.02TO

  0.002TO (thick line) – a). The spatial decay coefficient  ( ) versus a frequency in accordance with Eq.(6) for GaAs at two different anharmonicity factors   0.02TO (thin line) and   0.002TO (thick line) - b). (thin line) and

And equation determining function

 ( ) or the propagation length L( )   1 ( )

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 ( )  f 2 ( )  0,

(9)

where functions f1 ( ) and f 2 ( ) must be clear from Eqs.(5) and (6).

  p we have the complex frequency of the surface In case of a pure real wavenumber kSP polariton

 ( p)  iSP  ( p)  SP  ( p)  i( p) , SP ( p)  SP

(10)

where ( p) characterizes a temporal damping of the surface excitation. In this case we obtain from Eqs.(1) and (3) the equation of the fourth order with respect to the complex frequency of the surface polariton versus p 4 3 2 SP  ASP  BSP  CSP  D  0 ,

(11)

where A  i , B  (2 p c  P ) , C  i 2 p c , D  p c 2 2

2

2 2

P2

2 2

for Eq.(2) and A  i ,

2 2 B  [ p2c2 (   1)   0TO ]/   , C  i p2c2 (   1) /   , D  p2c2TO ( 0  1) /  

for Eq.(3). The Eq.(11) yields two pairs of complex conjugate solutions. The required

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137

Thermodynamics of Surface Electromagnetic Waves

solution is chosen so that it does not include the growing factors and be appropriate for the propagation waves, for instance as 

 ( p)t ]} exp[( p)t ] . exp{i[ pr  SP ( p)t ]}  exp{i[ pr  SP For numerical calculations, we take in Eqs. (2) and (3) the parameters corresponding to a typical

good

(P  2. 1016 rad / sec,  0.01P ) ,

metal

and

to

(TO  5.05 1013 rad / sec , LO  5.5 1013 rad / sec ,   0.01TO ,    11) ,

see

GaAs for

instance [38, 39]. At this point we mention the frequency of the quasistatic surface polariton

QP . The frequency QP

corresponds to the nonradiative Coulomb surface polariton as a

root of the dispersion equation Re{ ( )}  1 . For example, in case of the Drude and

QP  P / 2 and QP  TO ( 0  1) /(   1) , correspondingly for dissipationless systems (   0,   0 ). oscillatory models in Eqs.(2),(3)

Figure 1 exemplifies the relations between the pure real frequency  and the real part p -a) and the imaginary part  -b) of a wavenumber in accordance with Eqs.(5) and (6) for GaAs at two different anharmonicity factors  . The curves are typical for materials described by the dielectric functions in the oscillatory approach, Eq.(3). Herewith, figure 1a) shows the dispersion relation for the surface phonon polariton and the spatial decay coefficient versus a frequency is shown in figure 1b). Main features of this figures are the backbending [40, 41, 42] in figure 1a) and the strong spatial

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decay of surface phonon polaritons at the frequency

QP in

figure 2b). The backbending

disappears in case of the dissipationless medium supporting the surface polaritons. The backbending means an existence of the maximum wavenumber of surface polaritons in this case. This maximum wavenumber is determined by losses in a system under study. The slanting thin line in figure a) represents the light line. The horizontal dashed lines are situated at

TO , QP

and

LO

in these figures. It should be noted that the dispersion equation in

Eq.(1) is valid also for so-called Brewster mode despite of a sign  ( ) . Corresponding branch of the dispersion curve is shown at frequencies larger than the frequency of the in Figure 1a) and at frequencies smaller than

TO

LO

in the radiative frequency range of the

figure. Figure 2 exemplifies the relations between the pure real wavenumber p and the real part

 of the surface phonon polariton frequency and the imaginary part   SP  of a SP frequency in accordance with Eq.(11) at the same material parameters. Herewith, figure 2a) shows the dispersion relation for the surface phonon polariton in this case. The temporal decay coefficient versus a wavenumber is shown in figure 2b). The vertical dashed line in Figure 2b) is situated at p  TO / c .The dispersion curve in figure 2a) is different from the dispersion curve in figure 1a), where the backbending occurs. In case of good metals characterized by the Drude model in Eq.(2) a plane interface supports the surface plasmon polaritons. The surface plasmon polariton dispersion relations

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138

Illarion Dorofeyev

 ( p) , the spatial decay  ( ) and temporal decay ( p) coefficients are p( ) and SP demonstrated in Figures 3, 4. Figure 3 exemplifies the relations between the pure real frequency  and the real part p -a) and the imaginary part  -b) of a wavenumber in accordance with Eqs.(5) and (6) for aluminum at two different collision frequencies . The curves are typical for materials described by the dielectric functions in the Drude model, Eq.(2).

 ( p) in case of the Figure 2. The surface phonon polariton dispersion relation Re{SP ( p)}  SP p in accordance with Eq.(11) for GaAs at two different anharmonicity factors   0.02TO and   0.002TO – a). The temporal decay coefficient ( p) versus a wavenumber

pure real wavenumber

in accordance with Eq.(11) for GaAs at two different anharmonicity factors 

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and

 0.02TO (the curve 2)

  0.002TO (the curve 1) - b).

Figure 3. The surface plasmon polariton dispersion relation

Re{kSP }  p( )

in case of the pure real

 in accordance with Eq.(5) for aluminum at two different collision frequency   0.02P (thick line) and   0.002P (thin line) – a). The spatial decay coefficient  ( ) frequency

versus a frequency in accordance with Eq.(6) for aluminum at two different collision frequency

  0.02P (thick line) and   0.002P (thin line)- b).

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Thermodynamics of Surface Electromagnetic Waves The horizontal dashed lines are situated at

P

139

and QP  P / 2 in these figures. The

slanting thin line in figure a) represents the light line. In this case the dispersion equation in Eq.(1) is also valid for the Brewster mode despite of a sign  ( ) . Corresponding branch of the dispersion curve is shown at frequencies larger than the plasma frequency  P in Figure 3a). Figure 4 exemplifies the relations between the pure real wavenumber p and the real part

 of the surface plasmon polariton frequency and the imaginary part   SP  of a SP frequency in accordance with Eq.(11) at the same metal parameters. Herewith, figure 4a) shows the dispersion relation for the surface plasmon polariton in this case. The temporal decay coefficient versus a wavenumber is shown in figure 4b). The vertical dashed line in Figure 4b) is situated at p  P / c .The dispersion curve in figure 3a) is also different from the dispersion curve in figure 4a), where the backbending occurs. It should be emphasized that the backbending and maximum wavenumber of surface polaritons disappear in case of lossless materials (  relations kSP (SP ) and

 0,   0 ). In this case the dispersion

SP (kSP ) are identical.

In the presence of spatial dispersion, we took the modified oscillatory model [43] for nonconductors

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 (k ,  )    

2P , 2 TO   2  D( p 2  q 2 )  i

(12)

 ( p) in case of the Figure 4. The surface plasmon polariton dispersion relation Re{SP ( p)}  SP pure real wavenumber

p

in accordance with Eq.(11) for aluminum at two different collision frequency

  0.02P (thick line) and   0.002P (thin line) – a). The temporal decay coefficient ( p) versus a wavenumber in accordance with Eq.(11) for aluminum at two different collision frequency

  0.02P (the curve 2) and   0.002P (the curve 1) - b).

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140

Illarion Dorofeyev

where P  ( 0    )TO , D  2

2

TO / meff , meff  0.17me , TO  3.77 1013 rad / s and

 0  9.06 ,    5.8 typically for ZnSe chosen here only for definiteness and illustration purpose, k  p  q , and the hydrodynamic model for conductors [4] in a nonlocal case 2

2

2

with the same plasma frequency as in local case, with the Fermi velocity

vF  1.4 108 cm / s

P2 ,  2  i   2 ( p 2  q 2 )

 (k ,  )   B  where

 2  (3/ 5)v2F

for

(13)

  .

Taking into account that the spatial structure of the surface fields is determined by the wavevector k  { p, q  i} , we found allowed values of

   ( p,  ) associated with a

given p and  just as well as in [43]. From equations ( / c) and from Eq.(12) it follows that

2

 ( k ,  )  k 2 ,  (k ,  )  0

2 1,2 ( p,  )  (1/ 2)  A  A2  4 2  2P / Dc 2  ,

  ( p,  )   /   D   2B , 2 3



(14)

2 P

where A  ( p   2

  / c2 )  2B , A  ( p 2   2  / c 2 )  2B ,

2

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2 2B  ( 2  TO  Dp2  i) / D .

The three known roots for the hydrodynamic model in Eq.(13) are 2 1,2 ( p,  )  (1/ 2)  B  B 2  4 2P2 /  2 c 2  ,



 ,

(15)

 ( p,  )   /  B    , 2 3

2 P

where B  ( p   2

2

2 B

 B / c2 )  2B , B  ( p2   2 B / c2 )  2B ,

2

2B  ( 2   2 p2  i) /  2 in this case. It should be noted that the permittivity in Eqs.(12) and (13) is a pure real quantity at k   despite of a dissipation. The same statement is valid for the Lindhardt-Mermin dielectric function [44]. The mentioned models of dielectric functions in a local approach in Eqs.(2),(3) follow directly from Eqs.(12),(13) at k 0. In a nonlocal approach no the “stop band” [43] because the dielectric function  (k ,  ) is the function of a wavenumber. It was shown in the cited work that, for instance, within the band

TO ( p)    LO ( p) the propagating waves can exist despite of the sign of dielectric

function. Furthermore, no pure surface waves strongly localized near boundary, because the Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

141

Thermodynamics of Surface Electromagnetic Waves

exponential tails exp[i ( p,  ) z ] within a matter are leaking to a medium due to a complexity of the factors i ( p,  ) , including a pure imaginary one in spite a frequency range. That is why taking into account a spatial dispersion the surface-like and volume -like modes are mixed inside such a material. We would like to demonstrate the surface polariton dispersion curves for given dielectric function in Eq.(12) in case of a weak spatial dispersion obtained without of the so-called additional boundary conditions. In this case [1] the dispersion relation has a usual form 2 kSP 

 2  (k ,  ) ,` c 2  (k ,  )  1

where k  { p, i i } ,

(16)

i  i ( p,  ) , i means the i -th branch of waves within a nonlocal

medium. In our case we use two kinds of waves, because the third branch gives identically

kSP  0 due to equality  (k ,  )  0 for  3 ( p,  ) . Taking into account Eq.(12) in Eq.(16) the wavenumber and frequency of the surface phonon-polariton are both complex,

 and SP  SP   iSP  . In such a case the dispersion curve depends on the kSP  p  ikSP fixed conditions of an experiment or calculation [1, 40-42]. Furthermore, it should be bear in mind in calculations that Re{ i }  0 , assigning the near surface character of the modes under our study. We numerically solved Eq.(16) with Eq.(12) with a pure real frequency

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 followed by finding the complex roots p  ikSP  and vice versa, taking a pure real SP  SP   iSP  . Figure 5a) and wavenumber p followed by calculating the complex roots SP  SP 5b) show dispersion curves for these two cases. As well as in Figure 1a) and 2a) we have the backbending and corresponding maximum value of a wavenumber at finite losses in a system under study. Also the dispersion curves became identical at lossless systems (   0 ). As is known [1], dispersion of the volume polaritons is determined by the equation

 2 2   ( p, q,  )  k  2  ( p, q,  )   0 , c  

(17)

where k  p  q . In case of an isotropic and homogeneous medium we should take 2

2

2

k  p and q  0 in Eq.(17). It is easy to verify that the three dispersion equations directly 2 2 follows from Eq.(17) using Eq.(12), namely q1,2  1,2  0 and q3  3  0 .

2

2

Thus, we have two possible functional dependencies; one of them  ( p) gives three roots from equations 2  p 2c 2  2P  2  p 2c 2  p 2c 2TO ( p) 3 2 1,24  (i )1,2   TO ( p)  1,2   i    0,  1,2          

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(18)

142

Illarion Dorofeyev

Figure 5. Dispersion of the surface phonon polaritons in case of a weak spatial nonlocality. Dispersion relation Re{kSP ( )} in case of the pure real frequency two different anharmonicity factors 



in accordance with Eq.(16) for GaAs at

 0.02TO (thin line) and   0.002TO (thick line) – a).

Dispersion relation Re{SP ( p)} in case of the pure real wavenumber

p

in accordance with Eq.(16)

for GaAs at the same anharmonicities -b). 2 3  LO ( p)  i / 2 ,

(19)

2 2 2 2 LO ( p)  TO ( p)  2P /     2 / 4 and TO ( p)  TO  Dp2 . These equations determine complex frequencies 1,2,3    i of three branches of the bulk polaritons as Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

where

functions of the pure real wavenumber p . Another functional dependency k ( ) gives three roots from equations 2   2   2  i  2  2  TO   2  i 2P   2 4 k1,2   TO  2    k1,2     0, D c D   D  c 2    

k3  

2 TO   2  i

D

2P .  D

(20)

(21)

These equations determine complex wavenumbers k1,2,3  p  ik  of three branches of the bulk polaritons as functions of the pure real frequency  . Obviously, from Eqs.(18)-(21) directly follow analytical formulas for various limiting cases, for instance, in case of a transparent medium, when   0 . In this our paper we use only Eqs.(18),(19) determining the real and imaginary parts of the bulk polariton’s frequencies.

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Thermodynamics of Surface Electromagnetic Waves

143

Figure 6. Dispersion curves for the volume (VP) and surface (SP) polaritons in case of the weak spatial dispersion in according with Eqs.(16) and (17) using Eqs.(12),(14). Two Brewster’s modes (B1, 2) are shown within a domain of longitudinal

p   / c . Dashed lines show the dispersion of the transverse TO ( p)

and

LO ( p) optical phonons in Eq.(19). Slanting dashed lines show dependencies   cp ,

  cp /   ,   cp /  0

, correspondingly. Dotted line represents the dispersion of the

quasistatic polariton in according with Eq.(22). The imaginary part of the surface and volume phononpolaritons frequency is demonstrated in figure b) for the corresponding curves SP1, 2, VP1 and B1,2 in figure a).

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Figure 6 demonstrates the dispersion dependencies taking into account spatial dispersion for the surface polaritons from the implicit equation (16) numerically solved in the form  ( p) using Eq.(12) and for the bulk polaritons from explicit Eqs.(18),(19). Figure 6a) exemplifies the wavenumber dependence of the real part of the frequency for the volume (VP) and surface (SP) polaritons in case of the weak spatial dispersion in according with Eqs.(16) and (17) using Eq.(12), (14). Two Brewster’s modes (B1,2) are shown within a domain of p   / c , too. Dashed lines show the dispersion of the transverse

TO ( p) and longitudinal LO ( p) optical phonons. Slanting dashed lines show dependencies   cp ,   cp /   ,   cp /  0 , correspondingly. Dotted line represents the dispersion curve of the quasistatic polariton in according with Eq.(22). The imaginary part of the surface and bulk phonon-polariton frequency is demonstrated in figure 6b) for the curves SP1,2, VP1 and B1,2 from figure 6a). As it seen from these figures the curves SP1,2 and B2 intersect near the point ( TO , p  TO / c ). In vicinity of the point the curves oscillate, and these jumps are artificially smoothed out. It should be noted from Figure 6a) that in a quasistatic limit ( p   / c ) a dispersion curve for the surface phonon-polariton SP1,2 saturates due to Eq.(16) obtained without of additional boundary conditions [1]. There is more complicated dispersion equation, taking into account additional boundary conditions [43], and the wave number dependence of the quasistatic polariton in the above mentioned quasistatic limit is as follows

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144

Illarion Dorofeyev

Figure 7. Dispersion relation wavenumber values in range

 ( p) satisfying the equation Re{D( p,  )}  0 from Eq.(23) for 0  p  104 cm1 –a) and in range 104  p  106 cm1 –b). Slanting

straight lines in figure 7a) indicate dependencies   cp ,

  cp /   ,   cp /  0

,

correspondingly. 1

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 d     p  2P  QP ( p) QP     3 1   i B  , 2   d      2 D B  i   3 B  QP  

(22)

which is valid for the lossless (   0 ) medium at the conditions c  and p  0 . This dispersion is shown in Fig6a) by the dotted line SP. So far, we used the dispersion Eq. (1) in local approach or Eq. (16) for surface polaritons which is valid for very weak spatial dispersion. Now, we calculate the dispersion curves using more rigorous model accounting additional boundary conditions [43] as applied to an artificial nonlocal material with the cubic symmetry. For convenience, we rewrite here the dispersion equation (4.12) from [43] as follows

D( p,  )  (1   01 )(i B  1 )( p 2   3 2 )   ( 2   0 2 )(i B   2 )( p 2   31 )  ,

(23)

 p (i B   3 )( 2  1 )  0 2

where the dielectric functions

1,2 are defined in Eq.(12) with roots 1,2,3 , correspondingly,

 0  p 2   2 / c 2 . Because of the complexity of the function D( p,  ) , the Eq.(23) means that both the real D( p,  ) and imaginary D( p,  ) parts of the function must be equal zero. We numerically solved the implicit equations D( p,  )  0 and D( p,  )  0 at pure real wavenumbers p and frequencies  . Figure 7 exemplifies the dispersion relation

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145

Thermodynamics of Surface Electromagnetic Waves

 ( p) satisfying the equation D( p,  )  0 for essentially different range of wavenumber values. Slanting straight lines indicate dependencies

  cp ,   cp /   ,   cp /  0

, correspondingly in figure 7a). The conditions Re{ i }  0 assign the near surface character of the modes under study. It is clearly seen from Figure 7b) another kind of the backbending curve yielding in the additional surface polariton [1] at fixed frequency  between

TO and

QP . Figure 8 shows the dispersion relation  ( p) satisfying the equation D( p,  )  0 for the same range of wavenumber values as in Figure 7. Slanting straight lines in Figure 8a) also

  cp ,   cp /   ,   cp /  0 .

indicate dependencies

It should be emphasized that the surface mode in this figure saturates at the frequency

LO , differing from the usual surface polariton. Dispersion relations for surface plasmon polaritons supported by good metals in case of nonlocal response are known, for example from [45]. In our designations we have

D ( p,  ) 

2 2  c2





0

 dq  p2 q2   2  2 2 2 2 2  k  ( / c ) (k ,  ) ( / c ) t (k ,  )  k  ,

(24)

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 p2   2 / c2  0

 ( p) satisfying the equation Im{D( p,  )}  0 from Eq.(23) for 4 6 1 4 1 wavenumber values in range 0  p  10 cm –a) and in range 10  p  10 cm –b). Slanting Figure 8. Dispersion relation

straight lines in figure 8a) indicate dependencies   cp ,

  cp /   ,   cp /  0

,

correspondingly.

where k  p  q , 2

2

2

 (k ,  ) and  t (k ,  ) are the longitudinal and transverse dielectric

functions.

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146

Illarion Dorofeyev This equation implicitly determines the dispersion relation

 ( p) for the surface plasmon

polaritons. In the quasistatic regime ( c  ) a more simple dispersion equation follows from Eq.(24)

D ( p,  )  1 

2p







0

dq 0. k  (k ,  ) 2

(25)

We numerically solved the Eq.(24) using the hydrodynamic model in Eq.(13) putting

 (k ,  )   (k ,  )   t (k ,  ) . Figure 9 exemplifies the dispersion relation  ( p) satisfying the equation D( p,  )  0 in Eq.(24). It is clearly seen the wavenumber dependence of the surface polariton frequency. We do not show a picture corresponding to the equation D( p,  )  0 because no additional curves in the nonradiative ( p   / c ) region with the selected values of  and p . As the final important example of the surface polariton dispersion, we consider here a system bounded by two plane surfaces or a dielectric slab with thickness h and the dielectric function  f from Eq.(3) with

  0.02TO . This slab is surrounded by vacuum or air. A

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dispersion relation for a more general case is known from [3, 46]

 ( p) satisfying the equation Re{D( p,  )}  0 in Eq.(24) for 6 1 6 8 1 wavenumber values in range 0  p  5 10 cm –a) and in range 5 10  p  2 10 cm – b). Slanting straight line in figure 9a) indicates the dependence   cp . Figure 9. Dispersion relation

              D( p,  )  1  3 f 1  1 f   exp(2 f h) 1  3 f 1  1 f   0 ,               f 3  f 1 f 3  f 1  

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(26)

147

Thermodynamics of Surface Electromagnetic Waves where  1

and

 3 are

the

1, f ,3  p 2  1, f ,3 ( )( / c)2 Figure

10

dielectric

functions

of

surrounding

materials,

.

exemplifies

the

 ( p) in

dispersion

case 1   3  1 ,

1,3    p2  ( / c)2 in Eq.(26) at different thickness of the film. It is seen a splitting of the unique surface polariton dispersion curve on two surface modes due to their interaction within comparatively thin films. It is sometimes more convenient in numerical calculations to use other form of the dispersion relations for two splitting surface modes in the above considered case [3]

 f ( p,  ) Tanh[(1/ 2) f ( p,  ) h]  0,  ( p,  )  ( p,  ) D ( p,  )   f ( )  f Coth[(1/ 2) f ( p,  ) h]  0.  ( p,  ) D ( p,  )   f ( ) 

(27)

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We considered and wrote out the dispersion relations in this paragraph for plane interfaces because their simplicity and particular importance in practical applications. Peculiarities of the surface polariton dispersion in other geometrical cases can be found in the cited reviews and textbooks.

Figure 10. Dispersion

 ( p) of the surface polaritons in accordance with Eq.(26) in case 1   3  1 ,

1,3    p2  ( / c)2

at different thicknesses of the film

h  2 104 cm –a),

h  4 104 cm -b), h  6 104 cm -c), h   -d). The horizontal dashed lines are situated at

TO , QP

and

LO

from the bottom to upper side in the figures.

It should be emphasized that the dispersion equations directly determine the density of states of the surface waves and their thermodynamical functions in any approaches.

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148

Illarion Dorofeyev

Thermodynamic Functions of the Surface Normal Modes Spectral density of energy of the surface plasmon and phonon polaritons in case of thermodynamic equilibrium is calculated in [34, 35]. It is found that the spectral distribution of surface polaritons in equilibrium, depending on the optical properties of a medium, is quite differ from the Planck’s law for bulk photons. Temperature dependence of the surface energy density for two dimensional thermal electromagnetic fluctuations is differ from the temperature dependence of volume energy density for photons in equilibrium. Three dimensional fluctuations of thermally excited electromagnetic fields in vacuum near a sample and two dimensional thermal fluctuations of surface polaritons mainly occur at the frequency of the quasistatic surface polariton. A manifestation of the corresponding resonance in the spectral energy density of thermal three- and two dimensional electromagnetic fluctuations depends on the exponential factor in the mean energy of an oscillator. A general expression for the spectral density of states in a two-dimensional system is obtained in [34, 35] by analogy with a three-dimensional case [36, 37] usually employed in theory of solid states. This quantity can be written out as follows

D ( ) 

d k S , 2  (2 ) | k  |

where S is the surface of sample under study, d

(28)

k

is the differential element of a constant-

frequency line kSP ( ) in a two-dimensional wave-vector space, k  is the group velocity of the surface polariton(see the designations in [34, 35]). In a two-dimensional wave-vector space the value (2 ) / S corresponds to one allowed Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

2

state of k SP . Accounting dissipation in the system brings new features in the dispersion curve for surface polaritons [40-42]. As we have already illustrated in figures 1a). 3a) and 5a) of our previous paragraph, the main feature in this figures is a backbending of the dispersion curve at finite dissipation, which was observed experimentally at a fixed frequency and varying the angle [40]. An influence of finite dissipation rates on the DOS of surface polaritons is analyzed in [35]. Let’s recall the formula for DOS given in [35]. We consider an isotropic material, that is why the constant-frequency lines in a wavenumber space are the concentric circles in this case. The group velocity k  is a constant along the constant-frequency line and | k  || d / dkSP | . The circle length is

k

 2 | kSP | . Taking into account these

considerations, we can write from Eq.(28) the number of surface modes per unit frequency interval per unit surface

D( ) 

D ( ) | kSP | dkSP .  S 2 d

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149

Thermodynamics of Surface Electromagnetic Waves

First of all we consider both the real and imaginary parts of the surface polaritons wave number kSP ( )  p( )  i ( ) . In this case we have

p 2 ( )   2 ( )  dp( )   d ( )      . 2  d   d  2

D( ) 

2

(30)

Figure 11a) exemplifies the normalized DOS of surface phonon polaritons supported by the plane vacuum-GaAs interface in accordance with Eq.(30) and Eqs.(5),(6). Normalization is done to D(QP ) at the frequency of Coulomb surface polariton. The vertical dashed lines are situated at

TO , QP

and

LO

from the left to right side in the figures. We emphasize

that the spectral validity of the results is limited by the condition TO    QP . Strictly speaking the definition of DOS in Eq.(30) means negligibly small absorptions in a system of interest (   0 ). It is not very difficult to verify that the real and imaginary parts of the wavenumber of a surface polariton can be decomposed within the frequency range

 [TO , QP ] as follows p( )  a1  b1 2  c1 4  ... ,

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 ( )  a2  b2 3  c2 5  ... .

Figure 11. Normalized DOS

(31)

 ()  D() / D(QP ) of surface phonon polaritons supported by the

plane vacuum-GaAs interface in accordance with Eq.(30) – a) and Eq.(33) – b). Normalization is done to

D(QP ) at the frequency of Coulomb surface polariton. The vertical dashed lines are situated at

TO , QP

and

LO

from the left to right side in the figures.

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150

Illarion Dorofeyev

Figure 12. Normalized DOS

 ()  D() / D(QP )

of the surface phonon-polariton supported by

the vacuum-GaAs interface versus a normalized frequency

 / QP as calculated with use of

Eq.(30)(upper curve), Eq.(32) and Eq.(33)(bottom curve) at two different anharmonicities:

  0.01TO – a) and   0.001TO – b). Common normalization is done to D(QP ) with use Eq.(30). The vertical dashed line is situated at QP . That is why we can neglecting by the imaginary  ( ) part in Eq.(30) at the condition

  0 . As the next step instead of Eq.(30) we can write | p( ) |  dp( )   d ( )  D( )      , 2  d   d  2

2

(32)

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and then

D( )

| p( ) | dp( ) . 2 d

(33)

Using Eq. (5) in case of the transparent media (    0 ), we get from Eq.(33) the sought formula for the spectral DOS of surface polaritons

  ( )  d  ( )  D( )  02 D   , 2   ( )  1 2[ ( )  1] d 

(34)

where 0 ()   / 2 c is the two-dimensional (2D) spectral density of states with one 2D

2

polarization state. Figure 11b) shows normalized DOS  ()  D() / D(QP ) of the surface phononpolariton supported by the vacuum-GaAs interface versus a frequency calculated with use of Eq.(33) and Eq.(5). It is clearly seen two peaks in DOS. One larger peak is centered near the frequency of the quasistatic polariton QP . Additional smaller peak is connected with finite losses in our system due to an anharmonicity. We found that the smaller peak is centered near

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Thermodynamics of Surface Electromagnetic Waves

151

the frequency corresponding to the intersection point of the surface polariton wavelength and the propagation length. Figure 12 demonstrates normalized DOS  ()  D() / D(QP ) of the surface phonon-polariton supported by the vacuum-GaAs interface versus a normalized frequency

 / QP

as calculated with use of Eq.(30)(upper curve), Eq.(32)(middle curve) and

Eq.(33)(lower curve) at two different anharmonicities. This figure shows how influence the terms  ( ) and d / d in Eq.(30) determining a dissipation in a system on to the density of states. Next figure demonstrates a connection between the smaller peak of DOS as calculated with help of Eq.(33) with a dissipation strength of material supported the surface polaritons. Figure 13a) shows the normalized smaller peaks of DOS for GaAs as calculated with use of Eq.(33) at different anharmonicities  . The vertical dashed line fixes a frequency of the quasistatic polariton QP

 5.46 1013 rad / sec for this material at   0 . It is evidently

that the smaller  , the larger the peak of DOS and closer to

QP .

Figure 13b) shows the frequency positions of the peak maximum of DOS (thick line) from figure a) and of the intersection point(thin line) of the propagation length

L(,  )   1 (,  ) and wavelength  ( ,  )  2 p 1 (,  ) of the surface phononpolariton at the GaAs/Vacuum interface calculated with help of the formulas Eqs.(5), (6), (7) at different anharmonicity  . From this figure, we can conclude that the smaller peak of DOS as calculated with help of Eq.(33) or (34) is connected with dissipative properties of a system.

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The intersection point of L and  determines two domains, where L   and L   . Other words, the additional peak of DOS is determined by interplay between losses in a system and propagation conditions for surface polaritons. In the limit of   0 the additional peak merges with a peak of the normal mode at

 QP . The same regularity was found also for

the Drude model of dielectric function. Figure 6 in [35] exemplifies normalized DOS of the surface plasmon-polariton at different collision frequency  supported by the Al/Vacuum interface versus a frequency. It is also found two peaks in DOS. One peak is situated near the frequency of the quasistatic plasmon polariton. Location of the additional smaller peak in this case is determined by interplay between losses in a system and propagation conditions for the surface plasmon polaritons. The additional peak merges with the larger peak of the normal mode at the frequency of quasistatic polariton in the limit of   0 . We would like to emphasize that the finite dissipation rate in a system under study determine concrete and finite value of DOS and backbending in dispersion curve for surface polaritons. Knowledge of DOS allows defining the spectral energy density of surface polaritons [34, 35] by analogy with the Planck’s law for bulk photons as follows

uSP ( )  D( )(, T ), and the total energy density of surface polaritons

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(35)

152

Illarion Dorofeyev

Figure 13. Normalized smaller peaks of DOS for GaAs as calculated with use of Eq.(33) at different anharmonicities

  0.005,0.006,0.007,0.008,0.01,0.012,0.015,0.02TO

from upper to

bottom curves –a). The vertical dashed line is fixed at the frequency of quasistatic polariton

QP  5.46 1013 rad / sec for this material at   0 . Frequency positions of the peak maximum of

DOS (thick line) from figure a) and of the point of intersection (thin line) of the propagation length

L(,  )   1 (,  )

and wavelength  ( ,  )  2 p ( ,  ) of the surface phonon-polariton at the GaAs/Vacuum interface calculated with help of the formulas Eqs.(5), (6), (7) at different anharmonicity  . 1

2

U SP (T )   d D( )(, T ) ,

(36)

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1

where 1 and  2 determine the frequency range, where Re{ ( )}  1 . It is obviously, that other thermodynamic functions can be written by analogy with Eq.(35), (36) using DOS in Eq. (34). For example, for the free energy of the surface polaritons 2

FSP (T )  k BT  D( ) n  Z (, T )  d,

(37)

1

where

Z ( , T )   Exp(  / 2k BT )  Exp(  / 2k BT ) 

1

(38)

is the partition function. We would like to recall that the above described method of the DOS calculating is valid at very weak dissipative processes within a system under study. A general method of calculation of free energy and energy of the electromagnetic fields within spatially inhomogeneous and dissipative materials was developed in [22, 23]. The expression, for instance, for free energy can be represented as follows

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Thermodynamics of Surface Electromagnetic Waves

153



F (T )  kBT   ( ) n  Z ( , T )  d,

(39)

0

The key quantity of the Barash-Ginzburg theory [22, 23], determining each of thermodynamic functions, is the function  ( ) in Eq. (39), given by the expression



1





 ( )   Im    (  )d  n D(  ,  )  ,    

(40)

where  is the variable connected with integrals of motion, in particular, the wavenumber components

in

a

homogeneous

infinite

media

with

 ( )  L3 /(2 )3 and

d   k 2 dk sin  d d , D   D(i ) , where D(i ) is the dispersion equation, "i " means i

the branch of the natural modes of the system under study. For example [1], in an infinite homogeneous and dispersive media it is known two transverse eigenmodes of two independent polarizations, satisfying the dispersion equation D and one longitudinal eigenmode from the equation D

( )

( tr )

 k 2  ( / c)2  tr (, k )

  ( , k ) . An integration in

Eq.(40) is done over the volume   , separating the longwavelength part of the

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electromagnetic fields [22,23]. The normal modes of plane surface are the surface polaritons in the frequency range when the dielectric functions across the interface have opposite signs [1-5]. Because we know the dispersion relation for the surface modes, corresponding term to the free energy from Eq.(39) may be clearly found. Indeed, in this case we have in Eq. (40) that d 

 pdpd ,  ( )  L2 /(2 )2

D SP  p 2 

 2  ( ) , c 2  ( )  1

and in a local approach

Re{ ( )}  1 ,

(41)

that is why it follows from Eq.(40) that the sought for quantity per unit area

 ( )  



 SP 1 D SP  pdp Im   D   , 2 2 0    1

(42)

where

D SP 2   ( )  d  ( )   2   . 2  c   ( )  1 2[ ( )  1] d 

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(43)

154

Illarion Dorofeyev

It should be noted that the equation for free energy in Eq.(39) with Eq.(40) is valid for any dissipation strength. But, the quantity in Eq.(40) has no clear sense of the density of states in general [22-24], because this quantity may be of different sign for different frequency range. Nevertheless, in the limiting case of the transparent media, it is definitely the density of surface states within the specified frequency range. Namely, let’s turn to the transparent media ( Im{ ( )}  0 ). In this case we have from Eq.(41)

D SP  p 2 

 2  ( )  2  ( ) 2  p   i, (  0) , c 2  ( )  1 c 2  ( )  1

(44)

where   ( / c ) ( ) /[ ( )  1] , where  ( ) and  ( ) are the real and imaginary parts of the dielectric function. Applying Sohotskii's formula lim( x  i)1  P(1/ x)  i ( x) to Eq.(42), we obtain 2

2

2

0

the expression for the density of states of surface polaritons

 ( ) 

   ( )  d  ( )    , 2 c 2   ( )  1 2[ ( )  1]2 d 

(45)

identically to the result in [34, 35] obtained from the wellknown definition of density of states usually accepted in theory of solids. Another example we would like to refer to is the case of a plane-parallel film [2-5, 46]. In a quasistatic regime ( c  ) we have the following pair of dispersion relations for two

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modes

 (kSP ) and  (kSP ) of surface polaritons in a thin film of thickness

D( )  k  (2 / ) ArcTanh[ ( )] ,

(46)

D( )  k  (2 / ) ArcCoth[ ( )] .

(47)

Taking into account Eqs. (46), (47) and the definition in Eq.(40) we have  ( )   (  ) ( )   (  ) ( ) , where

 (  ) ( )  

 (  ) ( )  

1



2

1



2









0

0

 1 d  ( ) / d  k dk Im  (  ) , 1   2 ( )  D

(48)

 1 d  ( ) / d  k dk Im  (  ) . 1   2 ( )  D

(49)

By considering the same transition Im{ ( )}  0 we have from Eqs.(46) and (47)

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155

Thermodynamics of Surface Electromagnetic Waves

D(  )  k  (2 / ) ArcTanh[ ( )]  i ,

(50)

D( )  k  (2 / ) ArcCoth[ ( )]  i ,

(51)

where   (2 / ) |   /(   1) | . Thus, Eqs.(48) and (49) can be transformed as follows 2

 (  ) ( )  

1 d  ( ) / d  2 1   2 ( )

 (  ) ( )   The





0

1 d  ( ) / d  2  2 ( )  1

integrals

in

k  k  (2 / ) ArcTanh[ ( )] dk ,



these



0

(52)

k  k  (2 / ) ArcCoth[ ( )] dk

equations

are

not

equal

zero

in

(53)

case

of

(2 / ) ArcTanh[ ( )]  0 and (2 / ) ArcCoth[ ( )]  0 . It means that it must be 1   ( )  0 in Eq.(50) and  ( )  1 in Eq.(51), correspondingly. That is why we have from (54) and (55) the following densities of states in this case

 (  ) ( )  

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 (  ) ( )  

2

ArcTanh[ ( )]

d  ( ) / d , 1   2 ( )

(  QP ) ,

(54)

2

ArcCoth[ ( )]

d  ( ) / d , 1   2 ( )

(  QP ) ,

(55)

2

 2



identically to the result in [34], where QP is the frequency of a quasistatic plasmon-polariton satisfying the equation

 ( )  1 .

Figure 14 exemplifies the normalized function

 (,  )   (,  ) / max (,  ) in

Eq.(42) at different anharmonicities  in the oscillatory model of the dielectric function for GaAs in the frequency range

 [TO , QP ] , where Re{ ( )}  1 . The numbers near

curves correspond to the anharmonicity factor

  0.03TO  1 ,   0.02TO  2 ,

  0.015TO  3 and   0.01TO  4 . The curves in figure a) was normalized to max ( ,  ) at   0.01TO and to own maximum in figure b). The vertical dashed line represents position of the quasistatic surface phonon-polariton. The normalized function

 (, )   (, ) / max (, ) for good conductors in Eq.(42)

at different damping factor in the Drude model of the dielectric function is shown in Fig15. The numbers near curves correspond to the damping factor

  0.02P  1 ,

  0.01P  2 ,   0.005P  3 and   0.001P  4 . The curves in figure a) was

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156 normalized to

Illarion Dorofeyev

max ( , ) at   0.001P and to own maximum in figure b). The vertical

dashed line represents position of the quasistatic surface plasmon-polariton. It is clear from these figures that the larger the dissipation in the system under study, the larger the shift of

max ( ) of the function in Eq.(42), despite of the dielectric function

model.

Figure 14. Frequency dependence of the normalized function

 (,  )   (,  ) / max (,  )

in

Eq.(42) at different anharmonicities  in the oscillatory model of the dielectric function. The curves in figure a) was normalized to

max ( ,  )

at

  0.01TO

and to own maximum in figure b). The

  0.03TO  1 ,  3 and   0.01TO  4 . The vertical dashed line

numbers near curves correspond to the anharmonicity factor

  0.02TO  2 ,   0.015TO Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

represents position of the quasistatic surface phonon-polariton.

Figure 15. Frequency dependence of the normalized function

 (, )   (, ) / max (, ) for

good conductors in Eq.(42) at different damping factor in the Drude model of the dielectric function.

max ( , )

 0.001P and to own maximum in figure b). The numbers near curves correspond to the damping factor   0.02P  1 ,   0.01P  2 ,   0.005P  3 and   0.001P  4 . The vertical dashed line The curves in figure a) was normalized to

at 

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Thermodynamics of Surface Electromagnetic Waves

157

 (,  )   (,  ) / max (,  ) of the surface polaritons supported by the vacuum/GaAs interface at different  in figure a) as calculated with help of Eq.(42) Figure 16. Normalized function

and the normalized smaller peaks of DOS as calculated with use of Eq.(33) also at different anharmonicities in figure b).

In order to compare two definitions of DOS in Eq.(33) and in Eq.(42) within the frequency range

 [TO , QP ] , where the surface polaritons are supported by GaAs, we

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show the normalized function

 (,  )   (,  ) / max (,  ) at different  in Figure 16a)

as calculated with help of Eq.(42) and the normalized smaller peaks of DOS as calculated with use of Eq.(33) also at different anharmonicities in Figure 16b). The smaller the anharmonicity, the larger the peak in these figures. We can to observe a qualitative agreement between the curves. Both definitions give the same shifts of peaks versus anharmonicity. Both definitions give similar qualitative dependence versus frequency within the frequency range, where Re{ ( )}  1 . But, the usual definition of DOS gives the positively definite quantities in Eqs.(28)-(30), (32)-(34) in accordance with the sense of the density of states. In its turn, the function  ( ) in Eq.(42) can not be interpreted as the DOS, because its negative values within some frequency intervals. We recall that in a nonlocal approach no the “stop band” [43] and within the band

TO ( p)    LO ( p) the propagating waves can exist

despite of the sign of dielectric function. Furthermore, no pure surface waves strongly localized near boundary, because they are leaking to a medium due to a complexity of the factors i ( p,  ) , including a pure imaginary one in spite a frequency range. That is why taking into account a spatial dispersion the surface-like and volume -like modes are mixed inside such a material. In this case we should use all frequencies to calculate thermodynamic characteristics of surface polaritons. Figure 17 exemplifies the normalized function

 ( )   ( ) / max ( ) versus the normalized

frequency  / QP as calculated with help of Eq.(42) and with use of the nonlocal models of the dielectric functions in Eq.(12) – a) and in Eq.(13) – b). In figure b) this function is represented at different frequency collision rates. The vertical dashed lines are situated at

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158

Illarion Dorofeyev

TO , QP , LO in figure a) and at QP  P / 2 in figure b). It is clearly seen the qualitative difference between the DOS in Figure 11 and the function  ( ) in Figure 17. frequencies

It should be emphasized that both of the definitions of DOS above described are identical in case of transparent materials. It is necessary to make one important remark concerning an integration in Eq.(40), which is performed over some volume   , separating the longwavelength part of the electromagnetic fluctuations [22,23]. It means that the integration with respect to the variable

p in Eq.(42) is should be done up to some maximum value P / c conductors, where a is the interatomic distance, or

TO / c

pmax

pmax

a1 for

a1 for dielectrics,

 (k ,  ) tends to pure real value at p  in the nonlocal models of the dielectric functions in Eqs. (12) and (13). In this case the function  ( )  0 in taking into account that

Eq.(42). The exact magnitude of the upper limit of integration in local calculations with any given exactness can be established in comparison with corresponding calculations using the nonlocal models of dielectric functions. But, a calculation of the relative quantities is not very sensible to the choice of pmax .

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In a comparative sense, we calculated the function  ( ) for the whole set of bulk and surface modes described by dispersion relations in Eqs.(16), (17) and exemplified by Figure (6).

Figure 17. Normalized function

 ( )   ( ) / max ( ) versus the normalized frequency  / QP

as calculated with help of Eq.(42) and with use of the nonlocal models of the dielectric functions in

  0.02TO – a) and in Eq.(13) – b). In figure b) this function is represented at different frequency collision rates   0.01P ,0.07P ,0.05P from the bottom to upper curve. The Eq.(12) at

vertical dashed lines are situated at frequencies

TO , QP , LO in figure a) and at QP  P / 2

in figure b).

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159

Thermodynamics of Surface Electromagnetic Waves Figure 18 shows the frequency dependence

 ( ) for the bulk and surface modes; the

curve 1 corresponds to the longitudinal wave  ( ) /(3 10 ) with a scale correction factor, 3

the curve 2- to the two transverse waves

1tr ()  2tr () as it is calculated for the bulk

waves, and the curve 3 corresponds to [ 1 ()  2 ()] 10 with other correction factor tr

tr

5

for the surface waves. All calculations were done at fixed anharmonicity   0.02TO . The vertical dashed lines represent positions of the transverse optical phonon frequency

TO  3.77 1013 rad / s , QP  4.59 1013 rad / s

LO  4.711013 rad / s

the and

quasistatic the

at k  0 and

longitudinal

surface optical

phonon-polariton phonon

frequency

  0 in Eq.(12). The dimensionality of the function

 ( ) is equal cm (rad / s) , where r  2,3 for the surface or bulk states, r

1

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correspondingly.

Figure 18. Frequency dependence of the function  ( ) for the bulk and surface modes. The curve 1 corresponds to the longitudinal wave 

( ) /(3 103 ) with a scale correction, the curve 2- to the two

1tr ()  2tr () as it is calculated, and the curve 3 corresponds to [ 1tr ()  2tr ()] 105 with indicated correction factor. All calculations were done at fixed anharmonicity   0.02TO . The vertical dashed lines represent positions of the transverse optical transverse waves

phonon frequency TO

 3.77 1013 rad / s , the quasistatic surface phonon-polariton

QP  4.59 1013 rad / s

and the longitudinal optical phonon frequency

LO  4.7110 rad / s at k  0 and   0 in Eq.(12). The dimensionality of the function  ( ) is equal cm r (rad / s)1 , where r  2,3 for the surface or bulk states, correspondingly. 13

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160

Illarion Dorofeyev

U (T )  U SP (T ) / U SP (1000) of surface phonon polaritons supported by the plane interface “vacuum-GaAs” versus a temperature T at different definitions of Figure 19. Normalized energy

DOS in Eq.(42) – the curve 1, in Eqs.(30),(32) – the curves 2,3 and in Eq.(33) – the curve 4 in figure a). The same curves in comparison with the normalized energy of the black body photons in vacuum

U bb (T )

(the curve 5) in figure b). The normalization in figure b) is done to

U bb (100)

and to

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U SP (100) for each curve, correspondingly. First of all, it should be emphasized that the longitudinal modes are exist only within a matter due to their fully electrostatic character. In this sense, they are bounded states manifesting in the negative sign of the function  ( ) in whole frequency range. Taking into account the correction factor for them in Figure 18, they are most energetic modes of thermal electromagnetic fluctuations. The function  ( ) for the transverse bulk and surface modes has contributions of both signs. From our point of view the negative tails can be attributed to the bounded waves in some frequency range, which are evanescent inside a matter. The evanescent character of these waves is totally due to the lossy mechanism within a matter. It is easy to verify that the negative part of the function  ( ) tends to zero when   0 . In order to compare different definitions of DOS we numerically calculated the energy and free energy of surface phonon- and plasmon polaritons supported by a plane interface between a vacuum and a medium characterized by dielectric functions in Eqs.(2) and (3). Figures 19-23 show the normalized energy and free energy of the surface phonon- and plasmon polaritons as calculated with help of Eqs.(36),(37),(39) at different definitions of DOS in Eqs.(30),(32),(33),(42). The normalized energy U (T )  U SP (T ) / U SP (1000) of surface phonon polaritons supported by the plane interface “vacuum-GaAs” versus a temperature T is demonstrated in Figure 19a) at different definitions of DOS in Eq.(42) – the curve 1, in Eqs.(30),(32) – the curves 2,3 and in Eq.(33) – the curve 4. The same curves in comparison with the normalized energy of the black body photons in vacuum U bb (T )  

2

 kBT 

4

/15( c)3 (the curve 5) is shown in Figure 19b). The

normalization in this figure is done to U bb (100) for bulk photons and to U SP (100) for each

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161

Thermodynamics of Surface Electromagnetic Waves curve, correspondingly. An integration in Eq.(36) is limited by the frequencies

1  TO and

2  QP taking into account the validity condition Re{ ( )}  1 for surface phonon polaritons. It should be noted that the energy of surface phonon polaritons in BarashGinzburg theory 2

2

1

1

U SP (T )   d  ( )(, T )   d uSP ( )

(56)

follows from Eq.(39) for free energy. Figure 20 exemplifies the normalized energy of surface phonon polaritons supported by the plane interface “vacuum-SiC” versus a temperature at different definitions of DOS in Eqs.(30),(32),(33),(42). The normalizations are done as in Figures 19a), b). The optical characteristics

of

SiC

in

Eq.(3)

are

as

follows

TO  1.49 1014 rad / s

,

LO  1.82 10 rad / s,   8.9 10 s ,    6.7 from [47], the frequency of the 11 1

14

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quasistatic phonon polariton QP  1.78 1014 rad / s .

U (T )  U SP (T ) / U SP (1000) of surface phonon polaritons supported by the plane interface “vacuum-SiC” versus a temperature T at different definitions of DOS Figure 20. Normalized energy

in Eq.(42) – the curve 1, in Eqs.(30),(32) – the curves 2,3 and in Eq.(33) – the curve 4 in figure a). The same curves in comparison with the normalized energy of the black body photons in vacuum

U bb (T )

(the curve 5) in figure b). The normalizations are done as in Figure 18.

In calculations we used only the temperature dependent part of the mean energy of oscillator (T ) 

 /[ Exp(  / kBT )  1] , omitting the zero-point term  / 2 .

It is seen from Figures 19, 20 that the energies have similar temperature dependence despite of different definitions of DOS. Moreover the temperature dependence of energy in case of surface phonon polaritons is quite different from the case of equilibrium bulk photons in vacuum. The normalized free energies of the surface phonon polaritons versus a temperature as calculated with help of Eqs.(37),(39) at different definitions of DOS are represented in figures

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162

Illarion Dorofeyev

(21) and (22). Herewith, the normalized free energy F (T )  FSP (T ) / FSP (1000) of surface phonon polaritons supported by the plane vacuum-GaAs interface versus a temperature T is demonstrated in Figure 21a) at different definitions of DOS in Eq.(42) – the curve 1, in Eqs.(30),(32) – the curves 2,3 and in Eq.(33) – the curve 4. The curve 5 everywhere in figures (21) and (22) shows the normalized free energy of the black body photons in vacuum

Fbb (T )   2  kBT  / 45( c)3 . Figure 22a) shows the normalized free energy of surface 4

phonon polaritons supported by the plane vacuum-SiC interface versus a temperature T at different definitions of DOS. In figures 21a) and 22a) we used only temperature dependent parts of the free energy

FSP (T )  kBT 

QP

TO

D( ) n 1  Exp(  / k BT ) d,

(58)

where D( ) from Eqs.(30),(32) or (33),

FSP (T )  k BT 

QP

TO

 ( ) n 1  Exp(  / k BT ) d,

(59)

where  ( ) from Eq.(42). Figures 21b) and 22b) show the same dependencies, but including the zero-point term. In this case

FSP (T )  kBT 

QP

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TO

D( ) n  2Sinh(  / 2k BT ) d,

(60)

F (T )  FSP (T ) / FSP (1000) of surface phonon polaritons supported by the plane vacuum-GaAs interface versus a temperature T at different definitions of DOS Figure 21. Normalized free energy

in Eq.(42) – the curve 1, in Eqs.(30),(32) – the curves 2,3 and in Eq.(33) – the curve 4. The curve 5 in figures shows the normalized free energy of the black body photons in vacuum

Fbb (T ) . The curves

are calculated with help of Eqs.(58),(59) in figure a) and with help of Eqs.(60),(61) in figure b).

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Thermodynamics of Surface Electromagnetic Waves

163

F (T )  FSP (T ) / FSP (1000) of surface phonon polaritons supported by the plane vacuum-SiC interface versus a temperature T at different definitions of DOS as Figure 22. Normalized free energy directly as in Figure 20.

and

FSP (T )  kBT 

QP

TO

 ( ) n  2Sinh(  / 2kBT )  d,

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with DOS D( ) from Eqs.(30),(32) or (33) and

(61)

 ( ) from Eq.(42), correspondingly.

U (T )  U SP (T ) / U SP (100) of surface plasmon polaritons supported by vacuum-aluminum interface versus a temperature T at different definitions of DOS in Eq.(42) – the Figure 23. Normalized energy

curve 1, in Eqs.(30),(32),(33) – the curves 2,3,4 in figure a). In figure b) the normalized energy

U (T )  U SP (T ) / U SP (1000)

with other normalization factor and the normalized energy of

equilibrium photons (the curve 5) are shown.

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Illarion Dorofeyev

Numerical calculations show that the discrepancy between of two definitions in Eq.(28) and Eq.(40) in case of good metals with finite dissipation strength is quite essential. Figure 23 demonstrates the normalized energy of surface plasmon polaritons supported by vacuumaluminum interface. Herewith, the normalized energy U (T )  U SP (T ) / U SP (100) versus a temperature T is shown in Figure 23a) at different definitions of DOS in Eq.(42) – the curve 1, in Eqs.(30),(32),(33) – the curves 2,3,4. In Figure 23b) the normalized energy

U (T )  U SP (T ) / U SP (1000) is shown with other normalization factor. In this figure the normalized energy of equilibrium photons is also shown by the curve 5. Integration over a frequency range is done from

1  0 up to  2  QP in accordance with

the validity condition Re{ ( )}  1 for surface plasmon polaritons. As a final step, we compute the spectral power densities of surface plasmon polaritons at different DOS definitions to compare with the spectral power density of equilibrium photons in the Planck law ubb () 

3 /  2c3[exp(  / kBT ) 1]1 .

Figure 24 shows the normalized spectral power density of equilibrium photons in accordance with the Planck law versus a frequency - the curve 1 and spectral power density of

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surface plasmon polaritons u ( )  uSP ( ) / uSP (max) in accordance with Eq.(56) - the curve 2 and in accordance with Eqs.(29),(35)- the curve 3. Normalization is done to their maximum values in figure a) and to the maximum of the black body spectrum in figure b). It is seen from these figures that the Barash-Ginzburg theory gives the same spectral distribution of surface plasmon polaritons as in the Planck law for bulk photons in a vacuum. In its turn, Eqs.(29),(35) yield in a shift of the spectral power density maximum towards lower frequencies with respect to the Planck law. Moreover, along with the quantitative difference in the spectral distribution, these spectral power densities are qualitatively different as it clearly seen from Figure 24. It should be emphasized that the Barash-Ginzburg theory gives DOS in Eq.(45) identically equal to Eq.(34) in case of transparent materials when   0 and   0 in Eqs.(2),(3). But, the spectral shift in Figure 24a) exists despite of the dissipation factors in Eqs.(2),(3), that is why corresponding experiments would be very important. Our final remarks are concerned with the function  ( ) in Eq.(40). From our numerical calculations it follows that the negative tails of the function  ( ) in case of the transverse waves for 3D and 2D geometry are concerned with the dissipative conditions in a system of interest. In its turn, in case of the longitudinal waves this function is negative in all frequency range despite of a level of dissipation, see Figures (17),(18). We recall that the function  ( ) in Eq.(40) cannot be treated as the density of states because of accepting the negative values in general. Taking into account that the integrand in Eq.(39) or in Eq.(56) has a multiplicative form, we rewrite formally , for example Eq.(56), in another way as follows 



0

0

U (T )    ( )(, T )d   D( ) E (, T )d ,

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(62)

165

Thermodynamics of Surface Electromagnetic Waves

Figure 24. Normalized spectral power density of equilibrium photons in accordance with the Planck law versus a frequency - the curve 1 and spectral power density of surface plasmon polaritons in accordance with Eq.(56) - the curve 2 and Eqs.(29),(35) - the curve 3. Normalization is done to their own maximum values in figure a) and to the maximum of the Planck law in figure b).

where D( ) is explicitly the density of states, for instance the spectral density of states of free photons in vacuum with two independent polarizations

D( )  03D ( ) 

2 ,  2 c3

(63)

or in two-dimensional case this is correspondingly the two-dimensional spectral density of states with one polarization state

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D( )  02 D ( ) 

 , 2 c 2

(64)

and the term

E ( , T ) 

 ( ) ( , T )  E (  ) (, T )  E (  ) (, T ) 0 ( )

which has a dimensionality of energy. This energy can be both of a positive E

(65)

()

( , T ) and

negative value E ( , T ) in general. The negative values of energy correspond to bound states. In our case this is a subsystem of localized (evanescent) waves within a medium. Taking into account that the factor (, T) is the mean energy of an isolated oscillator, the ()

absolute value of the factor | () / 0() | shows how many of the elementary oscillators are excited within a dissipative medium at the temperature T due to fluctuations comparing with free space. The energy E(, T) can be treated as the field mean energy of the degree of freedom corresponding to the frequency  within a dissipative medium at the temperature T . It should be noted that the field oscillators are attributed to the photons inside a matter for

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Illarion Dorofeyev

the transverse waves, but no the longitudinal photons in case of the longitudinal waves. Taking into account Eqs.(39),(62) , an expression for the free energy  ( )    F (T )  k BT  0 ( ) n  Z ( , T )  0 ( )  d , 0  

(66)

and the formula (39) can be identically written as follows 

F (T )  k BT  0 ( ) n  Z ( , T )  d, 0

(67)

where Z ( , T ) is the partition function of electromagnetic excitations within a material, and

0 ( ) has a clear meaning of DOS from Eqs.(63),(64).

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CONCLUSION In this chapter we addressed to thermodynamic properties of surface electromagnetic waves supported by plane interfaces. We briefly described and illustrated related dispersion equations in different approaches known from literature. Spectral energy densities of surface plasmon and phonon polaritons and total specific energies in case of thermodynamic equilibrium are calculated using general definition of the DOS accepted in theory of solids and the Barash-Ginzburg theory for inhomogeneous and disspative media. It is demonstrated that the spectral distribution of surface polaritons in equilibrium, depending on the optical properties of the material, may be differ from the Planck’s law for bulk photons. Temperature dependence of the surface energy density of the two dimensional electromagnetic fluctuations is differ from the temperature dependence of volume density of energy for photons in equilibrium is also shown. It is known that three dimensional fluctuations of fields in vacuum near a plane interface and two dimensional fluctuations of surface polaritons mainly occur at the frequency of the quasistatic surface polariton. But, a manifestation of corresponding resonances in the spectral energy density of thermal fluctuations depends on the exponential factor in the mean energy of an oscillator. Based on the Barash-Ginzburg general formulae for free energy of the electromagnetic fields within inhomogeneous and lossy materials, thermodynamic functions of the interface modes are computed using dispersion equations in various local and nonlocal approaches. In particular, the energy and free energy of thermally stimulated electromagnetic fields of surface eigenmodes of a plane interface and of a plane parallel film are considered. A correspondence between the Barash-Ginzburg approach in calculations of thermodynamic properties of normal modes within spatially nonuniform dispersive and dissipative systems and the traditional textbook definition of energy via the density of states of eigenmodes of spatially nonuniform dissipationless systems is established. It is shown that the Barash-Ginzburg basic definition of free energy of the surface electromagnetic fields is identical to the related expression as derived from the wellknown definition of density of states usually accepted in theory of solids in the case of dissipationless materials. Dispersion relations for the surface states in different approaches are considered

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Thermodynamics of Surface Electromagnetic Waves and showed that negative values of the function

167

 ( ) in the general Barash-Ginzburg theory

can be concerned to the bounded states of fields within a material. The longitudinal bulk waves are bounded states manifesting in the negative sign of the function  ( ) in whole frequency range despite of dissipation. In its turn, the transverse fields inside bulk or surface systems contain only in part the coupled waves with a matter via some dissipative mechanism. It is follows that the Barash-Ginzburg theory gives qualitatively the same spectral distribution of surface plasmon polaritons as in the Planck law for bulk photons in a vacuum. In its turn, other considered approaches yield in a shift of the spectral power density maximum towards lower frequencies with respect to the Planck law. Moreover, along with the quantitative difference in the spectral distribution, these spectral power densities are qualitatively different as it clearly seen from demonstrated figures. This spectral shift exists despite of the dissipation factors in model dielectric functions that is why corresponding experiments would be very important.

REFERENCES [1] [2] [3]

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[4] [5] [6] [7] [8] [9] [10]

[11] [12] [13] [14] [15] [16] [17]

V. M. Agranovich, V. L. Ginzburg, Crystal optics with spatial dispersion, and excitons, Springer-Verlag,Berlin and New York (1984). V. M. Agranovich, D. L.Mills, (Eds) Surface Polaritons: Electromagnetic Wave at Surfaces and Interfaces, North - Holland, Amsterdam (1982). D. L. Mills and K. R. Subbaswamy, in Progress in Optics, Vol. XIX p.47, edited by E. Wolf, North-Holland Publishing company Amsterdam (1981). Edited by A. D. Boardman Electromagnetic surface modes, John Wiley & Sons (1982). J. M. Pitarke, V. M. Silkin, E. V. Chulkov and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007). H.B. Callen, T.A. Welton, Phys. Rev. 83 (1951) 34. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957). R. Kubo, Rep. Prog. Phys. 29, 255 (1966). S.M. Rytov, Theory of Electric Fluctuations and Thermal Radiation (Air Force Cambridge Research Center, Bedford, Mass., AFCRC-TR-59-162, 1959). M.L. Levin, S.M. Rytov, Teoriya Ravnovesnykh Teplovykh Fluktuatsii v Elektrodinamike (Theory of Equilibrium Thermal Fluctuations in Electrodynamics, Nauka, Moscow, 1967) (in Russian). E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Pt.2, (Butterworth-Heinemann, Oxford, 2002). S.M. Rytov, Yu.A. Kravtsov, V.I. Tatarskii, Principles of Statistical Radiophysics (Springer, Berlin, 1989). K. Joulain et al., Surf. Sci. Rep. 57, 59 (2005). A. I. Volokitin, B. N. J. Persson, Rev. Mod. Phys. 79, 1291 (2007). E.A. Vinogradov, I.A. Dorofeyev, Usp. Fiz. Nauk 45, 1213 (2009) [Sov. Phys. Uspekhi 52, 425 (2009)]. E.A.Vinogradov, I.A. Dorofeyev, Thermally stimulated electromagnetic fields from solids (Fizmatlit, Moscow, 2010) (in Russian). I.A. Dorofeyev, E.A.Vinogradov, Physics Reports, 504, 75 (2011).

Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

168 [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

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[30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47]

Illarion Dorofeyev R. Carminati, J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999). C. Henkel et al., Opt. Commun. 186, 57 (2000). E. Marquier, et al., Phys.Rev. B 69, 155412 (2004). I.A. Dorofeyev, E.A.Vinogradov, Laser Physics, 21, 1 (2011). Yu.S. Barash, Izv. Vyssh. Uchebn. Zaved., Radiofiz.[Sov. Radiophys.] 16, 1086 (1973). Yu.S. Barash, V.L. Ginzburg, Sov. Phys. Usp. 19, 263 (1976). V.L. Ginzburg, The propagation of electromagnetic waves in plasmas, 2nd ed., Sec.22, Pergamon, Oxford, (1970). L.D. Landau and E.M. Lifshitz, Statistical Physics, Pergamon, Oxford, (1969). E.N.Economou, Green’s functions in Quantum Physics, Springer-Verlag, Berlin, (1979). N.N Bogolyubov, S.V. Tjablikov, Dokl. Acad. Nauk SSSR 126, 53 (1959) [Sov. Phys. Dokl. 4, 589 (1959)]. D.N. Zubarev, Usp. Fiz. Nauk 71, 71 (1960) [Sov. Phys. Uspekhi 3, 320 (1960)]. V.L. Bonch-Bruevich, S.V. Tyablikov, The Green Function Method in Statistical Mechanics, North-Holland, Amsterdam, (1962). R. Balian, C. Bloch, Ann. Phys. 60, 401 (1970), 64, 271 (1971). G.S. Agarwal, Phys. Rev. A 11, 253 (1975). S.C. Ching, H.M. Lai, K. Young, J. Opt. Soc. Am. B 4, 1995 (1987). K. Joulain et al., Phys. Rev. B 68, 245405 (2003). Illarion Dorofeyev, Phys. Lett. A 375, 2885 (2011). Illarion Dorofeyev, Physica Scripta 84, 055003 (2011). J.M. Ziman, Principls of the theory of solids, Cambridge UP, Cambridge, (1972). C. Kittel, Introduction to solid state physics, Wiley, New York, (1996). E.A. Vinogradov, Usp. Fiz. Nauk 45, 1213 (2002) [Sov. Phys. Uspekhi 45, 1213 (2002)]. E. Palik, Handbook of Optical Constants of Solids, Academic Press, San Diego, (1991). E. T. Arakawa et al., Phys. Rev. Lett. 31, 1127 (1973). J. Le Gall et al., Phys. Rev. B 55, 10105 (1997). A. Archambault, et al., Phys. Rev. B, 79 (2009) 195414. A. A. Maradudin and D.L. Mills, Phys. Rev. B 7, 2787 (1973). G.W. Ford, W.H. Weber, Phys. Rep. 113, 195 (1984). K.L.Kliewer, R.Fuchs, Phys.Rev., 172, 607 (1968). D.L. Mills and A. A. Maradudin, Phys. Rev. Lett. 31, 372 (1973). W. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127 (1959).

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 © 2013 Nova Science Publishers, Inc.

Chapter 4

MAGNETIC FIELD ORIGINATED BY POWER LINES J. A. Brandão Faria1 and M. E. Almeida Pedro2 1

Instituto de Telecomunicações, Instituto Superior Técnico, Technical University of Lisbon, Portugal 2 CIE3, Instituto Superior Técnico, Technical University of Lisbon, Portugal

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ABSTRACT Danger to human health from living near to high-voltage power lines has been a matter of concern and controversy over the past years; exposure to magnetic fields produced by power lines has been suspected of increasing the risk of cancer. Guidelines, put forward by the International Commission of Non Ionizing Radiation Protection, have been established for safe public exposure to power-frequency magnetic fields. This chapter starts with electromagnetic field equations to explain how magnetic fields can be deleterious for human health, and how the operating frequency plays a decisive role for that matter. Next, an analysis of the magnetic field originated by the current-carrying conductors of a high-voltage single-circuit three-phase overhead power line is thoroughly developed. The analysis takes into account the effect of protective ground wires, the effect of earth return currents and, furthermore, incorporates the non-uniform character of the power line structure arising from conductor sagging between towers. For magnetic field evaluation purposes, matrix techniques are made use in order to implement multi-conductor transmission line theory –a key tool for this subject. Mitigation techniques usually employed to decrease magnetic field levels are also addressed, namely, mitigation loops with or without compensation capacitors. Graphical and numerical computation results concerning magnetic field evaluation are presented and discussed, not only for the fundamental power frequency of 50 Hz, but also for higher order harmonics, up to 800 Hz. In the latter case, balanced and unbalanced line loads are considered. Underground power cables do not have as a visual impact as overhead power lines. Nonetheless, they also originate a magnetic field above the ground surface. This aspect is also paid attention.

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1. INTRODUCTION Danger to human health from living near high-voltage power lines has been a matter of concern and controversy over the past years. Exposure to 50 Hz magnetic fields produced by overhead power lines has been suspected of increasing the risk of cancer. General accepted guidelines have been established for safe public exposure to powerfrequency magnetic fields. Complying with the recommendations issued by ICNIRP International Commission of Non Ionizing Radiation Protection - the reference level for the root mean square (rms) value of the magnetic induction field has been set at 100 T throughout the majority of the European Union countries, [1]-[2]. However, in some countries, limitations that are even more stringent are being enforced, for example, in Italy, a reference level as low as 3 T is now recommended for new power lines being built. The public concern about magnetic-field effects on human safety has triggered a wealth of research efforts focused on the evaluation of magnetic fields produced by power transmission lines [3]-[17]. Studies include the design of novel compact power-line geometries, the inclusion of auxiliary single or double loops for magnetic field mitigation in already existing power lines, the consideration of series-capacitor compensation schemes for enhancing field mitigation, the reconfiguration of power lines to high-phase operation, the influence of high-order harmonics, etc. However, many of the works presented, dealing with power lines, make use of several simplifying assumptions that, inevitably, give rise to inaccurate results in the calculated magnetic fields. Ordinary simplifications include: neglecting the earth currents, neglecting the ground-wires, replacing bundle phase-conductors with equivalent single conductors characterized by their geometric mean radius (GMR), replacing actual sagged conductors with average height horizontal conductors. Errors incurred by using some or all of the above mentioned simplifying assumptions may not be critical. Nonetheless, from the viewpoint of power utilities, even a small error may have severe economic repercussions regarding not only the width of the required rightof-way, but also, possible lawsuits for violation of the magnetic field reference levels. In any case, given the capabilities of current computers, there is no sound justification to keep utilizing poor models to represent multi-conductor transmission lines (MTL) and to miscalculate the magnetic field they create. At this point, we should add that powerful software programs have already been developed for 2D and 3D modeling of magnetic field shielding, as well as for the computation of the electric and magnetic fields produced by power lines. These software packages have proven well against actual field measurements. However, the utilization of software packages may pose a few problems. Firstly, such tools are not universally available. Secondly, most of them are based on numerical techniques that require increasing computation times as accuracy demands increase. Last, but not the least, the results they produce are opaque from the users’ point of view —results are what they are, independently of the understanding of the theoretical background the users may have (or not) about the phenomena under analysis. This chapter offers an analytical approach to the subject of power-line magnetic fields that is hoped to give the reader the necessary insight into the various facets involved in the problem.

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Magnetic Field Originated by Power Lines

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Figure 1. Cross-section of the power line used for exemplification purposes.

In this chapter we present a matrix based MTL model [16]-[19], where the effects of earth currents and ground wire currents are taken into account; moreover, actual bundle conductors and non-uniform sagged conductors are taken into consideration. Therefore, with this comprehensive model, accurate calculation of magnetic-field intensity distributions is made possible. Figure 1 depicts the cross-sectional view of a single-circuit three-phase overhead power line (400 kV, 1.4 GVA), which will be used in this chapter for exemplification purposes. The phase conductors are arranged in a flat configuration, each phase comprising a bundle of two sub-conductors (1a-1b, 2a-2b, 3a-3b), and a pair of two ground wires (G1-G2) The chapter is organized into ten sections, the first of which is introductory. Section 2 introduces the fundamental laws governing electromagnetic phenomena. Section 3 describes the standard procedure used for magnetic field evaluation in overhead power lines. An accurate matrix method for determining the conductor currents flowing in overhead MTL systems is developed in Section 4. Based on MTL results, a complete approach to the computation of power-line magnetic fields is presented in Section 5. Magnetic field mitigation techniques, employing mitigation loops with or without compensation capacitors, are dealt with in Section 6. Numerical results concerning the evaluation of overhead powerline magnetic fields (with and without mitigation techniques) are offered in Section 7, for the fundamental 50 Hz frequency. Section 8 is an extension of Section 7, where magnetic fields, produced by high-order harmonics up to 800 Hz, are computed, considering the case of balanced and unbalanced line loads. The problem of magnetic fields produced by underground three-phase cables is briefly addressed in Section 9. At last, Section 10 is devoted to conclusions.

2. ELECTROMAGNETIC FIELDS The key equations for the analysis of electromagnetic field phenomena are the Maxwell equations [20]-[21],

B    E   t     B  0

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(1a)

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J. A. Brandão Faria and M. E. Almeida Pedro

D    H  J  t     D  

(1b)

In (1a), the pair E, B defines a single entity: the electromagnetic field. Its characterization requires two vectors, the electric field strength E and the magnetic induction field B. From (1a) we learn that not only the magnetic induction has closed field lines, but also that time-varying magnetic induction fields do give rise to electric fields (so-called electric induction fields). In (1b), the pair  , J defines the field sources, without which no electromagnetic field can exist. The scalar  is the electric charge density, while J is the conduction current density a vector field associated with the movement of electric charges. In (1b), the auxiliary vectors D and H, respectively, the electric displacement vector and the magnetic field vector, are related to E and B through the so-called constitutive relations, which macroscopically characterize the material medium where the electromagnetic field is impressed. In its simplest form the constitutive relations can be written as

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D   E  B   H J   E 

(2)

The parameters , , and  denote the permittivity, permeability and conductivity of the medium, respectively. The particular values assigned to these parameters depend on the medium being considered (those values can be found in tabular form, for a variety of materials, in specialized literature dedicated to the analysis of the electromagnetic properties of materials). For a vacuum we have

  0,   0  4 107 H/m,    0 

109 F/m 36

For the important case of time-harmonic (sinusoidal) variations, where scalar and vector quantities can be symbolically represented by their complex amplitudes (or phasors) the equations in (1) take the form [20],

  E   jB    B  0

(3a)

 H  J  j D    D  

(3b)

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Magnetic Field Originated by Power Lines



B  Bx cos(t   x ) xˆ  By cos(t   y ) yˆ  Bz cos(t   z ) zˆ  Re B e jt

B  Bx e j x xˆ  By e

j y



yˆ  Bz e j z zˆ

(4a)

(4b)

where xˆ, yˆ , and zˆ are unit vectors for the x, y, and z directions. In (4a),  is the angular frequency,  = 2f, and f is the operating frequency. The rms value of a time-harmonic magnetic induction field is calculated as, [20],

Brms 

B  B* 2

(5)

Note that doing Brms  Bmax / 2 would be a mistake (unless  x   y   z ). In fact,

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the field described by (4a) is not a linearly polarized field. In general, B is an elliptically polarized field, where Bmax / 2  Brms  Bmax , [20]. In this chapter, we will not consider the presence of ferromagnetic materials, therefore  = 0 will be assumed everywhere. With regard to human tissues submitted to time-harmonic fields, we consider the conductivity and permittivity data available in [22], which result from parametric models developed by C. Gabriel et al. [23]-[25]. See Table 1, for f = 50 Hz and f = 1 kHz. From Table 1 we learn that the human body is a good dielectric medium ( >> 0) but a poor conductor1, tissue relaxation times    /  ranging from 1 s to 1 ms. Let us now address the basics of the calculation of electric and magnetic fields originated by a long single circular cylindrical wire immersed in the air ( = 0,  = 0) and oriented along z. The wire has a per unit length electric charge q(t) and carries an electric current of intensity i(t). Table 1. Electromagnetic parameters of some human tissues f = 50 Hz Conductivity [S/m]

Permittivity [F/m]

f = 1 kHz Conductivity [S/m]

Permittivity [F/m]

Bone cortical

2.00 102

7.85 108

2.01102

2.39 108

Brain grey matter

7.53 102

1.07 104

9.88 102

1.45 106

Brain white matter

5.33 102

4.68 105

6.26 102

6.18 107

Heart

8.27 102

7.67 105

1.06 101

3.12 106

Skin (dry)

2.00 104

1.00 108

2.00 104

1.00 108

Skin (wet)

4.27 104

4.54 107

6.57 104

2.84 107

Tissue

1

Metals (like copper, aluminum, gold, etc) are very good conductors, their conductivity is of the order of 107 S/m.

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Figure 2. Electric and magnetic fields produced by a charged long wire carrying a time-varying current. (a) Radial electric field. (b) Azimuthal magnetic field and companion axial electric induction field.

From   ( 0 E)   it can be shown [20]-[21] that the electric field produced by q(t) is a radial field given by

E(r , t )  E rˆ 

q(t ) rˆ 2 r 0

(6)

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where r is the radial distance measured from the conductor axis, and rˆ is the unit vector of the radial direction. See Figure 2a. When a poor conductive body (like the human body) is submitted to a low frequency electric field, an electric charge distribution appears at the surface of the body. The superposition of the primitive E-field in (6) with the E-field resulting from the body surface charges leads to a total electric field that practically vanishes inside the body. Harm can only result from low intensity surface currents flowing in the skin. For low-frequency regimes, the magnetic induction field originated by i(t) can be calculated, [20]-[21], from   (B / 0 )  J , yielding an azimuthal vector whose field lines are circumferences concentric with the wire axis

B(r , t )  B ˆ  0

i(t ) ˆ  2 r

(7)

where ˆ is the unit vector of the azimuthal direction. See Figure 2b. Since the permeability of the human body is not distinct from the one characterizing the surrounding medium (i.e.,  = 0), the magnetic field can freely penetrate into the body tissues, the same happening with the associated electric induction field. Taking into account that the problem is z-independent, the electric induction field, obeying to  E  B / t , must verify E  E zˆ , where E is evaluated from

E B  r t

(8)

For sinusoidal regimes of angular frequency , the above result translates into E  j  B dr and, using (7), we get Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Magnetic Field Originated by Power Lines

E(r )  jB(r )  G

(9)

where G is a geometrical factor, expressed in [m], which, for the case of a single long wire can be written as

r G  r ln    r0  where r0 is an arbitrary distance. At this stage, a parenthetical remark is in order: The electric induction field is an unambiguously defined field and, therefore, the constant r0 appears as a mystery. The thing is that the basic problem being offered here is an unrealistic problem. In fact, one single wire is just but a physical abstraction. A second wire must necessarily exist for the returning current. When both wires are taken into account, the arbitrary constant r0 disappears. Nonetheless, we can state, based on (9), that Erms   Brms . Since human tissues

display non-null conductivity, electric currents do circulate through them ( J   E ). Hence, because of Joule effect [20], energy is dissipated in the tissue volume (induction heating) –a deleterious result as far as human safety is concerned. The time-average power density at play at any point of the tissue, expressed in W/m3, is given by, [20],

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2 2 pav   Erms   ()  2 Brms

(10)

This shows that tissues’ induction heating is proportional to the square of the frequency and proportional to the square of the rms value of the magnetic induction field. Furthermore, it can be seen from Table 1, that tissues’ conductivity also tends to increase with the frequency –an added detrimental factor.

3. STANDARD POWER-LINE MAGNETIC FIELD EVALUATION Assuming that the overhead phase bundles are replaced with equivalent single conductors, assuming these conductors carry sinusoidal currents directed along the z-axis with complex amplitudes denoted by I1, I2 and I3, and assuming no other currents are present, the complex amplitude of the magnetic induction field vector at a point Q (xQ, yQ) above the ground is obtained, from Ampère’s law, as a simple summation of three terms

B

0 2

 I



  d 2k  yk  yQ  xˆ   xQ  xk  yˆ   3

k 1 

kQ

(11)



where dkQ denotes the distance between the center of phase conductor k and point Q (see Figure 3) Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Figure 3. Specification of coordinates required for the evaluation of field Bk.

d kQ 

 xk  xQ    yk  yQ  2

2

(12)

Note that in (11) and (12) the vertical coordinate yk is ordinarily defined as the average height above ground of conductor k, that is

yk 

 hk max  2  hk min 3

(13)

The rms value of the magnetic induction vector is obtained from (11) and (5),

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Brms  (B  B* ) / 2 .

4. COMPUTATION OF SYSTEM CURRENTS The standard procedure described above is not an accurate one. In fact, the result established in (11) ignores the influence of earth currents and ground wires currents. The result in (11) only takes into account the effect of overhead phase conductors and even this effect is not appropriately described, since perturbations due to conductor sag and conductor partition into sub-conductors have been disregarded. The first step required to conduct a correct analysis —prior to magnetic field computation— consists in the determination of all system currents based on prescribed phaseconductor currents IP  I1  I P   I 2   I 3 

(14)

This problem is, apparently, a complicated one for induction effects make each and every conductor current depend on all the remaining others. Multi-coupling can however be handled Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Magnetic Field Originated by Power Lines

easily by resorting to matrix techniques which have already proven effective in the analysis of MTLs, [18]-[19]. To start with, let us consider the frequency-domain transmission-line matrix equations for non-uniform MTLs (allowing the inclusion of the sag effect), [26]-[27],



d V  Z(, z ) I dz

(15a)



d I  Y(, z ) V dz

(15b)

where Z  and Y respectively denote the series-impedance and shunt-admittance matrices per-unit-length of the line. V and I are complex column matrices gathering the phasors associated, respectively, with all the voltages and all the currents of the line conductors.  Va  V   Vb   VG 

nP  Ia  nP ; I   Ib  IG  nG

nP nP nG

(16a)

where

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I a  Ib  I P and Va  Vb  VP

(16b)

In (16), subscript P refers to phase conductors, subscripts a and b refer to the partition of phase bundles into two sub-conductor sets, and subscript G refers to ground wires. In (16), nP and nG, denote respectively the number of phase bundles and the number of ground wires. For the line configuration in Figure 1, we have nP = 3, nG = 2. Because the standard procedure for computing Z  in (15a) has been established elsewhere, [28]-[30], details will not be gone into here, and, thus, only a brief summary is presented.

Z  jL  Z E  Zskin

(17)

The per unit length external-inductance matrix L is a frequency-independent real symmetric matrix whose entries are ( y j  yk )  ( x j  xk ) 0 2 yk  ln , L jk  0 ln 2 rk 4 ( y j  yk )2  ( x j  xk )2 2

Lkk 

2

(18)

where rk denotes conductor radius, and yj, yk and xj, xk denote the vertical and horizontal coordinates of the jth and kth conductors, respectively. Matrix ZE, the earth impedance correction, is a frequency-dependent complex square matrix whose entries can be determined using Carson’s theory [31] or, alternatively, the

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J. A. Brandão Faria and M. E. Almeida Pedro

Dubanton complex ground plane approach [30], [32]-[33]. The entries of ZE are defined in (19) (Z E )kk  j

2 2 0  p   ( y j  yk  2 p )  ( x j  xk ) ln 1   , (Z E ) jk  j 0 ln 2  yk  4 ( y j  yk )2  ( x j  xk )2

(19)

where p , the complex depth, is given by

p

1

(20)

j0 E

where  denotes the earth conductivity. Matrix Zskin is a frequency-dependent complex diagonal matrix whose entries can be determined by using skin-effect theory results for cylindrical conductors, [20]. For lowfrequency situations one will have

(Z skin )kk  ( Rdc )kk  j

8

(21)

0

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where (Rdc)kk denotes the per-unit-length dc resistance of conductor k. Because line conductors sag between towers, yk = yk(z), the matrix entries of L and ZE, defined in (18)-(19), vary along the longitudinal coordinate z. A parabolic expression [27] for conductors’ height as a function of z can be written as

yk ( z )  (hk )min   (hk )max

2

 2z   (hk )min    1 , for 0  z  s  s 

with the suspension towers placed at z = 0 and z = s, (see Figure 4).

Figure 4. Conductor sagging between towers along the line span s.

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179

Magnetic Field Originated by Power Lines At this point the following very important aspects deserve being emphasized:

a) At 50 Hz frequency (wavelength  = 6000 km) the wave-propagation effects are absolutely negligible, provided that the length l of the line section being considered for magnetic field evaluation purposes is a small fraction of . b) Phase-conductor currents IP have prescribed values, based on which all the remaining currents are computed. This signifies that all system currents are assumed zindependent. This amounts to saying that transversal displacement-currents among conductors are negligibly small, or, in other words, (15b) is equated to zero. This means that for the purpose of magnetic field evaluation only (15a) is relevant. Contrarily, if our aim were the evaluation of the electric field around the line, things would be reversed; the capacitive coupling among conductors described in (15b) would be crucial, and (15a) would be equated to zero. The segregation of the electric and magnetic effects is an adequate approach for quasi-stationary regimes (50 Hz), where wave-propagation phenomena are unimportant. c) The loop formed by the two ground wires is traversed by non-null time-varying magnetic flux originated by all the system currents; this fact implies that IG1  IG 2 . d) By the same token, the currents flowing in the sub-conductors belonging to a given phase bundle are, in general, different, therefore, in (16), I a  Ib . The line section under analysis has its near end at z = 0 and its far end at z = l (with l a multiple of the span length s). Integration of (15a) from z = 0 to z = l gives  z l  Vnear  Vfar   Z( z )dz  I    z 0  V Z Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.



(23a)

where I is assumed constant along z (absence of wave-propagation effects). The matrix equation in (23a) can be written explicitly, in partitioned form, as  Va (0)   Va (l )   Va   Z aa  V (0)    V (l )    V    Z  b   b   b   ba  VG (0)   VG (l )   VG   ZGa

Z ab Zbb ZGb

Z aG   I a  ZbG   I b  ZGG  IG 

(23b)

Z

The computation of the bus impedance Z in (23) is performed using a standard discretization technique [27], [34], [44], that consists in subdividing the entire line section under analysis into a large number of uniform line cells of very small length. For instance, if l is equal to Ns line spans (l = sNs), and each span is divided into N individual cells of length z = s/N, then matrix Z will be determined via N

Z  N s  Z( zi ) z  i 1

l N

N

 Z( zi ) i 1

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J. A. Brandão Faria and M. E. Almeida Pedro

where values for the entries of Z  are evaluated from (17)-(21) considering conductors’ heights given by (22), with the longitudinal coordinate discretized as zi  s(i  1) /( N  1) . Equation (23b) can be inverted, hence  I a   Yaa I   Y  b   ba  I G   YGa

Yab Ybb YGb

YaG   Va  YbG   Vb  YGG   VG 

(25)

Y

where Y  Z1 is the bus admittance matrix. Bearing in mind that the conductors belonging to a given phase bundle are bonded to each other, and that ground wires are bonded to earth (tower resistance neglected), we can make, in (25),

Va  Vb  VP and VG  0

(26)

Plugging (26) into (25) and adding the first two equations we find 1 I P  I a  Ib  (Yaa  Yab  Yba  Ybb ) VP  VP  Ypp IP

(27)

YPP

The set of equations (27), (26) and (25) allows for the determination of all system currents, based on the knowledge of prescribed phase currents IP, that is





(28a)





(28b)

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1 I a  (Yaa  Yab ) YPP IP 1 Ib  (Yba  Ybb ) YPP IP





1 IG  (YGa  YGb ) YPP IP

(28c)

The net current returning through the earth IE is the complement of the sum of all overhead conductor currents nG nP  nP IE   I ak  I bk  I Gk  k 1 k 1  k 1







   

(29a)

If —as it is ordinarily the case— the prescribed phase-conductor currents, (14), define a balanced three-phase set, then the net earth return current will reduce to

IE  

nG

 IG k 1

k

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(29b)

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Magnetic Field Originated by Power Lines

Earth currents are not localized ones, they spread deep in the soil with a density J E varying with x and y 0 

IE 

  J E ( x, y)  zˆ dx dy

(29c)

 

Even if the net current in the soil IE were zero the magnetic field effects of the corresponding current density J E would still be present.

5. ACCURATE POWER LINE MAGNETIC FIELD EVALUATION The complex amplitude of the magnetic induction field vector B in the space surrounding the overhead line is obtained by summation of several contributions B  Bcond  Bearth , Bcond   Ba  Bb   BG

(30)

BP

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where Bcond is the contribution associated with the currents flowing in the overhead line conductors, i.e., phase bundles and ground wires. This contribution is calculated in a manner similar to (11). Contribution of the phase bundles:

BP 

 Ia  2 k 1  d a2 Q  0

nP



k

 y

ak

 yQ

 xˆ   x

Q

 xa

 0

k

k

nP

 Ib

 yˆ    2   

k 1

k

2

 db Q

 y

k

bk

 yQ

 xˆ   x

Q

 xb

k



 yˆ   

(31)

where I ak and Ibk are the phasors of the currents in the sub-conductors belonging to the kth phase bundle, which are determined from (28a) and (28b). Contribution of the ground wires: BG 

0 2

 I

G   d 2   yG nG

k 1 

k

k

Gk Q





 yQ xˆ  xQ  xGk



 yˆ  

(32)



where IGk is the phasor of the current in the kth conductor of the ground-wire system, which is determined from (28c). Similarly to (11), yQ and xQ in (31)-(32) denote the coordinates of the target point Q where the field is to be evaluated (see Figure 3). However, the problem we now are dealing with is a three-dimensional one. From (22), due to conductor sag between towers, the ycoordinates of the overhead conductors are functions of z. This means that, in addition to yQ

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and xQ, the zQ coordinate of point Q must also be specified for field evaluation purposes. Information on zQ is necessary to determine ya ( zQ ), yb ( zQ ) and yG ( zQ ) . k

k

k

In (30) the contribution Bearth due to earth return currents, with density J E ( x, y) , is obtained using the complex ground plane approach, [30], [32]-[33]. For the evaluation of Bearth at point Q we need to sum up the contributions due to each and every virtual image of the overhead conductors considering a reference mirroring plane situated a complex depth p below the ground surface, (20). See Figure 5. Bearth 

ntotal

 Bk ( I k )

(33a)

k 1

where ntotal = nP(a) + nP(b) + nG. Each Bk contribution in (33a) describes an elliptically polarized field whose complex amplitude is obtained, with the help of Figure 5, through Bk 

0 2

 I  k 2  d kQ 



  yk  yQ  2 p  xˆ   xk  xQ  yˆ  

(33b)



where dkQ is a complex distance depending on p() , i.e., d kQ 

 xk  xQ 2   yk  yQ  2 p 2

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Note again that, according to (22), yk depends on zQ.

Figure 5. Specification of coordinates required for the evaluation of the k th conductor contribution to the Bearth field.

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Magnetic Field Originated by Power Lines

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6. MAGNETIC FIELD MITIGATION The results in Section 4 allow for the determination of all the conductor currents of the power line shown in Figure 1. The magnetic induction field produced by those currents can be evaluated at any place in space by resorting to the results in (30)-(33). In the case of old power lines, constructed before the restrictive regulations set by ICNIRP, it may well happen that the B-field magnitude does exceed the threshold levels at places where humans live, namely, when they walk on the ground near to the power line. Conceptually speaking this problem could be circumvented by placing a conductive screening plane beneath the line conductors, as in Figure 6a. According to Lenz’s law the induced currents in the screening plane would be such that a reaction magnetic field, opposing the magnetic field of line conductors, would be created, therefore dramatically reducing the total field observed nearby the ground surface. Obviously, for a myriad of reasons (mechanical, aesthetical, and cost), this is not a feasible solution. In reality, the desired screening effect can be partially fulfilled by placing one, or more, rectangular closed wire loops beneath the power line - the so-called mitigation loops, [5]-[7], [11]-[13], [16]. The wires of the loop run parallel to the z-axis and are closed at the tops. The mitigation loops are suspended from the power towers. In this chapter we consider the presence of a single mitigation loop. In Figure 6b (a modified version of Figure 1) L1 and L2 denote the circular cylindrical wires of the loop. In some situations, a series compensation capacitor Cs is included in one of the tops of the mitigation loop, [8], [14], [16]. The basic idea is to create a resonant circuit whose current is maximized, therefore providing an extra increase of the B-field of the loop, which opposes the power conductors’ B-field. The analysis of the new line configuration, shown in Figure 6b, follows the same rationale used in Sections 4 to 5, with the added complication that two more conductors are included (10 conductors instead of 8). Equation (16b) remains unaffected, but (16a) changes to:

 Va  V  V b  VG     VL 

nP nP nG nL

;

 Ia  I  I b  IG    IL 

nP nP nG nL

(34)

where nL = 2, and VL and IL are column matrices gathering the voltages and currents of the mitigation loop conductors.

V  I  1 VL   L1  ; I L   L1   S I L ; S    1 VL 2   I L2  where IL denotes the circulating current in the loop.

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J. A. Brandão Faria and M. E. Almeida Pedro

Figure 6. Screening techniques for reducing magnetic field effects. (a) A conductive plane under the power line. (b) A rectangular mitigation loop with longitudinal conductors L1 and L2 closed at the tops.

Equation (25) for the bus admittance changes to  I a   Yaa I  Y  b    ba I G   YGa     I L   YLa

YaL   Va 

Yab

YaG

Ybb

YbG

YbL   Vb 

YGb

YGG

YGL   VG 

YLb

YLG

YLL   VL 









(36)

Y

All the entries of the new bus admittance matrix Y must be re-computed from scratch. As to the voltage drop VL in the mitigation loop we can conclude, upon examination of the boundary conditions at both the near and far end of the line section (see Figure 7), that

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VL1    VL1  VL1  V  VL     L1      V   V  Z I  V V L1 C L L2    L 2  near  L 2  far 

(37)

from where we readily obtain ST VL  VL1  VL2  ZC I L

(38a)

K VL   ZC I L , K  SST

(38b)

where S was defined in (35), and ZC  jX s  1/ ( jCs ) is the impedance of the series-capacitor Cs inserted at the near-end of the loop. In (38), the upperscript T denotes matrix transposition.

Figure 7. Boundary conditions at the near and far ends of the mitigation loop, considering the possible inclusion of a compensation capacitor at the line near end. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Magnetic Field Originated by Power Lines

Note that if the loop conductors are short-circuited at z = 0 (capacitor absent) all we have to do is to enforce ZC = 0. Now, because of the presence of two more conductors, we have to re-compute all the currents in the MTL system. They are determined in a similar manner as in Section 4. Noting that Va = Vb = VP, VG = 0, and that Ia + Ib = IP, by summing the first two equations in (36) we get I P  (Yaa  Yab  Yba  Ybb ) VP  (YaL  YbL ) VL YPP

(39)

YPL

From the fourth equation in (36) we find I L  (YLa  YLb ) VP  YLL VL

(40)

YLP

Plugging (38b) into (40) transforms the latter equation into

K VL  ZC YLP VP  ZC YLL VL

(41a)

from where it results

VL  ( ZC (K  ZC YLL )1 YLP ) VP

(41b)

K LP

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Note that lim K LP  0 . Z C 0

This result is consistent with (38b), ensuring that VL = 0 when the loop is short-circuited at its near end (ZC = 0). Back substitution of (41b) into (39), allows for the determination of VP in terms of IP

VP  ZPPI P , ZPP   YPP  YPL K LP 

1

(42)

Taking into account that Va = Vb = VP, VG = 0, and making use of (41b) and (42), we rewrite (36) as  I a   Yaa I  Y  b    ba IG   YGa     I L   YLa

Yab Ybb YGb YLb

YaG YbG YGG YLG

YaL   Z PP I P  YbL   Z PP I P   YGL   0   YLL  K LP Z PP I P 

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J. A. Brandão Faria and M. E. Almeida Pedro

Ia   Yaa  Yab  YaLK LP  ZPP I P

(43a)

Ib   Yba  Ybb  YbL K LP  Z PP I P

(43b)

IG   YGa  YGb  YGL K LP  Z PP I P

(43c)

I L   YLa  YLb  YLL K LP  Z PP I P

(43d)

As in Section 5, the complex amplitude of the magnetic induction field vector B in the space surrounding the overhead line is obtained by summation of several contributions

B  Bcond  Bearth , Bcond  BP  BG  BL

(44)

The contributions BP and BG are evaluated as in (31)-(32), but where the currents there involved, Ia, Ib, and IG, are those determined in this Section, in (43). Contrary to the situation analyzed in Section 5, here the field Bcond includes the novel contribution BL due to the current in the mitigation loop (with or without the inclusion of the compensation capacitor). Contribution of the mitigation loop:

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BL 

0 2

 IL k

 dL2 Q  yL 2

k 1 

k

k

  yQ xˆ  xQ  xLk yˆ   

 

 

(45)

where I L1  I L and I L2   I L are the complex amplitudes of the currents in the mitigation loop, which are determined from (43d). The mitigation loop currents also affect the computation of the field Bearth . In fact, the result (33) in Section 5 must be modified in order to take into account the new total number (ten) of fictitious image filaments of current inside the soil.

Bearth 

Ntotal

  I







 Bk (Ik ) , Bk  20  dkQ2k  yk  yQ  2 p  xˆ   xk  xQ  yˆ   k 1

(46)

where Ntotal = nP(a) + nP(b) + nG + nL.

7. NUMERICAL RESULTS FOR THE FUNDAMENTAL HARMONIC We are going to apply the theory developed in the preceding Sections to the single-circuit three-phase power line with flat configuration depicted in Figure 6b. Table 2, [16], summarizes conductor characteristics.

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Magnetic Field Originated by Power Lines Table 2. Data on the line conductors Conductor number

Radius (mm)

x coordinate (m)

Maximum height (m)

Minimum height (m)

1a

15.9

-12.2

26.0

14.0

Rdc @ 50ºC (m/km) 57.3

1b

15.9

-11.8

26.0

14.0

57.3

2a

15.9

-0.2

26.0

14.0

57.3

2b

15.9

0.2

26.0

14.0

57.3

3a

15.9

11.8

26.0

14.0

57.3

3b

15.9

12.2

26.0

14.0

57.3

G1

7.3

-8.0

36.0

27.0

372

G2

7.3

8.0

36.0

27.0

372

L1

11.2

-12.0

16.0

7.0

131

L2

11.2

12.0

16.0

7.0

131

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A soil with an average conductivity  of 0.01 S/m has been considered. The distance between consecutive towers has been set at s = 300 m. The length of the mitigation loop (if present) covers three line spans, l = 900 m. The conductors of the mitigation loop are suspended beneath the outer phase conductors at a distance of 10 m below (distance measured at the towers site) — data from [6] refers 9.8 m. The prescribed phase-conductor currents IP are described by a balanced direct sequence three-phase set of 50 Hz sinusoidal currents, with 2 kA rms, that is,  1   I1      I P   I 2   2  2 e j 2 /3  kA   j 2 /3   I3  e 

(47)

To start with, we consider the standard evaluation procedure referenced in Section 3: substituting sagged phase bundle conductors with equivalent horizontal conductors with GMR = 35.66 cm placed at an average height hav =18 m, ignoring ground wires, ignoring earth currents, considering that the mitigation loop is absent. The rms value of the magnetic induction vector, at a target point Q of coordinates xQ = 0 and yQ = 1.80 m, has been obtained from (11) and (5), yielding Brms = Bstd = 22.25 T

(48)

The above identified point Q corresponds roughly to the position of the brain of a human being standing under the line conductors of the center phase. For comparison purposes the rms value of B referred to in (48) will be used as a standard (std). Table 3 summarizes the results concerning the complex amplitudes of all conductor currents, obtained by using the accurate methods developed in Sections 4 to 6. Results have been obtained considering two situations. First, the mitigation loop is supposed to be absent; second, the mitigation loop is present (but the compensation capacitor is still absent, ZC = 0).

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J. A. Brandão Faria and M. E. Almeida Pedro Table 3. Complex amplitudes of conductor currents (rms and phase values)

Without mitigation loop Conductor 1a 1b 2a 2b 3a 3b G1 G2 L1 L2 earth

With mitigation loop without compensation capacitor

rms (A)

phase (º)

rms (A)

phase (º)

994.36 1005.67 1003.83 996.40 1007.68 992.29 104.96 113.12 NA NA 38.98

0.32 +0.32 120.87 120.12 +120.93 +120.12 176.23 +16.37 NA NA 95.60

994.86 1005.18 1003.09 997.10 1007.43 992.58 97.77 105.17 241.52 241.52 38.98

0.32 +0.32 120.79 119.20 +119.85 +120.15 174.28 +16.03 164.19 +15.81 95.60

As to the evaluation of the rms value of the magnetic induction field at the target point Q (positioned at a mid-span, zQ = s/2 = 150 m), we obtained, from (30), (44), and (5) 

Without the mitigation loop:

Brms = 32.16 T = 1.45 Bstd

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

(49)

With the mitigation loop (but without capacitor compensation):

Brms = 26.73 T = 1.20 Bstd

(50)

It should be noted that for both cases examined the computed contribution of the field

Bearth is as small as 0.01 T (rms). This minor effect is a direct consequence of the very large penetration depth at 50 Hz, p  500 m. However, for higher frequencies and better conducting soils the contribution Bearth grows in importance. The result in (49) shows that the standard evaluation procedure gives a defective estimation of the actual field. The observed error of 45% is mainly due to the neglecting of the sag effect on conductors. The result in (50) shows the real effectiveness of the mitigation loop technique. The presence of the loop placed 10 m below beneath the outer phase conductors made the field at point Q to decrease some more 17%. As additional information, it deserves mentioning, that the effectiveness of the mitigation loop can be further enhanced by getting the loop closer and closer to the phase conductor set. To confirm this idea we plotted in Figure 8, [16], a normalized representation of Brms/Bstd against the height of loop conductors at the tower sites, keeping invariant conductor sags. The higher the loop is positioned the lower is the field at the target point Q.

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Figure 8. Normalized plot of Brms/Bstd against the height of the mitigation loop. The point marked with a circle corresponds to the data in Table 2 (hLmax = 16 m). [Courtesy of IEEE, [16]].

However, from a practical point of view, eventual insulation and air breakdown problems may prevent the loop to be brought very close to the phase conductors. Therefore, throughout the remaining of this chapter, we will keep assuming that the configuration coordinates of the loop are those listed in Table 2, i.e., hL  16 m and hLmin  7 m . max

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Keeping the mitigation loop at its stated position one can further reduce the magnetic field intensity at the observation point Q (xQ = 0, yQ = 1.8 m, zQ = 150 m) by inserting an appropriately chosen series-capacitor in the loop [6], [8], [16] recall Figure 7. In order to determine the optimal capacitance Cs of the capacitor to be inserted in the loop, we reevaluated field-B using the results established in Section 6, considering different values for ZC = jXs, with the reactance Xs running from 2  to 0. Graphical results depicted in Figure 9 show that the optimal situation (point P1) is characterized by Xs = 523 m, Cs = 6.086 mF, Brms = 23.76 T = 1.07 Bstd

(51)

The conclusion reached in (51) makes it clear that the decrease of Brms as compared to (50) is still significant an added improvement of 11%. Nonetheless, the capacitor compensation scheme may not be extraordinarily attractive. The reason is two-fold. One the one hand, the required capacitor would be expensive due to its high capacitance. On the other, we see from Figure 9, [16], that a mistake on the choice of Cs could inclusively lead to an unwanted increase of the B-field. For example, if we make Xs = 1.045  Cs = 3.046 mF, we will obtain Brms = 46.86 T = 2.11 Bstd (point P2). So far we have been concerned with the computation of the magnetic induction field at a particular target point (point Q with coordinates: xQ = 0, yQ = 1.8 m, zQ = 150 m). However, in order to have a complete grasp of the problem we still need to analyze the field distribution in the whole space. Bearing this in mind, we started by obtaining transversal and longitudinal profiles of the field intensity —see Figure 10, [16]. In Figure 10a we made zQ = 150 m (mid span), yQ = 1.8 m, and allowed x = xQ to continuously vary in the range 50 to 50 m. In Figure 10b, we made xQ = 0, yQ = 1.8 m, but allowed z = zQ to continuously vary in the range 0 to 300 m (a whole line span between two towers).

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Figure 9. Normalized plot of Brms/Bstd as a function of the reactance Xs of the compensation capacitor inserted in the mitigation loop. Points P1 and P2 define respectively the optimal and the worst situations. Point P3 corresponds to a short-circuited mitigation loop (capacitor absent). [Courtesy of IEEE, [16]].

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Figure 10 presents normalized plots of Brms/Bstd against the space coordinate that we have allowed to vary. Four curves, labeled (0), (1), (2), and (3), are represented. They correspond, respectively, to the following cases: standard basic approximation, accurate model without mitigation loop, accurate model with short-circuited mitigation loop, and accurate model with optimal compensation capacitor inserted in the mitigation loop. In Figure 11, [16], a transverse-plane two-dimensional representation of contour plots of field intensity measured at mid-span (z = 150 m) is presented. The curves define the 100 T reference level for the magnetic induction which cannot be exceeded at 50 Hz. Three curves are shown; all of them obtained using the accurate model developed in section in Sections 5 and 6, with and without mitigation loop, with and without compensation capacitor.

Figure 10. Representation of the normalized field intensity Brms/Bstd in space. (a) Transversal profile, taking zQ = 150 m, yQ = 1.8 m, and x  [50 m; 50 m] . (b) Longitudinal profile at xQ = 0, yQ = 1.8 m, and z  [0; 300 m] . Curve 0 (dashed line) corresponds to the standard basic approximation; curve 1 corresponds to the accurate model without mitigation loop; curve 2 corresponds to the accurate model with short-circuited mitigation loop; and curve 3 corresponds to the accurate model with optimal compensation capacitor inserted in the mitigation loop. [Courtesy of IEEE, [16]].

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Magnetic Field Originated by Power Lines

Figure 11. Transverse-plane 2D contour plots of Brms(x, y) = 100 T observed at mid-span. Curve labels 1, 2, and 3, have the same meaning as in Figure 10. [Courtesy of IEEE, [16]].

It may be noticed that the region where the field exceeds the reference level of 100 T (the interior of the contour plots) is near and around the phase-conductors. Nonetheless, it should be pointed out that the presence of the mitigation loop (intended to minimize the Bfield near to the ground surface) causes the 100 T reference contour to spread outside the phase-conductors area, encircling the mitigation loop conductors.

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8. ANALYSIS AND RESULTS FOR HIGH-ORDER HARMONICS The presence of nonlinear loads in power system networks is a recognized source of inevitable harmonic pollution, leading to waveform distortion, increased losses, misoperation of protective and metering equipment, and, in general, a degradation of power quality supply, [17]. Standards for limiting this harmonics content have been set in many countries, [36]. The limit values of the allowed distortion for each harmonic component depend on the order of the harmonic under analysis; in any case, for power transmission lines operating at 150/220/400 kV, harmonic distortion exceeding 2% is not permitted. As referred to in Section 2, magnetic field deleterious effects on human health, resulting from induction heating of human tissues, increase with the frequency. Accordingly, ICNIRP guidelines, [2], defined the rms value of the magnetic induction field reference level as Bref (μT) 

5000 f (Hz)

(52)

for frequencies in the range 25 Hz – 800 Hz. This means, for example, that for the 16th harmonic (f = 800 Hz) the reference level allowed for Brms has decreased to as low as 6.25 T. Since power quality requirements do not permit harmonic distortions to exceed 2%, one may be led to assume that the magnetic field originated by a given harmonic cannot also exceed 2% of the magnetic field computed at 50 Hz. We will show in this Section that such an assumption is not entirely correct.

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J. A. Brandão Faria and M. E. Almeida Pedro

For exemplification purposes we keep considering the single-circuit overhead power line (400 kV, 1.4 GVA) whose configuration is shown in Figure 6b, with line parameters given in Table 2. The mitigation loop is present, but the compensation capacitor is absent. The length of the structure is three line spans, l = 900 m. The computation of system currents for f  h  50 Hz (with h = 2, 3, , 16) follows the same procedure as indicated in the preceding Section. However, the approximate expression employed for the evaluation of the entries of the diagonal matrix Zskin in (21) is abandoned. Here we utilize, from [17], [20],

(Zskin )kk  ( Rdc )kk  k 

J 0 (k ) 2 J1 (k )

(53)

where J0 and J1 are, respectively, the Bessel functions of the first kind of order 0 and 1. In (53), the dimensionless complex quantity k depends on the frequency of the harmonic under analysis and on the dc resistance of the kth conductor

k 

0

(54)

j ( Rdc )kk

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The prescribed set of phase currents, written in matrix phasor notation, is  p1 e j1h   I1   h    I P  I a  Ib   I 2   2 I rms  p2h e j2 h     I3   p3 e j3h   h 

(55)

The corresponding time-domain currents are written explicitly as

  



 i1 (t )  p1  I rms 2 cos h1t  1 h h  h   i2h (t )  p2 h  I rms 2 cos h1t   2h  i3 (t )  p3  I rms 2 cos h1t  3 h h  h

 

(56)

where 1 and Irms characterize the fundamental 50 Hz frequency previously analyzed: 1  100 rad/s , and Irms = 2 kA. In (56), h represents the order of the harmonic under consideration, and pk and k are, h

h

respectively, the percentage of distortion and phase angle assigned to the hth harmonic in ik current, with k = 1, 2, 3. Once IP is given, all the remaining system currents Ia, Ib, IG, IL, and IE, are evaluated according to (43) and (29). The rms value of the magnetic induction field produced by all

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Magnetic Field Originated by Power Lines

currents at play is determined from (44) and (5). The target point Q where Brms is assessed is defined through xQ = 0, yQ = 1.8 m, and zQ = 150 m. Results for two different cases are obtained and examined. First case: A balanced three-phase load for which the currents in (56) not only have the same magnitude but also have correlate phase angles. Second case: A non-balanced load for which the currents in (56) are characterized by random parameters.

Balanced Load For the case of a balanced load, the set of prescribed currents in (56) is similar to the one in (47) for 50 Hz, that is

  p1h  p2h  p3h  ph   1h  0 ; 2h  h  4 / 3 ; 3h  h  2 / 3

(57)

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Considering the worst possible case we will take ph = 2%. For such small currents (40 A rms), one would be prone to estimate Brms at the target point Q to be around 0.53 T, i.e., 2% of the value reported in (50). As we will next see this happens to be true for some of the harmonics, but not for all of them. It is helpful to note that while the harmonics of order 3, 6, 9, 12, and 15, on i1, i2, and i3, define a homopolar sequence, the remaining harmonics define direct or inverse sequences. Hence, we have  1    j 2 /3   e  , for h = 2, 5, 8, 11, 14   j 4 /3    e  1  I1     I P   I 2   2 40A    1  , for h = 3, 6, 9, 12, 15  1   I 3     1    j 4 /3   e  , for h = 4, 7, 10, 13, 16   j 2 /3   e 

(58)

Numerical results of magnetic induction field calculation are offered in Table 4 for h = 2, 3, 4, 14, 15, 16. We can see that for the inverse and direct sequence harmonics the rms value of field B is around 2% of the one evaluated at 50 Hz, in agreement with a previous estimation. However, for the homopolar sequence, the field harmonics almost reach 4% of the 50 Hz value. In this case the currents in the power line structure are entirely symmetrical with respect to the vertical plane of symmetry x = 0.

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J. A. Brandão Faria and M. E. Almeida Pedro Table 4. Values of the magnetic induction field for several harmonic components

2 harmonic

14 harmonic

Homopolar sequence harmonics 15th 3rd harmonic harmonic

Brms

0.536 T

0.522 T

0.928 T

B/B50Hz

2.00%

1.95%

3.47%

Inverse sequence harmonics nd

th

Direct sequence harmonics 4th harmonic

16th harmonic

0.992 T

0.524 T

0.521 T

3.71%

1.96%

1.95%

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This fact makes the mitigation loop ineffective (IL = 0) and, in addition, the influence of the earth currents grows in importance. In conclusion: from the viewpoint of B-field calculations, the worst possible scenario corresponds to homopolar sequence harmonics where the actual Brms is almost two times bigger than previously assumed. Under these circumstances, the question that remains to be answered is if the reference level restriction for Brms, stated in (52), will or will not be obeyed for the highest homopolar harmonic. Fortunately, the answer is yes. Suppose that the 50 Hz fundamental currents were such that the critical 100 T level was reached. This would mean that a scaling factor of 3.74 = 100/26.73 would be required to affect all computed quantities. Therefore, the homopolar 15th harmonic (with 2% distortion) would originate a Brms value of only 3.71 T —a value that still does not exceed the limit Bref = 6.67 T, in (52). Another aspect deserving attention is the magnetic-induction field distribution along the x-transverse direction. For its analysis we considered that the target point, located at yQ = 1.8 m, zQ= 150 m, can move from x = 50 m to x = 50 m (a human walking perpendicular to the line).

Figure 12. Transverse distributions of the field intensity ratio B/B50Hz for points in space characterized by z = 150 m, y = 1.8 m, and x  [50 m; 50 m] , for the case of homopolar sequence harmonics: h = 3, 6, 9, 12, and 15. [Courtesy of Wiley, [17]]. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Magnetic Field Originated by Power Lines

Figure 12, [17], depicts a graphical representation of the ratio B/B50Hz as a function of x for the important homopolar case.

Non-Balanced Load Here, we are going to consider that the non-linear load of the power line is undetermined. The existing harmonics are characterized by amplitudes and phase angles randomly chosen. A statistical approach is now necessary since the problem cannot be handled analytically. For each harmonic order h, we let each of the distortion parameters p1 , p2h , p3 , to h

h

randomly vary in the range 0 to 2%. In the same way, we let each of the phase angles 1 , 2h , 3 , to randomly vary in the h h

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range 0 to 2. Any combination of these 6 uncorrelated random parameters constitutes an event. Events are created using a uniform-distribution pseudo-random number generator available in the MATLAB toolbox. For each harmonic under analysis a statistically meaningful number of events (104) were generated. The rms intensity of the B-field at the target point Q was evaluated for each event. Scatter plots distributions depicting values of B/B50Hz (in %) against an event counter were obtained for each harmonic order, from h = 2 to 16. At naked eye, all of the obtained scatter plots seem the same, no special distinguishing features being revealed. For this reason, only a single graphic is shown. Figure 13, [17], illustrates the scatter plot distribution for the highest-order harmonic.

Figure 13. Scatter plot distribution for the field intensity ratio B/B50Hz at the target point Q, for the 16th harmonic. A series of ten thousand events; each event representing a randomly generated non-balanced load, was considered. [Courtesy of Wiley, [17]].

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J. A. Brandão Faria and M. E. Almeida Pedro Table 5. Statistical data from scatter plot distributions

Harmonic 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th 15th 16th

Mean value 1.38% 1.38% 1.39% 1.39% 1.40% 1.41% 1.41% 1.42% 1.42% 1.43% 1.43% 1.43% 1.43% 1.44% 1.44%

Standard deviation 0.54% 0.54% 0.54% 0.55% 0.55% 0.55% 0.55% 0.56% 0.56% 0.56% 0.57% 0.57% 0.57% 0.57% 0.57%

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Statistical data such as the mean value and standard deviation were evaluated from the scatter plot distributions for all harmonic orders —see Table 5, [17]. The above results clearly show that, for non-balanced random loads, the B-field generated by any of the harmonics is weakly dependent on the harmonic order; there is a very slight, but consistent, increase of its mean value when the frequency increases —a fact that should be associated to the growing contribution of Bearh , (46). The mean value of the ratio B/B50Hz is approximately equal to ph / 2 where ph is the maximum value of the allowed harmonic distortion. Although the mean value of the ratio B/B50Hz never exceeds the 2% estimation, for some rare events it may reach 3.5% (see Figure 13) —a situation similar to the case of balanced loads with homopolar sequence harmonics.

9. UNDERGROUND POWER CABLES The standard procedure to evaluate the magnetic field due to underground power cables is based on Ampère’s law and is similar to the one described in Section 3 for overhead power lines. The approach assumes equal values of the magnetic permeability inside soil and air, and considers only the sinusoidal currents carried by the cable system with axial direction, the influence of earth currents being neglected [37]. Using this approach the complex amplitude of the magnetic induction field vector at the target point Q above the ground can also be determined using (11). Nevertheless, to perform an accurate evaluation of the magnetic field originated by power cables it is necessary to determine a general solution for the magnetic field in the soil. A first approximation due to Pollaczek [38] was developed for negligibly small size cross section cables. Afterwards, more general and more accurate solutions were developed [39]-[40], not only for one single cable but also for a set of three cables in flat configuration, respectively.

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197

First, a general field formulation was considered, based on Fourier integrals and series developments and later the Pollaczek approach was applied. Conditions to obtain enough accuracy using the Pollaczek approximation were established in [39]-[40], where it was shown that, for typical configurations and typical power frequencies, Pollaczek’s solution is adequate (errors below 1%) for frequency values bellow 1 kHz. This methodology, using Pollaczek’s approximation, was followed in [41]-[43] to evaluate the magnetic field above the ground surface due to a set of underground cable currents. Results presented in [41] show, on the one hand, that the accurate model and the standard model give similar results for homogeneous soils with  = 0, for low frequency currents (50/60 Hz). This is due to the fact that, for low frequency regimes, earth currents spread deep into the soil, and the magnetic field effects of earth currents are negligible. On the other hand, the utilization of the accurate model becomes mandatory for higher frequency and higher soil permeability values [41]-[42]. As referred to before, exposure to low frequency magnetic fields has been a matter of concern, in particular regarding the magnetic fields created by overhead power lines. Underground power cables often appear as an alternative to overhead transmission lines, in order to decrease magnetic field levels, particularly in suburban regions. In this section we evaluate and compare low frequency magnetic field originated by both transmission systems, under the same operation conditions and with similar geometric configuration. The standard procedure was used to evaluate the magnetic field originated by a 400 kV three-phase underground power cable whose configuration and data are illustrated in Figure 14. The soil conductivity is E = 0.01 S/m and the permeability is 0. The underground cable currents, assuming null currents flowing through the sheaths, are defined by a balanced direct-sequence three-phase set of 50 Hz sinusoidal currents, with 2 kA rms. The accurate model, without mitigation loop, was used to determine the magnetic field originated by the overhead line described in Figure 1. Figure 15 presents graphical plots of Brms against the x coordinate, taking zQ = 150 m, and considering two different values for yQ (0 m and 1.8 m).

Figure 14. Cross-sectional view of the 400 kV underground power cable used for exemplification purposes. Data parameters: h = 1.5 m; s = 21.8 cm, re = 7.4 cm, and E = 0.01 S/m.

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J. A. Brandão Faria and M. E. Almeida Pedro

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Figure 15. Graphical representation of Brms against x, using the accurate model without mitigation loop to characterize the overhead line (dashed lines), and the standard model to represent the underground cable (solid lines). Field profiles were obtained by considering zQ = 150 m, x[50 m, 50 m] , and two different values of yQ. Curves 1 and 3 correspond to yQ = 1.8 m, curves 2 and 4 correspond to yQ = 0 m.

Results obtained show that the underground cable Brms curves, when compared to the overhead line Brms curves, present a narrow shape and a significant dependence on yQ. The width of the curves is a consequence of the distance between phase conductors, which is much smaller in the underground cable. The dependence of Brms on yQ is more critical for the underground cable than for the overhead line, this is so because the target point Q is far away from the overhead line, but quite close to the underground cable. Figure 16(a) and (b) depict transverse-plane contour plots of the magnetic induction field intensity (rms values) for the overhead line and for the underground cable, respectively. The curves correspond to three different B-field levels: 100, 30 and 3 T. Results show that the field intensity due to the underground cable does not reach the ICNIRP reference value. In addition, the space regions where the field intensity exceeds 30 and 3 T are much smaller in size than the ones obtained with the overhead line.

Figure 16. Transverse-plane 2D contour plots of Brms(x,y). Curve 1 corresponds to 100 T, curves 2 corresponds to 30 T and curves 3 corresponds to 3 T. (a) Overhead line. (b) Underground cable. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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CONCLUSION This book chapter was dedicated to the topic of magnetic fields produced by power lines a matter of public concern and controversy over the past years, since the exposure to low frequency magnetic fields has been suspected of endangering human safety. Standard analytical procedures for the evaluation of magnetic fields produced by power lines utilize relatively simple models. Nowadays, considering the huge increase of computation capabilities there is no sound justification to keep employing such simple models. In this chapter we developed a comprehensive accurate model for the computation of magnetic fields which takes into account a large variety of effects, therefore permitting a rigorous evaluation of magnetic induction field levels. Our model includes the partition of bundle-phase conductors into sub-conductors, includes ground wire effects, includes the contribution of earth return currents, and includes conductor sagging effects between towers. Using this model, and considering a typical high-voltage single-circuit three-phase line configuration, we obtained numerical and graphical results concerning the evaluation of the magnetic induction field not only at a specific point in space but, also, obtained transversal and longitudinal magnetic field profiles. Two-dimensional field contour plots were obtained as well. In the case of old power lines, built before the restrictive regulations set by the International Commission of Non Ionizing Radiation Protection (ICNIRP), it may happen that magnetic field levels can exceed threshold settings. In this case, special techniques must be employed to reduce magnetic field effects. In this chapter, an analysis was conducted aimed at understanding the effectiveness of the so-called mitigation loop technique with and without compensation capacitors; advantages and drawbacks of the technique were discussed. Our analysis efforts were mainly focused on the fundamental 50 Hz frequency. Nonetheless, the presence of non-linear power-line loads, whether balanced or unbalanced, originates distorted line currents which translate into a set of higher-order harmonics. Since deleterious magnetic-field effects increase with the square of the frequency, an entire Section was also dedicated to the analysis of high-order harmonics effects in the range 100 – 800 Hz. Given the small magnitude of the harmonic distortion allowed by power quality standards, we showed that, even in the worst possible scenario of homopolar currents, there is no reason to fear that ICNIRP rulings on safe public exposure to low frequency magnetic fields be violated, as far as harmonics are concerned. Finally we addressed the problem of magnetic fields produced by underground cables. Results presented show that, in general, the magnetic field produced by underground cables is less intense than the field originated by overhead lines. The single exception occurs when the target point is positioned at the soil level and just above the cable.

ACKNOWLEDGMENT The authors wish to acknowledge IEEE and Wiley publishers for having granted, free of charge, the partial re-use of the material published by the authors in [16] and [17], respectively.

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REFERENCES [1]

[2]

[3]

[4] [5] [6] [7] [8]

[9] [10]

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[11] [12]

[13]

[14] [15] [16]

[17] [18]

Safigianni, A.; Tsompanidou, C. G. Measurements of electric and magnetic fields due to the operation of indoor power distribution substations. IEEE Trans. Power Del. 2005, vol. 20, 1800-1805. International Commission of Non Ionizing Radiation Protection. Guidelines for limiting exposure to time-varying electric, magnetic and electromagnetic fields. Health Phys. 1998, vol. 74, 494-522. Dahab, A. A.; Amoura, F. K.; Abu-Elhaija, W. S. Comparison of magnetic-field distribution of noncompact and compact parallel transmission-line configurations. IEEE Trans. Power Del. 2005, vol. 20, 2114-2118. Melo, M. O.; Fontana, E.; Naidu, S. R. Electric and magnetic fields of compact transmission lines. IEEE Trans. Power Del. 1999, vol. 14, 200-204. Memari, A. R.; Janischewskyj, W. Mitigation of magnetic field near power lines. IEEE Trans. Power Del. 1996, vol. 11, pp. 1577-1586. Memari, A. R. Optimal calculation of impedance of an auxiliary loop to mitigate magnetic field of a transmission line. IEEE Trans. Power Del. 2005, vol. 20, 844-850. Kalhor, H. A.; Zunoubi, M. R. Mitigation of power frequency fields by proper choice of line configuration and shielding. Electromagnetics. 2005, vol. 25, 231-243. Walling, R. A.; Paserba, J. J.; Burns, C. W. Series-capacitor compensation shield scheme for enhanced mitigation of transmission line magnetic fields. IEEE Trans. Power Del. 1993, vol. 8, 461-468. Celozzi, S. Active compensation and partial shields for the power-frequency magnetic field reduction. Int. Symp. EMC 2002. Rome, Italy, 2002. Stewart, J. R.; Dale, S. J.; Klein, K. W. Magnetic field reduction using high phase order lines. IEEE Trans. Power Del. 1993, vol. 8, 628-636. Cruz, P.; Izquierdo, C.; Burgos, M. Optimum passive shields for mitigation of power lines magnetic field. IEEE Trans. Power Del. 2003, vol. 18, 1357-1362. Clairmont, B; Fardanesh, B.; Hopkins, L.; Shperling, B.; Zelingher, S. Passive shielding loops for a multiple line corridor. CIGRE Study Committee 36 Colloquium. Foz do Aguacu, Brazil, 1995. Shperling, B.; Hopkins, L.; Fardanesh, B.; Clairmont, B.; Childs, D. Reduction of magnetic fields from transmission lines using passive loops. CIGRE International Conference, Report 36-103. Paris, France, 1996. Hopkins, L. Capacitor compensated loops for transmission line EMF reduction, IEEE PES TandD Conference. 1996, Los Angeles, CA, 1996. Budnik, K.; Machczynski, W. Contribution to studies on calculation of the magnetic field under power lines. Europ. Trans. Elect. Power. 2006, vol. 16, 345-364. Faria, J. B.; Almeida, M. E. Accurate calculation of magnetic-field intensity due to overhead power lines with or without mitigation loops with or without capacitor compensation. IEEE Trans. Power Del. 2007, vol. 22, 951-959. Faria, J. B.; Almeida, M. E. Computation of transmission line magnetic field harmonics. Europ. Trans. Elect. Power. 2007, vol. 17, 512-525. Faria, J. B. Multiconductor Transmission-Line Structures; Wiley: New York, NY, 1993.

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[19] Clayton, P. Analysis of Multiconductor Transmission Lines; Wiley: New York, NY, 1994. [20] Faria, J. B. Electromagnetic Foundations of Electrical Engineering; Wiley: Chichester, UK, 2008. [21] Solymar, L. Lectures on Electromagnetic Theory; Oxford Univ. Press: Oxford, UK, 1984. [22] IFAC. Dielectric Properties of Body Tissues. 2010. URL: http://niremf.ifac.cnr.it/ tissprop/ [23] Gabriel, C.; Gabriel. S.; Corhout. E. The dielectric properties of biological tissues: literature survey. Phys. Med. Biol. 1996, vol. 41, 2231-2249. [24] Gabriel, S.; Lau, R. W.; Gabriel, C. The dielectric properties of biological tissues: measurements in the frequency range 10 Hz to 20 GHz. Phys. Med. Biol. 1996, vol. 41, 2251-2269. [25] Gabriel, S.; Lau, R. W.; Gabriel, C. The dielectric properties of biological tissues: parametric models for the dielectric spectrum of tissues. Phys. Med. Biol. 1996, vol. 41, 2271-2293. [26] Faria, J. B. Multiconductor transmission lines. In: Editor Chang, K. Encyclopedia of RF and Microwave Engineering. vol. 4, 3335-3341; Wiley: New York, NY, 2005. [27] Faria, J. B. High frequency modal analysis of lossy nonuniform three-phase overhead lines taking into account the catenary effect. Europ. Trans. Elect. Power. 2001, vol. 11, 195-201. [28] Galloway, R. H.; Shorrocks, W. B.; Wedepohl, L. M. Calculation of electrical parameters for short and long polyphase transmission lines. Proc. IEE. 1964, vol. 111, 2051-2059. [29] Gary, C. Approche complète de la propagation multifilaire en haute fréquence par utilization des matrices complexes. EDF Bulletin de la Direction des Etudes et Recherches. 1976, vol. 3/4, 5-20. [30] Dubanton, C. Calcul approché des parametres primaries et secondaires d’une ligne de transport. EDF Bulletin de la Direction des Etudes et Recherches. 1969, vol. 1, 53-62. [31] Carson, J. R. Wave propagation in overhead wires with ground return. Bell System Tech. Journal. 1926, vol. 5, 539-554. [32] Déri, A.; Tevan, G.; Semlyen, A.; Castanheira, A. The complex ground return plane: a simplified model for homogeneous and multilayer earth returns. IEEE Trans. PAS. 1981, vol. 100, 3686-3693. [33] Deri, A.; Tevan. G. Mathematical verification of Dubanton’s simplified calculation of overhead transmission line parameters and its physical interpretation. Arch. Elektrotechnik. 1981, vol. 63, 191-198. [34] Faria, J. B. On the segmentation method used for analyzing nonuniform transmission lines: application to the exponential line. Europ. Trans. Elect. Power. 2002, vol. 12, 361-368. [35] Semlyen, A.; Shirmohammadi, D. Calculation of induction and magnetic field effects of three-phase overhead lines above homogeneous earth. IEEE Trans. PAS. 1982, vol. 101, 2747-2754. [36] IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems, ANSI/IEEE Std. 519-1992.

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[37] Vérité, J. C.; Bjorlow-Larsen, K.; Conti, R.; Deschamps, F.; Drugge, B.; Dular, P.; Garcia, F.; Pirotte, P.; Swingler, R. Magnetic field in HV cable systems  Systems without ferromagnetic component. Report of CIGRÉ Joint Task Force no. 36-01/21, 1996. [38] Pollaczek, F. Über das feld einer unendlich langen wechsel-stromdurchflossenen einfachleitung. Elektrischen Nachrichten Technik. 1926, vol. 3, 3339-3360. [39] Maló Machado, V.; Borges da Silva, J. F. Series-impedance of underground transmission systems. IEEE Trans. Power Del. 1988, vol. 3, 417-424. [40] Maló Machado, V.; Borges da Silva, J. F. Series-impedance of underground cable systems. IEEE Trans. Power Del. 1988, vol. 3, 1334-1340. [41] Maló Machado, V.; Almeida, M. E.; Neves, M. G. Accurate magnetic field evaluation due to underground power cables. Europ. Trans. Elect. Power. 2009, vol. 19, 11531160. [42] Marchante, P.; Maló Machado, V.; Almeida, M. E.; Neves, M. G. The influence of frequency and soil permeability on the magnetic field due to underground power cables. Europ. Trans. Elect. Power. 2010, vol. 20, 760-770. [43] Almeida, M. E.; Maló Machado, V.; Neves, M. G. Mitigation of the magnetic field due to underground power cables using an optimized grid. Europ. Trans. Elect. Power. 2011, vol. 21, 180-187. [44] Faria, J. B. The effect of power-line sagged conductors on the evaluation of the differential voltage in a nearby circuit at ground level, Progress in Electromagnetics Research M, 2012, vol. 24, 209-220.

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 © 2013 Nova Science Publishers, Inc.

Chapter 5

MICROWAVE HEATING FOR METALLURGICAL ENGINEERING Jingjing Yang1, Ming Huang1 and Jinhui Peng2 1

Wireless Innovation Lab, School of Information Science and Engineering, Yunnan University, Kunming, People’s Republic of China 2 Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, People’s Republic of China

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ABSTRACT As a sort of electromagnetic waves ranging from 300MHz to 3000GHz, microwaves have been widely used in wireless communication, radar, heating and sensing. Microwave heating is best known for heating food in the kitchen, and in the last two decades it has emerged as a ubiquitous tool in chemistry. Despite its broad technological importance, microwave heating remains an unpredictable tool because the detailed physics of the interaction between microwave and substance is poorly known. In this Chapter, we revisit the reflection and transmission of microwave by conducting medium. We show that when a large piece of metal is milled into particles and flours, it becomes a good microwave absorber. To reveal the mechanism behind this phenomenon, firstly, three models based on effective media theory, i.e., qusi-static model, equivalent parameter model and RC network models are studied. Then, a new equation is introduced to characterize the Debye and non-Debye relaxations under microwave irradiation. Some new physical phenomena including local field enhancement and temperature dependent relaxation time, etc., which exist in non-Debye materials can be explained by this equation. Finally, we show that the local field enhancement is a ubiquitous and nonlinear phenomenon in granular materials, which is relative to microwave power, boundary condition, constituent and micro-structure of the materials, etc., and this is the main reason that microwave assisted chemical reactions can take place at a much lower average temperature compared with conventional heating. Examples about the application of microwave heating in metallurgy engineering are given. These works lay a solid foundation for the development of microwave metallurgical engineering.

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1. INTRODUCTION

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Microwave heating has been well known for its advantages such as fast heating and volume heating [1]. It has been widely used in science and technologies especially in food engineering and chemical engineering. Since the 1980s, our group has been devoted to the study of the interaction between the microwave and materials. For example, a surface plasma generator is invented by Huang [2] et al. The reaction of metallurgical materials under microwave irradiation was studied by Peng [3]. Huang [4] studied the mechanism of the interaction between microwave and granular material. Yang [5] studied the electromagnetic properties of heterogeneous granular materials. Recently, a breakthrough was achieved in microwave metallurgical engineering, and the large scale, continuous and automation production were realized by our group [6].

Figure 1. (a) Simulation model of the waveguide loaded with a bulk metal. (b) Corresponding transmission and reflection coefficients of (a). (c) Simulation model of the waveguide loaded with metallic particles. Grey regions represent the metal particles, while the white regions represent dielectric materials. (d) Corresponding transmission and reflection coefficients of (c). The inset shows the electric field distribution in the metallic particles. Bright regions represent electric field with higher intensity.

To reveal the mechanism of the interaction between microwave and matter, we revisit the reflection and transmission of microwave by conducting medium, as shown in Figure 1. From Figure 1(a) and Figure 1(b) we can see that a bulk metal totally reflects the electromagnetic wave, that is, the transmission coefficient equals to zero, while the reflection coefficient equals to 1. When the bulk metal is milled into particles (Figure 1(c)), transmission coefficient does not equal to zero. Electromagnetic wave penetrates into the inner region of

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the particles, and is absorbed, as shown in Figure 1(d). Interestingly, when the shape of the particles are well designed and arranged periodically, the heterogeneous materials with effective permittivity and permeability ranging from negative to positive could be obtained. This kind of heterogeneous materials is named as metamaterials [7]. Simulation results of effective permittivity and permeability for the metamaterials constituted of square rings are given in Figure 2. The discovery of metamaterials opens up an avenue for control electromagnetic wave at will [8, 9].

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Figure 2. (a) Simulation model of metamaterials constituted of square rings. (b) Effective permittivity and permeability.

This chapter reveals detailed physics of the interaction between microwave and granular materials, and examples of minerals processing in microwave metallurgy engineering are given. The remainder of this Chapter is organized as follows. In section 2, effective permittivity of heterogeneous granular materials is simulated by using qusi-static model. In section 3, equivalent parameter model is established for simulating the effective permittivity and the frequency dependent characteristics are obtained. In second 4, the conducting and dielectric phase of the heterogeneous materials are modeled as resistors and capacitors, and a three dimensional LC network is established for simulating universal dielectric response of heterogeneous granular materials. In section 5, we introduce a new equation for characterizing the relaxation properties of heterogeneous materials under microwave irradiation. In section 6, local field enhancement effect predicted by the equation is further confirmed by numerical simulation. In section 7, several examples of minerals processing in microwave metallurgical engineering are given. The last section is a summary of this chapter.

2. QUSI-STATIC MODEL 2.2. Two Dimensional Qusi-static Model Figure 3 (a) and (b) show the scanning electron micrographs of fused zirconia and iron powder. They are all multi-phase granular heterogeneous materials. Taking the Qusi-static model as an example, the two phase heterogeneous materials can be modeled as a periodical square structure consisting of inclusion with permittivity  2 embedded in a dielectric matrix

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with permittivity  1 . Although the inclusion may be complicated in shape, we assume that it is a disk of radius r as shown in Figure 4. The complex relative permittivity of the inclusion is denoted as  2  1  ( /  0 )i , where  is the conductivity, is the angular frequency, and  8.85 1012 (F/m) is the permittivity of vacuum. The surface fraction of the inclusion is

denoted as A   r 2 / L2 . It is assumed that the unit cell, which has no free charges or currents, is constructed from nonmagnetic materials. The model space can simulate a capacitor by applying a potential difference between the top and bottom faces of the model space. We fix that and V2  0 , and assumed that V / n  0 on the other side faces. The effective permittivity was computed using the FEM software package COMSOL MULTIPHYSICS. The code involves finding the nontrivial solutions of Laplace’s equation   [ (r )V (r )]  0 . The effective permittivity corresponding to the direction of the applied

i.e.,  e   y ,

field,

  (V / n) dS   [(V S

i

i

e

2

is

obtained

by

integration

via

 V1 ) / L]S , where denotes the difference of potentials imposed in

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the y direction, is the size of the unite cell, and S is the surface of the unit cell perpendicular to the applied field.

Figure 3. Scanning electron micrographs of fused zirconia(a) and iron powder(b) [10].

Figure 4. A qusi-static model for simulating the effective permittivity of two-phase composite medium[10].

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Figure 5. (a) The dependence of the real part of the effective permittivity of conductor-dielectric compound ( A  0.3 , 1  1.5 ) as a function frequency and several values of conductivity  (s/m). (b) Same as in (a) for the imaginary part of the effective permittivity [10].

2.2.1. Influence of Conductivity on Effective Permittivity of Heterogeneous Materials In this section, effective permittivity of two phase heterogeneous materials is simulated based on the qusi-static model. Microwave absorbing property, the imaginary part of the effective permittivity is a key parameter which represents whether the materials can be heated up by microwave. In metallurgy engineering, the microwave absorbing property of granular materials can be enhanced by adding conducting phase such as anthracite or coke particulates. This is due to the factor that the conducting phase increases the loss factor of the composite, which represent the amount of input microwave power that is lost in the material by being dissipate as heat. For a representative set the values of conductivity  , its impact on absorbing properties of the conductor-dielectric compound was investigated. The results are shown in Figure 5(a) and 5(b). It is found that absorbing peak position of the compound is governed by the conductivity of the inclusion. The absorbing peak shows a blue shift with the increase of  , while the peak value keeps unchanged. As the conductivity of the inclusion is increased by a factor of ten, the frequency of the absorbing peak increases by the same factor. In fact, the frequency at which the absorbing peak occurs is proportional to the inclusion

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conductivity. It is worth noting that near the frequency of 2450MHz which is the most commonly utilized frequency for microwave heating, the composite material behaves as a good microwave absorber, when the conductivity of the inclusion phase is about 0.5 S/m.

2.2.2. Influence of Embedding Matrix Permittivity on Absorbing Properties In order to quantify the influence of the permittivity of the embedding matrix on absorbing property of the compound materials, we performed further calculations. For fixed conductivity and the surface fraction of the inclusion, the relation between effective permittivity and frequency was simulated for 1  1  3 , as shown in Figure 6. Significant enhancement of the   and   spectra is observed as 1 is increased. Besides, the peak position of shows a slight red shift with increase of 1 . It indicates that the change of dielectric

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permittivity not only influence the amplitude of the   and   spectra but also influence the peak position.

Figure 6. (a) Real part of the of the effective permittivity of conductor-dielectric compound (   0.5 , A  0.3 ) plotted against frequency at several values of 1 . (b) Same as in (a) for the imaginary part of the effective permittivity [10].

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2.2.3. Comparison of the Numerical Results with Theoretical Prediction For different values of the real part and imaginary part of the inclusion permittivity, effective permittivity of the two phase heterogeneous media is simulated and compared with prediction of classical rules. Maxwell-Garnett rule and Bruggeman formalism is given by Eqs. (1) and (2) [11].

e  2  3 f 2

(1  f )

1   2 1  2 2  f (1   2 )

(1)

2  e    f 1 e 0  2  2 e 1  2 e 1.4

(2)

(a)

1.3

'e

1.2 1.1 1.0 FEM results BS CP MG

0.9 0.8 0

20

40

60

80

(b)

FEM results BS CP MG

0.006

"e

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' 0.008

0.004

0.002

0.000 0

20

40

60

80

'2 Figure 7. Effective complex permittivity of the two-phase composite medium as a function of the real part of the complex permittivity of the inclusion. (a) Real part; (b) Imaginary part[14].

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Jingjing Yang, Ming Huang and Jinhui Peng Here, and denote the permittivity of inclusion and the substrate media;  e is the effective

permittivity of the mixture; f is the ratio of the inclusion. The mixing approach presented in [12] collects these two dielectric mixing rules into one family:

e  2 1   2  f  e   2  v( e   2 ) 1   2  v( e   2 )

(3)

where, is a dimensionless parameter. For different choices of v , the previous mixing rules are recovered. v  0 gives the Maxwell Garnett rule, v  1 gives the Bruggeman formula, and v  2 gives the Coherent potential approximation [13]. 1.45

(a) 1.40 1.35

'e

1.30 1.25 1.20 1.15

FEM results BS CP MG

1.10 1.05 0

10

20

"2

30

40

50

0.15 FEM results BS CP MG

0.10

"e

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(b)

0.05

0.00 0

10

20

"2

30

40

50

Figure 8. Effective complex permittivity of the two phase composite medium as a function of the imaginary part of the complex permittivity of the inclusion. (a) Real part; (b) Imaginary part [14].

In the simulation, the permittivity of the matrix phase (  1 ) is supposed to 1, complex permittivity of the inclusion is denotes as  2   2  0.03 j . The real part and imaginary part of the effective permittivity as a function of is shown in the panels (a) and (b) of Figure 7. In

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Figure 7(a) we found that increases with and reaches a saturation sate when  2  10 . The simulation results of are very close to that of the three classical rules, i.e., Maxwell- Garnet (MG), Bruggeman (BS), Coherent Potential (CP), when is less than 10. is close to the classical rule of MG, when is greater than 10. Figure 7(b) indicates that the values of  e obtained from the simulation model are in good agreement with the that of the three classical rules over the whole range of  1 , and there is a inflexion point at  2  5 , before which  e decreases sharply. For 1  1 and  2  3   2 j , effective complex permittivity as a function of is simulated as shown in Figure 8. Figure 8(a) indicates that increases with  2 , and it reaches a saturation status when  2  10 . The prediction of  e from the simulation model is close to both the classical rules of CP and MG, before the saturation point, while  e is close to the prediction of MG rule after the saturation point. From Figure 8(b), it is worth noting that reaches the peak value when  2  5 . Before the peak point, increases remarkably, after that it decreases gradually with  2 . The imaginary part of the permittivity is relative to the microwave power absorbed by the composite medium, and in general, the larger the imaginary part, the higher the efficiency of microwave heating. Therefore, the peak value of  e in Figure 8(b) indicates that the maximum dielectric loss of the composite medium can be achieved by tuning the inclusion component, which may lead to a maximum microwave heating efficiency.

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2.3. Three Dimensional Qusi-static Model Figure 9(a) shows the three dimensional qusi-static model of which the size is set to unity. It is composed of 30x30x30 cubic cells for simulating the inclusion and matrix elements. The inclusion elements are placed randomly in the matrix material by means of generating a series of uniformly distributed pseudorandom numbers which note the coordinates of the inclusion elements. The grey region denotes the inclusion with permittivity 1 , and the white region denotes the host material with permittivity  2 . Both materials are homogeneous, lossless, and isotropic. Similar to the two dimensional model, illustrated in the last section, the model space can simulate a parallel-plate capacitor by applying a potential difference between the top and bottom faces of the model space. We fix that to be and V2  0 , and assume that V / n  0 on the other side faces, as shown in Figure 9(b). The electrostatic energy of the parallel-plate capacitor can be calculated macroscopically by

We   z S (V2  V1 )2 / 2d ,

(4)

where S is the area of the surface exposed to the electric field and d is the distance between top and the bottom surfaces. It is obvious that the effective permittivity along the direction corresponding to the applied filed (  z ) can be obtained by calculating the total electrostatic energy ( We ) of the model. Solving the problem at hand means finding expressions for the

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scalar potential V and electric field E  V everywhere within the simulation domain based on the solutions of Laplace’s equation, i.e., [V ] , where  is the local permittivity distribution inside the simulation domain. Once the potential distribution is know, the electrostatic energy for each element can be obtained by integration via [15]

We (k )  1 2   k [(V x)2  (V y)2 ]dxdy ,

(5)

Sk

where and S k are the dielectric constant and surface of the kth element, respectively. The

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total electrostatic energy in the entire composite can be calculated by summation of all the elements, i.e.,

Figure 9. (a) The 3D simulation model with 30% volume fraction of inclusions. The gray region denotes the inclusion elements. The white region denotes the host material. (b) Boundary conditions of the simulation model. (c) Effective permittivity of the disordered model in the x, y, and z directions (  1 =10,  2 =1) [16].

We  We (k ) k

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In order to test the orientation dependence of the disordered model, the effective permittivity in directions x, y, and z are calculated by changing the polarization of the applied electric field. Results shown in Figure 9(c) indicate that the effective permittivities in the three directions are almost the same. As a consequence, the 3D disordered model is isotropic, and the effective permittivity is calculated by taking a statistical mean of the permittivity in the three directions:

 eff  ( x   y   z ) / 3

(7)

The simulation is performed based on the commercial finite element software ANSYS and the procedure sorted out  eff on a personal computer. The simulation model is meshed using the adaptive mesh technique. The finite element mesh consisted of hexahedral second order volume elements with 20 nodes per element and the degree of freedom as the projection of the voltage, V , at each node. Mesh convergence study was performed to confirm that the results were not dependent on the mesh. Figure 10 gives the convergence graph of effective permittivity as a function of total number of elements for fixed volume fraction ( f =30%,  1 =30,  2 =1). The solution varied considerably for total number of elements less than 27000

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but was found to be fairly stable after 27000 elements. Hence, the mesh with 27000 (182736 nodes) elements was selected as the appropriate choice for the computations. As a side node, we do point that the use of 10-node tetrahedral element doesn’t affect the simulation results providing that the mesh is dense enough to generate the same number of nodes. The inclusions may be embedded in the matrix with different geometric shapes. In order to study the influence of the geometric shape of the inclusions on dielectric properties of the composite medium, periodical models shown in Figure 11, consisting cubic inclusion, rounded cubic inclusion and sphere inclusion, are also simulated.

Figure 10. Conventional periodical models for calculating the effective permittivity of two-phase composites: (a) dielectric cubic model. (b) dielectric rounded cubic model. (c) dielectric sphere model.

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Figure 11. Effective permittivity as a function of total number of elements (

f

=30%,  1 =30,

 2 =1).

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2.3.1. Impact of Permittivity Contrast on Effective Permittivity For different values of inclusion phase and the substrate, effective permittivity of the disordered three-dimensional Qusi-static model is simulated and compared with that of the Bruggeman formula, Hashin-Shtrikman bound and the periodic model with cubic inclusion (PC). The relation between volume fraction and effective permittivity is shown in Figure 12. It is seen that at a low permittivity contrast ( 1  3 and  2  1 ) the simulation results are in

Figure 12. Comparison of the numerical results of the disordered model, periodical model and the classical mixing rules. PC presents the results obtain by the periodical model with cubic inclusion. (a) and  2  1 . (b) 1  10 and  2  1 . (c) 1  30 and  2  1 . The inset shows an expanded view of the region marked by the ellipse. (d) Relative errors of the effective permittivity to their mean value at each topological structure for the disordered model [16].

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good agreement with the prediction of Bruggeman formula and locate between the HashinShtrikman bounds. At a much higher permittivity contrast, simulation results of the three dimensional model are still in good agreement with the Bruggeman formula; at the lower volume fraction side, the effective permittivity is close to the lower limit of the HashinShtrikman bounds; at the higher volume fraction side, the effective permittivity is close to the upper limit. To investigate the influence of inclusion randomness on effective permittivity, ten topological structures are calculated for each volume fraction. The inset of Figure 12c shows the expanded view of the simulating results of the disordered model in the volume fraction range of 35%-40%.Figure 12(d) shows the relative errors of the calculated effective permittivity to their mean value at each topological structure. It can be seen that the relative errors locate in the range of -4%-3%, and they are smaller than 2% at larger volume fraction ( f >50%). It means that the procedure for calculating the effective permittivity is valid.

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2.3.2. Impact of Inclusion Shape on Effective Permittivity From Figure 12, it is interesting to observe that the computed effective permittivity of the periodical model with cubic inclusion nearly exactly coincides with the Maxwell-Garnett rule which is also the lower limit of the Hashin-Shtrikman bounds, even at high permittivity contrast and large volume fractions. This phenomenon is unusual, since the Maxwell-Garnett formula is often interpreted as the effective permittivity of sparsely distributed spheres with little mutual interaction.

Figure 13. Effective permittivity as a function of volume fraction for periodical model with rounded cubic inclusion (a) and sphere inclusion (b). PRC presents the results obtain by the periodical model with rounded cubic inclusion. PS presents the results obtain by the periodical model with sphere inclusion. The inset of (a) is the cross section of the rounded cubic inclusion. From bottom to up, the curves represent the permittivity contrast of and  2  1 , and  2  1 , and  2  1 , respectively.

To understand the impact of inclusion shape on effective permittivity, the effective permittivity of the periodical model with rounded cubic inclusion and sphere inclusion was simulated and compared with the prediction of Maxwell-Garnett formula, as shown in Figure 13. It is found that in the case of lower permittivity contrast, the effective permittivity values of the periodical models with rounded cubic inclusion and sphere inclusion coincide well with values predicted from Maxwell-Garnett formula. With the increase of permittivity contrast, both the two periodical models generate a larger effective permittivity over the Maxwell-

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Garnett rule. As shown in Figure 13(a), the obvious increase in effective permittivity of the periodical model with rounded cubic inclusion is observed when f  75%, at the permittivity contrast of 1  2  10 . For a much higher permittivity contrast of 1  2  30 , the obvious increase in effective permittivity is observed when f  65%. For the periodical model with sphere inclusion, Figure 13(b) indicates that the obvious increase in effective permittivity takes place when f  35% (respectively f  30%), at the permittivity contrast of (respectively 1  2  30 ). These results indicate that increasing the smoothness of the inclusion particles will results in the enhancement of the mutual interaction at a much lower volume fraction.

3. EQUIVALENT PARAMETER MODEL To investigate the frequency dependent characteristic of the effective permittivity of heterogeneous materials, an equivalent parameter model with random inclusion was developed by Kärkkäinen et al. [17]. Recently, based on the effective permittivity retrieval algorithm proposed by Simith et al. [18], we simulated the effective permittivity of the random heterogeneous materials using FE method [19].

3.1. Methodology

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The simulation model is shown as Figure 14. It is a two-dimensional TEM waveguide filled with a two phase composite. The permittivities of the matrix materials and the circular particle inclusions with radius of r  1 mm are supposed to be and i  16 , respectively. The length and width of the waveguide are 105mm and 35mm. Distances from the ports to the I composite, and j , are 35mm. and are propagation constants on port and j , respectively. In order to obtain the effective permittivity of the composites, S-parameter retrieval methods [18] have been used in our simulation. The simulation procedure consists of two steps.

Figure 14. Simulation model [19].

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Sii | Sii | exp( j(2i Ii  ii )),

(8)

S ji | S ji | exp( j ( i I i   j I j   ji )).

(9)

S  are calculated from electric fields on ports using the following equations: Sii 



(( Ec  Ei )  Ei* )dAi



( Ec  E*j )dAj

port i

S ji 



( Ei  Ei* )dAi ,

(10)

port i

port j



( E j  E *j )dAj ,

(11)

port j

where and are the electric field patterns of fundamental modes on ports and j , is the computed electric field on the port, including incident field and reflected field. Second, the effective permittivity (  eff ) is retrieved from the obtained S parameters:

 eff  n / z,

(12)

where is the refractive index, and z is the wave impedance of the composite. For inhomogeneous composite, n and can be found in terms of the scattering parameters as follows:

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n

z

1 1 cos 1[ (1  S11 S22  S212 )], kd 2S21 (T22  T11 )

(13)

(T22  T11 ) 2  4T12T21 2T21

,

(14)

where is the propagation constant in free space, is the thickness of the composite. The value of depends on Re( eff )  0 . parameters can be expressed in terms of parameters: T11  T21 

(1  S11 )(1  S22 )  S21S12 2S21

T12 

,

(1  S11 )(1  S22 )  S21S12 2S21

,

(1  S11 )(1  S22 )  S21 S12 (1  S11 )(1  S22 )  S21S12 T22  2S21 2S21 , .

To resolve phase ambiguities that result when the length of composite is greater than a wavelength in the effective medium, a modified version of Eq. (13) is available:

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n

1 1 {cos 1[ (1  S11 S22  S212 )]  2m }, kd 2S21

(12)

where is determined by following equation.

m  Re[

( S11  1) 2  S212 fi d ] , ( S11  1) 2  S212 c

(13)

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where is the excitation frequency, is the speed of light in free space.

Figure 15. Effective permittivity versus volume fraction for the composite with circular inclusions at the frequency of (a) 200 MHz and (b) 2 GHz [19].

3.2. Simulation Results For the equivalent parameter model with circular particle inclusions, effective permittivity as a function of volume fraction is simulated at the frequency of 200 MHz and 2 GHz, respectively. The simulation results are compared with the theoretical results of Eq.(3),

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as shown in Figure 15. It is seen that when the circular particles are arranged periodically, the effective permittivity of the composite is in good agreement with the Maxwell-Gamett rule (v=0). When the circular particles distribute randomly in the matrix materials, effective permittivity of the composite locates between the v=0 and v=1 bounds. At the frequency of 200 MHz and 2GHz, the simulation results can be fitted by Eq. (3) with v  0.25 and v  0.35 , respectively. In the simulation, 5 topological structures are calculated for each volume fraction. Comparing Figure 15(a) with 15(b), we can observe that deviation of the effective permittivity of the composite will be enlarged by increasing the frequency and the volume fraction of the inclusion. For the equivalent parameter model with square inclusions, simulation results are plotted in Figure 16. When the square inclusions are arranged periodically, the simulation results are in good agreement with the Maxwell-Garnett rule. When the inclusions are filled randomly in the matrix materials, the simulation results locate between v=0 and v=1 bounds. This is similar to the composite with circular inclusions. But comparing Figure 16 with Figure 15, we can observe that the permittivity of the composite is dependent on the shape of the inclusion. At the frequency of 200MHz and 2GHz, simulation results of the composite with square inclusions can be fitted by Eq.(3) with v  0.45 and v  0.55 , respectively. Besides, the standard deviations of the composite with square inclusions are much greater than that with circular inclusions especially at high frequency band. Figure 17 shows the effective permittivity of the simulation model as a function of frequency. It can be seen that effective permittivity of the composite with periodically arranged inclusions is independent on frequency, and the imaginary part equals to zero. But for the composite with randomly distributed inclusion phase, the real part of the effective permittivity increases with frequency. Interestingly, imaginary part of the effective permittivity does not equal to zero although the inclusion phase is lossless, as shown in Figure 17(b).

Figure 16. Effective permittivity versus volume fraction for the composite with square inclusions at the frequency of (a) 200 MHz and (b) 2 GHz [19].

4. RC NETWORK MODEL Although the simulation models illustrate in the above section can give a vivid picture of effective permittivity, they cannot predict universal dielectric response and the percolation

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threshold of heterogeneous materials. Universal dielectric response of heterogeneous materials was proved by Jonscher [20], and this work was published in Nature in 1977. More details can be found in [21]. After that, two dimensional RC network [22] was established for simulating the universal dielectric response. To investigate these characteristics of the heterogeneous materials, a three-dimensional RC network model [23, 24] which is much more consistent with the real structure of heterogeneous materials is developed by our Lab.

Figure 17. The effective permittivity of composite materials as a function of frequency: (a) the real part and (b) the imaginary part. Here, the volume fraction is 43% [19].

4.1. Model and Numerical Calculation The heterogeneous materials are modeled as a mixture of conducting phase and dielectric phase. The microstructure and the equivalent 3D RC network [23, 24] are shown in Figure 18. The black cubes represent the conductive phase, and light gray region represents the dielectric phase in Figure 18(a). The contacting two black cubes denote resistor, and the two black cubes connected by the light gray cube denotes capacitor. Figure 18(b) shows the equivalent circuit of the 3D RC networks for the heterogeneous materials, where light gray regions represent the two electrodes of the parallel plate capacitor.

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Figure 18. (a): Microstructure model of heterogeneous materials: the black cubes represent the embedded conductive phase; light gray cubes correspond to the dielectric phase. (b): Equivalent circuit of the 3D RC networks for the heterogeneous materials: the light gray regions correspond to the two electrodes of the parallel plate capacitor; all the resistors (R) and all the capacitors (C) were set to the single values 1 k  and 1 nF, respectively [24].

In order to study the dielectric response of the heterogeneous materials, we designate node 0 as a reference node. The voltage of node 1 relative to the reference node is defined as V1 , and is defined as the voltage of node with respect to the reference node. An ideal current source is applied across the two electrode plates. We now apply Kirchoff's current law (KCL) to node 0, 1, …, and node i . Beginning at node 0, we can write the following equations:

V1 R  jCV4  jCV7  jCV10  V13 R  V16 R  jCV19  V22 R  V25 R  i0  0

R  jCV4  jCV7  jCV10  V13 R  V16 R  jCV19  V22 R  V25 R  i0  0

and at node 1,

V1 R  (V2  V1 ) R  (V4  V1 ) R  jC (V10  V1 )  0 and finally, at node 28,

(V28  V3 ) R  jC (V28  V6 )  jC (V28  V9 )  (V28  V12 ) R  (V28  V15 ) R  jC (V28  V18 )  jC (V28  V21 )  jC (V28  V24 )  (V28  V27 ) R  i28  0 Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Rearranging, and define the impedance between nodes i and j as r(i, j) . Thus, the matrix equations of the 3D RC network model can be obtained:

AV  I

(14)

where V  [V1 ,V2 ,V3……,V28 ]T , I  [i1, i2 , i3 ,……, i28 ]T , i28  i0  1 , and

 c1,1 c1,2 c c2,2 2,1 A   c28,1 c28,2

c1,28   28 c2,28  1/ r (i, j ) i  j ci , j   j 1  1/ r (i, j ) i  j   c28,28 

Solving matrix eq. (14), the equivalent impedance, Z eq () , of the 3D RC network becomes:

Zeq    U ( ) i28  U ( ) i0

(15)

and the relative complex permittivity of the network is then obtained from the follow relation28:

 r ()   r ()  j r()  1 jZeq ()

(16)

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Where  r ( ) and  r( ) are the real part and the imaginary part of the normalized dielectric constants, respectively. When the number of components in one direction of the Cartesian Coordinate System equals to zero, the three dimensional RC network can be easily reduced to two dimensional case.

4.2. Simulation Results Dielectric response of the 3D RC network is simulated and compared with that of the 2D RC network model. Here, we assume that both the two models contain 1568, 2048 and 2592 components distributed randomly in the ratios of 5% R－95% C , 10% R－90% C and 15% R－85% C. The effective permittivity as a function of frequency is shown in Figure 19. It is seen that for both the 3D and 2D RC network models, the relation between frequency and can be divided into three regions. At low frequencies (106 Hz) bands, a frequency independent  r is observed. In the middle region,  r decreases with frequency. Interestingly, there is subtle difference between dielectric response of 2D RC networks and 3D RC networks. In Figure 19, it is observed the simulation results for 3D RC network model is a little discrete when the ratio of R is 5%. This is because for the same network size, the 3D RC networks in the ratio of 5%R and 95%C perform a much weaker

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randomicity than that of 2D RC network. This separation will be eliminated by increasing the size of the 3D RC networks.

Figure 19. Normalized relative dielectric constants of the RC network models for heterogeneous materials. (a): The relation between log  r and frequency. (b): The relation between log  r and frequency [24].

To study the percolation phenomena of the RC networks, the 3D network responses (2048 components, 15% R－85% C, 17% R－83% C,…, and 32% R－68% C) of randomly positioned resistors and capacitors were computed using eq. (16) and compared with the 2D networks responses (2048 components, 40% R－60% C, 42% R－58% C,…, and 61% R－39% C ). The relations between log  r and frequency are shown in Figure 20(a) and (b) for 3D and 2D RC networks, respectively. In order to understand the percolation phenomena of RC networks shown in Figure 20, the relationship between the permittivity and the ratio of R for four particular frequencies is shown in Figure 21. It can be seen from Figure 21 that the percolation threshold for 3D and 2D RC networks with 2048 components is (25  1)% and

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(50  1)%, respectively. The results are in good agreement with the literature results[22], and the percolation threshold of 3D network is the same as that computed by the CP formula.

Figure 20. The relation between

log  r and frequency. (a): 3D network (b): 2D network[24].

5. DIELECTRIC LOSS OF MATERIALS UNDER MICROWAVE IRRADIATION Dielectric loss is a key parameter which determines the microwave absorbing properties of heterogeneous granular materials under microwave irradiation. For polar molecules, the frequency dependence of the dielectric loss is based on the Debye relaxation mechanism for which the time domain response is given by

F (t )  exp(t /  ) where  and t is relaxation time and observation time, respectively.

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However, the dielectric loss does not obey equation (17) except in some liquid dielectrics and departs seriously from it in most solids. It is shown that some relaxation processes, particularly, chemical reaction kinetics, would follow the time domain response law:

Figure 21. The relation between

log  r and the ratio of R for four particular frequencies. (a): 3D

network (b): 2D network [24].

t F (t )  exp[( ) ]



(18)

While  equals 0.5, F (t ) is called slow relaxation, the slow response or non-Debye relaxation for which the relaxation mechanism is governed by the bound charges. Equation (18) was obtained in the absence of microwave irradiation. To understand the dielectric loss for non-Debye dielectric relaxation under microwave irradiation, a new equation is developed [25]. From Maxwell’s differential equations, ohm’s loss in dielectric medium of nonmagnetic materials is given by

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v

  E  Jdv 

v

   D E  (  H  )dv t

      D   [ H  (  E )    ( E  H )  E  ]dv v t Taking the time derivatives of and H  B , we have

 D E ( E  D)  E   B t t t  B H . ( H  B)  H   B t t t Then, we obtain

s

  ( E  H )ds 

 [

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v

   B  D    v [ H  t  E  t  E  J ]dv

1 1 ( E  D)  ( H  B)   E  Jdv v 2 t 2 t

The term on the left-hand side of this equation represents the power flowing on closed surface s. The first term on the right-hand side represents the electric energy and magnetic energy stored within the volume v . The second term on the right-hand side represents the power dissipated within the volume v . The third term on the right-hand side represents electric losses of material within the volume v . The fourth term on the right-hand side represents the magnetic losses of material within the volume v . Therefore, for electric dielectric material, the dielectric loss per unit volume is

   E 1  D Pd  ( E   D  ) 2 t t

(19)

Where E is electric field intensity vector. H is magnetic field intensity vector, D is electric flux density vector, B is magnetic flux density vector, J is volume current density vector, and volume v is bounded by surface s . If Debye dielectric relaxation mechanism is followed, and governed by the equation (17) and the process occurring under an electric field with would still follow the linear superposition principle, then

 t  t' [ exp( )]dt' t    '( ) E cos t  j "( )sin t ,

D(t )   h E (t )   l 

t



E (t ' ) 

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1  E cos t [ '( ) E cos t  j "( ) E sin t ] 2 t 1 Pd   "E 2 2 Pd 

(20)

where is the dielectric loss per unit volume based on Debye relaxation, is the high frequency permittivity of the materials, is the low frequency permittivity or static permittivity of the materials,  '( ) is the real part of the dielectric permittivity of the materials and

 '   h   l /1   2 2 , is the imaginary part of the dielectric permittivity of the materials and  "   l /(1   2 2 ) , the electric field E (t ) is switched on at and

 is the angular

frequency of microwave. If non-Debye dielectric relaxation mechanism is followed and governed by the Equation (18), the other conditions are the same with 2.2, then

 { exp[ (t  t ')  ]}dt ' t t  t '  12 cos(t ')( ) exp[ (t  t )  ]dt '

D(t )   h E (t )   l 

  h E (t ) 

l E t 2  

t



E (t ')



  t ' E cos(t )   "t E sin(t )

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Pt 

1 2 E2  2  t    E  t   cos(t )sin(t ) t   cos (t ) 2 2  t t 

 where  t   h  l 2   t  l 2



 0

t   t  t 

 

 0



(21)

1

 t   2   exp( t   )cos(t )dt   

1

 t   2   exp( t   )sin(t )dt   

Pt is the dielectric loss per unit volume based on the non-Debye relaxation. This equation developed by our Lab is named as HPJ equation [16]. From Eq. (20), we can observe that is directly proportional to frequency. For dipole molecular, the large the frequency is, the faster the rotation of the molecular will be, and then much more microwave power will be absorbed. However, for non-Debye materials, dielectric loss Pt given by Eq. (21) is a function of five variables, i.e., ,  "t , E ,  , and  . The first term of Eq. (21) indicates that if microwave frequency and relaxation time 1/  are in the same order of magnitude, the heating efficiency of microwave is irrelevant to frequency. This has been confirmed by many experiments. For example, we cannot say that microwave with frequency of 2450MHz has a higher heating efficiency that that of 915MHz. This is due to the factor that relaxation time is an inherent characteristic of materials, and it varies with temperature. Therefore, Eq.(21) is suitable for characterize the dynamic process of microwave

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heating. The second term of Eq. (21) indicates that the heating rate of microwave is directly proportional to the derivative of and  "t . As a consequence, high energy absorption will appear at the boundary between metal particles and dielectric. For instance, ball lightning plasmas is observed in activated carbon under microwave heating. Figure 22 shows the phenomena of ball lightning plasmas and plasma arcs after 1 min of microwave irradiation. The average temperature measured by thermocouple is 400-700 oC. With Eq. (21), local field enhancement effect in heterogeneous granular materials under microwave irradiation can be successfully explained. In what follows, numerical simulations are performed for further study the local field enhancement effect inherent in heterogeneous granular materials.

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Figure 22. Ball lightening plasmas and plasma arcs observed in activated carbon after 1min of microwave irradiation [26].

LOCAL FIELD ENHANCEMENT EFFECT To further confirm the local field enhancement effect predicted by Eq. (21), the electric field distributions in both the qusi-static model and the equivalent parameter model are simulated. Figure 23(a) shows the electric field distribution in a 2D qusi-static model with circular inclusions arranged into 10x10 arrays. In the simulation, the distance between two circles is 100 m , the surface fraction of the inclusion is 74.7%, the permittivity of the matrix and the inclusion is fix at 1  1 and  2  3  25 j . In Figure 23(a), the local electric field distribution is observed with enhancement into the small part between the circular inclusions. Maximum electric field intensity of the composite medium is 940.8v/m, which is about 18.8 times that of the medium without filling circular inclusion. Meanwhile, when subject to a constant applied electric field, the maximum absorbing power of the composite medium can be increased by 353 times. For fixed surface fraction (74.7%) of the inclusions, the influence of the imaginary part of the inclusion on the maximum electric field and dielectric loss of the composite medium was simulated as shown in Figure 23(b). It is observed that the imaginary

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part of the effective permittivity achieves the maximum value the point of  2  12 . Interestingly, the maximum electric field in the medium increases with  2 , and reaches a saturation state at the same inflection point. The maximum electric field of 1033.27v/m is achieved when the  2  50 , which is 20.7 times that of the medium without filling circular

1200

0.06

1000

0.05 0.04

Emax

800

0.03

"e

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inclusion. Obviously, the microwave absorbing power of the medium is increased by 426.9 times. As a consequence, the inner heat source can be enhanced by increasing the dielectric loss of the composite medium. Figure 24 shows electric field distribution in the heterogeneous materials obtained by using the equivalent parameter model. In the simulation, permittivity of the permittivity of the matrix and the inclusion phase is supposed to be  e  1 and i  16 . In Figure 24(a), the circular particles are distributed periodically in the matrix materials. It is seen that the electric file distribution is in good agreement with qusi-static model. In Figure 24(b), the inclusion particles are distributed randomly in the matrix material, and the volume fraction is 13%. Local field enhancement phenomenon can also be observed. The peak electric field is located between two particles. In Figure 24(b), volume fraction of the inclusion phase is increased up to 43%, and much more hot spot can be observed compared with Figure 24(a).

600

0.02 400

Emax

0.01

"e

200

0.00 0

10

20

 "2

30

40

50

Figure 23. (a) Local electric field distribution in the qusi-static model. (b) Imaginary part of the effective permittivity and maximum electric field of the composite materials versus imaginary part of the inclusion [14].

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We have also investigated the electric field distribution in the heterogeneous granular materials in a multimode cavity. The simulation model is given in Figure 25(a). The heterogeneous granular materials formed into pellet is located at the center of the cavity on a stock of a microwave oven with thickness of 10mm. Geometry size of the cavity is axbxc=265mmx275mmx190mm. The microwave oven is excited by a rectangular waveguide with dxexf=78mmx18mmx55mm, operating at TE10 mode. Frequency of the excitation source is 2450MHz. Since the whole structure is symmetric about the x-axis, only half the cavity, half the sample substance and half the waveguide are modeled using the commercial software Ansys. We supposed that the heterogeneous granular material is a mixture of Fe2O3 and the reductant C, which is formed into pellet with radius r. Permittivity and permeability of Fe2O3 [27] is 1  10  0.1 j ， 1  2  0.6 j . Permittivity of C is 2  145  80 j [28]. In the

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simulation, material parameters of Fe2O3 and C are assigned randomly to each meshgrid by generating a series of uniformly distributed pseudorandom numbers with “1” denotes the inclusion phase (C) and “0” denotes the inclusion phase (Fe2O3). Simulation model of the sample substance is shown in Figure 25(b).

Figure 24. Electric field distribution in the heterogeneous materials simulated by using the equivalent parameter model. (a) Periodic distribution (13% volume fraction ); (b) Random distribution (13% volume fraction ); (c) Random distribution (43% volume fraction ).

Figure 25. (a) Simulation model of the microwave oven; (b) FEM elements in the sample. White region denotes C. Dark gray region denotes Fe2O3[5]. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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With the increase of the volume fraction of inclusion phase (C), the electric field distribution in the pellet is simulated as shown in Figure 26. In Figure 26, local field enhancement phenomenon in the mixture of Fe2O3 and C can be clearly observed. Moreover, we can see that with the increase of reductant C, the distribution of electric field moves towards the surface of the pellet. According to the effective medium theory, this is due to the factor that increasing the volume fraction of C increases the dielectric loss tangent of the mixture, which will lead to lower penetration depth. As a consequence, the volume fraction of C possesses an optimum value, at which a uniform distribution of electric field can be obtained. Comparing Figure 26(b) with Figure 26(a), (c) and (d), we can observe that for the mixture of Fe2O3 and the reductant C, a uniform electric field distribution can be achieved when the volume fraction of C is about 20%. Local electric field enhancement will result in a rapid rise of local temperature. According to Arrhenius law, i.e., k  A0 exp(W / RT ) , local

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reaction rate k increases with local temperature T , and consequently, localized superheating induced by microwave irradiation leads to localized reaction rate enhancements. Therefore, compared with conventional heating, chemical reactions under microwave irradiation can take place at a low average temperature.

Figure 26. Electric field distribution in the sample. (a)C=10%. (b)C=20%. (c)C=30%. (d)C=40% [5].

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7. APPLICATION OF MICROWAVE HEATING IN METALLURGY ENGINEERING

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In the past three decades, our group has been devoted to the study of the application of microwave heating in metallurgy engineering. These include microwave plasma processing of materials, microwave-assisted process for preparation of titania-rich materials, preparation of direct reduction iron by microwave heating and the preparation of activated carbon with large surface area, etc. Two examples are given as follows. In the field of metallurgy engineering the advantages of microwave heating are not only reflected in the grinding process for improving the grindability of mineral, but also in the reduction and leaching process for reducing the reaction time. We have investigated the influence of microwave heating on the grinding of Panzhihua ilmenite ore [29]. In the experiment, 40g sample was heated by microwave with power of 1kW for 30s and followed by water quenching. SEM photograph shown in Figure 27 indicates that intergranular fractures occur between ores and gangues after microwave treatment, which would liberate minerals from each other effectively. The subsequently magnetic separation trials show that the recovery rate increased from 44% for raw ore to 72% after microwave treatment.

Figure 27. l SEM photograph of the ilmenite ore treated by microwave heating [29].

The microwave-assisted process for preparation of titania-rich materials can be divided into four steps: carbon-bearing pellets preparation, microwave reduction, beneficiation and then microwave-assisted hydrochloric acid leaching. A comparison between microwaveassisted reduction and conventional reduction in small scale experiment is show in Table I [30]. It is evident that microwave-assisted reduction is much more efficient than the conventional one. For instance, the chemical rate enhancement factor (Q) is 79.06 at the temperature of 1153K. Moreover, the microwave-assisted reduction could be carried out at a much lower temperature than traditional heating.

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Table 1. Chemical Rate Enhancement Q at Different Temperatures [30] T(K) 1153 1173 1223 1273 1323 1373 1422

kc 1.50x10-4 2.30x10-4 5.10x10-4 1.34x10-3 3.05x10-3 5.94x10-3 1.18x10-2

km 1.18x10-2 1.18x10-2 1.18x10-2 1.18x10-2 1.18x10-2 1.18x10-2 1.18x10-2

Q= km / kc 79.06 51.61 23.27 8.86 3.89 2.00 1.00

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For microwave-assisted carbothermic reduction of ilmenite, under the optimum experimental conditions [31-34] of coke-14%, adhesive-5%, agglomerant-3%, carbon-bearing pellets-20kg, microwave power-19.2kw, reduction temperature-1150 oC, and reduction time150 min, the content of TiO2 in the carbon-bearing pellets was 53.92%. We found that the grade of the titanium-rich residue can be upgraded to 72.01% TiO2 when subject to a union process of ore milling separation. The XRD pattern of the titanium-rich residue is given in Figure 28, which shows that the major phases are two forms of titanium oxide, rutile and anatase. At the same time, a Ti2O5 phase is found together with Fe, Mg and Ca. Microwaveassisted acid leaching was conducted under the conditions of titanium-rich residue: 80g, leaching time: 20 min, particle size: 48-74μm, HCl concentration: 10%, solid-liquid ratio: 1:12. After solid/liquid separation, calcination, grain agglomeration processes, the titania-rich materials was obtained, of which the XRD pattern was shown in Figure 29. It indicates that rutile and anatase titanium dioxide is the major phases of the titania-rich materials. Silicate is observed as a minor phase.

Figure 28. The XRD pattern of the titanium-rich residue. 1-TiO2 (Rutile), 2- TiO2 (Anatase), 3-MgTi2O5, 4-CaTi2O5, 5-FeTi2O5[32].

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Figure 29. XRD results of the titanium-rich material. 1-TiO2 (Rutile), 2- TiO2 (Anatase), 3-Ca2(Mg0.7, Fe0.5) 1.7SiO7[32].

Microwave-assisted acid leaching was compared with that under traditional heating, as shown in TABLE II. It indicates that the maximum leaching ratio of residual iron by conventional heating was 52.4%, while Ca and Mg nearly could not be leached out. The maximum leaching ratios of residual iron, Mg and Ca by microwave heating were 95.8%, 89.12% and 52.2%, respectively. The leaching ratios of Fe and Mg by microwave heating are 1.82 and 57.8 times that by conventional heating. It is apparent that the leaching ratios of Fe, Ca and Mg are enhanced greatly. This is due tot the factor that solid particles crack under microwave irradiation and make the leaching sufficiently to remove Ca and Mg. Chemical analysis shows that the titania-rich materials contain 92.73% TiO2, 0.13% MnO, 0.8% total Fe, as well as 0.207% the sum of CaO and MgO. The titania-rich materials prepared under microwave heating can be used as feed stock in chlorination process to produce TiCl4, which is the most important intermediate material for producing titanium white and titanium sponge. Table 2. Comparison between Traditional Leaching and Microwave-assisted Leaching [33]

HCl (%) Temp.(oC) Solid-liquid ratio Time (min) grain size (μm) Leaching rate of Fe (%) Leaching rate of Ca (%) Leaching rate of Mg (%) Apparent activation energy kJ/mol)

Traditional leaching

Microwave-assisted leaching

15 96 1:30 200 63~75 52.4 55.40

10 160 1:12 120 48~74 95.43 52.17 88.98 44.38

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CONCLUSION In this chapter, microwave heating mechanism of heterogeneous granular materials is investigated, and examples of microwave metallurgy engineering are given. Main conclusions are shown as follows. a) The interaction between microwave and materials cannot be simply explained by Debye theory. For materials with non-Debye relaxation, the new equation derived in our previous work is suitable for characterizing their relaxation properties under microwave irradiation. b) Effective media theory is a power full tool for characterizing electromagnetic properties of heterogeneous granular materials. However, this theory does not involve the inner characteristics of heterogeneous granular materials under microwave irradiation. c) Local field enhancement effect reveals the inner properties of heterogeneous granular material. Based on this effect, we successfully explained why chemical reaction in microwave metallurgy process take place at a much lower average temperature compared with conventional heating.

ACKNOWLEDGMENTS

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This work was supported by the National Natural Science Foundation of China (Grant No. 61161007) Scientific Research Fund Major Project of the Education Bureau of Yunnan Province (Grant No. ZD2011003), and the Natural Science Foundation of Yunnan Province (Grant No. 2011FB018).

REFERENCES [1] [2] [3]

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Grant E H. Microwave: Industrial，Scientific，and Medical Applications. BostonArtech House Inc, 1992. J. Feng, M. Huang, X. H. Li, Coupled surface plasma generator, CN88208620.0, 1988. M. Huang, Research on the mechanism and application of the interaction between microwave and granular materials, Ph.D. thesis, Kunming University of Science and Technology 2006. J. H. Peng, The interaction kinetics of metalurgy materials under microwave irradiation, Ph.D. thesis, Kunming University of Science and Technology 1991. J. J. Yang, Fundamental research and simulaiton on the electromagnetic properties of heterogeneous materials, Ph.D. thesis, Kunming University of Science and Technology 2010. J.H. Peng, L. B. Zhang, S. H. Guo, Y. X. Hua, M. Huang, S. P. Liu, Noval microwave metallurgy applicator and its key technology. Second Prize of 2010 Annual National Award for Technological Invention.

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[8] [9]

Jingjing Yang, Ming Huang and Jinhui Peng R. A. Shelby, D. R. Smith, S. Schultz, Experimental verification of a negative index of refraction, Science, 2001, 292 (5514), 77-79. N. I. Zheludev, The road ahead for metamaterials, Science, 2010, 328(5978): 582–583. M. Huang, J. J. Yang, Microwave Sensor Using Metamaterials in: Wave Propagation, A. Petrin (Ed.), In Tech Inc. Austria, 2011, Ch. 2 pp.13-36.

[10] J. J. Yang, M. Huang , Z. Y. Wu, J. H. Peng, Microwave absorbing properties and electric field distribution of conductor-dielectric compound, The Proceedings of ISAPE 2008, Kunming, Yunnan, China, 2008, 673-676. [11] A. H. Sihvola and J. A. Kong, Effective permittivity of dielectric mixtures, IEEE Trans. Geosci. Remote Sensing, 1988, 26(4): 420- 429. [12] A. Sihvola, Self-consistency aspects of dielectric mixing theories, IEEE Trans. Geosci. Remote Sensing, 1989, 27(4): 403–415. [13] R. J. Elliott, J. A. Krumhansl, and P. L. Leath, The theory and properties of randomly disordered crystals and related physical systems, Rev. Mod. Phys., 1974, 46(3), 465– 543. [14] J. H. Peng, J.J. Yang, M. Huang, J. Sun, Z. Y. Wu, Simulation and analysis of the effective permittivity for two-phase composite medium, Front. Mater. Sci. China, 2009, 3(1): 38-43. [15] Y. H. Cheng, X. L. Chen, K Wu, S. N. Wu, Y. Chen and Y. M. Meng, Modelling and simulation for effective permittivity of two-phase disordered composites, J. Appl. Phys., 2008, 103(3): 034111. [16] J.J. Yang, M. Huang, C. F. Yang, J. H. Peng, J. H. Shi, Electromagnetic properties of heterogeneous materials and the local electric field enhancement effects, Materials Review, 2009，23(12): 1-4. [17] K. K. Kärkkäinen, A. H. Sihvola, and K. I. Nikoskinen, Effective permittivity of mixtures: numerical validation by the FDTD method. IEEE Trans. On Geoscience and Remote Sensing, 2000, 38 (3): 1303-1308. [18] D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Electromagnetic parameter retrieval from inhomogeneous metamaterials, Physical Review E, 2005, 71(3): 36617. [19] J. Sun, M. Huang, J. H. Peng, W. W. Niu, Libo Zhang, The Simulation of the Frequency-Dependent Effective Permittivity for Composite Materials, ISAPE 2010, Guangzhou, China, Nov. 29-Dec. 2, 2010, p.701-704. [20] A. K. Jonscher, The 'universal' dielectric response, Nature, 1977, 267: 673 – 679. [21] A. K. Jonscher, Dielectric relaxation in solids, J. Phys. D: Appl. Phys., 1999, 32(14): R57. [22] D. P. Almond, C. R. Bowen and D. A. S. Rees, Composite dielectrics and conductors: simulation, characterization and design, J. Phys. D: Phys., 2006, 39(7): 1295. [23] Z. Xiao, M. Huang, J. H. Peng, Y. F. Wu, Modelling the universal dielectric response in heterogeneous materials using 3-D RC networks, Acta Physica Sinica, 2008，57(2): 957-961. [24] M. Huang, J. J. Yang, Z. Xiao, J. Sun, J. H. Peng, Modelling the dielectric response in heterogeneous materials using 3D RC networks, Mod. Phys. Lett. B, 2009, 23(25): 3023–3033. [25] M. Huang, J. H. Peng, J. J. Yang, J. Q. Wang, A new equation for the description of the dielectric losses under microwave irradiation. J. Phys. D: Appl. Phys, 2006, 39(10): 2255-2258.

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[26] J.A. Menéndez, E.J. Juárez-Pérez, E. Ruisánchez, J.M. Bermúdez, A. Arenilla, Ball lightning plasma and plasma arc formation during the microwave heating of carbons, Carbon,2011, 49(1): 346–349. [27] V. D. Buchelnikov, D. V. Louzguine-Luzgin, A. P. Anzulevich, et al. Modeling of microwave heating of metallic powders, Physica B, 2008, 403(21-22): 4053-4058. [28] X. D. Chen, G. Q.Wang, Y.P. Duan, S. H. Liu, B. Wen, Carbon black coated with barium titanate via sol-gel and its electromagnetic characters, Journal of functional materials, 2006, 9(37): 1404-1407. [29] S. H. Guo, G. Chen, J. H. Peng, J. Chen, D. B. Li, L. J. Liu, Microwave assisted grinding of ilmenite ore, Trans. Nonferrous Met. Soc. China, 2011, 21(9): 2122-2126. [30] Y.X. Hua, C.P. Liu, Microwave-assisted carbothermic reduction of ilmenite, Acta Metallurgica Sinica, 1996, 9(3): 164-170. [31] M. Y. Huang, J. H. Peng, M. Huang, S. M. Zhang, Y. Li, Y. Lei., Research on microwave-absorbing characteristic of mixtures about different proportions of carbonaceous reducer and ilmenite in microwave field,The Chinese Journal of Nonferrous Metals, 2007, 17(3): 467-480. [32] M.Y. Huang, The process and mechanism for preparation of the titanium-rich material using ilmenite concentrate with high CaO and MgO content, Ph.D. thesis, Kunming University of Science and Technology 2008. [33] J.H. Peng, J. J. Yang, M. Huang, M. Y. Huang, Microwave-assisted reduction and leaching process of ilmenite, The Proceedings of ISAPE2008, Kunming, Yunnan, China, 2008, 1781-1784. [34] S.H. Guo, W. Li, J. H. Peng, M.Y. Huang, L. B. Zhang, S. M. Zhang, M. Huang, Microwave-absorbing characteristics of mixtures of different carbonaceous reducingagents and oxidized ilmenite, Int. J. Miner. Process., 2009, 93(3-4): 289-293.

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 © 2013 Nova Science Publishers, Inc.

Chapter 6

EXTREMELY LOW FREQUENCY ELECTROMAGNETIC FIELD AND CYTOKINES PRODUCTION M. Reale and P. Amerio1 Dept of Experimental and Clinical Sciences, Dept of Aging Medicine and Science (DMSI), Dermatologic Clinic, University "G.d'Annunzio" Chieti-Pescara, Chieti, Italy

1

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ABSTRACT Cytokines are proteins that interact with cells of the immune system in order to regulate the body's response to disease, infection, inflammation, and trauma. Once induced, cytokines help determine how the immune system should respond and to what degree, and their overproduction or inappropriate production can affect the immune response. Some cytokines act to make disease worse (proinflammatory), whereas others serve to reduce inflammation and promote healing (anti-inflammatory). The effects of Extremely Low Frequency (ELF) 50/60 Hz EMF, produced by many sources, e.g., transmission lines and all devices containing current-carrying wires, including equipment and appliances in industries and in homes, on human health remain unclear. There are many reports that ELF-EMF may modulate the immune response affecting human health. Studies of the possible health effects of EMF has been particularly complex and did not provide straightforward answers. Although the mechanism of this interaction is still obscure it has been shown that ELF-EMF can cause changes in cell proliferation, cell differentiation, cell cycle, apoptosis, DNA replication and expression. The effects of EMF may be useful and harmful depending on the intensity and frequency of the field, the period of exposure and the organism itself. A complete understanding of electromagnetic field effects on organisms helps in curing numerous illnesses as well as protecting from dangerous effects of electromagnetic fields. This review summarizes the effect of EMF exposure on cytokines production, although further studies are required to shed light on the mechanism by EMF regulate immune response influencing cytokines production.

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INTRODUCTION As consequence of technological developments and urbanization in the second half of the 20th century, the magnetic fields generated by electrical equipment are many times higher than those occurring naturally. The frequencies of the elettromagnetic fields (EMF) normally encountered by the population are 50 Hz (in Europe and much of the world) or 60 Hz (in the United States). Background of 50 Hz magnetic fields generated by electrical wires and domestic apparels in typical homes vary between 0.01 and 1 mT, with appliances generating fields of 0.1–100 mT [1, 2]. One may differentiate between occupational and residential sources, and evidences are showed that these artificial EMF may contribute to a new form of pollution. The EMF emitted by domestic appliances are generally undetectable at a distance of 1 m, in fact EMF are directly proportional to the current flowing in the wire and are very weakly attenuated by the objects they encounter, although they decrease rapidly in magnitude with distance from the source. The international agency for the research on cancer (IARC) has classified EMF as a potential cancinogen in 2001, based on pooled analysis of epidemiological studies that have demonstrated a small but consistent correlation between increasing time spent near electromagnetic generating sources and certain forms of cancer. Childhood leukemia and hormone dependent cancers such as breast and prostate cancers appear to be among the most frequently EMF associate cancers [3-6]. More recently the World Health organization has claimed that research studies did not support this evidence, however aknowledged IARC classification. Some concerns remain for people exposed to EMF and thus is imperative to understand the mechanism of EMF-tissue interaction. As the immune system is involved in the control of cancer development and other diseases, many studies have focused on whether or not exposure to EMF may affect immunological functions promoting cancer or disease development. Several studies have examined various immune cell parameters but with conflicting findings. To further complicate the matter it seems that different EMF may have different actions on different cells. These studies have been conducted in vivo and in vitro on different types of cell and have verified possible potentiation of cancer cell growth [7]. On the other hand some experimental evidence have found that EMF exposure may be beneficial such as in prostate cancer inducing cell lines apoptosis [8]. Many other are the biological effects of EMF, researchers have shown that there are frequencies that applied in controlled ways have beneficial actions to the body. Thus, pulsed electromagnetic fields in low frequency and intensity range (Gauss or micro-Tesla) increase oxygenation to the blood, improve circulation and cell metabolism, improve function, pain and fatigue from fibromyalgia [9], help patients with treatment-resistant depression [10], and may reduce symptoms from multiple sclerosis [11]. EMFs has been commonly used in the field of orthopedics for the treatment of non-union fractures and failed fusions, taking advange of the evidence that pulsed EMF accelerates the re-establishment of normal potentials in damaged cells [12] increasing the rate of healing, reducing swelling and improving the osteogenic phase of the healing process [13]. Moreover they promote the proliferation and differentiation of osteoblasts [14]. Long-lasting relief of pelvic pain of gynaecological origin has been obtained consistently by short exposures of affected areas to the application of a magnetic induction device producing short, sharp, magnetic-field pulses of a minimal amplitude [15] and researchers have shown that EMF improved cell survival

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after ischemic shock, and 90% reduced ischemic damage and subsequent disability [16, 17]. Electrophysiological abnormality and cognitive dysfunction associated with Alzheimer's disease appear reduced with frequency specific pulsed electromagnetic fields [18]. Due to these effects in the body, EMF have been used extensively in many other conditions and medical disciplines.

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ELECTROMAGNETIC FIELD, HOW DOES IT WORK? The mechanisms by which EMFs interact with living tissues are currently unclear. This depending upon by variability in the intensity of EMFs and in the different exposure durations. It is generally accepted that 50/60 Hz EMF do not transfer energy to cells in sufficient amounts to directly damage DNA leading to genotoxic effects. However DNA may function as a Fractal antenna which confers to it a high reactivity to EMF [19]. Previous studies have showed that low-frequency EMFs can act at the cellular level and have suggest that the membrane may be the primary site of interaction with consequently changes in the intracellular Ca2+ concentration [20-23]. The potentials between the inner and outer membrane of the living cell within the body, are of about 70 mV. When cells are damaged, these potentials change causing the attraction of fluids into the interstitial area and swelling or oedema. The application of pulsed magnetic fields may help the tissues to restore normal potentials at an accelerated rate, thus aiding the healing of most wounds and reducing swelling faster. The most effective frequencies found by researchers so far, are very low frequency pulses of a 50 Hz. These, if gradually increased to 25 pulses per second for time periods of 600 seconds (10 minutes), condition the damaged tissue to aid the natural healing process. This EMF conditioning works though several mechanism including: cellular proliferation and differentiation [24-28], DNA synthesis [29, 30], RNA transcription [31], protein expression [32], protein phosphorylation [33], ATP synthesis [34], cell damage and apoptosis [35-37], micro-vesicle motility [38], inhibition of adherence [39], metabolic activity [40], hormone production [41], antioxidant enzyme activity [42], redox-mediated rises in NFkB [43, 44], tromboxane release [45], CD markers and cytokines expression [46-48]

CYTOKINES All cytokines are secreted or membrane-bound small proteins with low molecular weight, that regulate the growth, differentiation and activation of immune cells and may act as regulators of responses to infection, inflammation, and trauma. Their most important functions seem to be local effects, modulating the behavior of adjacent cells (paracrine) or the cell that secretes them (autocrine), but in some cases there are significant effects on distant organs or tissues (endocrine). Despite the fact that most cytokines have been described and initially named on the basis of a single biological function, many are multifunctional molecules and their activities include regulating cell activation, hematopoiesis, apoptosis, cell migration, and cell proliferation. The effect of an inflammatory response is dictated by the balance between pro- and anti-inflammatory mediators. Pro-inflammatory cytokines such as interleukin-1beta (IL-1β), interleukin 6 (IL-6), and Tumor Necrosis Factor α (TNF-α) are

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responsible for early responses and amplify inflammatory reactions, whereas antiinflammatory cytokines, which include interleukin-4 (IL-4), interleukin-10 (IL-10), and interleukin-13 (IL-13), have the opposite effect in that they limit the inflammatory responses. Any cellular alterationn by biological, phisical or chemical agent. provokes changes in local cytokine expression and release. In these settings, cytokines function to stimulate a host response. The increasing complexity of pro- and anti-inflammatory cytokine/chemokine networks has made it crucial to examine them simultaneously and to consider the loss of their balance as a pathogenetic mechanism in diseases. This is aimed at controlling the cellular stress and minimizing cellular damage. The cytokine "controlled" microenvironment in the tissue may also impact several stages of cancer formation and progression. As the mixture of cytokines that is present in the tumour microenvironment shapes host immunity, therapeutic manipulation of the cytokine environment constitutes one strategy to stimulate protective responses. Many studies have investigated the EMF effect on release of growth factors and cytokines [49-51]. Overall, this contribution provide insight into current areas of debate in the interface between EMF and health and EMF effect on cytokines related to health or disease, such as on present intriguing prospects for future therapeutic developments in a variety of disease areas.

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MAGNETIC FIELD EXPOSURE AFFECTS CYTOKINES PRODUCTION WHICH DEPENDS UPON CELL TYPE The variability of the data on EMF-tissue interaction is great. This effect is mainly due to the fact that experimental setup and exposure conditions differed strongly from study to another even if many studies used a 50 Hz signal. The differences in the findings between these studies can partially be explained by use of T signals compared to the milliTesla (mT) ranges. 5 T was chose because common daily exposure to EMF will mainly be experienced in comparable field strengths, ranging from 0.07 T for average residential power-frequency magnetic fields in homes in Europe, to about 20 T under power lines [52]. Studies were designed to look for possible effects of acute exposure to 50-Hz magnetic fields (10 μT) on the IL-1β, interleukin 2 (IL-2), IL-6, interleukin-1 receptor antagonist (IL-1RA), and the interleukin-2 receptor (IL-2R) production. The effect of continuous and intermittent (1 h “off” and 1 h “on” with the field switched “on” and “off” every 15 s) exposure to magnetic fields was evaluated in blood samples of young men (20–30 years old). Results showed that exposure to 50-Hz magnetic fields (10 μT) significantly increases IL-6 when subjects were exposed to an intermittent magnetic field. However, no effect has been observed on interleukin IL-1β, IL-2, IL-1RA, and IL-2R [53]. The 7.5 Hz repetitive single pulse waveforms with pulse duration of 300�sec added to osteoblast culture can significantly increased cell count. The transforming growth factor-1 (TGF-1) concentrations in culture medium after 2-day, 3-day and 4-day were significantly affected by different intensities of EMF stimulation. These results support findings in the literature suggesting that EMF treatment may have a stimulatory effect on the osteoblast growth [54]. Correct frequency and waveform are important [55], but the intensity of the exposure should also be considered. Li et al. [56] reported that increase of TNF- and IL-1

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Extremely Low Frequency Electromagnetic Field and Cytokines Production

243

in osteoclast-like cells is related to the intensity of the electrical field. However, in osteoblasts coltures, EMF irradiation induced an increase of TGF-1 release, which was not related to the intensity of the magnetic field. Results from Gomez-Ochoa et al. [57] indicate that the application of EMF to the culture of fibroblast-like cells derived from mononuclear peripheral blood cells does not inhibit the production of inflammatory cytokines (IL-6 and IL-8), while drastically reduce the production of cytokines, IL-1 and TNF-, of macrophagic origin. These data reveal the inhibition of the production of inflammatory type of cytokines by activated macrophages, an action that is followed by the increase of IL-10 on day 21, probably because of the effect of EMF on a residual population of CD4+ lymphocytes. Using a magnetic field generated by a pair of circular coils powered by the generator system, which produced the input voltage of pulse, Ongaro et al. [58] were able to demonstrate that EMFs significantly modulate the release of both inflammatory and antiinflammatory cytokines in human osteoarthritic synovial fibroblasts (OASFs), with decreased IL-6 production in the presence of IL-1, suggesting that cytokine production may be one of the most important mechanism altered by EMFs in these cells. Interestingly, when EMFs and an adenosine agonist (Ars) were used in combination these inhibitory effects were significantly increased with the increase of IL-10 production beeing the most importan effect. The Ongaro's studies showed for the first time that EMFs can significantly modulate the behavior of human (OASFs), by inhibiting their inflammatory activities and suggest that the adenosine pathway is involved in mediating EMF effects, supporting the conclusion that the EMF-induced increase in adenosine receptor number is involved in the regulation of at least inflammatory mediators in OASFs. In particular, the EMF effects on IL-1-induced cytokine IL-6, IL-8 and IL-10 production are mainly mediated by the EMF-induced increase in A3 adenosine receptors. However, as the A3 adenosine antagonist did not completely abrogate the EMF effect on IL-6, this suggests that EMFs can also act by different signaling pathways. They have speculated that ‘‘in vivo,’’ the inhibition of pro-inflammatory pathways, exerted by EMFs and ARs, resulted in the suppression of the expression of matrix degrading enzymes, thus contributing to the EMF chondroprotective effects. The authors have concluded that EMFs display anti-inflammatory effects in human OASFs, by modulating inflammatory and anti-inflammatory parameters. Peripheral blood mononuclear cells (PBMCs) have been used frequently to study effects of EMF on the cell methabolism, inflammatory response since these are good producer of citokines [59-61]. There are controversies in the literature: some studies show an increase in IL-1, IL-2, IL-6 and TNF, whilst others have shown a decreased production of these and other cytokines such as IFN and IL-10. The exposure of PBMC to extremely low frequency EMFs with intensity of 2.5 mT, with average time variation of the order of 1T/s and with induced voltage of about 2 mV, increased both the spontaneous and the phytohemagglutinin (PHA)or 12-O-tetradecanoylphorbol-13-acetate (TPA)-induced production of IL-1 and IL-6 [48]. In another study, Cossarizza et al. [47] suggest that EMFs increase lymphocyte proliferation by increasing utilization of interleukin-2 (IL-2) and increasing expression of IL-2 receptor on lymphocyte cell membranes. In fact, when PBMC were exposed to 50-Hz EMFs for 12 h, the levels of neither IL-1, nor IL-2 were increased. Moreover after 24h of incubation the IL-2 concentration was similar in EMF-exposed and unexposed PBMC cultures, and only after 48h, in those cultures which responded to EMF

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exposure with increased [3H] TdR incorporation, a marked decrease in IL-2 was observed. Indeed, the concentration of TNF decreased significantly immediately after the exposure period. Other studies showed that in PBMC stimulated with PHA immediately before the exposure to EMFs the IL-1, TNF and IL-2 levels were significantly higher at the end of the 24 and 48 h EMF exposure, and cells subjected to three 15-min cycles of EMF, each exposure being followed by 105 min without a field, for a total of 6 hr, released unchanged levels of IL-2, IFN and TNF during the first 48 hr of incubation respect to unexposed cells. This indicates that brief exposure to EMF has no significant effect on PBMC. Unstimulated PBMCs exposed to EMFs with a frequency of 50 Hz and a potency of 3 mT for 12 h have not significantly increased release of either IFN or IL-6 after 12 and 24 h. In contrast, after PHA challenge, the cells expressed elevated responses to EMFs exposure, with both the proliferative responses and the release of cytokines significantly increased [62-64]. In the study of Jonai et al. [65], trends of greater production of cytokines IL-1 and IL-2 were noted for PBMCs exposed to 50 Hz EMF at 1 mT, 3 mT to 10 mT and 30 mT selected as levels seen in the occupational setting. For IL-1, though production by samples exposed to 50 Hz was higher for all exposure levels, statistical significance was detected only for 1 mT and 3 mT exposure levels. No statistically significant difference in the amount of IL-2 produced was noted in EMF-exposed cells for all intensities. The same trend of higher productivity of IL-6 in the EMF-exposed samples was reported at of 1 mT, 3 mT, and 10 mT. No distinct trend of difference in IL-10 production was detected between EMF-exposed and shamexposed cells. TNF- have been shown to be consistently lower in the cells exposed to magnetic fields at 1 mT, 3 mT, 10 mT and 30 mT. Some experiments were aimed at investigationg the effect of EMF on PBMC in “in vivo” conditions. Thus, reduced IL-2 and IFN- release was obseved in PHA stimulated PBMC by housewives, exposed for a mean period of 13 years, in their residences to EMFs (with range 500 KHz-3 GHz) emitted by radio-television broadcasting (4.3 + 1.4 V/m, while the exposure in the nearby area was 0). The relative magnitude of nA(C) and nA(H) can be estimated through

( nA( C )  nA( H ) )(  mA   mP )  N (  m ( C )   m ( H ) ) < 0 (N= nA(C) + nA(H)). Here χmA (χmP) is the magnetic susceptibility of diamagnetic (paramagnetic) components and χm(C) and χm(H) the magnetic susceptibility of cancerous cell and healthy cell respectively, χm(C) < χm(H) , for example, χm(C).=-7.76 , χm(H) =-7.16 for human throat[24]. So, nA(C) > nA(H), and from (42) we have

 

( jγ  Fγ )

(H )

  ( jγ  Fγ )

(C )

(43)



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This means the cancerous cell has higher entropy production than the normal under static magnetic field. The introduction of static magnetic field is no helpful in the reversal of entropy flow. But the gradient magnetic field forces are exerted to the diamagnetic（most of organisms）and paramagnetic (mainly the Fe-containing haemoglobin) components of a cancerous cell in opposite directions. A malignant tumour in the fast growing period attracts many new mini blood vessels to get enough alimentation and oxygen. The metabolism and alimentation supply of cancers could be affected when they are placed in the gradient magnetic field [24]. 6. The change of entropy production caused by applied electromagnetic field includes two parts. The first is the direct effect of the external force field,   s (5) d , that has been calculated in this section. The second is the indirect effect of the field which induces the change of biochemical processes and finally causes the additional entropy production. The latter will be discussed in next section.

EXPERIMENTAL MEASUREMENT OF ENTROPY PRODUCTION IN CELLS UNDER ALTERNATING ELECTRIC FIELD The entropy production of living organism can be obtained through measurement of the heat generated by the system when the entire organism is placed inside the calorimeter for the measurement. In principle, based on the measurement of specific heat capacity of the system C and the temperature change one can calculate the entropy increase through S   dT . T However, the measurement of C is difficult for a living cell since the volume of cell is small and it exists in the culture medium. Simultaneously，the measurement of such a small temperature change in the problem is not easy. Another method is indirect calorimetry measurement which calculates heat that living organisms produce from their production of carbon dioxide and nitrogen waste or from their consumption of oxygen. We put forward a new method that allows thermal data to be obtained on living cells [26]. It involves heating the sample (normal or cancerous cells) by alternating electric field and recording the heat

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flow either into or from the specimen. Then the entropy production of normal and cancerous cells can be deduced. The cancerous or normal cells were cultured and suspended with the medium and the suspensions were transferred to 96 pores plate, and incubated for 60 min in an incubator at 37℃. Then the 96 pores plate was placed on the electric field for 300s and the change of temperature TF (t) (t = 0 to 300s) was recorded by the temperature transducer. The control group was placed in the same apparatus without electric field and the change of temperature

TC (t) was also recorded. The heat transfer from the cell outward (denoted by Q (C ) in case without alternating electric field or under alternating electric field, the outgoing direction being positive) can be calculated from Fourier's law of heat conduction

dQ   A(T  Tenv ) dt

(44)

or

Q ( F )   A (TF  Tenv )dt

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Q(C )   A (TC  Tenv )dt

(45)

where is room temperature, is the surface area of the sample, is heat conductivity (in unit thickness). To subtract the effect from medium the culture medium alone (without cells in it) was also put in an incubator at 37℃ for 60 min, then placed on the electric field 300s or without electric field exposure respectively and the change of the temperature was recorded by the transducer. Thus the contribution of the heat transfer from the medium was obtained and can be subtracted. Hereafter

Q ( F ) and Q (C ) will represent the net heat transfer from

the cell only; that is, the contribution from culture medium has been subtracted. The entropy change of a cell during a definite time interval is denoted by S or for a cell under alternating electric field or without electric field applied, respectively. It can be divided into two parts (F )

S (C)  SnT (C )  ST (C ) ,

(46)

where ST and ST are heat-exchanging entropy (conduction entropy ) with the (F )

(C )

environment (the incoming direction being positive), and SnT (C ) and are entropy increase of a cell except the heat-exchanging part. From eq (45) we obtain

S ( F )  S (C )  (ST ( F )  ST (C ) )   F

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(47)

325

Electro-magnetic Field Induced Entropy Production in a Cell

 F =SnT ( F )  SnT (C )  F

(48)

is the net entropy increase of a cell apart from heat-exchanging terms which

includes all kinds of entropy production interior of a cell due to external forces. can be obtained by the measurement value of

ST ( F )   

dQ( F ) , TF

ST (C ) and

Q (C ) and Q ( F ) .

ST (C )   

dQ(C ) TC

(49)

Inserting (44) into (49) we obtain

ST (C )  ST ( F ) = ATenv (t0 ) 

1 1 （ - )dt TC TF

t0 +300 s

t0

T (t ) t0 +300 s = A env 0  (TF  TC )dt TF TC t0

(50)

It is interesting to note that the environmental temperature occurs in the equation only as a factor Tenv (t0 ) . Since  A keeps a constant in measurement and the variation of environmental temperature during each experiment (300s) can be neglected and Tenv (t0) for different rounds of experiments can be chosen as a constant, the conduction entropy Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

difference

ST (C )  ST ( F ) is

fully determined by the integral in eq(50), i.e., by the

variation of the temperature difference of cells. While the time evolution of the temperature of the cell is decided by  F , so one may assume is only a function of  F . Considering that

(ST (C )  ST ( F ) ) is a small quantity and it vanishes as  F =0 one can adopt linear

approximation to simplify the result and deduce

 F  k (ST(C )  ST( F ) )

(51)

where k is a constant （k>1）, independent of field strength . The coefficient 1/k represents the fraction of field-induced entropy production in a cell transferring to conduction entropy flowing from the cell. By using Eqs.(47) (48) and (51), we obtain

S ( F )  S (C )  (k  1)(ST (C )  ST ( F ) )

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Liaofu Luo and Changjiang Ding

30

20

-15

SEEP (10 J/(K*s))

MDA-MB-231 MCF10A

10

0 0

5

10

15

20

25

30

35

40

45

electric field strength (v/cm)

Figure 1. The relation between Scaled Electro-induced Entropy Production rate (SEEP) and electric field strength. 5

4

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EEPR

3

EEPR 2

1

0 0

5

10

15

20

25

30

35

40

45

electric field strength (v/cm)

Figure 2. The relation between Electro-induced Entropy Production Ratio (EEPR) and electric field strength.

Thus the entropy change can be deduced through the measurement of conduction entropy

(ST (C )  ST ( F ) ) . For a pair of normal cell and cancerous cell we have (S ( F )  S (C ) )(cancer ) (ST (C )  ST ( F ) )(cancer )  (S ( F )  S (C ) )(normal ) (ST (C )  ST ( F ) )(normal )

if the k value is same for two cell types. Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Electro-magnetic Field Induced Entropy Production in a Cell

327

For a pair of cells taken from the same tissue, human breast epithelial cell MCF10A and breast cancer cell MDA-MB-231, or human hepatoma cell line HL-7702 and hepatic cancer cell line SMMC-7721, the entropy production was measured at alternative electric field strength 5V/cm, 10V/cm, 15V/cm, 20V/cm, 25V/cm, 30V/cm, 35V/cm and 40V/cm, respectively.[26] Considering the total number of cells is about (0.15-0.45)×106 in our experiment and the experimental time is 300s, we divide the measured entropy difference ( ST (C )  ST ( F ) ) by

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0.3 × 106 cells and by 300s and name it as the Scaled Electro-induced Entropy Production rate (SEEP) which represents the entropy production rate for a cell due to external electric field apart from a factor (k-1). The relations between SEEP and electric field strength for breast cells (cancerous MDA-MB-231 and normal MCF10A ) are shown in Figure 1. It was found that the nearly same relations occur for hepatic cells (cancerous SMMC-7721 and normal HL7702). We conclude that both SEEPs of MDA-MB-231 and SMMC-7721 monotonically increase with electric field strength at 5-40V/cm, while both SEEPs of MCF10A and HL7702 change non-monotonically, showing a peak at 5-30V/cm. The ratio is named Electro-induced Entropy Production Ratio (EEPR). The relation of EEPR with electric field strength for breast cells (MDA-MB-231 / MCF10A) is given in Figure 2. The EEPR for hepatic cells (SMMC-7721/ HL-7702) shows the same relation. We conclude that the EEPRs for both cell lines are smaller than 1 in a large range of field strength from 5 to 25V/cm. In previous section by calculating   s (5) d (the dissipation of alternating electric field energy in a cell) we found that the entropy production rate of the cell monotonically increases with electric field strength (eq (25)) and made an order-of-magnitude estimate of the rate for a typical cell. Now, by inspection of Figure 1, we find that the experimental SEEPs are in accordance with the theoretical estimation of cell entropy production. Moreover, the field strength dependence of SEEP for MDA-MB-231 and SMMC-7721 is consistent with the theoretical calculation for cancerous cells. However, for normal cells MCF10A and HL-7702 the experimental result indicates a peak existing at 5-30V/cm which cannot be interpreted by the dissipation of alternating electric field. In fact, the experimental SEEP of a cell under electric field exposure generally consists of two parts, one is the direct entropy production which comes from the dissipation of the electric field energy in cell medium; another is indirect entropy production which comes from the change of biochemical processes caused by the external field. We know that the cell metabolism, typically the ATP synthesis, changes with applied electric field [27,28] and the metabolism pathways are different between cancer and normal cells [3, 29-30]. If the ATP synthesis in a normal cell is more sensitive to the electric field at some given range of field strength, then the observed peak of SEEP at 530V/cm for MCF10A and HL-7702 can be explained. The present experiment proved that as the 5-25V/cm alternating electric field is applied the field-induced entropy production rate for normal cells exceeds that for cancerous cells about 10-14 J/degree sec (Figure 1) which is in the order of the total entropy production of a cell without applied field. As a result, the direction of the entropy flow may be reversed between cancerous and normal cells under electric field exposure. The entropy flow is the carrier of information flow. The change of entropy flow direction may have therapeutic effect and provide opportunities for anticancer therapy.

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CONCLUSION 1, The Shannon information quantity is the projection of Boltzmann thermodynamic entropy from the microscopic phase-space to its subspace spanned by macroscopic variables that describe the chemical, morphological, structural and physiological state of the cell. The entropy flow is the carrier of the information flow. The entropy-information flow contains two parts: the drift flow and the diffusion flow. The information flow is directed from the high entropy state to the low entropy state. Generally, the normal cell is in low-entropy state (ordered state) and has lower entropy production while the cancerous cell is in high-entropy state and has higher entropy production. So, in case of no external field, the entropy flow is always directed from the cancerous cell at its surrounding normal cells which may carry and propagate the harmful information of the cancer. It is expected that the harmful effect brought about by the entropy flow can be blocked by the change of the relative entropy production rates between cancerous and healthy cells (the reversal of entropy current between them) through some specially devised mechanism. 2, By calculating the dissipation of alternating electromagnetic field energy in a cell we demonstrated in theory that several volt/cm low-frequency alternating electric field or 104 Gs alternating magnetic field with moderate frequency can effectively induce the additional entropy production the order of which is comparable with the entropy production for a cell without external field applied. Define the product of conductivity and inverse permittivity square as the entropy production threshold (EPT) of a cell. We predict that when the EPT of a cancerous cell is lower than that of its adjacent healthy cell then the entropy flow (information flow) direction can be reversed as the organism is irradiated under appropriate alternating electromagnetic field. 3, We proposed a novel method for measuring the entropy production of living cells. Through heating the sample by alternating electric field and recording the heat flow from cells we measured and compared the entropy productions of cancerous and normal breast (or hepatic)cells respectively. The experimental results proved that both for cells MCF10A/MDA-MB-231 and HL-7702/SMMC-7721 the normal-to-cancerous ratio of fieldinduced entropy production is obviously larger than 1 in a large range of field strength from 5 to 25V/cm. These results indicate the huge differences existing in the electric-field response of entropy production between two kinds of cells. It gives direct experimental support on the theoretical prediction that the appropriate electric-field exposure can change the relative entropy production rates between cancerous and normal cells and thus reverse the direction of entropy flow between them.

REFERENCES [1] [2] [3]

Schrödinger E. What is Life? Physical Aspects of Living Cell. University Press, Cambridge 1948. Luo LF. Theoretic-Physical Approach to Molecular Biology, Shanghai Scientific and Technical Publisher 2004. Luo LF. Entropy production in a cell and reversal of entropy flow as an anticancer therapy. Front Phys. 2009,4(1):122-136.

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Electro-magnetic Field Induced Entropy Production in a Cell [4]

[5] [6] [7] [8] [9] [10] [11] [12] [13]

[14] [15] [16]

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[17]

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[20] [21]

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Luo LF; Molnar J; Ding H; Lv XG; Spengler G. Physicochemical attack against solid tumors based on reversal of direction of entropy flow. Diagnostic Pathology 2006, 1:43. Luo LF; Molnar J; Ding H; Lv XG; Spengler G. Ultrasonic absorption and entropy production in biological tissue. Diagnostic Pathology 2006, 1:35. Glansdorff P; Prigogine I. Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley Interscience: New York, 1978. Nicolis BG; Prigogine I. Self-organization in Nonequilibrium Systems. Wiley Interscience: New York, 1977. Reichl LE. A Modern Course in Statistical Physics. Univ of Texas Press, Austin 1980. Gardiner CW. Handbook of Stochastic Method (2nd edition)，Springer, 1985. Xing XS. Dynamical statistical information theory. Science in China, Ser G. 2005，35(4):337-368. Frohlich H. Theory of Dielectricity. Oxford 1949. Polevaya Y, et al. Time domain dielectric spectroscopy study of human cells II. Biochim et Biophys. Acta. 1999, 1419:257-271. Barsamian ST; Reid BL; Thornton BS. Origin of dielectric discretness during the development of Dacus tryoni and its reversal by a carcinogen. IRCS Med. Sci. 1985, 13: 1103-1104. Sha L; Ward ER; Stroy B. A review of dielectric properties of normal and malignant breast tissue. Proc IEEE Sourtheast Con 2002,457-462. Haemmerich et al. In vivo electrical conductivity of hepatic tumours. Physiol. Meas. 2003, 24:251-260. Beebe SJ; Fox PM; Rec LJ et al. Nanosecond pulsed electric field (nsPEF) effects on cells and tissues: apoptosis induction and tumor growth inhibition. IEEE Transactions on Plasma Science, 2002, 30(1): 286-29 Jordan A; Scholz R; Wust P et al. Presentation of a new magnetic field therapy system for the treatment of human solid tumors with magnetic fluid hyperthermia, J. Magn. Magn. Mater., 2001,225:118-126. Foster KR. Thermal and nonthermal mechanisms of interaction of radio-frequency energy with biological systems. IEEE Trans. Plasma Sci. 2000, 28:15-23. Simeonova M; Wachner D; Gimsa J. Cellular absorption of electric field energy: influence of molecular properties of the cytoplasm. Bioelectrochemistry 2002, 56:215218. Kotnik T; Mikalavcic D. Theoretical evaluation of the distributed power dissipation in biological cells expposed to electric fields. Bioelectromagnetics 2000, 21: 385-394. Jaroseski MJ; Gilbert R; Heller R. Electrochemotherapy: an emerging drug delivery method for the treatment of cancer. Advanced Drug Delivery Reviews 1997, 26: 185197. Sergio Rodriguez-Cuevas et al. Electrochemotherapy in primary and metastatic skin tumours. Archives Medical Res. 2001, 32: 273-276. Larkin J; Soden D; O’Sullivan GC et al. Combined electric field and ultrasound therapy as a novel anti-tumour treatment. European J Cancer 2005, 41: 1339-1348.

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[24] Zhen FQ et al. Experimental studies on ultralow frequency pulsed gradient magnetic field inducing apoptosis of cancer cell and inhibiting growth of cancer cell. Science in China (series C) 2002, 45:33-40. [25] Ding CJ; Luo LF. A proposal on anticancer therapy based on reversal of entropy flow through magnetic field. Proceedings of the First International Conference on BioMedical Engineering and Informatics (BMEI2008), 2008, vol 1, 483-487. [26] Ding CJ; Luo LF. Experimental study of entropy production in cells under alternating electric field. Chinese Phys. Letters, 2012, 29 (8) 088701. [27] Berg H. Electrostimulation of cell metabolism by low frequency electric and electromagnetic fields. Bioelectrochem. Bioenerg. 1993, 31:1-25. [28] Berg H. Possibilities and problems of low frequency weak electromagnetic fields in cell biology. Bioelectrochem. Bioenerg. 1995, 38:153-159. [29] Molnar J, Thornton BS, Thornton-Benko E, Amaral L, Schelz Z, and Novak M. Thermodynamics and electro-biologic prospects for therapies to intervene in cancer progression. Curr. Cancer Ther. Rev. 2009, 5: 158-169. [30] Warburg O. On the origin of cancer cells. Science 1956, 123: 309-314.

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 © 2013 Nova Science Publishers, Inc.

Chapter 10

AN EVALUATION OF NEUROTOXICITY MARKERS IN RAT BRAINS, USING A PRE-CONVULSIVE MODEL AND EXPOSURE TO 900 MHZ MODULATED GSM RADIO FREQUENCY María Elena López-Martín1*and Francisco José Ares-Pena2# 1

Morphological Sciences Department, Faculty of Medicine, University of Santiago de Compostela, Santiago de Compostela, Spain 2 Applied Physics Department, Faculty of Physics, University of Santiago de Compostela, Santiago de Compostela, Spain

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ABSTRACT Studies of cerebral activity in humans and in animal models after exposure to the modulated radio frequency (RF) of mobile phones have often indicated alterations of normal physiology and signs of toxicity in the nervous system. In recent years, in our laboratory has carried out consecutive experiments to investigate how exposure to radiation similar to that of mobile phones affects the cerebral activity of rats previously exposed to a state of pre-excitability in their neuronal activity. An experimental radiation system was designed, involving a standing wave chamber built to maintain constant electromagnetic parameters and provide stress-free exposure to nonthermal levels of radiation. Rats were given an intraperitoneal injection of a subconvulsive dose of picrotoxin to create a pre-convulsive experimental model and then the animals were exposed to 900MHz GSM radio frequency in the radiation chamber for two hours. Afterwards, they suffered convulsions and showed marked increases in neuronal activity in the neocortex, paleocortex, hippocampus and thalamus. Clinical differences were also found in the electroencephalographic (EEG) signals and in c-Fos expression in the brains of rats exposed to modulated and unmodulated GSM radiation. The most marked effects of GSM radiation on c-Fos expression in picrotoxin-treated rats were in the limbic structures, olfactory cortex and subcortical * #

[email protected] [email protected]

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María Elena López-Martín and Francisco José Ares-Pena areas, the Dentate Gyrus and the centro-lateral nucleus of the intralaminar nuclear group of the thalamus. Animals not treated with picrotoxin and exposed to unmodulated radiation presented higher levels of neuronal activation in cortical areas. Morphological examination revealed that most rat brain areas except the limbic cortex have shown an important increase in neuronal activation 24 hours after picrotoxin and radiation. Three days later, radiation effects were still evident in the neocortex, Dentate Gyrus and CA3, but had diminished in the limbic cortex (entorhinal and pyriform). During this period, glial activity increased, with convulsions observed in radiated rats treated with picrotoxin. Our findings of neurotoxicity markers in a sub-convulsive model of rat brains exposed to radiation indicates how exposure to mobile phone radiofrequency fields may induce changes in brain tissue that is physiologically susceptible to electrical instability. These results suggest that the effects of mobile phones on at-risk populations should be thoroughly studied.

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1. INTRODUCTION In today’s world there are more than four billion users of mobile telephones and the effects of non-ionizing radiation emissions on health are still unclear. Though the threat may be low, any health risk from mobile phones could affect untold thousands of users. Much of the research in this area is aimed specifically at identifying any connection between mobile phones and brain cancer [1]. However, for a decade now the World Health Organization has been recommending research to ascertain links between mobile phone use and other pathologies, such as neurodegenerative illnesses in adults or the effects of wireless radiation on the juvenile human nervous system [2-4]. The design of the experimental research in our laboratory over the last few years is based on earlier experimental results from studies of animals and human volunteers, indicating that radio frequency fields emitted by mobile telephones could alter the physiology of the nervous system [5-8]. Many controversial mechanisms have been proposed to explain the interaction of modulated radio frequency signals with the central nervous system (CNS), such as neuronal damage related to increased permeability of the hematoencephalic barrier [9] and increased cerebral blood flow [10]. Our study examined the effects of two hours of radiation on rats pre-disposed to convulsions, due to an injection of a sub-convulsive dose of picrotoxin, an antagonist of the GABA-A receptors [11]. Radiation was applied in an experimental chamber specifically designed to study these animals under exposure conditions similar to those of the Global System for Mobile Communication (GSM), with frequencies of 890-960 MHz and pulse modulation at 217 Hz [12]. Radiation effects were evaluated by looking for signs of convulsions in the rats (EEG studies were proposed in some cases) and subsequent post-mortem immunohistochemical tests of the relevant anatomic areas of the rat brains. Specifically, we looked for: 1) expression of the c-Fos biomarker as an indication of neuronal activation and 2) glial reactivity as a parallel indicator of neuronal damage in anatomical circuits, caused by convulsions. To rule out the existence of thermal effects, the intensity of absorption in the rat brains and bodies was calculated from experimental data for specific absorption rates (SAR) and the results obtained from a commercial ‘phantom rat’ software model [13].

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2. RESULTS A) SAR Calculation and Measurement of the Power Absorbed by Small Animals in the Experimental Set-Up for 900MHz GSM Standing Waves

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Radiation is present as standing waves in the high megahertz or low gigahertz frequency bands [14] and therefore could have effects that are qualitatively or quantitatively different from those of travelling waves. The standing wave apparatus described here facilitates direct measurement of the power absorbed by the animal. By assuming local SARs to be approximately proportional to wholebody mean SAR, this measurement can be used to correct organ-specific SARs from simulated numerical phantoms.

Figure 1. Diagram of the experimental set-up. The signal generator, spectrum analyser and power meters are from Agilent (Models E4438C, E4407B and E4418B, respectively), the linear power amplifier is from Aethercomm, and the directional couplers are from Narda (Model 3282B-30). TA, transmitting antenna; RA, receiving antenna. The origin of coordinates is located at the centre of the chamber floor.

The experimental set-up shown in Fig. 1 consists of a non-metallic device chamber (NMD) of methacrylate placed inside a metallic box with dimensions large enough to minimize additional stress to the animal. The frequency, amplitude and modulation of the microwave signal are initially established by the signal generator, which is connected to the

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transmitter antenna (TA) by an amplifier. A receiving antenna (RA) is connected to the spectrum analyzer in order to monitor field stability and safeguard against spurious signals. The subsystem is formed by directional couplers at the incident and receiving ends, sensors and power meters, which make it possible to measure the power absorbed by the animal. The experimentally measured powers are then used to calculate the Specific Absorption Ratios (SARs) of the radiated animals with the aid of a commercial FDTD (Finite Difference in Time Domain) application [13]. In order to determine the optimum positioning of the animals within the geometry of the radiation region, the field distribution within the radiation region is first calculated with commercial FDTD software [13], removing the receiver antenna during the numerical simulation so that only the transmitter antenna remains. A λ/4 monopole transmitter antenna was designed for this kind of simulation and the radiation region was limited by a perfect electric conductor (PEC), or the metallic box illustrated in Figure 1. As noted above, the measurements of the actual power absorbed by the experimental rat can be used to apply a correction factor to the local SAR predictions calculated by numerical simulation. Specifically, we calculate an estimated local SAR, SARE, from the expression SARE = SARS × (WBMSARE)/(WBMSARS) = SARS × (PE/WE)/(PS/WS) (1)

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where SARS is the simulated SAR, WBMSARE and WBMSARS are the experimental and simulated whole body mean SARs, PE and PS are the absorbed powers, and WE and WS are the weights of the experimental and simulated rats. We assume local SARs to be proportional to whole-body mean SAR, at least in the small, 200–250 g weight range relevant to this study. The SARs were mainly used to establish that local power absorption was nowhere near sufficient to create thermal effects, thus great accuracy in SAR values was unnecessary.

B) Evaluation of the Effects of Mobile-Phone-Type Radiation on the Cerebral Activity of Seizure-Prone Animals 1.B) Effects in Rats Exposed to 2 Hours of Gsm-Modulated Radiation at 900 MHz and Intensity Similar to That Emitted by Mobile Phones The Global System for Mobile communication (GSM) is generally operated at carrier frequencies in the near-gigahertz range (890–960 MHz), with pulse modulation at 217 Hz [12]. In this study, we investigated the effects of 2 h of this type of radiation on rats made seizure-prone by injection of a subconvulsive dose of the GABA-A antagonist picrotoxin [11]. The effects of radiation were evaluated by observing whether the rats suffered seizures (supported in some cases by electroencephalography) and postmortem immunochemical testing of relevant brain areas for expression of c-Fos, a sensitive marker of neuronal activation [15] that is produced in these brain areas by seizures [16]. Whole-body SAR power absorption measurements were obtained experimentally and used to scale the results of calculations performed for a commercial ‘phantom’ rat [13].

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After 5 min exposure, all the irradiated picrotoxin-treated rats began to exhibit myoclonic jerks. In all but two rats, these were followed by intermittent seizures during 20–30 min. This behavior was reflected by generalized and continuous spike-and-wave trains in the EEGs conducted during the seizures. Non-irradiated picrotoxin-treated rats (Group 2) exhibited bursts of motor activity lasting from 3 to 5 min, after which they remained immobile but alert. The EEGs for rats from this group exhibited isolated spikes or very short bursts of spikes, but no more than minimal signs of seizure. Rats not treated with picrotoxin (Groups 3 and 4) showed initial stress attributable to immobilization, but did not exhibit any abnormal activity or signs of seizure, and none of the EEGs recorded from these groups showed spikes. The average experimental SAR values calculated for picrotoxin-treated and untreated irradiated rats are listed in Table I Table I. Mean Absorbed Power and SAR Values for the Four Experimental Groups Rat group

Whole body Peak 1-g-averaged Mean W/kg W/kg Picrotoxin-treated 0.15 0.85 Untreated 0.24 1.30

Mean W/kg 0.27 0.42

Brain Peak 1-g-averaged W/kg 0.31 0.47

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c-Fos Expression

Figure 2. Photomicrographs of DAB-stained transverse sections of the brains of picrotoxin-treated rats that had been exposed to GSM radiation for 2 h. The effects were clearly visible on the granular layer of the dentate gyrus (DG) and hippocampal areas CA1 and CA3.

c-Fos values in irradiated picrotoxin-treated rats were almost double those found in nonirradiated picrotoxin-treated rats, except that in the hippocampus the difference was greater. Irradiated picrotoxin-treated animals had significantly higher c-fos counts than non-irradiated picrotoxin-treated animals in both the frontal cortex and the parietal cortex. In neither the

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piriform nor the entorhinal cortex did radiation per se have a statistically significant influence on counts, but in both these areas it significantly modified the effect of picrotoxin. In the dentate gyrus, there was a marked difference in c-fos counts between the irradiated picrotoxin-treated rats and all the other groups. A similar pattern was found in hippocampal area CA1.In CA3, the c-fos counts of irradiated picrotoxin-treated rats were on average more than double those in any other group, but the major effect was due to picrotoxin treatment. Though radiation itself had no statistically significant effect on counts in the centrolateral thalamic nuclei, it significantly increased counts in both the centrolateral and the centromedial nuclei among picrotoxin-treated rats.

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2. B) Differences in the Effects of Exposure to Unmodulated and Pulse-Modulated GSM Radiofrequency in Picrotoxin-Injected Rats The principal argument for non-thermal mechanisms concerns identification of an experimental effect that occurs or is observed in relation to low energy, and the results of previous studies have suggested that the action of pulse-modulated RF fields such as those emitted by mobile phones can alter nervous system physiology [5,17] In a previous study, we found that rats pretreated with subconvulsive dose of the γaminobutyric acid (GABA) antagonist picrotoxin and then exposed to GSM radiation showed significant alterations in various indicators of brain activity, including clinical indicators, EEG indicators, and c-Fos levels in the brain [18]. These effects cannot be attributed to heating because the SAR was insufficient to cause bulk heating of tissue; which suggests that GSM radiation may affect brain activity. The objectives of the present study were to discover whether the effects of pulse-modulated GSM on brain activity differed from those of nonmodulated radiation at the same wavelength and to study c-Fos expression in seizure-related anatomical circuits. Power Absorption Table II records the mean absorbed power, mean SARs in brain and body, and peak SARs averaged for 1 gr of body and brain. All SAR values are well below thermal values. Table II. Mean Absorbed Power and SAR Values for the Four Experimental Groups.

Group PT+ GSM PT+ Unmod No-PT+ GSM No-PT+ Unmod

Mean absorbed Power (mW) 7.74 63.98 13.67 64.79

Mean SAR in brain (W/Kg) 0.03 0.26 0.05 0.26

Peak SAR averaged in 1 gr of Brain (W/Kg) 0.03 0.30 0.06 0.29

Mean SAR in body (W/Kg) 0.03 0.26 0.05 0.25

Peak SAR averaged in 1 gr of body (W/Kg) 0.14 1.40 0.28 1.39

Clinical Behavior and Electroencephalograph Results Non-picrotoxin-treated non-irradiated rats showed initial stress attributable to immobilization but did not exhibit any abnormal activity or signs of seizure, and none of EEGs recorded from these groups showed abnormalities. Picrotoxin-treated non- irradiated rats showed bursts of motor activity lasting between 5 and 10 min, after which the rats remained immobile but alert. EEGs showed isolated spikes or very short burst of spikes but no more than minimal sigs of seizure.

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Figure. 3. Schematic drawings of transverse sections of the rat brain, showing the anatomical regions in which nuclear c-Fos expression was measured in (A) at the 9.2-mm level (interval coordinates) in cortical areas (frontal cortex, FR1; parietal cortex, PAR1; piriform cortex, PIR); in (B) at the 5.7-mm level in hippocampal areas (dentate gyrus, DG; CA1; CA3; and the central medial, CM, and central lateral, CL, nuclei of the thalamic intralaminar nuclear group) and in (C) at the 4.2-mm level in the entorhinal cortex, ENT.

Non picrotoxin-treated GSM-irradiated rats showed initial stress but did not exhibit any abnormal activity or signs of myoclonic jerks. Picrotoxin-treated GSM-irradiated rats began to exhibit myoclonic jerks of the head and the body within 10 min of administration of picrotoxin. The myoclonic jerks persisted for long periods, but only two animals exhibited intermittent and generalized convulsions for 20-30 min. This behavior was reflected in the EEG by short-duration polyspikes or continuous spike-and-wave discharges during the seizures. Non-picrotoxin-treated rats exposed to unmodulated radiation (no-PT/UNMOD) showed alternating periods of immobility and activities such as sucking and small head movements, with no abnormalities in the EEG recordings. Picrotoxin-treated rats exposed to unmodulated radiation (PT/UNMOD) exhibited aggressiveness and motor activity that started a few

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minutes after picrotoxin administration and lasted about 10 min. Two rats had occasional myoclonic head jerks and movements of forepaws after 20 min, but only one rat showed generalized seizures. The EEGs of these rats showed short-duration polyspikes or continuous spike-and-wave discharges.

c-Fos Expression

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C-Fos Expression in the Entire Brain A two-way analysis of variance using radiation and picrotoxin as factors for evaluating the proportion of c-Fos-immunopositive neurons (henceforth c-Fos expression) in the entire brain indicated c-Fos expression to be significantly higher in picrotoxin-treated animals than in non-picrotoxin-treated animals. However, irradiation had different effects in the different groups (treated and non-treated animals considered together). Expression of c-Fos did not differ in groups receiving modulated (PT + GSM and no-PT + GSM) and unmodulated radiation (PT + UNMOD and no-PT + UNMOD), but there were significant differences between these groups and the non-irradiated groups. The effect of GSM radiation increased the magnitude of the difference in c-Fos expression between PT and non-PT rats: expression was very high in GSM/PT rats and low in GSM/no-PT rats. In contrast, there were no significant differences between UNMOD/PT and UNMOD/no-PT rats or between noRAD/PT and no-RAD/no-PT rats C-Fos Expression in Different Brain Regions All brain areas presented c-Fos expression after picrotoxin treatment, with or without irradiation. In all areas, the mean c-Fos expression in PT + GSM rats was higher than PT + No-RAD rats, with twofold increases in some areas and even greater differences in the hippocampus. In the neocortical areas, c-Fos expression was similar for picrotoxin-treated rats exposed to GSM and unmodulated radiation (UNMOD), and in the remaining frontal areas c-Fos expression was higher in rats exposed to GSM than in rats exposed to unmodulated radiation. In rats not treated with picrotoxin, c-Fos expression did not differ significantly between the GSM and no-RAD groups but was markedly higher in the UNMOD group. 3. B) Neurotoxic Biomarkers after Acute Exposure to GSM Radiation at 900MHz in Picrotoxin-Treated Rats In this experiment we looked for signs of neural stress on cerebral activity after GSMmodulated radiation at 900 MHz in a picrotoxin-treated rat model, using positive immunochemical testing for neuronal (c-Fos) and glial fibrillary acidic protein (GFAP) cells. We tested the chronological response cascade at 90 min, 24 h and 3 days, for expression of the c-Fos protein, which is provoked by different noxas such as ischemia [19], epileptic seizures [20] or cerebral trauma [21]. We also tested for GFAP reactivity in brain tissues.

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Table III. Description of experimental groups Group 1: Group 2: Group 3: Group 4: Group 5: Group 6: Group 7: Group 8: Group 9: Group 10: Group 11: Group 12:

Picrotoxin treated (PT) +irradiated(IR) , slaughtered and studied after 90min Picrotoxin treated (PT) + non-irradiated (NIR), slaughtered and studied after 90 min Non-picrotoxin treated (NPT) + irradiated (IR), slaughtered and studied after 90 min Non-picrotoxin treated (NPT) + non-irradiated (NIR), slaughtered and studied after 90 min Picrotoxin treated (PT) + irradiated (IR), slaughtered and studied after 24 h Picrotoxin treated (PT) + non-irradiated (NIR), slaughtered and studied after 24 h Non-picrotoxin treated (NPT) + irradiated (IR), slaughtered and studied after 24h Non-picrotoxin treated (NPT) + non-irradiated (NIR), slaughtered and studied after 24h Picrotoxin treated (PT) + irradiated (IR), slaughtered and studied after 3 days Picrotoxin treated (PT) + non-irradiated (NIR), slaughtered and studied after 3 days Non-picrotoxin treated (NPT) + irradiated (IR), slaughtered and studied after 3 days Non-picrotoxin treated (NPT) + non-irradiated (NIR), slaughtered and studied after 3 days

Exposure and Power Absorption Five minutes after i.p. administration of 2mg/kg of picrotoxin (Sigma) adjusted to individual animal weight (groups 1,2,5,6,9 and 10), or of vehicle only (groups 3,4,7,8,11 and 12), the animals were immobilized in methacrylate tubes and placed in a 150 x 46 x 70 cm radiation cage (with a commercial transmitting antenna incorporated) that had previously been calibrated to enable measurement of the radiation absorbed by the animals [17,22; 23]. Animals in groups 1,3,5,7,9 and 11 were then radiated for 2h with 900 MHz pulse-modulated GSM RF at 1000 MW. All SAR values were below the European Union legislation limits [24] for thermal values in the brain (Table III).

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Table IV. Mean absorbed power and SAR values for the six experimental groups

Type

1 3 5 7 9 11

PT+IR/90 m NPT+IR/90 m PT+IR/24hs NPT+IR/24hs PT+IR/3days NPT+IR/3days

Mean Weight absorbed (g) Power (mW) 178.37 189.41 192.67 202.33 186.17 201.60

209.95 211.83 225 228 199.98 230.66

Mean Peak SAR SAR in averaged brain in 1 gr (W/Kg) of brain (W/Kg) 1.32 1.38 1.32 1.37 1.44 1.35

1.48 1.55 1.49 1.54 1.62 1.52

Mean SAR in body (W/Kg) 0.74 0.78 0.74 0.77 0.81 0.76

Peak SAR averaged in 1 gr of body (W/Kg) 4.09 4.28 4.11 4.25 4.47 4.19

C-Fos Expression Ninety minutes after radiation, the mean c-Fos expression in PT + IR rats was higher than in PT + NIR rats, showing twofold increases in some areas. However, in two of the three hippocampal areas studied this relation was inverted: PT + NIR rats showed higher mean cFos expression levels than PT + IR rats. After 24 h most brain areas showed an important increase in the mean c-Fos expression of picrotoxin treated rats, with similar values for PT + IR or PT + NIR rats. Finally, after three days average c-Fos expression in the dentate gyrus, CA1, neocortex and piriform cortex was similar in PT + IR and PT + NIR rats. Conversely,

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after three days there was an important decrease in mean c-Fos expression in the entorhinal cortex of picrotoxin treated rats.

GFAP Expression in Different Brain Regions Three days after radiation the mean GFAP expression in PT+IR rats was higher than in PT+NIR rats in both the neocortex and the paleocortex. However, in the three hippocampus areas, PT+IR and PT+NIR rats showed similar mean GFAP expression levels.

Figure 4. Photograph of the GFAP immunomarkers for PT + IR in the parietal cortex.

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3. DISCUSSION Rat brains in a pre-convulsive state induced by the antagonist picrotoxin and exposed to GSM at 900 MHz presented important signs of clinical, electrophysiological and morphological neurotoxicity. These results should be interpreted within the experimental context of the study: an RF signal was applied in a controlled environment, with maximum impact to the rat’s head. The radiation system emitted a stationary wave that traveled continuously within a metal chamber and that interacted with cerebral electrical instability in the rat head, increasing the pre-disposition to discharge. A modulated RF signal that is not absorbed by the chamber and that acts repeatedly on the medium makes the neuronal response of the animals more obvious in a brain that is already altered, so that the evidence and effects of a possible health risk are enhanced. By controlling the physical environment and the type of signal emitted, substantial biological results were observed.

A Sub-Thermal Model in a Stationary Wave Chamber There is abundant scientific research and literature on the thermal and non-thermal effects of the exposure of living organisms to electromagnetic fields. European Union legislation on public exposure restricts RF energy on the body surface to no more than 1ºC, with a

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maximum value of 4 W/kg in the entire body [25]. The animals in this experiment experienced sub-thermal SAR values for body and brain well below the European and Spanish maximum limits [22]. At no point in this study were there signs of stress induced by neurotoxicity from manifest hyperthermia in the animals. The energy absorption values per animal, obtained with a mixed formula of numerical calculations and experimental measurements, indicate that heating did not occur [18,22]. Thus, in the absence of a thermal increase that might mask sub-thermal biological effects, we were able to study cerebral effects in this neurological rat model and examine the basic mechanisms of non-ionizing radiation in relation to the frequency and modulation of the wave and how it interacted with cerebral tissue.

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Convulsions and EEG Alterations in a Sub-Convulsive Model with Picrotoxin-Treated Rats Exposed to GSM at 900 MHz The transitory state of pre-excitability induced by the picrotoxin, which blocked the Clchannels of the GABA-A receptors [11], combined with two hours of modulated GSM RF caused myoclonuses and spike-and-wave trains, coinciding with convulsions in the animals [18,26]. However, unmodulated radiation did not cause convulsions or EEG alterations in radiated animals that were previously injected with picrotoxin [26]. After experimentally studying effects on human volunteers, other authors have also suggested that the modulated RF pulses emitted by mobile telephones alter the physiology of the nervous system [27,6,28]. They indicate that some aspect of the pulsation of the RF signal may be interfering with the normal processes of the neuronal electrophysiology of the brain. Mobile telephone radiation at normal intensity levels has been found to affect EEG patterns in humans during memory tests, sleep or stimulus response [28-30]. Recent studies of epileptic patients have shown increased EEG activity in alpha, beta and gamma rhythms [31] and interhemispheric modulation of the alpha rhythm in the dominant hemisphere related to patient exposure to GSM radiation [32]. If these results are confirmed by a larger body of research, then mobile telephone emissions could have significant implications for the cognitive-motor functioning of epileptic persons. At this point, based on alterations in human EEG patterns and the sub-convulsive rat model used in our lab, we can affirm that the interaction of a physiology susceptible to electrical instability with a modulated RF signal produced changes in cerebral activity. The repercussions of this on epileptic persons should be rigorously examined to determine if they constitute a risk group what might require greater safety precautions against exposure to electromagnetic fields.

Neuronal and Glial Activation in Rat Brain Tissue Injected with a Sub-Convulsive Dose of Picrotoxin and Exposed GSM Radio Frequency at 900 MHz The morphological study of rat brains in a pre-convulsive state, induced by injection of a sub-convulsive dose of picrotoxin, that were exposed to GSM radiation revealed an important increase in positive c-Fos cell counts. This is attributed to an increase in neuronal activation

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related to alteration of the electrophysiological parameters of the animal brains [18]. The cFos transcription factor is a sensitive neuronal activation marker that appears in cerebral tissue just after convulsions [33]. Its specific distribution varies according to the type of convulsions [16]. Very high c-Fos recounts have been observed in areas of the neocortex, paleocortex, hippocampus and thalamus of rat brains treated with picrotoxin and exposed to radiation [18]. Mausset-Bonnefont et al.2004 also described how acute exposure to highintensity GSM radiation at 900 MHz affects the GABAergic and glutamatergic systems of rat brains. This suggests that radiation may especially affect the GABAergic system in picrotoxin injected animals. Modulatd radiation may act as a periodic peripheral stimulus that increases the vulnerability of neuronal circuits, especially if GABAergic circuits have already been weakened by the effects of picrotoxin [18]. Neuronal activation, measured by the c-Fos recount in picrotoxin-treated animals exposed to modulated GSM radiation, was much more intense than in animals injected with the antagonist but exposed to unmodulated GSM [26]. GSM pulsed modulation seemed necessary for provoking convulsions in picrotoxin-injected animals, increasing c-Fos levels by means of a mechanism not mediated by temperature variations [34]. GSM radiation had specific effects in the various regions of the brain. In the neocortex, neuronal activation was similar with or without GSM pulsed radiation, but in the paleocortex there was marked c-Fos expression caused by GSM radiation. In our opinion, these results indicate that the paleocortex is especially sensitive to pulsed radiation such as that of GSM and that pulses play an important role in the progression of neuronal activation of convulsions. In the sub-cortical regions of the hippocampus, CA1, CA3 and dentate gyrus, the GSM effect was very apparent in the high levels of c-Fos expression in picrotoxin-treated rats. This effect was due to neuronal activation of the limbic system of the hippocampus and extra-hippocampal regions, caused by GSM radiation with pre-convulsive rat models in our study, along with the effect of other non-competitive GABA-A antagonists [35] or cholinergic agonists [36]. It suggests that anatomic structures may follow an excitation circuit that travels along the perforant pathway [26] when propagating convulsive activity. The weak c-Fos expression in the thalamus nuclei indicate that it may play a more variable role in synchronizing this neuronal circuit. The chronological response in the picrotoxin-induced sub-convulsive rat brain model 90 minutes, 24 hours and three days after radiation showed increases in c-Fos expression for all areas studied. Ninety minutes after radiation, c-Fos expression was greater in the neocortex, paleocortex, CA1 and CA3, with a positive interaction between radiation and treatment. This suggests that the electrochemical instability in the rat brains was fostered in combination with radiation [37]. Upon exposure to GSM radiation at 900 MHz, the GABA-A receptors and the affinity of the NMDA glutamate receptors decreased [8]. Given that the GABAergic is an inhibitory neurotransmission system and that the glutamatergic system is excitatory, it is possible that imbalance occurs between the two systems when exposed to GSM radiation. This imbalance may lead to blockage of GABA-A channels affected by picrotoxin and induce greater c-Fos expression in animals treated with this drug and then radiated. Increased neuronal activation continued in almost all areas 24 hours after radiation. Radiation was not found to be a significant factor, but picrotoxin treatment was. The hyperexcitability induced by the GABA-A antagonist was more persistent than the effects of radiation.

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The effects of radiation decreased in the hippocampus and piriform cortex three days after exposure, which agrees with findings described by other authors working with GSM radiation at 900 MHz [38]. The combined effect of the non-competitive picrotoxin antagonist and radiation depend on the temporal modification of the excitability of the GABA-A receptors and may be related to the interaction of the receptor sub-unit with picrotoxin [39]. The effects of neuronal activation appear to have been compensated in all regions studied, except the paleocortex areas where recovery was slower. This effect was increased by the combined action of picrotoxin and radiation, indicating that the joint action of these two agents create a scenario of extreme vulnerability for provoking a potentially neurotoxic action. Intense GFAP expression three days after radiation indicated activation of the glia, especially in the neocortex and paleocortex of animals injected with picrotoxin. Other authors also reported an increase in GFAP expression in the cortex, the hippocampus and the striatum at higher SARs three days after animals were radiated [8]. The decreasing gradient of radiation (effects are more intense in superficial regions than in deeper anatomical structures) clearly influenced the greater glial activation in the cortex than in other parts of the brain. Furthermore, the combined action of radiation and drugs had less effect in deeper regions of the brain such as the hippocampus [40, 10, 41]. A statistical interaction of picrotoxin with radiation in the paleocortex indicates that radiation is potentiated in the presence of the electrochemical lability resulting from treatment with picrotoxin [11]. The decrease in GABA-A receptor affinity after GSM radiation at 900 MHz [8] may activate astrocytic mechanisms, derived from an excitatory-inhibitory imbalance in the cerebral neurotransmission systems that act on the NMDA receptors of the cortical astroglia [42]. Another possible radiation mechanism that may affect the brain is calcium metabolism. It appears in several studies of GSM low frequency amplitude modulation at 217 Hz and 8.24 Hz, with maximum effects around the critical modulation frequency of 16 Hz [43,44]. GSM modulation may cause the calcium fluctuations that occur in astrocytes during convulsive crises [45]. It appears to be transmitted in waves through the astrocyte syncytium [46,47]. In spite of the anatomical differences between rats and humans in terms of cerebral morphology and size, which imply significant differences in dosimetry, our results indicate that the c-Fos protein and glia markers are activated by the combination of stress effects from non-thermal SAR, caused by radiation and the noxious action of picrotoxin in brain tissue. The nervous pathways of epileptic persons tend towards electrical instability, suggesting that they may be especially sensitive to electromagnetic radiation. The implications of this sensitivity for epileptic persons using mobile telephones may not coincide with the implications of findings for brain tissue of rats treated with picrotoxin. However, recent studies have found a significant increase in electroencephalographic activity within the alpha, beta and gamma bands of epileptic patients exposed to controlled electromagnetic radiation [31]. In our studies, the neurotoxicity found in cerebral tissues of sub-convulsive models of rats exposed to radiation indicates how mobile telephone radio frequency may induce potentially reversible changes in brains susceptible to electrical instability [48]. The findings of this study suggest the need for rigorous examination of the effects of mobile telephone radiofrequency on epileptic persons.

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[8]

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[9]

[10]

[11]

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[15] Morgan, JI; Curran, T. Stimulus-transcription coupling in the nervoussystem: involvement of the inducible proto-oncogenes fos and Jun, Annu. Rev. Neurosci., 1991, 14, 421–451. [16] Willoughby, JO; Mackenzie, L; Medvedev, A; Hiscock,J. Distribution of fos-positive neurons in cortical and subcortical structures after picrotoxin-induced convulsions varies with seizure type, Brain Res.,1995, 683:73–85. [17] Beason,RC; Semm, P. Responses of neurons to an amplitude modulated microwave stimulus, Neurosci. Lett., 2002, 333 (3): 175–178. [18] López-Martín, E; Relova-Quinteiro, JL; Gallego-Gómez, R; Peleteiro-Fernández, M; Jorge-Barreiro, FJ; Ares-Pena, FJ;GSM radiation triggers seizures and increases cerebral c-Fos positivity in rats pretreated with subconvulsive doses of picrotoxin. Neurosci. Lett., 2006; 398(1-2):139-44. [19] Neumann-Haefelin, T; Wiessner, C; Vogel, P; Back, T; Hossmann, KA; Differential expres sion of the immediate early genes c-fos, c-jun, junB, and NGFI-B in the rat brain following transient forebrain ischemia. J Cereb Blood Flow Metab, 1994,14 (2):206– 16. [20] Kiessling, M; Gass, P; Immediate early gene expression in experimental epilepsy. Brain Pathol., 1993;3(4):381–93. [21] Hayes, RL; Yang, K; Raghupathi, R; McIntosh, T.K; Changes in gene expression following traumatic brain injury in the rat. J. Neurotrauma, 1995,12(5):779. [22] López-Martín, E; Bregains, J; Jorge-Barreiro, FJ; Sebastian-Franco, JL; Morenopiquero, E; Ares-Pena, FJ; An experimental set-up for measuremen to the power absorbed from 900MHz GSM standing wave by small animals, illustrated by applicationto picrotoxin-treated rats. Prog. Electromagn. Res. PIER, 2008, 87:149–65. [23] Trastoy-Rios, A; Lopez-Martin, E; Jorge-Barreiro, FJ; Sebastián-Franco, JL; Ribas Ozonas, B; Moreno-Piquero, E, Ares, F; Experimental setup for exposures to a 900MHz-GSM radiation: application to small animals. In: Proceedings of international conference on Electromagnetic Fields, Health and Environment–EHE06 in Madeira Island (Portugal), 2006; 119–23. [24] Royal Decree 1066/28-9-2001, 1999, 36217–27. [25] ICNIRP. Guidelines for limiting exposure to time varying ,electric,magnetic and electromagnetic fields up to 300 GHz. Health Phys., 1998,74,494-522. [26] López-Martín, E; Bregains,J; Relova-Quinteiro,J.L; Cadarso-Suárez, C;Jorge-Barreiro, F.J; Ares-Pena, F.J; The action of pulse-modulated GSM radiation increases regional changes in brain activity and c-fos expression in cortical and subcortical areas in a rat model of picrotoxin-induced seizure proneness. J. Neurosci. Res., 2009; 87(6): 1484– 99. [27] Huber, R; Graf, T; Cote, KA; Wittmann, L; Gallmann, E; Matter, D; Schuderer, J; Kuster, N; Borbély, AA; Achermann, P. Exposure to pulsed high-frequency electromagnetic field during waking affects human sleep EEG. Neuroreport, 2000, 20:11(15):3321-5. [28] Schmid, MR; Loughran, SP; Regel, SJ,; Murbach, M; Bratic Grunauer, A; Rusterholz, T; Kuster N, Achermann, P. Sleep EEG alterations: effects of different pulse-modulated radio frequency electromagnetic fields. J. Sleep Res., 2012, 21(1):50-8. [29] Krause, CM; Björnberg, CH; Pesonen, M; Hulten, A; Liesivuori, T; Koivisto, M; Revonsuo, A; Laine, M; Hämäläinen, H. Mobile phone effects on children’s event-

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María Elena López-Martín and Francisco José Ares-Pena related oscillatory EEG during an auditory memory task. Int J Radiat Biol., 2006;82(6):443-50. Vecchio, F; Buffo, P; Sergio, S; Iacoviello, D; Rossini, PM; Babiloni, C. Mobile phone emission modulates event-related desynchronization of α rhythms and cognitive-motor performance in healthy humans. Clin. Neurophysiol., 2012, 123(1):121-8. Relova, JL; Peleteiro, M; Pertega, S; Vila, JA; López-Martín, E, Ares, F; Effects of cell-phone radiation on electroencephalographic spectra of epileptic patients. IEEE Antennas Propag. magazine, 2010,52(6):173-9. Vecchio, F; Tombini, M; Assenza G, Pellegrino, G; Benvenga, A; Babiloni, C; Rossini, PM; Mobile phone emission increases inter-hemispheric functional coupling of electroencephalographic alpha rhythms in epileptic patients. Int. J. Psychophysiol., 2012, 84(2):164-71. Morgan, IJ; Curran, T; Proto-oncogene transcription factors and epilepsy, Trends Pharmacol. Sci., 1991, 12 (9):343–349. Curcio, C; Ferrara, M; Moroni, F;D´Inzo, G;Bertin; M; De Gennaro, L. Is the brain influenced by a phone call? An EEG study of resting wakefulness. Neurosci Res., 2005, 53:265-270. Eells, JB; Clough, RW; Browing, RA; Jobe, PC. Comparative fos immunereactivity in the brain after forebrain, brainstem, or combined seizures Neuroscience, 2004, 123:279292. Mraovitch, S; Calando, Y. Interactions between limbic, thalamo-striatal-cortical, and central autonomic pathways during epileptic seizure progression. J. Comp. Neurol., 1999, 411(1):145-61. Hossmann, KA; Hermann, DM. Effects of electromagnetic radiation of mobile phones on the central nervous system. Bioelectromagnetics, 2003, 24:49–62. Brillaud, E; Piotrowski, A; de Seze, R. Effect of an acute 900 MHz GSM exposure on glia in the rat brain: a time-dependent study. Toxicology, 2007, 238(1):23–33. Bell-Horner, CL; Dibas, M; Huang, RQ; Drewe, JA; ligands with recombinant GABA (A) receptors. Brain Res. Mol. Brain Res, 2000,76(1):47–55. Huber, R; Schuderer, J; Graf, T; Jutz, K; Borbély, AA; Kuster, N. Radiofrequency electromagnetic field exposure in humans: estimation of SAR distribution, effects on sleep and heart rate. Bioelectromagnetics, 2003,24:262–76. Christ, A; Chavannes, N; Nikolski, N, Gerber, H-U; Pokovik, K; Kuster, N. A numerical and experimental comparison on human head phantoms for compliance testing of mobile telephone equipment. Bioelectromagnetics, 2005,26:125–37. Lalo,U; Pankratov, Y; Kirchhoff, F; North ,RA; Verkhratsky, A; NMDA receptors mediate neuron-to-glia signaling in mouse cortical astrocytes. J. Neurosci., 2006,26(10): 2673–83. Blackman, CF; Benane, SG; Elder, JA; House, DE; Lampe, JA; Faulk, JM; Induction of calcium- ion efflux from brain tissue by radiofrequency radiation: effect of sample number and modulation frequency on the power-density window. Bioelectromagnetics, 1980;1(1):35–43. Kittel, A; Siklow, L; Thuroczy, G; Somosy, Z. Qualitative enzyme histochemistry and microanalysis reveal changes in ultrastructural distribution of calcium and calcium activated ATP-ases after microwave irradiation of the medial habenula. Acta Neuropathol., 1996, 92:362–8.

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[45] Solá, C; Barrón, S; Tusell, JM; Serratosa,J; The Ca2+/calmodulin signaling system in the neural response to excitability. Involvement of neuron and glial cells. Prog. Neurobiol., 1999, 58(3):207–32(review). [46] Cornell-Bell, AH; Finkbeiner, SM. Ca2+ waves in astrocytes. Cell Calcium, 1991, 12(2– 3):185–204. [47] Innocenti, B; Parpura,V; Haydon, PG; Imaging extracellular waves of glutamate during calcium signaling in cultured astrocytes. J Neurosci., 2000, 20(5):1800–8. [48] Carballo-Quintás, M; Martinez-Silva, I; Cadarso-Suarez, C; Alvarez- Folgueiras, M; Ares- Pena, FJ; Lopez-Martín, EA.Study of biomarkers after acute exposure to GSM radiation at 900MHz in the picrotoxin model of rat brain. Neurotoxicology, 2011, 32:478-494.

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Chapter 11

THE EFFECT OF SETTLEMENT REOCCUPATION ON ELECTROMAGNETIC INDUCTION DATA SETS IN ARCHAEOLOGY Daniel P. Bigman University of Georgia, Athens, GA, US

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ABSTRACT This chapter compares results of electromagnetic induction surveys from two archaeological contexts, Drake’s Field and Southeast Plateau, located at Ocmulgee National Monument in Macon, GA. One is a single component area and the other a multi-component area. This survey was conducted to understand large, landscape scale, human settlement patterns in an efficient, cost effective manner without disturbing the archaeological record. I carried out field tests using a soil conductivity meter in continuous data collection mode at a frequency of 12150 Hz. I collected 6 to 9 measurements per meter and spaced transects 1 m apart. The conductivity meter recorded more variation in apparent conductivity values (mS/m) for the reoccupied site (Southeast Plateau). The two data sets differed in interpretability of horizontal grey scale plots and single traces of apparent conductivity values. Drake’s Field resembled similar surveys of single occupation sites. I could interpret anomalies as specific features and patterned clusters of anomalies as buildings. However, 4,000 years of human reoccupation on the Southeast Plateau left a high density of archaeological remains including postholes, hearths, burials, storage pits, and garbage pits. The density of features results in overlapping electromagnetic signatures and anomalies cannot be attributed to specific feature types nor can the location of a specific anomaly be accurately determined. Despite the difficulty in interpreting electromagnetic data sets from reoccupied sites, an important recognition came from this comparison: archaeological sites containing multiple reoccupations yield a specific and recognizable electromagnetic signature. This signature reflects the complicated subsurface modifications made by humans throughout history and can be distinguished from contexts of single occupancy and presumably from unoccupied zones. Archaeologists could potentially use this method for rapid assessment of occupational intensity or length.

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INTRODUCTION Archaeologists have applied electromagnetic fields in the prospection of archaeological remains for half a century. Early work in electromagnetic applications for archaeology focused on the identification of individual archaeological features [Colani 1966; Colani a nd Aitken 1966; Howell 1966; Tite 1961]. Recent developments in instrumentation and data processing software have allowed archaeologists to map entire sites or settlements. In ideal conditions, high density data sets provide accurate plan view maps of entire abandoned communities [see Bigman 2012; Clay 2001; Kvamme and Ahler 2007; and Witten et al. 2003 as examples]. Such data sets help answer anthropological questions regarding the use of space, sociopolitical relationships, landscape preferences, and how the built environment intersects with cultural institutions. Unfortunately, not all archaeological contexts provide conditions amicable to crisp, clean, interpretable data sets. Noisy, “un-interpretable” data sets still provide information, especially if the source of noise is relevant to the occupational history. This chapter compares the results of electromagnetic induction surveys from two archaeological contexts, Drake’s Field and Southeast Plateau, located in Ocmulgee National Monument in Macon, GA (Figure 1). Native Americans occupied Drake’s Field once. This occupation dates to the historic Creek period [1680-1720]. Native Americans occupied the Southeast Plateau during every major Native American period from approximately 3000 BC to AD 1200. The electromagnetic data sets from these two sites differ in interpretability and distribution of apparent conductivity values. The results of these surveys indicate that multiple occupations create overlapping electromagnetic signals and individual anomalies are difficult to isolate. However, archaeologists can identify areas subjected to multiple occupations even if they cannot identify individual features or structures. First, I provide background on the study areas and summarize the history of investigations from the two survey areas. I next present the methods used to carry out the surveys. Finally, I present the results of the two surveys, compare grey scale plots, traces, and histograms, and discuss the differences between single and multiple occupation sites.

STUDY AREAS Ocmulgee National Monument is a famous archaeological park located just north of the Ocmulgee River in central Georgia (Figure 1). It was excavated in the 1930s as part of the New Deal to put people back to work during the American Great Depression [Walker 1994]. Following these excavations, the government preserved the site as Ocmulgee National Monument. Ocmulgee is the fourth-largest (70 ha) mound site in the eastern United States [Hally and Williams 1994] and there is evidence of human occupation dating from the PaleoIndian period (approximately 11,000 BC) [Kelly 1938] through the American Civil War [Iobst 2009]. Native Americans re-occupied Ocmulgee during almost every major cultural period until approximately AD 1720 [Hally 1994]. However, people did not occupy every area of the site throughout time. Native Americans gave differential preference to some areas throughout time while neglecting other areas.

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Figure 1. Location of Ocmulgee National Monument, Drake's Field, and Southeast Plateau.

Figure 2. Excavation history of Drake's Field and location of EM induction survey.

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DRAKE’S FIELD

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Drake’s Field is located on a bluff top in the western portion of Ocmulgee National Monument, just north of the Funeral Mound (Mound C) (Figure 1). The parcel was converted into a series of baseball fields during the second half of the 20th century and the land was gifted to Ocmulgee National Monument in 1991. The National Park Service investigated the area following the donation and placed fifty shovel tests measuring 40 cm in diameter along the outer edge of Drake’s Field at an average depth of 57 cm [Cornelison 1992] (Figure 2). Forty-seven of these tests yielded artifacts. Historic Creek ceramics were abundant. Only one ceramic sherd dated to a pre-historic occupation. The National Park Service placed two small test units at the southern edge of the plot [Cornelison 1992]. One measured 1 m x 1 m and archaeologists excavated it to a depth of 67 cm. The other measured 0.5 m x 0.5 m and was excavated to 55 cm below the surface. These also primarily yielded historic Creek artifacts.The National Park Service revisited the area south of Drake’s Field the following year. Cornelison [1993] excavated five shovel tests to the west of the Funeral Mound parking lot in response to the construction of a new parking lot curb (Figure 2); all contained historic Creek pottery. An earlier project also yielded similar results. Gordon Willey excavated 15 test pits in 1937 to the west of the Funeral Mound (Figure 2). Most of the artifacts recovered from Willey’s stratified excavations consisted of Historic Creek (Ocmulgee Fields and Walnut Roughened) ceramics (AD 1680-1720) [Fairbanks 2003 [1956]:36]. The investigations I reviewed here indicate that Native Americans occupied Drake’s Field during the historic Creek period. All three projects recovered an abundance of historic Creek ceramics. No other occupational period was represented in any significant quantity. Drake’s Field is an area with a single, short lived occupation.

Figure 3. Excavation history of Southeast Plateau and location of EM induction survey.

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SOUTHEAST PLATEAU The Southeast Plateau consists of two consecutive spurs separated from each other by a large erosional gully (Figure 3) located in the eastern portion of Ocmulgee National Monument (Figure 1). The spurs are each bisected by the park’s paved tour road. Mound E, a small earthen pyramid, is located on the Southeast Plateau. Willey excavated four trenches on the Southeast Plateau in 1937 and 1938 (Figure 3). He expanded two of these trenches into excavation blocks after uncovering trash pits, but failed to identify any structures [Ingmanson 1965]. Willey recovered fiber tempered ceramics indicative of a Late Archaic (approximately 3000 BC) occupation [Ingmanson 1965]. His data also suggest that Native Americans reoccupied the Southeast Plateau several times throughout the Woodland (approximately 1000 BC-AD 900) and Early Mississippian (approximately AD 900-1200) periods [Ingmanson 1965]. This proposition is based on Willey’s recovery of elaborately stamped sand tempered pottery (Swift Creek) indicative of the Woodland period and shell tempered plain pottery (Bibb Plain) indicative of the Early Mississippian period. The review of Willey’s results suggests the site saw numerous reoccupation events throughout a 4000 year period. Woodland and Mississippian occupations may have disturbed stratigraphic levels of earlier occupations [Ingmanson 1965:23], creating a complicated archaeological record. The Southeast Plateau reflects an area that was occupied for an extended period of time possibly up to a total of several centuries.

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METHODS I carried out both surveys using a GEM-300 conductivity meter manufactured by GSSI, Inc. The instrument recorded apparent conductivity values measured in mS/m every 1/8th of a second at a frequency of 12150 Hz. Coils are spaced 1.67 m apart and the instrument prospects approximately 2 m at this frequency. The surveyor held the conductivity meter at waist height and oriented the instrument horizontal to the ground surface and perpendicular to the transect direction. Data was collected in a snake-line, where the surveyor traversed neighboring transects in alternating directions. The sampling interval ranged from 6 to 9 readings per meter and the transect interval equaled 1 m. I collected full transects lengths using 20 m fiduciary markers to minimize the effects of staggering due to inconsistencies in surveyor speed. The survey block on Drake’s Field (Figure 2) measured 50 m x 75 m (3750 m2) and the survey block on Southeast Plateau (Figure 3) measured 20 m x 75 m (1500 m2). Table 1.Central tendencies and standard deviations of experimental apparent conductivity data sets Coil Orientation Perpendicular Parallel Difference Between Directions

Mean (mS/m) 8.033333 7.121296 0.912037

Median (mS/m) 7.97037 7.08148 0.88889

STD (mS/m) 0.457511 0.329155 0.128356

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Following Bevan [1998:34], I did not readjust the directional alignment of the transmitter and receiver coils every alternating transect because changes in coil orientation should not affect apparent conductivity readings due to reciprocity. Furthermore, constant readjustment may unbalance the instrument [Clay 2006]. To test this I conducted an experiment by collecting two data sets (160 readings each) while holding the instrument at two different coil orientations (perpendicular and parallel). The central tendencies and standard deviation of values for each direction are similar (Table 1). Both the mean and median varied by less than 1 mS/m and the difference in standard deviation was less than 0.13. This suggests that not readjusting the coil orientation will not have a substantive effect onthe data and subsurface soil variation can still be accurately mapped. Zeroing out the mean of each survey block should create two comparable data sets. I downloaded data to MagMap2000 and used the software to orient transect lengths and position. I then plotted each survey block using Surfer 9.0. A weighted average of the data points from each 0.5 m was used as the grid value. The data points closest to the center of each raster cell carried more weight than those on the raster cells periphery. This process smoothed the data. I processed the two survey blocks using ArchaeoSurveyor 2.0 software and generally followed the processing procedures from Gaffney and Gator [2003] and Kvamme [2006]. I filtered the data first and enhanced data plots second. Data were de-spiked to remove noise and de-striped to account for drift, horizontal striping, or unintended variations in instrument height.I enhanced the data by doubling the X axis (interpolation) to create a denser data set and clipped each survey block at 3 STD.

Figure 4. Grey scale plot of apparent conductivity values collected from Drake's Field with interpretations.

Figure 5. Grey scale plot of apparent conductivity values collected from Southeast Plateau illustrating significant variation in background values.

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Figure 6. Three traces from Drake's Field survey illustrating high level of interpretability of apparent conductivity data. Larger anomalies represent possible Creek buildings and smaller isolated anomalies represent possible pits or burials.

RESULTS Individual anomalies detected in Drake’s Field can be isolated and interpreted as specific types of archaeological remains.The data indicate that Drake’s Field consisted of burials/pits and Native American structures that presumably date to the historic Creek occupation (Figure 4). Numerous small anomalies of low apparent conductivity reflect probable burials or pits (Figure 4). These types of features are often excavated and refilled with the same host material. The fill is less compact than the surrounding matrix and is more porous. Water drains quickly through these features leaving pores filled with air. Air is highly resistive and produces lower apparent conductivity readings. Archaeological remains in pits and burials such as bone, shell, ceramics, lithics, and wood are also resistive and may contribute to overall lower apparent conductivity [Bigman 2012:35]. Three anomalous clusters of high and low apparent conductivity in Drake’s Field may reflect the remains of historic Creek buildings (Figure 4). Excavations of a Creek structure at Ocmulgee suggest that Creek set wooden wall posts into individually excavated postholes [McNeil 2006]. These excavations also identified numerous archaeological features associated with structures. National Park Service archaeologists uncovered interior pits and

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fire basins [McNeil 2006] and excavations at other Creek sites uncovered burials below house floors [Scott 2007]. The close proximity and abundance of features should produce patterned clusters of anomalous readings such as those recorded in Drake’s Field. The clusters I identified with the soil conductivity meter are generally square in shape. Creek typically erected square domestic structures [Scott 2007] often clustered together into groups of three or four structures [Hudson 1976:213-214] similar to the cluster of possible Creek buildings on Drake’s Field. The data set from Southeast Plateau is noisy and individual anomalies cannot be interpreted as specific archaeological remains (Figure 5). The distribution reflects the overlapping electromagnetic signals produced by cultural modifications over 4000 years. While it is tempting to interpret several patterns from the apparent conductivity map in the multi-occupational context, I should remain cautious. Confidence in interpreting specific anomalies as pits or architectural features is minimal and the only ways to increase confidence is by surveying the site using additional near surface geophysical prospection techniques or excavation.

Figure 7. Three traces from Southeast Plateau survey illustrating high variability in apparent conductivity values and difficulty of identification of individual anomalies.

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A comparison of traces from both surveys also illustrates the ease of interpretation from single occupation sites compared to sites of multiple occupations. Figure 6 shows a trace from Drake’s Field. This trace shows individual anomalies separated from each other and each conforms to an expected signature. The isolated low apparent conductivity values represent pits or burials while the cluster of highs and lows reflects a Creek building. Figure 7 shows a trace from Southeast Plateau. Anomalies are not separated from each other and may represent the overlapping signals of closely spaced or disturbed archaeological features. It is impossible to tell where one anomaly or cluster of anomalies begins and ends. Opposing signals from different features may cancel each other out, in whole or in part, due to the averaging effect of soil conductivity meters. However, the comparison of the two survey blocks indicates that areas of single occupations and those of multiple occupations each have an identifiable signature. Survey results across space can inform archaeologists of occupational length and guide archaeologists during more destructive archaeological investigations. Figure 8 shows a histogram of apparent conductivity from Drake’s Field. Data are tightly clustered around a central tendency reflecting the clean background in the gray scale plot. The thin tails reflect archaeological features; cultural modifications in the sub-surface. This histogram conforms to the expected distribution of a short, single occupation where much of the subsurface remains unmodified. Figure 9 shows a histogram of apparent conductivity values from the Southeast Plateau. There is a bi-modal distribution that spreads data values in the first standard deviation further from the central tendency. This contributes to wider variation in the background of the grey scale plot making the data difficult to interpret.

Figure 8. Histogram of apparent conductivity values from Drake's Field showing high frequency of values about the central tendency.

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Figure 9. Histogram of apparent conductivity values from Southeast Plateau showing bi-modal distribution.

These findings are significant for three reasons. First, the rapid collection of EM induction data at archaeological sites is quicker, more efficient, less time consuming, and less destructive than traditional excavation. Large excavation blocks can take an entire field season or multiple field seasons to complete without heavy machinery. The cost of renting heavy machinery such as a back hoe can be substantial and sometimes difficult for academic departments or cultural resource management firms to obtain. Also, removal of artifacts and disturbance to the archaeological record from excavation or stripping with heavy machinery is an irreversible process. I surveyed Drake’s Field in approximately 2 hours and the Southeast Plateau in approximately an hour and fifteen minutes including grid setup and the archaeological record remains intact. Second, geophysical survey in general and EM induction specifically allows archaeologists to investigate significantly more area than excavation. The amount of space one can cover lets archaeologists answer anthropological questions at larger scales relating to power relationships, social inequality, the use of space, and human/environment interaction. For example, the Southeast Plateau is located near Walnut Creek, a feeder stream of the Ocmulgee River. The early occupations on the Southeast Plateau would have been small and the immediate landscape relatively free of other human inhabitants. The earliest settlers probably choose a convenient place on the landscape near a water source but still high on the bluff top to be defensible and drain water quickly. As the settlement sizes grew during subsequent occupations such as the Late Woodland, Early Mississippian, or Historic Creek, areas like the South Plateau could not support the entire population. New areas needed to be occupied. Third, my study identifies a new application of electromagnetic fields for archaeological purposes: measuring relative occupational length across archaeological sites. Archaeologists have primarily used electromagnetic induction survey to map spatial

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The Effect of Settlement Reoccupation on Electromagnetic Induction Data Sets … 359 distributions of possible features and relate them in a meaningful way for social science. Although most archaeological geophysical data sets are interpreted through a synchronic lens, some researchers have begun to make significant strides in diachronic interpretation. Walker [2009] made inferences regarding settlement pattern changes using differing magnetic signatures mapped with a gradiometer that represent structures from two different occupations and Goodman et al. [2009] argued that ground penetrating radar has the resolution to differentiate between architectural types that vary through time. Not all sites are conducive to these techniques and the length of occupation from these sites is less than the Southeast Plateau. The current study marks the first time that relative lengths of occupation have been correlated with EM induction signatures and clarity of data. Excavation had a monopoly on temporal information, but geophysical prospection is making breakthroughs in this area. My study has several limitations. None of the anomalies identified in either survey have been ground truthed. There is a possibility that some anomalous readings variation in underlying geology or natural features. Also, prior to being protected as Ocmulgee National Monument, the grounds were subjected to historic disturbance including plowing, historic houses, and Drake’s Field’s use as a community recreational area may influence electromagnetic readings. The manufacturing of the baseball field could have introduced more or less variation into the data set. While I believe the most important contributor to the data sets from Drake’s Field and the Southeast Plateau is occupational length, the reader should be aware of some other possible sources of variation

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CONCLUSION Noisy EM induction data sets that are difficult to interpret are still useful and provide information on human occupation, settlement, and use of landscapes. Ideal survey conditions on single occupation sites using EM induction can provide detailed maps of site layout and interpretable information on spatial relationships of features and buildings. However, limiting surveys to ideal survey conditions biases our collective understanding of past human behavior. Using EM induction to map the distribution and density of anomalies across landscapes can inform our understanding of human behavior, cultural habits, and human/environment interaction through time. Did people prefer certain areas and why did they reoccupy them? Why were other areas devoid of human settlement until more recently? Mapping variation of EM conductivity anomaly density can inform such questions. Paired with more traditional lines of archaeological evidence gathered through excavation, EM induction survey becomes a powerful tool for mapping long term human settlement patterns. This project identified an EM signature of overlapping low amplitude signals for archaeological sites with multiple occupations that may be applied to other geographical and cultural contexts. EM induction should remain an important tool in the archaeologist’s tool kit that helps supplement other geophysical techniques and more traditional archaeological data.

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Daniel P. Bigman

ACKNOWLEDGMENTS I would like to thank Ben Steere and Mark Williams for reviewing the chapter. Their insightful comments improved the paper. I would also like to extend my appreciation to the National Park Service, Ocmulgee National Monument, and the Muscogee Nation for their continued support. Equipment for the project was provided by the University of Georgia’s Laboratory of Archaeogeophysics and Archaeometry and the University of Georgia’s Laboratory of Archaeology.

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REFERENCES Bevan, B. W. 1998 Geophysical Exploration for Archaeology: An Introduction to Geophysical Exploration. Midwest Archaeological Center Special Report 1. Lincoln, N. E. Bigman, D. P. 2012 The Use of EM Induction for Locating Graves and Mapping Cemeteries: An Example from Native North America. Archaeological Prospection 19:31-39. Clay, R. B. 2001 Complementary Geophysical Survey Techniques: Why Two Ways are Always Better Than One. Southeastern Archaeology 20:31–43. Clay, R. B. 2006 Conductivity Survey: A Survival Manual. In Remote Sensing in Archaeology: An Explicitly North American Perspective. Edited by J. K. Johnson, pp. 79-108.University of Alabama, Tuscaloosa. Colani, C. 1966 A New Type of Locating Device. I-The Instrument. Archaeometry 9:3-8. Colani, C. and M. J. Aitken 1966 A New Type of Locating Device. II-Field Trials. Archaeometry 9:9-19. Cornelison, J. 1992 Trip Report for the Archaeological Investigations at the Mound C Parking Lot at O. C. M. U., 3/12/92 – 3/13/92, S. E. A. C. Accession Number 1002, O. C. M. U. Accession Number 147, Report on file, Southeast Archaeological Center, National Park Service, Tallahassee, Florida. Cornelison, J. 1993 Final Trip report on archaeological testing at Drake’s Field, Ocmulgee National Monument, Georgia, July 27 to July 29, 1992, S. E. A. C. Accession Number 1044, O. C. M. U. Accession Number 148, Report on file, Southeast Archaeological Center, National Park Service, Tallahassee, Florida. Fairbanks, C. H. 2003 [1956] Archaeology of the Funeral Mound, Ocmulgee National Monument, Georgia. University of Alabama Press, Tuscaloosa. Gaffney, C., and J. Gater 2003 Revealing the Buried Past: geophysics for archaeologists. Stroud, Tempus. Goodman, D., S. Piro, Y. Nishimura, K. Schneider, H. Hongo, N. Higashi, J. Steinberg, and B. Damiata. 2009 G. P. R. Archaeometry. In Ground Penetrating Radar: Theory and Applications, edited by Harry M. Jol, pp. 479-508. Elsevier; Amsterdam. Hally, D. J. (Editor) 1994 Ocmulgee Archaeology:1936-1986. University of Georgia Press, Athens. Hally, D. J,.and M. Williams 1994 Macon Plateau Site Community Pattern. In Ocmulgee Archaeology 1936-1986, Edited by David J. Hally, pp. 84-95. University of Georgia Press, Athens.

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The Effect of Settlement Reoccupation on Electromagnetic Induction Data Sets … 361 Howell, M. 1966 A Soil Conductivity Meter. Archaeometry9:20-23. Hudson, C. 1976 The Southeastern Indians. University of Tennessee Press, Knoxville. Ingmanson, J. E. 1965 Mound E., Southeastern Plateau, and Middle Plateau Fortifications Ocmulgee National Monument. Manuscript on file, Southeast Archaeological Center, National Park Service, Tallahassee, Florida. Iobst, R. W. 2009 Civil War Macon: The History of a Confederate City. Mercer University Press, Macon. Kelly, A. R. 1938 A Preliminary Report on Archaeological Explorations at Macon, Ga. Bulletin 119, Bureau of American Ethnology, Anthropological Papers, No. 1. Smithsonian Institute, Washington D. C. Kvamme, K. L. 2006 Data Processing and Presentation. In Remote Sensing in Archaeology: An Explicitly North American Perspective, edited by J. K. Johnson. University of Alabama Press, Tuscaloosa. Kvamme K. L.,and Ahler S. A. 2007Integrated remote sensing and excavation at the Double Ditch State Historic Site, North Dakota. American Antiquity 72:539–561. McNeil, J. 2006 Archaeological Investigations on the Middle Plateau, Ocmulgee National Monument, Macon, Georgia, S. E. A. C. Accession Number 1683, O. C. M. U. Accession Number 232, Report on file, Southeastern Archaeological Center, National Park Service, Tallahassee, Florida. Scott, R. J. 2007 Interpreting Changes in Historic Creek Household Architecture at the Turn of the Nineteenth Century.In Architectural Variability in the Southeast, edited by C. H. Lacquement, pp. 166-187. University of Alabama Press, Tuscaloosa. Tite, M. S. 1961 Alternative Instruments for Magnetic Surveying: Comparative Tests at the Iron Age Hill-Fort at Rainsborough. Archaeometry 4:85-90. Walker, C. P. 2009 Landscape archaeogeophysics: a study of magnetometer surveys from Etowah (9BW1), the George C. Davis site (41CE19), and the Hill Farm Site (41BW169). Unpublished dissertation, Department of Anthropology, University of Texas, Austin. Walker, J. 1994 A Brief History of Ocmulgee Archaeology. In Ocmulgee Archaeology 1936-1986, edited by David J. Hally, pp. 15-35.University of Georgia Press, Athens. Witten, A., G. Calvert, B. Witten, and T. Levy 2003 Magnetic and Electromagnetic Induction Studies at Archaeological Sites in Southwestern Jordan. Journal of Environmental and Engineering Geophysics 8:209-215.

Reviewed by: Mark Williams, University of Georgia. Benjamin A. Steere, University of West Georgia.

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In: Electromagnetic Fields Editors: Myung-Hee Kwang and Sang-Ook Yoon

ISBN: 978-1-62417-063-8 c 2013 Nova Science Publishers, Inc.

Chapter 12

N EW C OOPERATIVE E FFECTS IN S INGLE - AND T WO -P HOTON I NTERACTIONS OF R ADIATORS WITH E LECTROMAGNETIC B ATH Nicolae A. Enaki∗ Quantum Optics and Kinetic Processes Lab Institute of Applied Physics Academy of Sciences of Moldova, Chisinau, Republic of Moldova

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Abstract Two types of resonances between the spontaneous and induced emissions by twoand single photon transitions of three inverted radiators from the ensemble are proposed to accelerate the collective decay rate of the entangled photon pairs generated by the system relative the dipole-forbidden transition. The influence of the bath temperature to such processes is studied. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipole-forbidden transitions of third atom. Second effect corresponds to the scattering situation, when the difference of the excited energies of two dipole-active radiators are in the resonance with the dipole-forbidden transitions of third atom. These effects are accompanied with the interferences between single- and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions.

The new cooperative effect between the radiators consisted of dipole active A, S and R subsystems and dipole forbidden transitions of D subsystem is established in the process of three particle spontaneous emission (see Figure 1 A and B). This book is devoted to the new type of three particle collective spontaneous emission in which the decay rate of three atomic subsystems is proportional to the product of the numbers of atoms in each subsystem ∗

The Author thanks for invitation E-mail address: [email protected]; http://www.qol.asm.md

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Ns Nr Nd . The quantum kinetics takes into consideration both the correlations between three subsystems S, R and D and single and two-photons cooperative effects between the atoms of each sub-ensemble. The three particle cooperative interaction through the vacuum of EMF takes place in the process of mutual influences of the single photon polarization of S and R atomic subsystem with the polarization of the D atomic ensemble relatively the two-photon cooperative emission. To understand this effect it is carefully studied the new correlation function between the polarization of three different radiators from S, R and D subsystems. In order to avoid the confusion with Dicke super-fluorescence or two-photon super-fluorescence, in this report it is proposed to study the cooperative effect only between one dipole forbidden atom (D atom) and two dipole active atoms S and R (the radiators S and R don’t enter in the resonance one with another). In this case only one possibility appear between such three particle ensemble : to enter in the resonance one with another according to the conservation laws: 2ω0 = ωr + ωs and 2ω0 = ωa − ωs which correspond to the two-photon resonances and scattering resonances between the three particle, respectively. Figure 1 the resonance between the two-photon transitions of D atomic subsystem and the two dipole active systems, R and S is represented in Figures A and B. Three atoms D, R and S are situated at relative distances rds , rdr and rrs. The exchange energies between the subsystems in two-photon resonance 2ω0 = ωr + ωs , and the scattering resonance 2ω0 = ωa − ωs are given by energetic schemes A and B. Two types of resonance between the spontaneous emissions by two- and single photon transitions of three inverted radiators from the ensemble are proposed to accelerate the collective decay rate of the entangled photons generated by the system relative the dipole-forbidden transition. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipole-forbidden transitions of third atom. Second effect corresponds to the scattering situation, when the difference between the excited energies of two dipole-active radiators is in the resonance with the dipole-forbidden transition of third atom. These effects are accompanied with the interferences between single- and twoquantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions.

1.

Introduction

2.

Cooperative Three-Particle Resonance and Its Representation by Master Equations

Let us consider the interaction of three subsystems of radiators A, R, S, and D through the vacuum of EMF. The first two groups of radiators, R and S, prepared in excited state |er i ⊗ |es i can pass into Decke super-radiance regime [7] relatively the dipole active transitions ea → ga, er → gr and es → gs at frequencies ωa , ωr and ωs (Figures 1 A , B). According to the Figure 1 A the excited D atom relatively the dipole forbidden transition 2d → 1d passes in the ground-state |1di simultaneously generating two quanta under the influences of first two atomic subsystems and vacuum fluctuation of EMF. This transition takes place through the virtual levels, which we replaced by the state |3di with opposite symmetry relative the ground |1di and excited |2di states. An example of two-photon spontaneous decay may be

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New Cooperative Effects in Single- and Two-Photon Interactions . . .

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Figure 1. The resonance between the two-photon transitions of D atomic subsystem and the two dipole active systems, R and S is represented in figures A and B. Three atoms D, R and S are situated at relative distances rds , rdr and rrs. The exchange energies between the subsystems in two-photon resonance 2ω0 = ωr + ωs , and the scattering resonance 2ω0 = ωa − ωs are given by energetic schemes A and B. the transition relative the states with same symmetry |(n + 1)Si → |nSi through the virtual state |(n + 1)P i (see [28], [6]). The new possibilities of cooperative emissions can be observed in the resonance interaction between the dipole active radiators of R, S subsystems and dipole forbidden of D subsystem in two situations: A. The emission frequencies of the dipole active and dipole forbidden radiators satisfies the resonance condition ωr + ωs = ωd . Here ωr , ωs are the transition frequencies of R, S dipole-active radiators and ~ωd = 2~ω0 is the energy distance between ground |nSi and excited |(n + 1)Si states of the dipole forbidden transition of D radiator (see Figure 1 A) the dipole active radiators satisfy the scattering condition ωa − ωs = ωd . As it is represented in Figure 1 B, the transition energy of the dipole active atom A is larger than the transition energy of atoms S and D. Here, the two-photon resonance between the dipole active subsystems A and S is more effective, when the intermediate state of atom D has the small de-tuning from resonance ∆ = |(E3 − E2 )/~ − ωs |. Here, we discuss the condition for which, the pure super-fluoresce of the small number of radiators [50]–[49], in the subsystems R, S and D enter into interaction during the delay time of cooperative spontaneous emission of each subsystem so that inhomogeneous broadening of exited atomic states can be neglected, τr,i  T2,i. Here τr,i = τ0 /Ni is the collective time for which the polarization of the i subsystem become macroscopic, T2,i is the de-phasing time of the subsystem i, which include the reciprocal inhomogeneous and Doppler-broadened line-width, i ≡ S, R, and D (see, for example, the papers [49]– [51]). These conditions can be achieved using laser cooling method [45], [46] for three atomic ensembles represented in Figures 1 A and B. Let us suppose, that delay time of the super-radiant pulse is less than T2,i, we will drop the terms connected with de-phasing time T2,i from the kinetic equations. In this situation, considering, that the conservation energy law is established between the transitions of three atoms: ~(ωr + ωs ) = 2~ω0 (according

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Nicolae A. Enaki

to Figure 1 A) and ~(ωr − ωs ) = 2~ω0 (according to Figure 1 B), one can propose the following Hamiltonian of interaction of radiators with EMF ˆ =H ˆ 0 + λH ˆI, H

(2.1)

where the free and interaction parts are represented below c0 = H

X k

cI = − λH − − − +

~ωk b ak†b ak +

Na XX

Nr X j=1

b zj + ~ωjr R

l=1

bzl + ~ωls A

  b +b (da , gk )A j ak exp i(k, rj )

Ns X l=1

~ωls Sbzl +2~

N X

ω0 Dzm ,

(2.2)

m=1

k n=1 Nr XX k

j=1

  b +b (dr , gk )R j ak exp i(k, rj )

Ns XX  (ds , gk ) Sbl+ b ak exp[i(k, rl)] k

l=1

N X X

k1 ,k2 m=1 N X X

k1 ,k2 m=1

  b +b qb (k1 , k2){D ak1 exp i(k1 + k2 , rm) m ak2 b

n o   − † bm qs (k1 , k2 ) D b ak2 b ak1 (1−δk1 ,k2 )exp i(k1 −k2 , rm) +H.c. . (2.3)

Here we have the first-order gk = Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

Na X

qb (k1 , k2) = qs (k1 , k2) =

p 2π~ωk /V λ , and second order

(d31 , gk1 )(d32 , gk2 ) (d31 , gk2 )(d32, gk1 ) + , 2~(ω32 + ωk1 ) 2~(ω31 − ωk2 ) (d31 , gk1 )(d32 , gk2 ) (d31 , gk2 )(d32, gk1 ) + ~(ω32 − ωk1 ) ~(ω31 + ωk1 )

interaction constants. b ak and b ak† are annihilation and creation operators of EMF photons with wave vector k, polarization λ and frequency ωk ; da, dr and ds are dipole momentum transitions between the ground and excited states for A, R and S atomic subsystems; d32i and d31 are dipole momentum transitions in the three-level system of the atomic sub-ensemble D. The excitation and lowering operators of A, R, S, and D atomic − subsystems satisfy the commutation relations for SU (2) algebra [Jbl+ , Jbj ] = 2Jlz δl,j ; ± ± cl ± cl ± , Sbl ± or D [Jblz , Jbj ] = ±Jbl δl,j , where Jbl± is equivalent with operators of Aˆ± , R bz , Sbz and Dz operaatomic subsystems. The inversion operator Jbz is one of the Aˆz , R tors, respectively. The operators of EMF satisfy the commutation relation [b ak , b ak†0 ] = δk,k0 ; [b ak†, b ak†0 ] = 0, where k = (k,λ) is the wave vector and polarization of the photon. A. In comparison with the paper[54], here we will take into consideration simultaneously both effects connected with the influence of dipole active atoms A , S and A on the two photon spontaneous emission of dipole forbidden D subsystem for a finite temperature of the system.

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367

B. Another attractive effect corresponds to the situation when the dipole active subsystems A, S and R are non-equidistant so that Dicke cooperative effects between each subsystem are negligible. Considering that exist the large number of possibilities between the subsystems S and A and subsystems S and R so that it is satisfied the two photon resonances cooperative conditions ωd = ωa,l − ωs,m and ωd = ωs,l + ωr,m for different atomic pairs Al and Sm ; Rm and Sl respectively. In this case three particle cooperative effects become significant and dipole active atoms drastically can modify the the two-photon transition in the system D. b Let us now consider the Heisenberg equation for the mean value hO(t)i = b b h0, Ψa(0)|O(t)|0, Ψa(0)i of an arbitrary atomic operator O(t), where |0, Ψa(0)i = |0i|Ψa(0)i is the initial state of EMF and radiator subsystems. Indeed considering that at initial time t = 0 the EMF is in the vacuum state, we can represent the Heisenberg equab tion for the mean value of the atomic operator hO(t)i through the normal product of EMF operators N

a XX b  dhO(t)i (da, gk ) ˆ+ ˆ =−i [Al (t), O(t)]b ak (t) exp[i(k, rl)] dt ~

−i −i

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−i

k l=1 N r X (dr , gk ) l=1 Ns X l=1

~



 ˆ + (t), O(t)]b ˆ ak (t) exp[i(k, rl)] [R l

 (ds , gk ) ˆ+ b ak (t) exp[i(k, rl)] [Sl (t), O(t)]b ~

N XX   +  qb (k1 , k) b (t), O(t)]b b ak (t)b exp i(k1 + k, rm) [D ak (t) m 1 ~ k1 ,k m=1

N XX   †  qs (k1 , k) + bm b ak (t) +i exp i(−k1 + k, rm) b ak1 (t)[D (t), O(t)]b ~ k1 ,k m=1

b + → O). b + H.c. (O

(2.4)

Taking into account, the action of vacuum parts of operators b ak (t) and b ak† (t) on the vacuum state of EMF b ak (0)|0iph = h0|b ak†(0) = 0, we can partially eliminate the free parts of EMF field operators from the equation of the atomic operators. According to the interaction part (2.3) of Hamiltonian (2.1), let us represent the solution of the Heisenberg equation for EMF † operators b ak (t) and b ak (t) through the sources and free operator parts ak (t) = b b ak (0) exp[−iωk t] + b aks (t), b ak†(t) = [b ak (t)]†,

(2.5)

where b akv (t) = b ak (0) exp[−iωk t] and b aks (t) are the vacuum and source parts, respectively. Here, the source part is represented through the atomic polarization operators of the system b aks (t) = 2i

Z N X X qb (k1 , k) n=1 k1

~

0

t

  − b (t − τ )b dτ exp − i(k1 + k, rn) − iωk τ D ak†1 (t − τ ) n

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Nicolae A. Enaki −i

N XZ X

t

  dτ exp − i(k1 − k, rn) − iωk τ

n=1 k1 0



qs (k1 , k) b − qs (k, k1) b + × Dn (t − τ )b ak1 (t − τ ) + Dn (t − τ )b ak1 (t − τ ) ~ ~ Zt Na X i(da, gk ) b − (t − τ ) + dτ exp[−i(k, rl) − iωk τ ]A l ~ l=1

+

Nr X l=1



0

 − i(dr , gk )  b (t − τ ) − i(k, rl) − iωk τ R l ~ N

s i(ds , gk ) X + ~

Zt

j=1 0

  dτ exp − i(k, rj ) − iωk τ Sbj− (t − τ ), †,s

b ak (t) = [b aks (t)]+.

(2.6)

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We are interested in the description of three particle resonances represented in Figures 1 A and B. It is not difficult to observe that, such resonances appear in the third order of the interaction constant λ of the Hamiltonian (2.1). The terms of perturbation theory proportional to the constants (ds , gk )q(ωk1 , ωk ) give main contribution in the two-photon resonance between the atomic subsystems D and S,R. The conventional Born-Marcoff approximation in the right hand site of the equation (2.4) is reduced to the divergent expressions for cooperative rates of subsystems of radiators. To observe these divergences, let us firstly approximate the right hand site of the equation (2.6) using the traditional Born–Marcoff approximation [48], [8] Na

b aks (t) = +

+

(da, gk ) X − Al (t) exp[−i(k, rl)]ζ ∗ (ωk − ωr ) ~ (dr , gk ) ~ (ds , gk ) ~

+2

l=1 Ns X

N X X n=1 k1

−

l=1 N r X

N X X n=1 k1

j=1

b − (t) exp[−i(k, rl)]ζ ∗ (ωk − ωr ) R l

Sbj− (t) exp[−i(k, rj )]ζ ∗ (ωk − ωs )

  (qd (k1 , k) b − ak†1 (t) exp − i(k1 + k, rn) ζ ∗ (ωk + ωk1 − 2ω0 ) Dn (t)b ~ 





qs (k1, k) b − Dn (t)b ak1 (t)ζ ∗ (ωk − ωk1 − ωd ) ~  qs (k, k1) b + ∗ + (2.7) Dn (t)b ak1 (t)ζ (ωk − ωk1 + ωd ) . ~ exp − i(k1 − k, rn)

The small parameter in this approximation is the ratio of retardation time to cooperative spontaneous emission times of the subsystems, τ /τi  1. Here iζ(x) = i Pr /x + πδ(x) Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

New Cooperative Effects in Single- and Two-Photon Interactions . . .

369

is the Heitler function [8], [9]. The function i Pr /x represents the k-summation in analogy with Cauchy principal value [48]. Let us firstly apply the approximation (2.7) to two-photon resonance between the radiators A, S, R and D. Introducing the operators ( 2.7) in equation (2.4) and consecutively eliminating the boson operators of EMF, it obtains the following equation for operator O(t) with three particle cooperative rates Na XX b  dhO(t)i (da , gk )2 b + b A b − (t) exp[i(k, r −rl )]iζ ∗ (ωa −ωk ) = [Aj (t), O(t)] j l 2 dt ~ k l,j=1

+

Nr XX  (dr , gk )2 b + b R b −(t) exp[i(k, rj −rl )]iζ ∗ (ωr −ωk ) [Rj (t), O(t)] l 2 ~ k l,j=1

+

Ns XX  (ds , gk )2 b + b Sb − (t) exp[i(k, rj −rl )]iζ ∗ (ωs −ωk ) [Sj (t), O(t)] l 2 ~ k l,j=1

+2

N XX  qb2 (k, k0 ) b + b D b − (t) [Dj (t), O(t)] l 2 ~ k,k0 l,j=1   × exp i(k − k0 , rj − rl ) iζ ∗ (2ω0 − ωk − ωk0 )

+ 2i

Nr N X Ns X XX (ds , gk0 )(dr , gk )qb (k, k0 )

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k,k0 n=1 l=1 l=1 × iζ ∗ (ωr − ωk )iζ ∗ (ωs

− 2i

~3

− b + (t), O(t)]R b b− [D n j (t)Sl (t)

  − ωk0 ) exp i(k, rn − rl ) + i(k0, rn − rl )



N XX XX (dr , gk )(ds , gk0 )qb (k, k0 ) k,k0 m=1 l=1 j=1

×

~3

h

 − b + (t), O(t)] b D bm Sb + (t)[R (t) iζ ∗ (ωr −ωk )iζ(ωs −ωk0 ) j

l

i  b + (t)[Sb + (t), O(t)] b D b − (t) iζ ∗ (ωs − ωk )iζ(ωr − ωk0 ) + R m j l   × exp i(k, rj ) + i(k, rl ) − i(k + k0 , rm)

N i XX X (da , gk )(ds , gk0 )qs (k0 , k) ~3 0 m=1 l,j=1 k,k   × exp − i(k, rj ) + i(k, rl ) + i(k − k0 , rm )

 b + (t)[A− (t), O(t)] b × { Sbl+ (t)D iζ(ωs − ωk0 )iζ(2ω0 + ωk0 − ωk ) m j D E b D b + (t)A b − (t) iζ(2ω0 + ωk0 − ωk )iζ ∗ (ωa − ωk )}} − [Sbj+ (t), O(t)] m l   i X X − 3 (ds , gk0 )(dr , gk )qs (k, k0 ) exp − i(k, rn − rj ) + i(k0 , rn − rl ) ~ k,k0 j,l,n=1

+  − ∗ b (t)[D b n−(t), O(t)]S b 0 A j l (t) iζ(ωa − ωk )iζ (ωs − ωk )

+

b + → O). b + H.c. (O

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(2.8)

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We observe that in the right hand part of the equation () the third-order terms contain resonance between the single-photon radiators A, B and two-photon radiator D, described − b b − b− b+ b + (t), O(t)]D b by the correlation functions hSbl+ (t)[R m (t)i, h[Dn (t), O(t)]Rj (t)Sl (t)i j − (t)i. b + (t)[Sb + (t), O(t)] b D bm These terms contain the product of the functions and hR j l [Pr /(ωr − ωk )][Pr /(ωs − ωk0 )] which describe the principal value in the integration procedure on the variables k and k0 . It is not difficult to observe that the summation on the ~k and k~0 vectors of the right hand site of this equation give us the divergent expressions. In order to avoid such divergences we propose in next section the new method of elimination of field operators in the nonlinear interaction of atoms with vacuum field. As follows from the normal arrangement of the operators in equation (2.4) and expression (2.5), the free parts of the boson operators are partially eliminated. To obtain the master equation for atomic subsystem, we must totally eliminate the vacuum parts of EMF operators from the expression (2.4). According to generalized equation (2.4) is impossible to move the b + (t), O(t)]b ak1 (t)b aks (t)i, befree part b akv1 (t) of the operator b ak1 (t) in the correlation h[D m cause it doesn’t commute with the operator b aks (t). The similar situation is observed after the substitution of exact solution (2.6) in the master equation (2.4). It is observed that in b D b n(t − τ )b the correlation like h[hSb + (t), O(t)] ak†1 (t − τ )i, the operator b ak†1 (t − τ ) must be permuted in the right hand part of this correlation. The quantum approach for the elimination of the vacuum part of EMF operators in nonlinear interaction with vacuum field is proposed in Section (3.). This method gives us the possibility to eliminate the vacuum parts of the bi-boson operators in similar situations. The master equation (3.14) for three atomic subsystems in interaction through the vacuum of EMF is obtained, taking into account the normal ordering of annihilation and creation operators of EMF in the correlation functions of bi-boson EMF operators. At the end of this section we observe, that the three particle cooperative effects described above can be experimentally observed if we will find the conditions under which the single photon cooperative effect becomes negligible. Indeed consider that systems A, S and R consist from the discreet number of two level atoms which don’t enter in the resonance with which other. Due to the large detuning from resonance between the atoms of each subsystem |ωjα − ωlα |τα  1, one can neglect the cooperative effects between atoms of subsystems A , S and R.gust the three-particle cooperative effects become significant if we consider that in the subsystems S and R and subsystems S and A exist the enough pairs of atoms so that the energies of this atomic pairs satisfy the three particle resonance conditions represented in fig. 2 ωsj + ωrl = 2ω0 and ωal − ωsj = 2ω0 . In this case the cooperative effects in the first three terms in the master equation (2.8) are absent.

3.

Elimination of Boson Operators of EMF Taking for “T = 0” Temperature of the System

In this section we propose to eliminate the vacuum field operators without Born -Marcoff approximation. This method gives us the possibility to eliminate the vacuum parts of the bi-boson operators in similar situations. The new master equation (3.14) without the Maroff approximation for the three-atomic subsystems in interaction through the vacuum of EMF is obtained, taking into account the normal ordering of annihilation and creation operators

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371

of EMF in the correlation functions. At the end of the last Section 2. it is emphasized that the three particle cooperative effects described above can be experimentally observed if we found the conditions under which the single photon cooperative effect becomes negligible. Let us eliminate the EMF field operators from generalized equation (2.4). Introducing the solution (2.5) in the generalized equation (2.4) we obtain the following partial elimination of boson operators of EMF from the correlations Zt

N X (n31 , eλ1 )(n32 , eλ)qb (ω1 , ω) ~ n=1 k1 0

+  
 b (t), O(t)] b D b − (t − τ ) exp − i k1 + k, exp[−iωk τ ] × [R n l ( N X (n31 , eλ )(n32 , eλ)   1 × i exp − i(k1 − k, rn) ~ n=1

+  b (t), O(t)] b D b n−(t − τ )b × qs (ω1 , ω) [R ak1 ,s (t − τ ) l

X

+  b (t), O(t)]b b aks (t) = 2i [R l

dτ exp[−iωk τ ]

N

r

+  i(dr , gk ) X b (t), O(t)] b R b − (t − τ ) exp[−i(k, rl)] [R + l l ~

l=1

 Ns X

+  i(ds , gk ) b (t), O(t)] b Sb − (t − τ ) + exp[−i(k, rj ) [R , (3.1) j l  ~ j=1

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+  X b (t), O(t)]b b ak0 (t)b [D aks (t) ' m ×

(

Zt

k1 0

N X

  dτ exp − iωk τ − i(k1 + k, rn)

 2i(n31 , eλ1 )(n32 , eλ )qb (ω1 , ω) b + b ak0 (t)D b − (t − τ )b [Dm (t), O(t)]b ak†1 (t − τ ) n ~ n=1 X (dr , gk )

 b + (t), O(t)]b b ak0 (t)R b − (t − τ ) +i [D m l ~ l=1 )  (ds , gk ) b + − b ak0 (t)Sb (t − τ ) exp[−i(k, rl)] . (3.2) [Dm (t), O(t)]b + l ~

Here, we have represented the interaction constant in two-quantum interaction of Dsubsystem through the polarization vectors of the modes k1 and k2 : g(k1, k2 ) = (n31 , eλ1 ) (n32 , eλ ) qb (ω1 , ω), where n3α = d3α/d3α. Looking carefully in the right hand site of these expressions, we observe that full EMF operator b ak1 doesn’t commute with source part [b ak1 (t), Jbls (t − τ )] 6= 0, where Jb is one of the operators of radiator subsystems. We ak (t), representing the correlation of the can eliminate the free parts of operators b ak1 (t) and b s (t)i and hA(t)b b ak (t)b b ak (t)b aks (t)i. It is not diffia ak1 (t)b equation (2.4) in two forms hA(t)b 1 k cult to observe that this representation doesn’t solve the problem of simultaneous elimination of vacuum parts of both operators b ak1 and b ak (t). Here, according to our representation, b operator can be represented through the operators of the equation the atomic operator A(t) +(t), O(t)]. b = [D bm b (2.4) in the following way A(t) Observing that the source part of EMF

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operator b aks (t) is expressed through the linear combination of retardation atomic operator b according to with the formal solution (2.6), we can represent these operators through B(t) − − b is the operator Sb (t − τ ) or R b (t − τ )). In r this situation, the elimination of free (B(t) j l parts of both operators can be made according to the lemma.

Lemma 1. If Bose b ak (t) and b ak+ (t) operators lie between two operators of atomic b 1 ) and B(t b 2 ) belong to other time moments, t1 and t2 , the elimination of the subsystem A(t free part of these operators yielded to the following expression for the correlation



 b 1 )b b 2 ) = A(t b 1 )b b 2) A(t ak (t)B(t aks(t)B(t

 b 1 )[b b 2 )] , − exp[−iωk (t − t2 )] A(t aks(t2 ), B(t (3.3)



 b 1 )b b 2 ) = A(t b 1 )b b 2) A(t ak+ (t)B(t ak†,s(t)(t)(t)B(t

 b 1 ), b b 2) . − exp[iωk (t − t1 )] [A(t a †,s(t1 )]B(t k

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Proof. The commutations in (3.3) play the highest role in the bi-photon spontaneous emission, and such commutations bring the main contribution to the two-photon resonances between three particles. The problem is reduced to the elimination of vacuum part lies b 1 ) and B(t b 2) between the operators A(t



 b 1 )b b 2 ) = A(t b 1 )(b b 2) . A(t ak (t)B(t akv (t) + b aks (t))B(t Since b ak (t) = b akv (t) + b aks (t) we will represent the vacuum part b akv (t) = b ak (0) exp[−iωk t] through the vacuum operator at time moment t1 . Taking into account the identity (2.6), we can represent the vacuum part in the following form  akv (t) = b b akv (t2 )e−iωk (t−t2 ) = b ak (t2 ) − b aks (t2 ) e−iωk (t−t2 ) . After the substitution of hatavk (t) into the correlation it is obtained the expression





 b 1 )b b 2 ) = A(t b 1 )b b 2 ) + e−iωk (t−t2 ) A(t b 1 ){b b 2) . A(t ak (t)B(t aks (t)B(t ak (t2 ) − b aks (t2 )}B(t

We observe that operator ak (t2 ) commutes with the operator B(t2 ). Consequently, taking into account, that b 2 )|0i = B(t b 2 )b b ak (t2 )B(t ak (t2 )|0i

it is easily obtained that



 b 1 ){b b 2 ) = − B(t b 2 )[b b 2 )] . A(t ak (t2 ) − b aks (t2 )}B(t aks(t2 ), B(t This identity proofs the Lemma (3.3).

Let us describe the resonance represented by Figure 1 A. This lemma (3.3) can be used in the single photon terms (3.1) of generalized equation (2.4) for correlab +(t), O(t)]b b ak (t)Sb − (t − τ )i, h[D b + (t), O(t)]a b b− tion functions like h[D k (t)Rl (t − τ )i and n j j b + (t), O(t)] b D b − (t − τ )b h[R ak†1 (t − τ )i. Indeed, taking into account the lemma (3.3), the n j above correlation functions can be represented through atomic operators D E D E b + (t), O(t)]b b ak (t)Sb − (t − τ ) = [D b + (t), O(t)]b b aks (t)Sb − (t − τ ) [D n n j j

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New Cooperative Effects in Single- and Two-Photon Interactions . . . D E b + (t), O(t)] b b − (t − τ )] , −e−iωk τ [D [b a (t − τ ), S ks n j D E D E † b + (t), O(t)]a b b − (t − τ ) = [R b + (t), O(t)]b b a † (t − τ )D b − (t − τ ) [R (t − τ ) D n n j j k ks D E  − † −iωk τ + b (t), O(t)], b b n (t − τ ) −e [R b aks(t) D j

373 (3.4) (3.5) (3.6)

b + (t), O(t)] b D b −(t − τ )b ak†1 (t − τ )i. Indeed, taking into account the lemma (3.3), the and h[R n j above correlation functions can be represented through atomic operators. The interaction between the EMF, and the radiator subsystems can be found in the third order of interaction constants (dr , gk )(ds , gk )q(ω1 , ω2 ), respectively. According to this condition, the smooth correlation functions can be obtained only for the following terms of expressions (3.4) and b + (t − τ 0 )[R b +(t), O(t)] b D b n− (t − τ )i. b − (t − τ 0 )[D b + (t), O(t)] b Sbn− (t − τ )i and hR (3.6): hR j j l l Other terms of these expressions give a contribution in the higher order of decomposition on the small parameter λ (see the interaction part of the Hamiltonian (2.1)). The lemma (3.3) is non-applicable for correlation functions represented in the expression (3.2) in which it is eliminated simultaneously the creation and annihilation boson operators belong to different time moments:

+  † b (t), O(t)]b b ak (t)D b − (t − τ )b [D ak1 (t − τ ) n j and its hermit conjugate

 b n+ (t − τ )b b b −(t)] . b ak1 (t − τ )D ak†(t)[O(t), D j

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To eliminate the vacuum part of operators b ak (t) and b ak†(t0 ) let us formulate the following rule.

b 1 ) contains the creation operators of EMF Lemma 2. If the arbitrary operator A(t b 2 ) contains the annihilation operators of EMF the elimination of vacuum part of and B(t b 1 ) and annihilation b ak (t) or creation b ak†(t) operators situated between these operators A(t b 2 ) takes place according to Lemma (3.3). In the opposite situation, we can represent B(t b 1 ) through the product of the atomic operator A(t1 ) with annihilation field the operator A(t operators b 1 ) = A(t b 1 )b A(t ak1 (t1 )b ak2 (t1 ) · · ·b akn (t1 )

b 2 ) through the product of creation field operators with the atomic and the operator B(t b operator B(t2 ) so that b 2 ) = B(t b 2 )b B(t ak†1 (t2 )b ak†2 (t2 ) · · · b ak†m (t2 ).

Here, the elimination of vacuum part of the operators b ak (t) and b ak†(t) can be represented through the following identities n



  b 1 )b b 2 ) = A(t b 1 )b b 2 ) −exp[−iωk (t−t2 )] A(t b 1 )[b b 2 )] A(t ak (t)B(t ask (t)B(t aks(t2 ), B(t 

b 1 )B(t b 2 )b ak†m (t2 ) − · · · ak†2 (t2 ) · · · b − δk,k1 A(t o

b 1 )B(t b 2 )b ak†m−1 (t2 ) , (3.7) ak†2 (t2 ) · · ·b − δk,km A(t ak†1 (t2 )b

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n



  b 1 )a† (t)B(t b 2 ) = A(t b 1 )a†,s (t)B(t b 2 ) −exp[iωk (t−t2 )] [A(t b 1 ), b b 2) A(t ak†,s(t1 )]B(t k k

 b 2) − · · · − δk,k1 A(t1 )b ak2 (t1 ) · · ·b akn (t1 )B(t

o b 1 )b b 2 ) . (3.8) − δk,kn A(t ak1 (t1 )b ak2 (t1 ) · · · b akn−1 (t1 )B(t

Proof. Considering the lemma (3.3), we can represent the third correlation function b 1 )b b 2 )i of expression (3.7) in the following form hA(t ak (t)B(t



 b 1 )b b 2 ) = A(t b 1 )b b 2) A(t ak (t)B(t aks (t)B(t

 b 1 )[b b 2 ) − B(t b 2 )b + exp[−iωk (t − t2 )] A(t ak (t2 )B(t aks (t2 )]

 b 1 )[b b 2 )] . (3.9) − exp[−iωk (t − t2 )] A(t aks (t2 ), B(t

According to the explicit expression of the operator,

b 2 ) = B(t b 2 )b B(t ak†1 (t2 )b ak†2 (t2 ) · · · b ak†m (t2 ),

let us introduced it in the second term of the right hand site of expression (3.9). Following the commutation rules of boson operators of the EMF, the operator b ak (t2 ) can be permuted in the right hand site of the correlation function. Considering that (b aks (t2 ) + b akv (t2 ))|0i = s b ak (t2 )|0i, this term becomes

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D

E † b 1 )b b 2 )b A(t ak (t2 )B(t b ak1 (t2 )b ak†2 (t2 ) · · ·b ak†m (t2 ) D E b 1 )B(t b 2 )b = δk,k1 A(t ak†2 (t2 ) · · ·b ak†m (t2 ) + · · · D E b 1 )B(t b 2 )b ak†1 (t2 )b + δk,km A(t ak†2 (t2 ) · · · b ak†m−1 (t2 ) D E b 1 )B(t b 2 )b + A(t ak†1 (t2 )b ak†2 (t2 ) · · · b ak†m (t2 )b aks (t2 ) . (3.10)

Introducing this relation in expression (3.10), it is not difficult to observe, that the new b 1 )b b 2 )i coincides with the expression (3.7) from the expression for correlation hA(tr ak (t)B(t lemma. The similar procedure of permutation of vacuum part of creation operator b ak†(t) demonstrates the identities (3.8) of Lemma 2.

After the substitution of the source part of the EMF operators (2.6), the next step conb +(t), O(t)]b b a †(t − sists in the elimination of operator b ak†(t − τ 0 ) from the correlation h[R j k b − (t − τ 0 )i of the first term of equation (2.4). According to lemma (3.3) and taking τ 0 )D m into account only the resonance terms in the right hand site of equation (2.4), it is not difficult to observe that in the third order of the interaction constant λ the term proportional to (ds , gk )qb (ωk1 , ωk ) describes the two-photon resonance between the atomic subsystems D and S,R. Neglecting the terms proportional to the λ4 , we obtain the following two-photon resonance between S, R and D subsystems D

b + (t), O(t)]b b a †(t − τ 0 )D b − (t − τ 0 ) [R m j k

E

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New Cooperative Effects in Single- and Two-Photon Interactions . . . N

s i(ds , gk ) X = ~

Zt

l=1 0

dτ exp[iωk (τ − τ 0 )]

D

b + (t), O(t)] b Sbl+ (t − τ )[R j

375 

 E b +(t), O(t)] b Sb+ (t − τ ) D b − (t − τ 0 ) . (3.11) + θ(τ − τ 0 )[R m j l

Replacing in expression (3.11) the operator of S subsystem with operators of R atoms, it is obtained the similar correlation (3.11) from the second term of equation (2.4). As follows from the representation (2.6) and generalized (2.4), the procedure of elimination of EMF field operators must continue in the last term of expression (2.4) too. For b ak (t)R b j (t − τ )i, it is obtained the same resonances in the third b + (t), O(t)]b correlation, hD m 1 order of small Ns Z 0

+  i(ds , gk ) X b m (t), O(t)]b b ak (t)R b j (t−τ ) = [D dτ 0 exp[−iωk1 τ 0 )] 1 ~ l=1 D n oE + + 0 b b b b b j (t−τ ), S b + (t−τ 0 )] . (3.12) × [Dm (t), O(t)] (Sl (t−τ )Rj (t−τ ) − θ(τ 0 −τ )[R l

According to lemma (3.7) from the last term of equation (2.4), it is obtained the following contribution to two-photon cooperative decay diagrams of D subsystem

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D

E b + (t), O(t)]b b ak (t)D b − (t − τ )b [D ak†1 (t − τ ) n j D E † b + (t), O(t)]b b aks (t)D b − (t − τ )b = [D a (t − τ ) n j k1 D  E † − b + (t), O(t)] b b − exp[−iωk τ ] [D b a (t − τ ), D (t − τ )b a (t − τ ) ks n j k1 D E + − b b b − δk,k1 [Dj (t), O(t)]Dn (t − τ ) .

(3.13)

Let us consider the scattering resonance represented in the Figure 1 B. Following the same representation of the right hand site of equation (2.4), we can easily eliminate the free b +(t), O(t)] b part of boson operators from the correlations hb ak†1 (t)[D b aks (t)i. m Neglecting the non-resonance terms in equation (2.4) according to the expressions (3.11, (3.12) and (3.13), we obtain the following master equation for arbitrary operator O(t) in the thread approximation of the interaction constant λ Nr

Na

X X



 d b bzl (t), O(t)] b b zj (t), O(t)] b ~ωls [A hO(t)i = i ωjr [R +i dt j=1

+i

Ns X l=1

+

X

Na X

k l,j=1

(da , gk )2 ~2

 b ~ωls [Sbzl (t), O(t)] + 2i

Zt 0

l=1

N X

m=1

b ω0 [Dzm , O(t)]

  +  b (t), O(t)] b A b − (t − τ ) dτ exp − iωk τ + i(k, rj − rl ) [A j l

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Nicolae A. Enaki

Zt Nr XX   +  (dr , gk )2 b (t), O(t)] b R b − (t − τ ) + dτ exp − iωk τ + i(k, rj − rl ) [R j l 2 ~ k l,j=1

0

Zt Ns XX

+  (ds , gk )2 b (t), O(t)] b Sb − (t − τ ) + dτ exp[−iω τ + i(k, r − r )] [ S k l j j l ~2 k l,l=1

0

Z N X X   qb2 (k, k0 ) +2 dτ exp − i(ω + ω )τ k k 1 2 ~2 k1 ,k2 l,j=1 0

+    − b b b × [Dj (t), O(t)]Dl (t − τ ) exp i(k1 + k2 , rj − rl ) t

−2i

t Zt X X qb (k, k0 ) Z +i dτ dτ 0 3 ~ k,k0 j,l,n=1 0 0     × exp i(k, rn − rj ) − iωk τ exp i(k0, rn − rl ) − iωk0 τ 0 h

+  b n (t), O(t)] b R b −(t − τ )Sb − (t − τ 0 ) × (ds , gk0 )(dr , gk ) [D j l

+ i b (t), O(t)] b Sb − (t − τ )R b − (t − τ 0 ) +(dr , gk0 )(ds , gk ) [D n j l N XX XX qb (k, k0 ) k,k0 m=1 j=1 l=1

Zt

dτ

1 ~3

Zt

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×

+i

~3

0

0

Zt 0

  exp − i(k, rm −rl )+i(k0, rj −rm )

  dτ exp iωk τ − iωk τ 0 − iωk0 τ 0

 Dn  b +(t), O(t)] b × (ds , gk )(dr , gk0 ) Sbl+ (t − τ ), [R j o E b +(t), O(t)] b Sb + (t − τ ) D b − (t − τ 0 ) +θ(τ − τ 0 )[R m j l D  b + (t − τ ), [Sb + (t), O(t)] b +(ds , gk0 )(dr , gk ) R j l  E 0 b+ + − 0 b b b +θ(τ − τ )[Sj (t), O(t)]Rl (t − τ ) Dm (t − τ )

X X

k,k0 j,l,n=1

dτ

0

Zt 0

  dτ 0 qs (k, k0 ) exp − i(k, rn − rj ) + iωk τ

 × exp i(k , rn − rl ) − iωk0 τ 0 (ds , gk0 )(da, gk ) 

+ − b b (t − τ )[D b − (t), O(t)]S (t − τ 0 ) × A 

0

n

j

Zt

l

t−τ Z 0

N XX XX 1 −i dτ 0 dτ exp[−iωk τ − iωk0 τ 0 ] 3 ~ k,k0 m=1 j=1 l=1 0 0    × (ds , gk )qs (k, k0 ) exp i(k, rm − rl ) + i(k0 , rj − rm )

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New Cooperative Effects in Single- and Two-Photon Interactions . . . D E − 0 b− 0 b + (t), O(t)]D b ×(da , gk0 ) [A (t − τ ) S (t − τ − τ ) m j l   0 +(ds , gk0 )qs (k , k) exp i(k, rm − rl ) + i(k0, rj − rm ) D E + + 0 b− 0 b b b ×(da , gk ) [Sj (t), O(t)]Dm (t − τ )Al (t − τ − τ ) b + → O). b +H.c. (O

377

(3.14)

This equation can be used for estimating the exchange integrals between the dipole-active radiators A, S, R and dipole-forbidden atom D as this is represented in Figure 1 A and B. After the integration of the right hand site of expression (3.14) on the waive vectors and time in accordance with Section 5., we can obtain the master equation (3.14). The exchange integrals between three particles situated at distances represented in Figures ?? and 7 are estimated in the Section 5.. In the next section we will study the influence of finite temperature on the three particle cooperative processes.

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4.

Correlation Between Single and Two-Photon Cooperative Processes for Finite Temperature

The equation (3.14) for the atomic operators O(t), describing the cooperative interaction between the dipole active and dipole forbidden atoms in two-photon resonance and scattering processes, is obtained for T = 8 by using the methods of eliminations the boson operators. This equation takes into account the interaction of correlation between three dipole active radiator subsystems A, S and R and dipole forbidden transitions of D-radiators represented in Figure 1). Let’s now consider the influence of the finite temperature T on the three particle correlations described by the master equation (3.14). In order to avoid cascade transition through real level |3 > let us consider the situation when the position of this level is so hairy that induced real transition from excited and ground states becomes impossible due to small temperature of the EMF system (kb T  ~ω32 ). The influence of two-photon processes on the single photon for zero temperature was taken into account in the Section 3.. From a physical point of view it is important to found the temperature interval for which the single and two-quantum exchange integrals between the radiators have the same magnitude. In order to study this situation in this section we propose the method of projection operator technique [29] for obtaining the master equation of atomic subsystem in single and twophoton interaction with EMF [30]. The elimination of the Bose operators b ak (t) and b ak†(t) for zero temperature of the photon subsystem in the first term of the Lemmas (3.3) and (3.7) was already studied in the literature [54]. This method becomes complicated in the application for three particle resonance our problem for the finite temperature. In order to estimate the three particle interaction for finite temperature we will examine the situation in which one and two-quantum interactions with the thermostat are taken into account simultaneously. In this case it is necessary to eliminate from the density matrix equation the boson operators from the single and two photon interaction the EMF operator combinations for the finite temperature. According to the Hamiltonian (2.1) we proposed the equations for the density matrix of the total system of radiators in interaction with a

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Nicolae A. Enaki

nonzero temperature bath of EMF. In the interaction picture this equation is i~ where

  ∂ ρˇ(t) ˇ (t), ρˇ(t) , =λ H I ∂t

o n o b ot H b I exp − i H b ot . H ~ ~ Let P be the projection operator for the complete density matrix ρˇ(t) on the vector basis of a free EMF subsystem ρs (t) = P ρˇ(t), and ρb (t) = P¯ ρˇ(t), where ρs(t) and ρb (t) are slower and rapidly oscillating parts of density matrix, respectively, P = 1 − P. It can be shown that P 2 = P and PP = 0. Recognizing that for t = 0 an electronic subsystem does not interact with lattice vibration, we define the projection operator ˇ I (t) = exp H

ni

P = ρph ⊗ T rph {· · · },

(4.1)

where the trace is taken over the phonon states, and ρ0 = ρe (0) ⊗ ρph(0), where ρph(0) = ˇ 0ph )/kbT ] and represent the Gibbs distributions for free EMF subsystem, exp[(F0ph − H ˇ 0ph = P ωk a ρsr (0) is non-equilibrium distribution for source subsystem; H ˘+ ak and F0ph k˘ k

are the Hamiltonian and free energy for photon subsystem. In this case one can define the slow part of density matrix as, ρs (t) = ρ0 ⊗ W (t), where W (t) = T rr {ρ(t)} is the density matrix of the electronic subsystem. The equations for the matrix ρs(t) and ρb(t) are ∂ρs(t) = −iλPLI (t){ρs (t) + ρb (t)}, ∂t ∂ρb(t) i~ = −iλPLI (t){ρs (t) + ρb (t)}, ∂t

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i~

(4.2) (4.3)

ˇ I (t), . . . ]/~ is the interaction part of Liouville operator. Following where λLI (t) = [H the known procedure of elimination of the rapidly oscillating part of the density matrix, we integrate equation (4.3) with respect to the ρb(t) and substitute the resultant solution in equation (4.2) ∂ρs (t) i~ = −λ2 P ∂t

Zt 0

dτ Li (t)U (t, t − τ )Li(t − τ )ρs (t − τ ),

where U (t, t − τ ) = T exp



− iλP

Zt

t−τ

(4.4)

 dτ1 Li (τ ) .

The quantum correlation between the single and two-photon interaction of atoms with the thermal EMF can be found in the third order of the expansion on the small parameter λ of the right hand side of equation (4.4). Confining ourselves to the second and third order of the expansion in the small parameter λ we represent the evolution operators U (t, t − τ ) and ρs (t − τ ) in the following approximate form U (t, t − τ ) ≈ 1 − iλP

Zt

dτ1 Li (τ1 ),

t−τ

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(4.5)

New Cooperative Effects in Single- and Two-Photon Interactions . . .

379

and 2

ρs (t − τ ) = ρs (t) + λ P

Zτ 0

dτ1 Li (t − τ1 )

t−τ Z 1 0

dτ2 Li (t − τ1 − τ2 )ρs(t − τ1 − τ2 ). (4.6)

Upon substitution of equations (4.5) and 4.6) in equation (4.4), in the third order of small parameter λ the equation for ρs (t) becomes ∂ ρs (t) = − λ2 P ∂t + iλ

3

Zt 0

Zt 0

dτ Li (t)Li(t − τ )ρs (t)

dτ1

Zt

t−τ1

dτ2 PLi(t)Li (τ2 )Li (t − τ1 )ρs (t).

(4.7)

Let us represent the Liouville operator through single- and two-photon interaction parts with the thermal bath b I1 (t), . . . ]/~ + [H b I2 (t), . . . ]/~. LI (t) = [H

Now the the single photon Hamiltonian can be represented through the annihilation and ˇ I1 (t) = H ˇ − (t) + H ˇ + (t) respectively, so that creation EMF operators H I1 I1

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ˇ − (t) = − H I1

Na X XX

(dβ , gk )Jˇβ+ (t)ˇ ak (t) exp[i(k, rj )],

β=s,r,a k n=1 ˇ + (t) H I1

ˇ − (t)]+ . = [H I1

(4.8)

ˇ Jˇ+ = R ˇ + ; Jˇ+ = Aˇ+ . Following the Here the atomic operator is equivalent to Jˇs+ = S; r a similar representation one can divide the two-photon interaction part of the Hamiltonian ˇ I2 (τ ) = H ˇ b− (τ ) + H ˇ s− (τ ) + H ˇ b + (τ ) + H ˇ s+ (τ ), where (2.1), H I2 I2 I2 I2 ˇ b− (τ ) = − H I2

ˇ s− (τ ) H I2

=

N X X

qb (k1 , k2 )

k1 ,k2 m=1

n  o + ˇm ak1 (τ ) exp i(k1 + k2 , rm) , × D (τ )ˇ ak2 (τ )ˇ N X X

(4.9)

qs (k1 , k2 )

k1 ,k2 m=1

n  o ˇ + (τ )ˇ × D a†k1 (τ )ˇ ak2 (τ )(1−δk1,k2 ) exp i(k2 −k1 , rm) , m

ˇ b+ (τ ) = [H ˇ b− (τ )]+; H I2 I2

ˇ s+ (τ ) [H ˇ s− (τ )]+, H I2 I2

According to this procedure (4.9) we can find from the first term of the right hand site of the equation (4.7) the following expression Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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Nicolae A. Enaki

1 ∆ρ1 = − 2 ~

Zt 0

dτ

nh i ˇ + (t)H ˇ − (t−τ )ρs(t)+P H ˇ − (t)H ˇ + (t−τ )ρs(t) PH I1 I1 I1 I1

h io ˇ + (t)ρs(t)H ˇ − (t−τ )+P H ˇ − (t)ρs (t)H ˇ + (t−τ ) +H.c., (4.10) − PH I1 I1 I1 I1

which contains the single photon transition between the ground and excited states of atomic subsystems A, S and R. In the similar way one can represent the two -quantum transition of D subsystem in the thermal EM field in the following form

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Zt h i 1 ˇ s+ (t)H ˇ s− (t−τ )ρs(t)+P H ˇ s−(t)H ˇ s+ (t−τ )ρs(t) ∆ρ2 = − 2 dτ P H I2 I2 I2 I2 ~ 0 h i ˇ s+ (t)ρ(t)H ˇ s−(t − τ ) + P H ˇ s− (t)ρs (t)H ˇ s+ (t − τ ) − PH I2 I2 I2 I2 h i ˇ b+(t)H b− (t − τ )ρs(t) + PH b−(t)H b+ (t − τ )ρs(t) + PH I2 I2 I2 I2 h i b+ b− b− b+ − PHI2 (t)ρ(t)HI2 (t−τ )+PHI2 (t)ρs (t)HI2 (t−τ ) +H.c., (4.11) which represents the single and two- photon cooperative interaction between the radiators of D subsystem. Let us now study the third order contribution in the right hand site of the equation (4.7) Taking into account that the trace of an odd number of boson operator is zero, ˇ†k a ˇ† a T rph {ρ0a ˇk3 a ˇk4 ˇak5 } = 0, it is not difficult to observe that the projection of the oper1 k2 ˇ ˇ I2 H ˇ I2 takes a zero value too. In the third order of the small parameter ator product P HI1 H b I1 and L bI2 must be found from the terms like λ the contribution of Liouville operator L b b b P LI1 LI2 LI1 ρbs (t). Representing single photon interaction Hamiltonian through the creation and annihilation photon parts (4.8) and introducing the similar representations for the two-photon parts of the interaction Hamiltonian (4.8) and (4.9) in the expression (4.7), we obtain the following contribution in the third order of the small parameter λ ∆ρ3 = iλ

3

Zt

dτ1

0

Zτ1 0

dτ2 PLI (t)LI (t − τ2 )LI (t − τ1 )ρs(t).

Representing this expression through bi-photon and scattering parts ∆ρ3 = ∆ρb3 +∆ρs3 3 , we can reduce the third order matrix ∆ρ3 through excitation or lowering operators of single and two-photon subsystems A, S, R and D, respectively. For example two-photon resonance represented in Figure 1 A can be described by the following diagrams ∆ρb3 = iλ3

Zt 0

dτ1

Zτ1 0

n R− b+ dτ2 PLS− I1 (t)LI1 (t − τ2 )LI2 (t − τ1 )ρs(t)

S− b+ + PLR− I1 (t)LI1 (t − τ2 )LI2 (t − τ1 )ρs(t) b+ S− + PLR− I1 (t)LI2 (t − τ2 )LI1 (t − τ1 )ρs(t) b+ R− + PLS− I1 (t)LI2 (t − τ2 )LI1 (t − τ1 )ρs(t)

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381

b+ R− + PLI2 (t)LS− I1 (t − τ2 )LI1 (t − τ1 )ρs(t)

o b+ S− + PLI2 (t)LR− I1 (t − τ2 )LI1 (t − τ1 )ρs(t) + H.c.

(4.12)

R− b− ˇ R− ˇ R− Here λLR− I1 (t) = [HI1 (t), . . . ]/~, LI1 (t) = [HI1 (t), . . .]/~ and LI2 (t) = ˇ b− (t), . . .]/~ represent the Liouville operators of the interaction part of the R, S and [H I2 D atoms expressed through EMF annihilation and atomic lowering operators for single and two-quantum interactions with thermal bath. In the similar situation one can take into account the resonance contribution of A and S subsystem in the scattering process represented in the Figure 1 B

∆ρs3

= iλ

3

Zt 0

dτ1

Zτ1 0

n S+ s+ dτ2 PLA− I1 (t)LI1 (t − τ2 )LI2 (t − τ1 )ρs(t)

A− s+ + PLS+ I1 (t)LI1 (t − τ2 )LI2 (t − τ1 )ρs(t) s+ S+ + PLA− I1 (t)LI2 (t − τ1 )LI1 (t − τ2 )ρs(t) s+ A− + PLS+ I1 (t)LI2 (t − τ1 )LI1 (t − τ2 )ρs(t) A− S+ + PLs+ I2 (t)LI1 (t − τ1 )LI1 (t − τ2 )ρs(t)

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S+ A− + PLs+ I2 (t)LI1 (t − τ1 )LI1 (t − τ2 )ρs(t)} + H.c.,

(4.13)

ˇ s− where λLs− I2 (t) = [HI2 (t), . . . ]/~ is the Liouville parts for two-photon scarpering process ˇ A− of D atomic subsystem and λLA− I1 (t) = [HI1 (t), . . . ]/~ corresponds to the single photon transition in A atom described by the Hamiltonian parts (4.8) and (4.9), respectively. The scattering resonance can be represented by the diagram in which must take place the conservation law ωa − ωs = 2ω0 . We can find these diagrams of interaction between the A, S and D atoms in the following way. Considering that the trace of the odd number of boson operator is zero, T rph {ρ0 ˇ a†k a ˇk2 a ˇ†k } = 0, one can observe that the projection of 1 3 ˇ I1 H ˇ I2 P = 0. Following this procedure of calculation of mean the operator product P H value of boson operators, it is observed that only the projections give the main contribution ˇ I1 H ˇ I1 P 6= 0 and P H ˇ I2 H ˇ I2 P 6= 0 . PH So in conclusion we observe that the trace of the right hand site of the expressions (4.10), (4.11) gives us the following representation of density matrix of atomic subsystem W (t) = W (1) + W (2)(t) + W (3,1)(t) dW (t) dW (1)(t) dW (2)(t) dW (2,1)(t) = + + . dt dt dt dt Here taking in to account the trace on the thermal EMF bath   T rph ρph ˇak a ˇ†k1 = (Nk + 1)δk1 ,k ; T rph ρpha†k1 ak = Nk δk1 k

(4.14)

we found the following contributions to master equation from the single photon interaction (4.10) Zt Nα X X X     dW (1) (t) (dα, gk )2 = dτ exp i(ω −ω +iε)τ exp i(k, r −r ) k α j l dt ~2 α=s,r,a l,j=1 k

0

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Nicolae A. Enaki n    − o − + + × Nk Jˇαj , [W (t), Jˇαl ] + Jˇαj , W (t)Jˇαl + H.c., (4.15)

− + where Jˇαj and Jˇαl are excitation and de-excitation operator of α-atomic subsystems Nk =   ~ωk 1/[exp kB T − 1] is the mean number of photons in the mode k for finite temperature T , kB is the Boltzmann constant. The index in the equation (4.15) takes the values α = a, s, r which correspond to A, S, and R radiator subsystems. The two-photon transition include induce and scattering processes stimulated by thermal bath. According to the expression (4.11) the exchange integrals between the radiators of D subsystem can be represented by simple calculated

1 ∆ρ2 = −ρ0 2 ~

N X N X   qs (k1 , k2 )qs (k4 , k3 ) exp i(k2 −k1 , rm)

X

k1 ,k2 ,k3 ,k4 m=1 l=1



 × exp − i(k3 − k4 , rl ) (1 − δk1 ,k2 )(1 − δk4 ,k3 )

Zt

dτ

0

  − + ˇ (t)D ˇm × Tr a ˇk4 (t)ˇ a†k3 (t)ˇ a†k1 (t − τ )ˇ ak2 (t − τ )ρph D (t − τ )W (t) l  † − ˇ (t)W (t)D ˇ + (t − τ ) − Tr a ˇk1 (t − τ )ˇ ak2 (t − τ )ˇ ak4 (t)ˇ a†k3 (t)ρph D m l  † + † − ˇ ˇ + Tr a ˇk1 (t)ˇ ak2 (t)ˇ ak4 (t − τ )ˇ ak3 (t − τ )ρph Dm (t)Dl (t − τ )W (t)   + † † − ˇ ˇ − Tr a ˇk4 (t − τ )ˇ ak3 (t − τ )ˇ ak1 (t)ˇ ak2 (t)ρph Dm (t)W (t)Dl (t − τ ) Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

1 − ρ0 2 ~

X

N X N Z X

t

dτ qb (k1 , k2 )qb (k4 , k3)

k1 ,k2 ,k3 ,k4 m=1 l=1 0

    × exp i(k2 + k4 , rm) exp − i(k3 + k1 , rl )  − ˇ (t)D ˇ + (t − τ )W (t) × T r{ˇ a†k1 (t)ˇ a†k3 (t)ˇ ak4 (t − τ )ˇ ak2 (t − τ )ρph D m l  ˇ − (t)W (t)D ˇ + (t − τ ) − Tr a ˇk4 (t − τ )ˇ ak2 (t − τ )ˇ a†k1 (t)ˇ a†k3 (t)ρph D m l  + † † − ˇ ˇ + Tr a ˇk4 (t)ˇ ak2 (t)ˇ ak1 (t − τ )ˇ ak3 (t − τ )ρph Dm (t)Dl (t − τ )W (t)  +  † † − ˇ (t)W (t)D ˇ (t−τ ) +H.c. ak2 (t)ρph D − T r ˇak1 (t−τ )ˇ ak3 (t−τ )ˇ ak4 (t)ˇ m l

So that after the trace on the EMF variables we obtain for scattering  † a)ˇ a†k3 (t − τ )ρph ˇk1 (t)ˇ ak2 (t)ˇ (1 − δk1 ,k2 )(1 − δk4 ,k3 )T r a

= Nk1 (Nk2 + 1)(1 − δk1 ,k2 )(1 − δk4 ,k3 )δk4 ,k1 δk3 ,k2 ,

and two photon transitions    ˇ†k4 = (Nk1 + 1)(Nk3 + 1) δk1 k2 δk3 ,k4 + δk1 ,k4 δk3 ,k2 ; k2 6= k4 , T r ρph a ˇk1 ˇak3 ˇa†k2 a    ˇk3 = Nk1 Nk3 δk1 ,k2 δk3 ,k4 + δk1 ,k4 δk3 ,k2 ; k2 6= k4 , T r ρph a ˇ†k2 ˇa†k4 ˇak1 a

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383

we obtain the following contribution in the collective processes between the radiators of D subsystem with thermal fields N   dW (2) (t) 1 X X = 2 qs (k1 , k3)qs (k1 , k3) exp i(k3 −k1 , rm −rl ) dt ~ k1 ,k3 m,l=1

×

Zt 0

n  −   +  ˇ , [W (t), D ˇ + ] + Nk D ˇ W (t), D ˇ− dτ Nk1 Nk3 D m m 3 l l

 − o   + ˇ , W (t)D ˇm + Nk1 D exp i(ωk3 − ωk1 − 2ω0 )τ l

N N Z 1 X XX −2 2 dτ qb (k1 , k3)qb (k3 , k1 ) ~ k1 ,k3 m=1 l=1 0  n ˇ − [D ˇ + , W (t)] × exp i(k3 + k1 , rl − rm) Nk1 Nk3 D m l o   + ˇ − W (t)D ˇm − (Nk1 + Nk3 + 1)D exp − i(ωk3 + ωk1 − 2ω0 )τ l n o ˇ + [D ˇ − , W (t)] + (Nk + Nk + 1)D ˇ +D ˇ − W (t) + Nk1 Nk3 D m m 1 3 l l   × exp i(ωk3 + ωk1 − 2ω0 )τ + H.c. t

(4.16)

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In this expression the operators of EMF bath are totally eliminated for a finite temperature of the bath. Let us now found the contribution of the third orderly expansion on the small parameter λ. We can divide this contribution in the two parts according to Figure \ref{figure 1}1 A and B dW (2,1)(t) dW (2,1b)(t) dW (2,1s)(t) = + , (4.17) dt dt dt The trace on the EMF states of the right hand cite of expressions (4.12) gives the expressions like these n o T r ˇak1 (t)ˇ a†k2 (t − τ2 )ˇ a†k4 (t − τ2 )ˇ ak3 (t − τ1 )ρph   = Nk3 (Nk1 + 1) δk4 ,k3 δk2 ,k1 + δk4 ,k1 δk2 ,k3   × exp − i(ωk3 + ωk1 )τ2 + iωk3 τ1 , o n a†k2 (t − τ1 )ˇ a†k4 (t − τ1 )ρph ak3 (t − τ2 )ˇ T r ˇak1 (t)ˇ   = (Nk3 + 1)(Nk1 + 1) δk4 ,k3 δk2 ,k1 + δk4 ,k1 δk2 ,k3   × exp − i(ωk3 + ωk1 )τ1 + iωk3 τ2 .

After the combination of the terms on the right hand site of expression (4.12), we can obtain the following explicit correlations between S, R and D subsystems h i dW (2,1b)(t) 2i X X =− 3 exp i(k1 , rj − rm) + i(k3, rl − rm) dt ~ k1 ,k3 j,l,m

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Nicolae A. Enaki n   +  ˇ , [D ˇ − , W (t)] × (ds , gk1 )(dr , gk3 )qb (k1 , k3 ) Nk1 Nk3 Sˇl+ , R m j  o ˇ +, D ˇ − W (t)] + (Nk1 + Nk3 + 1) Sˇl+ , [R m j ×

Zt

dτ1

×

Zt

0

Zt 0

  dτ2 exp − i(ωk3 − ωs )τ1 − i(ωk1 − ωr )τ2

n  −  + +   +  ˇ , R ˇ , [Sˇ , W (t)] + Nk [R ˇ , W (t)Sˇ +], D ˇ− + Nk3 Nk1 D m 1 m j j l l    − o ˇ + ], D ˇ− + D ˇ , W (t)Sˇ+R ˇ+ + Nk3 [Sˇl+, W (t)R m m j j l

+

Zt 0

0

dτ2

dτ1

Zt

0 t−τ 2 Z 0

  exp i(ωk1 − ωr )τ2 + i(ωk3 − ωs )τ1 

dτ1 exp[−i(ωk3 − ωs )τ2 + i(ωk1 − ωr )τ1 ]

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n   +    ˇ , [D ˇ − , W (t)] + Nk Sˇ+ , [R ˇ +, D ˇ − W (t)] × Nk3 Nk1 Sˇl+ , R m 1 m j j l    − o ˇ − ]R ˇ+ + D ˇ W (t)R ˇ + , Sˇ+ + Nk3 Sˇl+ , [W (t), D m j m j l   + exp − i(ωk1 − ωr )τ2 + i(ωk3 − ωs )τ1 n  +  +   + + −  − ˇ , Sˇ , [D ˇm ˇ , [Sˇ , D ˇ mW (t)] × Nk3 Nk1 R , W (t)] + Nk3 R j j l l   +   − o − ˇ+ + ˇ+ ˇ ˇ ˇ ˇ + Nk1 Rj , [W (t), Dm]Sl + Dm W (t)Sl , Rj +H.c. (4.18)

The scattering cooperative term between the A, S and D subsystems in the representation (4.17), can be obtained from the expression (4.13), taking the trace on the EMF subsystem operators n o Tr a ˇ†k4 (t)ˇ a†k1 (t − τ2 )ˇ ak3 (t − τ2 )ˇ ak2 (t − τ1 ) (1 − δk1 ,k3 )   = Nk3 Nk1 (1 − δk1 ,k3 )δk4 ,k3 δk1 ,k2 exp i(ωk3 − ωk1 )τ2 + iωk1 τ1 , o n a†k4 (t − τ1 ) (1 − δk1 ,k3 ) a†k1 (t)ˇ ak3 (t)ˇ T r ˇak2 (t − τ2 )ˇ   = (Nk3 + 1)(Nk1 + 1)(1 − δk1 ,k3 )δk4 ,k3 δk1 ,k2 exp iωk2 τ2 − iωk4 τ1 Taking this into consideration, the scattering part of the density matrix in the right hand site of expressions (4.13) (4.17) gives us the following explicit contribution in (4.17) h i dW (2,1s)(t) i X X exp i(k1 , rj − rm ) − i(k3 , rl − rm ) = 3 dt ~ k1 ,k3 j,l,m n   −  ˘ ˇ− × (ds , gk3 )(da, gk1 )qs (k1 , k3 ) Nk1 Nk3 A˘+ j , Sl , [Dm, W (t)]    o ˘ −, D ˇ − W (t)] − Nk A˘+ , [S˘−, W (t)D ˇ −] , [ S + Nk3 A˘+ m 1 m j j l l

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 Zt 0

Zt

Zt

Zτ1

− 2i

dτ1

  dτ2 exp i(ωs − ωk3 )τ2 + i(ωa − ωk1 )τ1

0

dτ1

0

385

0



dτ2 sin (ωs − ωk3 )τ1 + (ωa − ωk1 )τ2





   − −    ˇ ˘ ˇ − ˘− + Nk3 Nk1 A˘+ + Nk3 A˘+ j , Dm [Sl , W (t)] j , Dm [Sl , W (t)]     + − −  − ˘− ˇm ˘ ,D ˇ mS˘ W (t) + Nk1 A˘+ , [ D , S W (t)] + A j j l l ×

Zt

t−τ Z 2

dτ2

0

h i dτ1 exp i(ωa − ωk1 )τ2 − i(ωs − ωk3 )τ1

0

   −    ˇ , [A ˘+ , W (t)] + Nk S˘− , [W (t), A ˘+]D ˇ− + Nk3 Nk1 S˘l− , D m m 1 j j l   −   −  + ˇ− + ˇ− ˘ ˘ ˘ ˘ + Nk3 Sl , [W (t)Aj , Dm] + Sl , W (t)Aj Dm

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×

Zt

dτ2

0

t−τ Z 2 0

  dτ1 exp − i(ωs − ωk3 )τ2 + i(ωa − ωk1 )τ1

  −  + −   −  ˇ , A˘ , [S , W (t)] + Nk D ˇ , [A ˘+, S − W (t)] + Nk3 Nk1 D m m 1 j j l l   −   − ˘+ + − ˘− ˇ ˘ ˇ ˘ + Nk3 Dm , [W (t), Sl ]Aj − v[Dm, Sl W (t)Aj ×

Zt

dτ1

0

Zt 0

  dτ2 exp i(ωs − ωk3 )τ1 − i(ωa − ωk1 )τ2 + H.c. (4.19)

The master equation (4.14) represents the behavior of atomic systems A, S, and R in two photon resonance with D subsystem. Let us now find the connection of this equation with equation (3.14) from the last section. Indeed for zero temperature , T = 0, the mean value of the photon numbers is zero Nk = 0. In this case we obtain the following expression for the master equation (4.14) Zt Nα X X X   (dα, gk )2 dW (t) dτ × exp i(ω − ω + iε)τ + i(k, r − r ) = k α j l dt ~2 α=s,r,a l,j=1 k

0

N  −  X X   qb (k1 , k3)2 + × Jˇαj , W (t)Jˇαl − exp i(k3 − k1 , rm − rl ) 2 ~ k1 ,k3 m,l=1  −  + + ˇ− ˇ W (t)D ˇm ˇm + W (t)D Dl × exp − i(ωk3 + ωk1 − 2ω0 )τ D l   2i X X − 3 (ds , gk1 )(dr , gk3 )qb (k1 , k3 ) exp i(k1 , rj −rm )+i(k3, rl −rm ) ~ k1 ,k3 j,l,m

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386

Nicolae A. Enaki ×

(Z t 0

+

Zt    + −  ˇ ,D ˇ mW (t) dτ1 dτ2 exp − i(ωk3 −ωs )τ1 −i(ωk1 −ωr )τ2 Sˇl+ , R j

Zt

0

dτ1

0

Zt 0

  −  ˇ , W (t)Sˇ+R ˇ+ exp i(ωk1 − ωr )τ2 + i(ωk3 − ωs )τ1 D m j l

Z t t−τ Z 2    −  ˇ m W (t)R ˇ + , Sˇ+ + dτ2 dτ1 exp − i(ωk3 −ωs )τ2 +i(ωk1 −ωr )τ1 D j l 0

0





 +

ˇ − W (t)Sˇ+ , R ˇ + exp − i(ωk1 − ωr )τ2 + i(ωk3 − ωs )τ1 D m j l +

)

  i X X (ds , gk3 )(da, gk1 )qs (k1 , k3 ) exp i(k1 , rj − rm ) − i(k3 , rl − rm ) 3 ~ k1 ,k3 j,l,m

×

(Z t

dτ2

0

t−τ Z 2 0

   ˇ − ˘− dτ1 exp i(ωa −ωk1 )τ2 −i(ωs −ωk3 )τ1 A˘+ j , DmSl W (t)

Zt t−τ Z 2    ˘+ D ˇ− + dτ2 dτ1 exp − i(ωs −ωk3 )τ2 +i(ωa −ωk1 )τ1 S˘l− , W (t)A m j 0

0

) Z t Zt   −  ˇ − + H.c. (4.20) + dτ1 dτ2 exp i(ωs − ωk3 )τ1 − i(ωa − ωk1 )τ2 S˘l W (t)A˘+ j , Dm Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

0

0

In the next section 5. we will discuss the situation, where the two-quantum exchange integral have some as the single quantum interaction between particles of extended system of radiators. In this case the dependence of the exchange integral of temperature has interesting peculiarities. The cooperative exchange between the electrons increases with increasing temperature. In other words the effective interaction implicitly depends on temperature through the mean number of bosons, Nk , in the bath. This is one of the main differences between the single quantum exchanges (4.15), and the two-quantum exchanges (4.16) between the radiators in super-radiance. The temperature dependence is very important for the formation and mutual influences of the super-radiance and super-conducting states [52]. In order to understand these effects, the influence of temperature on the exchange parameters between the radiators in the next section it is analyzed.

5.

Exchange Integrals for Single- and Two-Photon Processes and their Interference

1. To estimate all exchange integrals between three particles in generalized equations (3.14) and (4.14) let us remember method used in the well-known correlation functions between two radiators in single-photon interaction with the vacuum of EMF studied in papers [15],[20] and [8]. In the first two terms of (4.14) the causality in the process of interaction

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New Cooperative Effects in Single- and Two-Photon Interactions . . .

387

between the radiators through the vacuum of EMF can be estimated taking into account the retardation effect. Indeed integrating, firstly, the right hand part of the equation (4.15) on the wave vector k , we obtain the following expression for single photon exchange integral between j and l radiators Z∞ Z Zt
  d2α 3 Kα(j, l) = ω dω dΩ 1 − (e , n ) dτ exp i(ω − ω )τ k k k d α k α k (2π)2 ~c3 0 0 h    − i   − + + ˇ ˇ ˇ × Nk Jαj , [W (t), Jαl + Jαj (t), W (t)Jˇαj exp iωk rjl cos θ . (5.1)

Here, ωα is the emission frequency relatively the dipole active transitions of the A , R and + − ˜+ , R ˜− S atomic subsystems; α = α, r, s; for I = r operators J˜αj , J˜αl corresponds to R j l and for I = s these operators correspond to S˜j+ , S˜l− . Introducing the new variable, υ = ωk − ωα , and consideration that Nk and ωk3 are the smooth functions, one can approximate under the ωk − integral with their mean values ωα3 and Nωα = 1/[exp[~ωα/(kB T )] − 1] respectively. In this approximation we obtain the following expression of single-photon exchange integrals Z∞

−ωα

  dv exp iv(τ − rjl cos θ/c)

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'

Z∞

−∞

  dv exp iv(τ − rjl cos θ/c) = 2πδ(τ − rjl cos θ/c). (5.2)

As follows from the definition of Dirac δ((τ − rjl cos θ/c)) function, the spherical angle θ must be considered between 0 and π/2, cos(θ) ≥ 0 for non-zero value of exchange integral between the radiators (5.1). After the integration on the angle θ and retardation time τ , it is obtained the following expression for (5.1) ω 3 d2 Kα(j, l) = α 3α 2~c

Zπ 0

dθ n

Zt 0

dτ sin θδ(τ − rjl cos θ/c)

 −   − o + + × Di(θ) Nα Jˇαj , [W (t), Jˇαl ] + Jˇαj (t), W (t)Jˇαj

Zπ h ∂ i   ωα3 d2α exp iωαrjl cos θ dθ sin θΘ(cos θ)D = jl 3 2~c ∂ωi 0 n    − o − + + × Nα Jˇαj , [W (t), Jˇαl ] + Jˇαj (t), W (t)Jˇαj n    − o 1 − + + = χα (j, l) Nωα Jˇαj , [W (t), Jˇαl ] + Jˇαj (t), W (t)Jˇαj . 2τα

(5.3)

Here τα and χα (j, l) are the spontaneous emission time and the exchange integral between radiators in the single-photon emission respectively [8] h ∂ i 3 exp[iω r /c] − 1 1 4d2 ω 3 α jl = α 3i ; α = a, s, r; χα (j, l) = Djl . (5.4) τα 3~c ∂ωα 4 iωi rjl /c

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The expressions Dα(ξα) and Djl [∂/∂ωi] in equation (5.3) and (5.4) are defined below  h ∂ i  c2 ∂ 2 2 2 Djl = 1 + cos (ξα) + (3 cos ξα − 1) 2 , ∂ωα rjl ∂ωα2 Dα(ξα ) = 1 + cos2 ξα − cos2 θ(3 cos2 ξα − 1),

(5.5)

where cos ξα is the scalar product between the unit vectors along the direction of dipole momentum of the j (or l) atom, ndα = dα /dα, and the direction of the distance between the j and l atoms, njl = rjl /rjl . We have considered here that the directions of the vectors ndα are parallel. 2. The third term in the right hand site of the equation (2.4) describes the two-photon exchange integral between the dipole-forbidden transitions of D radiator and other two dipole active radiators. This integral was estimated in paper [21] taking into account the traditional Born-Marcoff approximation. Here, we will estimate this correlation between radiators j and l, which takes into account the interaction causality relative the distances |rj − rl | ∼ λs(r) . Integrating first on the wave vectors k1 and k2 we obtain for twoquantum exchange integral between j and l radiators 2V 2 Kb = (2π)6

Z2π 0

Z∞

× k32 dk3

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0

dϕ1

Zπ

dθ1 sin θ1

0

Z∞

k12 dk1

0

Z2π

dϕ3

0

Zπ

sin θ3 dθ3

0

Zt

  (n31 , eλ1 )2 (n23 , eλ2 )2 qb2 (ω1 , ω3 ) dτ exp − i(2ω0 − ω1 − ω3 )τ 2 ~ 0   × exp i(k3 + k1 ), (rm − rl ) Gb (k1 , k2, m, l). (5.6)

Here the operator

 −   −  + + ˇ , [W (t), D ˇm ˇ , W (t)D ˇm Gb(k1 , k2 , m, l) = Nk1 Nk3 D ] + (Nk1 + Nk3 + 1) D . l l

is defined in the equation (4.16). After this approximation, we can easily integrate the expression (5.6) on the variables k1 and k2 . Indeed introducing the new variables xi = ωki −ωi as in single photon exchange integral (5.2) in consideration that Nk1 ≈ Nk3 ≈ Nω0 is the smooth operator it is obtained the following expression for Vjld V 2 ω04 qb2 (ω0 , ω0 ) Kb(m, l) = 2 (2)4 π 2 c6 ~2

Zt 0

×

Zπ 0

dτ

Zπ

dθ1 sin θ1

0

dθ2 sin θ2 D0 (θ1 )D0 (θ2 )δ(τ − rml cos θ1 /c)δ(τ − rml cos θ2 /c)   × exp iω0 rml (cos θ1 + cos θ2 )/c Gb (k0 , k0 , m, l)  2 ω 6 d2 d2 c 1 1 ' 0 6 312 12 + 2c ~ rml ω31 − ω0 ω32 + ω0

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New Cooperative Effects in Single- and Two-Photon Interactions . . . 389  ∂  exp[−2iω r ] − 1 0 ml 2 × Gb (k0 , k0 , m, l)Dml , (5.7) ∂ω0 −2iω0 rml where expressions D0 (θ1 ) and Djl (∂/(∂ω0) are defined in (5.5). As follows from the definition of Dirac δ(x) -function representation (5.7), the integrals on the angles θ1 and θ2 are limited by the causal conditions cos θ1 ≥ 0 and cos θ2 ≥ 0. These conditions give us the possibilities to limit the integrals on the angle and the retardation time on the right hand site of the equation according to this causality (5.7). According to this, we obtain the following approximated expression for Kd (j, l) Kd (m, l) =

1 χ (j, l)Gb(k0 , k0 , m, l), 2τd d

(5.8)

where

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2 n 2 o2 ω 7 d2 d2  1 1 1 0 23 31 = + , τd 3 π~2 c6 ω32 + ω0 ω31 − ω0 h ∂ i exp[2iω r /c] − 1 32 πc 0 jl χd (j, l) = 2 D2 2 ω0 rjl ∂ω0 iω0 rjl /c

(5.9) (5.10)

is the exchange integral and τ1b two-photon spontaneous emission rate defined in the exd pression (5.9). When the distance between the radiators rjl is less than the emission wavelength, λ0 , it is not difficult to observe that the real and imaginary parts of the exchange function (5.10) diverge. The real part of the exchange integral χd (j, l) describes the biphoton spontaneous emission rate and must tend to 1, when j = l. According to the Kd (j, l) expression, the real part of this integral tends to cooperative emission rate 1/(2τd) for small values of relative distances between the radiators rjl /λ0  1. To take into account this effect, we must estimate the real part of this integral for the small values of the distances, rjl /λ0 < 1. Let us, firstly, integrate on the retardation time the expression (5.6) in Born–Marcoff approximation [21]. In this case, we obtain the following expression for Fd (j, l) = 0 we obtain the non-divergent expression for Vjln;asd . Neglecting the − − e (t) and Se (t) the similar expression is retardation, rnl xi /c, in the smooth operators R j l b (n, j, l) can obtained and for generalized equations (3.14). The correlation function Ursd now be easily represented by the expression b Ursd (n, j, l) =

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Here for ωs ' ωr 1 b τsrd

i d U (j, l, m)K D(j, m, l). b 2τsrd

 n 4 o2 ω 3 (ω )3 d d d d  1 1 r s r 23 31 s , = + 3 2~2 c6 ω32 + ωs ω31 − ωr

(5.13)

is the cooperative emission rate (5.13) of three atoms belong to S, R and D subsystems located at relative distances rnj , rnl  λi. The exchange between three particle m, j and l situated at distances rnj , rnl is described by the correlation function  3 2 h ∂ i h ∂ i U b (j, l, m) = − Dml Dmj 4 ∂ωs ∂ωr [exp[−iωr rmj /c] − 1][exp[−iωs rml /c] − 1] × . (5.14) ωr ωs (rmj /c)(rml /c) It is not difficult to observe that this function tends to unity, when the relative distances between the radiators ωr rmj /c and ωs rml /c tend to zero. This procedure of representation of exchange integral give us the possibility to remove the divergences of the last terms of generalized equation (2.8). The correlations in the right hand sites of equations (4.18) and (3.14)  +  +  + + −   − b b , [S , DmW (t)] d K + Nk3 R R (j, m, l) = Nk3 Nk1 Rj , Sl , [Dm, W (t)] j l

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and

m

j

1

m

l

393

j

l

  +    cS (j, m, l)= Nk Nk S + , R b , [D − , W (t)] +Nk S + , [R b +, D − W (t)] K m m 3 1 1 j j l l     b + + D − W (t)R b +, S + , +Nk3 Sl+ , [W (t), D −]R m j j l

describe the cooperative action of the D subsystem other the dipole-active subsystems S and R. atomic operators, respectively, we obtain the following expression VSR = − ×

  2i X X exp i(k3 , rl −rm )−i(k1, rj −rm ) (ds , gk3 )(dr , gk1 )qb (k1 , k3 ) 3 ~ k1 ,k3 j,l,m

Zt

t−τ Z 2

dτ2

0

0

n   cS (j, m, l) dτ1 exp − i(ωk3 − ωs )τ2 + i(ωk1 − ωr )τ1 K

o   d + exp − i(ωk1 − ωr )τ2 + i(ωk3 − ωs )τ1 K R (j, m, l) . (5.15)

Representing in expression (5.15) the sum on k through integral, we obtain the following correlation function between the j, l and m atoms Z Z V V ~2 d23 d31 ds dr (2π)4 X 3 = −2i ω dω ω33 dω3 q˜b (ω1 , ω3 ) 1 1 (2π)3 (2π)3 c6 ~ 3 22 V 2 ∞

VSR

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j,l,m 0

×

Z1

−1

dx1

Z1

−1

dx3

Zt 0

dτ2

∞

0

t−τ Z 2 0

n     cS (j, m, l) dτ1 exp i(ω3 − ωs )τ2 exp − i(ω1 − ωr )τ1 K

o    d + exp − i(ω1 − ωr )τ2 exp i(ω3 − ωs )τ1 K (j, m, l) R h ∂ i h ∂ i   × Dml Djm exp iω3 rml x3 /c − iω1 rjm x1 /c . (5.16) ∂ω3 ∂ω1 

Replacing the new variables u1 = ω1 − ωr ; u3 = ω3 − ωs in (5.16) and the smooth √ amplitudes ω12 ω32 ω1 ω3 qb (ω1 , ω3 ) and Nk3 , Nk1 with expressions with fixed frequencies √ around which is picked the Lorentz function ωs2 ωr2 ωs ωr qb (ωs , ωr ) and Nω3 Nωr we of course obtain the similar integrals. Indeed according to the definition of δ-functions (5.2) we get VSR = −i

1 d d d d X 23 31 s r ωs3 ωr3 q˜b (ωs , ωr ) 2 c6 ~ 2

Z1

j,l,m

Z1

Zt

× dx1 dx2 dτ2 −1

−1

0

t−τ Z 2 0

n cS (j, m, l)δ(τ2 −rmj x3 /c)δ(τ1 −rml x1 /c) dτ1 K

+d KR (j, m, l)δ(τ1 − rmj x3 /c)δ(τ2 − rml x1 /c)

o

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394

Nicolae A. Enaki h ∂ i h ∂ i     × Dml Djm exp − iωs rml x1 /c exp iωr rjm x3 /c ∂ωs ∂ωr

the magnitude of which can be estimated from zero values of the arguments of the Dirac δ-functions. According to these, we obtain that the angles θ1 and θ2 , which describe the possible propagation directions of first and second photons, must satisfy the inequalities x1 > 0 and x2 > 0, where cos(θi ) = xi , i = 1, 2. As follows from the above expression for the larger values of time t we obtain the expression b VSR =−

 i X d c Vb (j, l.m) K R (j, m, l) + KS (j, m, l) , b 2τsrd j,l,m

(5.17)

0 is the three particle cooperative rate (5.13) between three atoms belonging where 1/τsrd to S, R and D subsystems defined in (5.13). The integration procedure V (j, l.m) on the direction of the emitted photons can be estimated in the similar form

 2  ∂   ∂  3 V (j, l, m) ' Djm Dml 4 ∂ωs ∂ωr [exp[−iωs rml /c] − 1][exp[iωr rjm /c] − 1] × . ωs ωr (rjm /c)(rml/c) b

(5.18)

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All expressions for exchange integrals described in points 3 are used in the master equation (4.14 ). 4. Let us now consider the scattering interaction between the radiators, which is represented by the master equation (4.19). The exchange energy between the D and S , R subsystems is represented in the last two terms of equation (4.19). The modification of the collective decay rate of the radiators under the influence of the single-photon emissions of the S and A atomic subsystems on the scattering process of the D subsystem is described by the expression

s Vsad

= 2i

t X X Z k,k0 j,l,n=1 0



dτ

Zt 0

  dτ 0 exp − i(ωs − ωk3 )τ2 + i(ωa − ωk1 )τ1

 b Ds (m, j, l), × exp i(k1, rj − rm ) − i(k3, rl − rm ) (ds , gk3 )(da , gk1 )qs (k1 , k3 )K (5.19)

where

 −  + −   −  ˇ , A˘ , [S , W (t)] +Nk D ˇ , [A ˘+ , S −W (t)] b s (m, j, l)= Nk Nk D K m m D 1 1 3 j j l l    − −  − ˇ , S˘ W (t)A˘+ . ˇ , [W (t), S˘ −]A˘+ − D +Nk D 3

m

l

j

m

l

j

Following the similar procedure of integration of the right hand site of expression (5.19) as in the point 4, we introduce the new variables u1 = ω1 − ωa ; u3 = ω3 − ωs . Following the similar procedure of integration of the right hand site of expression (5.19) as in the point 4, we obtain

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New Cooperative Effects in Single- and Two-Photon Interactions . . . 395 n X  −  + −  i s ˇ , A˘ , [S , W (t)] Vsad = s Vs (j, m, l) Nωs Nωa D m j l 2τsrd j,l,n=1  −   −   − − o ˇ , [A ˘+, S −W (t)] + Nωs D ˇ , [W (t), S˘ −]A˘+ − D ˇ , S˘ W (t)A˘+ , + N ωa D m m m j j j l l l

where

1 s τsad

  4 2 2d d d d ω 3 (ω )3  1 1 a s a 23 31 s + = 3 c6 ~ 2 ω32 − ωs ω31 + ωs

(5.20)

the spontaneous cooperative rate between D, R and S at small distances relatively the emission wavelength of anti-Stokes photon λr (5.20). The exchange integral at the large distance relatively the wavelength λr is described by the expression  3 2 h ∂ i h ∂ i Vs (j, m.l) = Dmj Dml 4 ∂ωr ∂ωs (exp[−iωs rml /c] − 1)(exp[iωarmj /c] − 1) × . (5.21) ωs ωa (rml /c)(rmj /c) The influence of D atom on the spontaneous emission of R and S dipole active radiators can be represented by the expressions

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U s (j, m, l) =

  i X X exp i(k , r − r ) − i(k , r − r ) 1 j m 3 l m ~3 k1 ,k3 j,l,m  b s (j, m, l) ×(ds , gk3 )(da, gk1 )qs (k1 , k3) Q A

 Zt Zt   × dτ1 dτ2 exp i(ωs − ωk3 )τ2 + i(ωa − ωk1 )τ1 +2i

0

0

Zt

Zτ1

dτ1

0

b Ss (j, m, l) +K

where

Zt

dτ2

Zt

dτ2

0

b s (j, m, l) +K A

0

0

t−τ Z 2



dτ2 sin (ωs − ωk3 )τ1 + (ωa − ωk1 )τ2





  dτ1 exp − i(ωs − ωk3 )τ2 + i(ωa − ωk1 )τ1

0 t−τ Z 2 0

   dτ1 exp i(ωa − ωk1 )τ2 − i(ωs − ωk3 )τ1 ,

  −    − ˘− ˇ m , [S˘−, W (t)] +Nk A˘+ , D ˇm b As (j, m, l) = Nk Nk A˘+ , D [Sl , W (t)] K 1 3 3 j j l    + − −  ˇ − ˘− ˘ ˇ ˘ + Nk1 A˘+ j , [Dm, Sl W (t)] + Aj , Dm Sl W (t) ,      − ˘ + ]D ˇ− ˘+, W (t)] +Nk S˘− , [W (t), A ˇ , [A b s (j, m, l) = Nk Nk S˘− , D K m 1 m 1 3 S j j l l     − − ˘ +, D ˇm ˘+ D ˇm ] + S˘l− , W (t)A + Nk3 S˘l− , [W (t)A j j    − b As (j, m, l) = Nk Nk A˘+ , S˘− , [D ˇm Q , W (t)] 1 3 j l

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Nicolae A. Enaki

Figure 2. The real parts of exchange integrals Vsrd and Usrd , defined in expressions (7.1) are plotted as a function of relative distance between radiators x = ωs r/c.    + −  ˘− ˇ − ˘ ˘ ˇ− + Nk3 A˘+ j , [Sl ,Dm W (t)] − Nk1 Aj , [Sl , W (t)Dm] .

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Using the calculation method proposed in the points 1 − 3 , we can obtain the following expression for cooperative emission time and the exchange integral between three radiators  s  i n s s b (j, m, l) + Q b s (j, m, l) Uasd (j, m, l) = s U (j, m, l) K A A 4τsad o b s (j, m, l) , + U ∗s (j, m, l)K (5.22) S where the exchange integral is represented by analytical expression h ∂ i  3 2 h ∂ i U s (j, m, l) = − Dmj Dml 4 ∂ωs ∂ωa c2 [exp[iωarjm /c] − 1][exp[iωs rml /c] − 1] × . ωr ωs rmj rml

(5.23)

The analytical representations of the exchange integrals, Vs (j, n, l) and U s (j, m, l), are introduced in the master equations (4.14) and (3.14). These estimations of exchange integrals between the radiators give us the possibilities to reduce the divergences, connected with angular causality at distances larger than the wavelength of emission photons. The exchange integrals obtained above can be used for description of cooperative interaction between the dipole forbidden and dipole active subsystems of radiators in two-photon excitation. Indeed passing again from Schrodinger to Heisenberg pictures T r[W (t)O(0)] = T r[W (0)O(t)], we obtain from master equation for density matrix (4.14) the complimenter equation

where

b b (0)(t) dO b (21b)(t) dO b (21s)(t) dO(t) dO = + + . dt dt dt dt Nα X 1 X b (0)(t)  dO i b b = H0 (t), O(t) + χα (j, l) dt ~ 2τα α=a,s,r l,j=1

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(5.24)

New Cooperative Effects in Single- and Two-Photon Interactions . . . n  +   o − + − b b × Nωα Jbαl (t), [O(t), Jˇαj (t)] + Jblα (t) O(t), Jbjα (t)

397

N n  +  1 X b (t), [O(t), b ˆ −(t)] + χd (j, l) Nω20 D D j l 2τd l,j=1  o b + (t) O(t), b b −(t) + (2Nω0 +1)D D j l

+

Z∞ 0

N n X d d 1 − + (Nω1 + 1)N2ω0+ω1 D (t), O(t) D dω1 m (t) l 2τS (ω1 ) l,m=1  o d d + − + Nω1 (N2ω0+ω1 + 1)D (t) O(t), D (t) χS (ω1 , m, l) m l

b + → O). b + H.c. (O

(5.25)

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All parameters and collective exchange integrals between the radiators belonging to S, R and D subsystems are defined in the points 1 and 2. This equation can be used for description of interaction between the dipole forbidden and dipole active subsystems of radiators. We give here for comparison the real part of the single-photon exchange integrals Re[χα (j, l)] = sin(ωαrj,l /c)/[ωαrj,l /c] of A, S and R dipole active atomic subsystems, defined in the expression (5.3) Ns  N Nr X ˆ (21b)(t) dO i XX Ub (j, m, l) =− b dt 2τsrd m=1 j=1 l=0 n   +  ˆ b −(t)], S b + (t) , R b (t) D × Nωs Nωr [O(t), m j l  −   +  + + + b b ˆ b b b ˆ b −(t)] + Nωr Sl [Dm (t), O(t)], Rj (t) + Nωs Rj (t) Sl [O(t), D m o b + (t)Sb + [O(t), ˆ b −(t)] +R D m j l n   +  − bm b + (t) , R b (t) (t)], S + Ub∗ (j, l, m) Nωs Nωr [O(t), D j l    − o + + b b b b + (Nωs + Nωr + 1) [O(t), Sl (t)], Rj (t) Dm (t)

 Ns N Nr X  −   i XX b b m (t) b +(t), O(t)] − b ,D Vb (j, l.m) 2Nωs Nωr Sbl+ (t), [R j 2τsrd m=1 j=1 l=0  +    − b (t), O(t)], b b −(t) +Nω Sb + (t), [R b +(t), O(t)] b b (t) + Nωr Sbl+ (t) [R D D m s m j j l n   + + + + b (t), O(t)] b D b − (t) + Nω R b (t) [Sb (t), O(t)], b b −(t) + Sbl (t)[R D m s m j j l  o  +  b (t), [Sb + (t), O(t)] b b − (t) + R b + (t)[Sb + (t), O(t)] b D b − (t) + N ωr R D m m j j l l b + → O). b + H.c. (O

(5.26)

All collective exchange integrals between the radiators belonging to S , R and D subsystems are defined at the point 3. This equation can be used for description of interaction between the dipole forbidden and dipole active subsystems of radiators. We give Electromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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here for comparison the real part of the single-photon exchange integrals Reχr (j, l) = sin(ωi rj,l /c)/[ωirj,l /c] of S and R dipole active atomic subsystems, defined in the expression (5.3). The spontaneous emission time of the dipole forbidden radiators τd is described by the expression (5.9). The exchange integrals between radiators j and l , χi (j, l), are defined in expressions (5.4), (5.10), (5.14) and (5.18) of representation 1 − 4. Indeed, representing the exchange integral between three atoms in the similar form as in the paper [21], we can find the cooperative emission rates between three atoms belonging to S , R and D subsystems situated at small distance r  λ0 (5.13). Let we consider the situation, when atomic subsystems R and S, with a dimension less than the emission wavelength λI , are situated at equal distance r relatively the dipoleforbidden ensemble D with the same dimension. Considering that the distances r between subsystems rsd and rrd may have the identical magnitude as the emission wavelength of photons from the system, we can represent the three particle exchange integrals between the radiators, R, S and D described by (5.17) and (5.14) in the form b Vsrd =

b 0 τsrd τsrd , U = exp[−iω r/c] , srd s b (r) τsrd(r) τsrd

(5.27)

in which

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  1 c2 ∂ 2 1 2 2 = 2 1 + cos (ξr ) + (3 cos ξr − 1) 2 b (r) r r ∂ωr2 τsrd   c2 ∂ 2 2 2 × 1 + cos (ξs ) + (3 cos ξs − 1) 2 r ∂ωs2 [exp[−iωs r/c] − 1][exp[iωr r/c] − 1] , (5.28) × ωs ωr r is the distance between R, S and D subsystems. If we consider that the directions of the dipole transition vectors ds , d32 and dr , d31 coincide, we can replace the coefficients 1 + cos2 (ξr )Rand 3 cos2 ξr − 1 in the relation (5.28) with their mean values 1 h1 + cos2 (ξr )id = 4π dΩ[1 + cos2 (ξr )] = 4/3; h3 cos2 (ξr ) − 1id = 0. In this case, we obtain simpler dependence of exchange integral between three radiators τbsr (r) as the function of the distance r 1 b (r) τdsr

=

1 [exp[−iωs r/c] − 1][exp[iωr r/c] − 1] . ωs ωr (r/c)2

b τsrd

b Here 1/τsrd is the cooperative emission time of three atoms belonging to S, R and D subsystems situated at a relatively small distance r  λ. Let us now found the part of the master equation (5.24) for resonance scattering interaction between the absorbed and emitted photons by the dipole active subsystems S and A and D. In this situation, the scattering part of the master equation for the case represented in Figure 7 can be represented by the expression N Na X Ns b (21s)(t) dO i XX = s Vs (j, m, l) dt τsad m=1 j=1 l=0

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New Cooperative Effects in Single- and Two-Photon Interactions . . . 399    −    − − c+j (t) , S c+j (t) Sb − (t) b bm b (t) + Nωa [O(t), b bm × Nωa Nωs [O(t), D (t)], A D (t)], A l l    c+ j (t) [O(t), c+ j (t)[O(t), b b − (t)], S b − (t) + A b b −(t)]Sb − (t) +Nωs A D D m m l l  n X    i c+j (t) , Sb − (t) b b −(t)], A + s Us (j, m, l) 2Nωa Nωs [O(t), D m l 2τsad m,j,l=1 n   −  c+ j (t)], S c+j (t) Sb − (t) b b − (t) D b (t)+Nω [O(t), b b − (t)], A +2Nωs [O(t), A D m a m l l  o   − − c+j (t)], S c+j (t)] bm b b − (t) + Sb − (t)D bm b −D (t) [O(t), A (t)[O(t), A l l n   −  − c+j (t) , S b bm b (t) + Us∗ (j, m, l) Nωa Nωs [O(t), D (t)], A l  −    c+ j (t) D c+ j (t), [O(t), b (t), [O(t), b b − (t)] +Nω D b − (t) A b b − (t)] +Nωs A S S m a m l l o − − c + b b b b + → O), b + A j (t)Dm (t)[O(t), Sl (t)] + H.c. (O (5.29)

where the last two terms in the master equation (5.29) describe the scattering process of emitted photons by atoms S and A. When the atom D is in the excited state, the emitted Stokes photon by an atom of system S can be absorbed by the radiator D so that three radiators pass into the ground state generating two anti-Stokes photons with energies E0 = 2~ωr . The opposite situation can be observed when D atom is prepared in the ground-state. In this case, the absorption of the anti-Stokes photon of R excited atom is accompanied by generation of another Stokes photon by atom D according to Figure 7. Let us consider the situation when the radiators D, R and S are situated in the separate volumes with the dimension less than the emission wavelengths as this is represented in Figure 7, we can consider rnj = rnl = r. In this case the exchange integrals can be approximated with the following expressions Vs (r) '

λr λs {exp[−2iπr/λr] − 1}{exp[2iπr/λs] − 1} 4π 2 r 2

and U s (r) ' −

λr λs {exp[2iπr/λr] − 1}{exp[2iπr/λs] − 1} , 4π 2 r 2

where λr and λs are the emission wavelength of R and S radiators, respectively; r is the distance between the subsystem D and S, R ensembles. The master equations (2.8) and (5.24) can be used for description of cooperative interaction between the dipole forbidden and dipole active subsystems of radiators in two-photon excitation. Of course some differences between these equations exists . It is not difficult to observe this for T=0 . Forthe equations (2.8) and (3.14) we observe the new correlation  − (t) in three particle interaction case of the Fig. ?? . This b b +(t) D bm Sbl+ (t)], R term [O(t), j term gives some contribution in the correlation function of three-particle interaction. We will discuss this in the section 7..

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6.

Two-Photon Super-Radiances of Inverted Atomic System

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Dicke’s study [7] was first which predicted the possibility of collectivization of an excited ensemble of two-level atoms in one-photon spontaneous decay. This effect, which has come to be called super-radiance, has become the focus of extensive theoretical and experimental investigation in the literature. As it is demonstrated in the last experimental and theoretical studies (see for example [14]–[17], two-level atoms in an inverted quantum state can pass into regime of collective light generation, due to interaction through fluctuations of the vacuum of electromagnetic field. In this case the rate of photon generation becomes proportional to N 2 , and achieves the maximal value, when the inversion takes zero value. Here N is the number of atoms in the system. The present section reports the possibility of collectivization of an ensemble of atoms inverted with respect to the dipole-forbidden transitions in the process of two-photon emission of the excited states |2i of atomic ensemble. Let us consider cooperative emission only for one atomic subsystem described by equation (5.24) in which the subsystems A, S and R are absent. Here we propose the new method of de-correlation of three particle correlations is proposed taking into account the Fermi and Bose proprieties of Pauli spin operators, used in the description of atomic ensemble [53]. From the master equation (5.25) it is easy to obtain the following chain of equations for two-photon dipole-forbidden cooperative transitions for temperature T = 0

+   d b 1 X b (t)D b − (t) χd (i, j) D Dzj (t) = − i j dt 2τd i

+  b (t)D b − (t) , + χ∗d (i, j) D j i  X



  1 d b+ b− b + Dzi (t)D b − (t) Di (t)Dj (t) = χd (i, l) D j l dt τd l

+  b (t)D b zj (t)D b − (t) , ... + χ (j, l) D d

i

(6.1)

l

b zj , D b + , and D b − are respectively the inversion, creation and annihilation and so on. Here D j j operators for the D atomic subsystem. Let firstly consider the system consisted of two atoms in the excited state. As in onephoton super-radiance it is possible to obtain a closed system of equations for two atoms situated at the distance r21 at the second step of the chain (6.1) 1 1 d Z(t) = − (1 + Z(t)) − V (t), dt τd τ1 d 1 1 4 V (t) = − V (t) + Z(t) + Y (t), dt τd τd τ1 d 1 1 2 Z(t) + V (t). Y (t) = − Y (t) − dt τd 2τd 2τ1

(6.2)

b z2 (t)i is the inversion of atoms, Here we introduce the new variables: Z(t) = hDz1 (t)i+hD + − + − b b b b V (t) = hD2 (t)D1 (t)i + hD1 (t)D2 (t)i is the cooperative rate of emission, Y (t) = b 1z (t)D b 2z (t)i is the correlation function of inversions for the first atom and the second hD

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401

one. Using the initial conditions for variables: Z(t = 0) = 1, V (t = 0) = 0, Y (t = 0) = 1/4, it is obtained the following solution of the system (6.2) 4J 2 −2τ 1 − J −(1−J)τ 1 + J −(1+J)τ e + e + e − 1, 1 − J2 1+J 1−J 4J 1 − J −(1−J)τ 1 + J −(1+J)τ V (τ ) = − e−2τ − e + e , 1 − J2 1+J 1−J 1 + J 2 −2τ Y (τ ) = e 1 − J2 1 − J −(1−J)τ 1 + J −(1+J)τ − e − e + 1/4, 2(1 + J) 2(1 − J) Z(τ ) = −

(6.3)

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where J = τ0 /τ1 , τ = t/τ0 . To estimate the dependence of the two-photon cooperative exchange integral between the atoms situated at the distance r12 , we make the following approximation in the expression for the cooperative parameter n. First we average the exchange kernel χ12 (x) over the directions of the dipole momentum d~ and then one can approximate x2 (ω21 − x)2 ≈ (ω21 /2)4 . In this case we obtain the following relation for parameter J  c 2  c ω r   ω r  21 12 21 12 J =3 sin − cos . r12 ω12 r12 ω12 c c We observe that at a big distance relative to parameter c/ω21 the exchange integral J 2 ). In other words the oscillates as a function of distance r12 (J ∼ − cos(ω21 r12 /c)/r12 two-photon cooperative exchanges between the two atoms can inhibit or enhance the spon2 . taneous emission as a function of the distance between the atoms and decreases as 1/r12 Let us suppose, that all the atoms are located within a volume the linear dimensions of which are small compared to the wave length λmin = 2πc/ω21. In this case J ≈ 1 and the solution of the system of equations (6.2) takes the form Z(τ ) = 2(1 + τ )e−2τ − 1,

V (τ ) = 2τ e−2τ , 1 Y (τ ) = (1 − 4τ e−2τ ). 4

(6.4)

Now we consider a more general case, when the number of atoms in the concentrated system is larger than one. For a correct description of super-radiance it is necessary to use the quantum treatment of atomic behavior. In this case, the number of equations for higher order correctors in the chain (6.2) drastically increase. From Fokker–Planck equation [52], which corresponds to the concentrated system of radiators, follows, that by increasing the number of radiators the relative value of quantum fluctuations decreases. The method of decoupling of a chain of equations (6.2) can be found, when the atoms in interaction through EMF contains a small parameter. Such a small parameter can be proposed at the initial stage of super-radiance. In a similar way as in the theory of ferromagnetism, in this case, it is absent the small parameter useful for all time intervals of super-radiance process. The quantitative theory of decoupling of a chain of equations (6.2)

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till now is absent but in many cases it is necessary to take into account the intrinsic symmetry of correctors, when is proposed the method of decoupling. The traditional method of decoupling connected with negligible value of quantum fluctuations of inversion

+  +  b (t1 )D b zm (t2 )D b − (t3 ) = D b (t1 )D b − (t3 ) hD b zm (t2 )i. D (6.5) j j l l

Of course this method of de-correlation gives the mistakes for the correlation function of three particles, when label j coincide with m or m = l. In the situation, when this three particle correlation passes in to two particle correlation the decoupling gives an evident error



 b j (t1 )D b l (t3 ) /2; Dj (t1 )Dzm (t2 )Dl (t3 ) =− D j=m; t1 =t2 (6.6)



 b b b b j (t1 )D b l (t2 ) /2. Dj (t1 )Dzm (t2 )Dl (t3 ) =− D

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l=m; t3 =t2

The value of errors, which is made of one atom in this decomposition can be estimated by the expression 1 b j (t)i2 . δ = − hD 4 At the maximum of super-radiance process, when the inversion achieves zero value, b j (t)i = 0, the error parameter δ achieve maximal value. In order to avoid these difficulhD ties from three particle correlation (6.5) is separated all possible two particle correlations (6.6) for which j = m; and m = l before the decomposition (6.5) is used. Taking into account the intrinsic symmetry of three particle correlations developed in the papers[33]–[37] for the Green function theory of ferro-magnetism, we proposed the new type of de-correlation [40], [40] which takes into account Bose and Fermi proprieties of spin operators. Indeed, taking into account, that the atomic operators have Bose proprieties for different particles, b −D b+−D b +D b − = 0, D j j l l and Fermi proprieties for the same particle,

b −D b++D b +D b − = 1; (R+ )2 = (R− )2 = 0, D j j J j j j

b zm (t) through anti-normal order of creation and annihilation let us represent the inversion D − + b b operators, Dm and Dm b−D b+ b zm = 1 − D D m m. 2 In this circumstance the three particle correlation is represented in the following form

+  b (t1 )D b zm (t2 )D b − (t3 ) D j l

+ 

+  − − b b b b b + (t2 )D b − (t3 ) . = Dj (t1 )Dl (t3 ) /2 − Dj (t1 )Dm (t2 )D m l In a following step we uncouple the last correlation in analogy with Wick theorem for Boson and Fermi operators developed in papers [36]–[38]

+  − + b (t1 )D bm bm b − (t3 ) D (t2 )D (t2 )D j l

+  +  −  +  − + b (t1 )D bm b m (t2 )D b − (t3 ) + D m b (t1 )D b − (t3 ) . (6.7) ≈ D (t2 ) D (t )D (t ) D 2 2 m j j l l

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Taking this in to account it is not difficult to observe that the particle correlation take the next de-correlation form

+  b (t1 )D b zm (t2 )D − (t3 ) D j l

+ 

 +  +  − b (t1 )D b − (t3 ) D b zm (t2 ) + D b (t1 )D bm b m (t2 )D b − (t3 ) . ≈ D (t2 ) D (6.8) j j l l

Ignoring the quantum fluctuation of operator Dzi (t) by decoupling method (6.5) from the chain of equations (6.2) it obtains the next system of equations d 1 1 hDzj (t)i = − hD zj (t)i + dt τd 2  X



 1 − − χd (i, j) Di+ (t)Dj− (t) + D + (t)D (t) , j i 2τd i

 d + 1 Di (t)Dj− (t) = − hD + (t)Dj− (t)i dt τd i

 1 X + χd (i, l)hDzi(t)i Dl+ (t)D − j (t) τd l

 − + χd (j, l)hDzj (t)i D + (t)D (t) , i l

(6.9)

In the system of equation (6.8) the first terms in both equations take into account the correct express of the correlations (6.6), obtained after separation of the two-particle correlations from three particle one.For simplicity we will consider a concentrated system of atoms with dimensions much smaller than the minimum radiation wavelength. In this case we observe that the coefficient lim F (j, l) = 1/2τd , Copyright © 2013. Nova Science Publishers, Incorporated. All rights reserved.

j→l

doesn’t depend on the atomic position. According to this the new collective operators can be introduced in the system (6.8) D + (t) =

N X

− R+ j (t); D (t) =

j=1

N X

D− j (t); Dz (t) =

j=1

N X

D jz (t).

j=1

According to the generalized equation (5.24), and quasi-classical condition (6.5), the quasiclassical Bloch vector is conserved 

 N N + 1 = Z(t)(Z(t) − 1) + D + (t)D − (t) , 2 2

where Z(t) = hD z (t)i is the inversion of the atomic system relatively the dipole forbidden transition. In this case we obtain the well-known super-fluorescent equation for the atomic inversion  d 1 1  2 Z(t) = − (Z(t) + N/2) + Z (t) − N 2 /4 , (6.10) dt τ0 τ0

the solution of which is

Z(t) = −

ht − t i N 0 tanh , 2 2τR

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(6.11)

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Nicolae A. Enaki

where t0 = τR log N is the delay of the collective radiation pulse of the photon pair and τR =τd/N is the collectivization time of the ensemble of atoms in the two-photon spontaneous decay process of the |2i excited state of the ensemble. It follows from the solution (6.11), that the ensemble of atoms collectively emits photon pairs in the spectral region (0, ω21) with total energy ~(ωk1 + ωk2 ) = ~ω21 . The emission rate of such photon pairs is equal to ht − t i d N 0 V21 = − Z(t) = − sech2 . (6.12) dt 4τr 2τR Let us apply the decoupling (6.8) to the chain of equation (6.2). In this case it is obtained the following system of equations 

X 

 d hDzj (t)i = − F (i, j) Di+ (t)Dj− (t) + Dj+ (t)Di− (t) , dt i

 d + Di (t)Dj− (t) dt h X

 +  + i (6.13) − − =2 F (i, l) hDzi (t)i Dl+ (t)D − (t) − D (t)D (t) D (t)D (t) j i i j l l

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 h

+  +  + i − − − + F (j, l) hD zj (t)i D i (t)Dl (t) − D i (t)D j (t) Dj (t)D l (t) .

For a concentrated system of radiators one can obtain from the system of equation (6.13) takes the form 2 2 d 2 d d2 Z(t) + Z(t) Z(t) − Z(t) = 0. (6.14) dt2 τ0 dt N dt This equation (6.14) defers from the traditional expression (6.11), obtained in the neglecting of quantum fluctuations of inversion during the super-fluorescence process. In this equation d is present the new term N2 ( dt Z(t)) the physical interpretation of which, can be obtained after the partially integrated of the equation (6.14) with initial condition dZ(t)/dt = −N/τ0 ; Z(t) = N/2  2Z(t)  N  d N N Z(t) = (N − 1) exp − Z(t) + . (6.15) dt eτ0 N τ0 2

According to this equation one can construct the dependence between the decay rate dZ(t)/dt and inversion Z(t). As follows from equation(6.15) this dependence becomes non-univocal functional. As follows from equation (6.15) and 3 the maximum of depen˙ dence Z(Z) is shifted to increasing the number of atoms in the system in accord with following three dimensional dependence f (x, y) = y(y − 1) exp[2x − 1] − y 2 (x + 0.5). The extremum of the function Z(N ) for which the super-radiance achieved the maximal decay rate is  N − 1 i Nh Zextr (t) = 1 − ln 2 . 2 N By increasing the number of atoms N  1 the maximum of super-radiance is displeased from zero value of traditional theory with value proportional with the number of atoms in the system N Zmax (t) = [1 − ln 2] = 0.153N. 2

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Figure 3. The representation of right hand site of equation (6.15) as function of relative inversion and number of atoms f (x, y) = (y −1) exp[2x−1]−y(x+0.5), where f (x, y) = d τ0 dt x(t); y = N and x = Z/N . The dynamical description of the proposed model consists in the fact, that the maximal value of super-radiance is achieved earlier than in point Z = 0 described by the Decke model in which is used the semi-classical methods of decoupling of equation chain (6.9). This effect can be connected with large quantum fluctuations, which are taken into account in the system of equations (6.13). As follows from the solution of semi-classical equation (6.14) the maximal value of super-radiance intensity is achieved in the time moment t0 = τr ln N and is equal with Imax = N 2 /(4τd). For estimation of the intensity of the maximum of super-radiance we can replace the inversion Z with the value Zmax , in equation (6.15) and considering that maximal of two-photon super-radiance corresponds to the derivation −dZ/dt in point Z = Zmax we get Imax =

N2 (1 − ln 2). 2τ0

This intensity is less than the super-radiance intensity obtained using the traditional decoupling. We can find the analytical comparison of the solutions of equations (6.15) and (6.11). For this let us decompose the exponential function in equation (6.15) near the superradiance maximum taking into account the small parameter Z(t)/N h Z(t) i Z(t) Z 2 (t) exp 2 = 1+2 +2 +··· . N N N2

(6.16)

Taking into account only the second order of decomposition on the small parameter Z(t)/N in the right hand site of the equation (6.16), the equation (6.15) pass in the next approximaElectromagnetic Fields: Principles, Engineering Applications and Biophysical Effects, Nova Science Publishers, Incorporated, 2013. ProQuest Ebook

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