Superfluid: How a Quantum Fluid Revolutionized Modern Science 3031426517, 9783031426513

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J. G. Weisend II

How a Quantum Fluid Revolutionized Modern Science

Superfluid

J. G. Weisend II

Superfluid How a Quantum Fluid Revolutionized Modern Science

J. G. Weisend II Dept of Industrial Production, Lund University Accelerator Division, European Spallation Source Lund, Sweden

ISBN 978-3-031-42651-3    ISBN 978-3-031-42652-0 (eBook) https://doi.org/10.1007/978-3-031-42652-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover credit: Biwa Studio/Gettyimages This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

To Steve Van Sciver who started me on this journey and To Shari, who has taken it with me

Acknowledgements

The creation of this book required the assistance of many people. I greatly appreciate their efforts which have improved this work and made the process more enjoyable. A number of friends and colleagues  – Susan Breon, Dimitri Delikaris, Michael DiPirro, Sam Harrison, Mats Lindroos, Tom Peterson and Shari Weisend  – have read a draft of the book, made valuable suggestions and looked for errors. Any remaining errors are, of course, mine alone. The editorial team at Springer – Sam Harrison, Ragavendar Mohan, Tom Spicer and Cindy Zitter – was very supportive of this book and provided help whenever asked. My colleagues at the European Spallation Source and Lund University were also supportive of my efforts on this book. A special thank you to Steve Van Sciver, who first introduced me to cryogenics and superfluid helium and who has remained a friend and colleague over the years. My family  – Shari, Rachel, Nick, Alex, Patrick, Kelsey and Lovisa –has been through a number of book projects with me and has been tolerant, not only of the time this work took, but also of having me explain whatever I have just recently learned. As always, their support makes this book possible.

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Contents

1 I ntroduction  1 2 A Brief Tour of Cold  3 3 D  iscovery 11 4 Explaining  He II: Quantum Mechanics and the Two-Fluid Model 17 5 What If You Had a Bucket? 23 6 M  oving Heat 29 7 General  Weirdness: Fountains, Porous Plugs, Second Sound and Films 35 8 E  arly Applications 43 9 The Fabulous 80s: Tore Supra, IRAS and CEBAF 49 10 Can You Paddle a Canoe in He II? – Engineering Studies 73

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11 Colliders: Super, Large and Otherwise 83 12 ILC, TESLA, & SRF Everywhere 97 13 A Superfluid Space Odyssey115 14 H  igh Field Magnets127 15 Th  e Other Superfluid135 16 Th  e Future141 Suggestions for Further Reading145 I ndex 147

About the Author

J. G. Weisend II  is a Senior Accelerator Engineer at the European Spallation Source and Adjunct Professor at Lund University in Sweden. A specialist in cryogenic engineering, he has worked at the Superconducting Supercollider Laboratory, the Centre D’Etudes Nucleaires Grenoble, the Deutsches ElecktronenSynchrotron Laboratory (DESY), the Stanford Linear Accelerator Laboratory (SLAC), the US National Science Foundation and Michigan State University. His other books include: He is for Helium, Cryostat Design (ed), Cryogenic Safety (with T.  Peterson) and Going for Cold: A Biography of a Great Physicist, Kurt Mendelssohn (with G.T.  Meaden). He resides in Sweden and California.

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1 Introduction

Unless you are a specialist or watch a lot of obscure YouTube videos, you have probably never heard of He II (pronounced “helium two”) or superfluid helium. However, this substance, a unique liquid form of the element helium, is produced and used in multi-ton quantities to enable much of modern science. He II cools the superconducting magnets that contain the particle beams at the Large Hadron Collider (LHC) at CERN. It is the go-to coolant for superconducting radiofrequency cavities that are used in accelerators that produce X-ray lasers and intense neutron beams for the study of materials and that accelerate heavy ions for the study of rare isotopes and nuclear astrophysics. Since the temperature of He II is below that of the background temperature in space, He II was used in space-based infrared telescopes and experiments that made significant advances in understanding the universe. Altogether, He II is at the heart of more than a dozen large-scale scientific facilities worldwide, representing an investment of tens of billions of dollars. The expected, and more importantly unexpected, discoveries from these facilities in the areas of new materials, drug development, biology, chemistry and physics will affect both daily life and our understanding of the universe. This little-known liquid is, in reality, one of the enabling technologies of the future. He II is a manifestation of quantum mechanics and exhibits at times amazing behaviors. It can flow up the side of a container against gravity, can move through small openings without friction, and can transfer heat extremely efficiently via a mechanism not seen elsewhere in nature. He II contains quantized vortices that can be used in fundamental studies of turbulence.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_1

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The discovery of He II and the explanation of its behavior began in the 1930s and involved many leading experimental and theoretical physicists, including Lev Landau, Richard Feynman, Peter Kapitza and Kurt Mendelssohn. Starting in the 1960s, efforts turned to using the properties of He II to solve technical problems, such as cooling superconductors. This led to a range of engineering studies, related technological developments and increasingly large-scale applications of He II. This book tells the story of He II. It describes the discovery of the fluid, the observation and understanding of its behavior, the development of underlying theory and the evolution of He II from a laboratory curiosity to an industrial scale coolant. The current and possible future applications of He II are described. Like all science and engineering, the story of He II is a human story, and the role that personalities, politics, communication, cooperation and competition play in the development of He II is captured here as well. The race to liquefy air, the Second World War, the development of the atomic bomb and the desire to find and measure the most fundamental particles in nature are all part of the story. This work is meant for the general reader. It does not assume any expertise in physics, engineering or mathematics. There are a number of technical monographs on He II (see suggestions for additional reading) but this book is something else. It is an attempt to illuminate for the general public a little-­ known area of science and engineering and show why it matters. As it turns out, it is also a good story.

2 A Brief Tour of Cold

You have been on the edges of the ultracold. You have seen tanker trucks on the highway, frequently white and labeled “liquid nitrogen”, “liquid oxygen” and more rarely “liquid helium”. If you ever had a Magnetic Resonance Imaging (MRI) scan at the hospital, you were, although likely nobody told you, surrounded by a superconducting magnet cooled by liquid helium. It is possible that some of the natural gas you use at home was at one point stored or transported as ultracold liquefied natural gas (LNG). These were all brushes with the multibillion dollar cryogenics industry. Cryogenics is the science and engineering of the ultracold, and the first question to ask is: “How cold are we talking?” In science and engineering, we typically use the Kelvin temperature scale. In this scale, 1 K equals 1 °C + 273.15. Thus, room temperature is approximately 300  K.  In comparison, at atmospheric pressure, oxygen becomes a liquid at 90  K (−183  °C), nitrogen at 77  K (−196  °C), hydrogen at 20  K (−253 °C) and helium at 4.2 K (−269 °C). The field of cryogenics is generally defined as applying to phenomena below 120 K (−153 °C). There are two aspects of the Kelvin scale that are immediately important to our story. The first is that we use the symbol K but never °K, and we discuss the temperature as kelvin, not degrees kelvin. More fundamentally, 0  K (−273.15 °C) is a physical limit. Just as we can never go faster than the speed of light in a vacuum we can never go below 0 K. In fact, the laws of thermodynamics show that you can’t even reach 0 K although you can get very close with the current record being approximately 38 picokelvin (0.000000000038 K). As will be seen, our subject, He II or superfluid helium, extends into these near 0 K temperatures.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_2

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What is He II? He II is the second liquid phase of the helium 4 isotope. This statement, while a correct answer on a physics quiz, needs some unpacking. We are all familiar with the concept that matter occurs in phases, the most common being liquid, gas and solid. In the case of water, we call these phases liquid water, steam and ice. The universe is more complicated than this, however. For example, depending on pressure and temperature, water ice can form in up to 20 different crystalline phases. The existence of a second liquid phase in helium has, as we shall see, very important fundamental and practical implications. For the moment though, consider Fig. 2.1 This figure shows the different phases of helium as a function of pressure and temperature. Overall, the figure is relatively simple; we see the vapor phase, two liquid phases (He I and He II) and a solid phase.

Fig. 2.1  Helium Phase Diagram. The horizontal axis plots temperature in kelvin, while the vertical axis shows pressure in either kiloPascals (left) or atmospheres (right). The diagram shows the four phases of helium: solid, vapor, liquid He I and liquid He II. Note that very high pressures are needed to form solid helium, and He II, a liquid, exists all the way down to 0  K.  From Helium Cryogenics, S.W. Van Sciver, Springer (2012)

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Under certain conditions, He II exhibits superfluidity; that is, it flows without resistance. Thus, He II is frequently also referred to as superfluid helium, although this is not strictly correct.1 In addition to the existence of He II, whose story is told below, Fig. 2.1 shows another important feature of helium; unless high pressures (approximately 20 times that of normal atmospheric pressure) are applied, helium remains a liquid (in the form of He II) all the way down to 0 K. From an engineering viewpoint, liquids are much more useful as coolants than solids. For example, liquids can be pumped and will penetrate small spaces. Helium is the only substance that remains a liquid down to near absolute zero. The reason for this, like the existence of the He II liquid phase, is a result of quantum mechanical effects. The fact that helium remains a liquid down to these extremely low temperatures is, as will be seen, part of what makes it so useful. There is one remaining feature of our definition of He II above. This is the comment about the helium 4 isotope. Elements exist in different isotopes. Isotopes of a given element have the same number of protons in their nucleus but differing numbers of neutrons. The number of protons in an element is indicated by the atomic number, while the total number of protons and neutrons is given by the mass number. In the case of helium, there are only two isotopes. By far, the most common isotope of helium contains two protons and two neutrons, resulting in a mass number of four, and is thus known as helium 4, whose symbol is 4He. It is this common version of helium that we will address in this book. The other isotope of helium contains 1 neutron and 2 protons and is thus known as helium 3 (3He). This isotope is exceedingly rare, making up only 0.1 part per million of naturally occurring helium. This isotope will be discussed in a later chapter of the book and does become superfluid under certain conditions. So, to review, 4He and 3He are different isotopes of the element helium, while He II (note the use of a Roman numeral) is not an isotope but rather the second liquid phase of the 4He isotope. With definitions out of the way, the next step is to understand the state of cryogenics at the time of the discovery of He II. Cryogenics really started as a field when researchers in the late 19th and early twentieth centuries competed to liquefy the so-called permanent2 atmospheric gases, for example oxygen, nitrogen and neon. There was no compelling economic or societal need for this effort, but technology and scientific  However, “Superfluid” makes a better book title than “He II”  These were called permanent because they couldn’t be turned into liquid merely by increasing the pressure on them at room temperature. 1 2

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theory had developed to the point where liquefying these gases was possible. Reaching lower temperatures and liquefying gases became a point of institutional and national pride, and the race to accomplish these feats resembled the race to the North and South poles or the race to climb the highest mountains taking place at approximately the same time. Of course, once these gases were liquefied, particularly on an industrial scale, then uses were found for them. An example is the extensive use of oxygen and nitrogen in steel mills and chemical plants. Along the way, new techniques for cooling, storing and working with materials at these temperatures were developed together with a better scientific understanding of the universe at these temperatures. These developments formed the basis of the field of cryogenics. We will see this interplay between application and research again and again in the story of He II.  The process of scientific discovery will result in new technologies; these technologies will in turn drive or enable new discoveries. The composition of air plays a role in this story. Table 2.1 shows the typical composition of dry air, that is, air with all water vapor removed. Table 2.1 does not include pollutants such as dust or sulfur dioxide, and due to rounding errors, the percent of components may not add up to 100%. The main takeaways should be that 99.9% of dry air is made up of just three components: oxygen, nitrogen and argon and that the rare atmospheric gases neon, krypton and xenon occur in vanishingly small amounts. As we will see, helium, as usual, is a special case. Hydrogen, due to its chemical reactivity, does not appear as an atmospheric gas but was easily available, and theory showed that it likely had a low liquefaction temperature. Oxygen was first liquefied in 1877 independently and nearly simultaneously by Louis Paul Cailletet in France and Raoul Pictet in Switzerland. Cailletet’s technique was to compress oxygen gas to roughly 20 times that of atmospheric pressure and then cool the high-pressure container in a bath of Table 2.1  Typical composition of dry air Component

Percent by volume

Nitrogen Oxygen Argon Carbon dioxide Neon Helium Methane Krypton Xenon

78 21 0.9340 0.0415 0.001818 0.000524 0.000187 0.000114 0.0000086

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liquid ethylene at a temperature of 169 K. When the pressure was suddenly reduced to atmospheric pressure, the cold oxygen gas cooled further and dropped below its liquefaction temperature of 90 K. This approach of compressing a gas, cooling it with a colder substance and then expanding the gas to a lower pressure for additional cooling is a fundamental technique of cryogenic refrigeration and is used in much more sophisticated machines today. However, Cailletet’s machine could only produce bursts of liquid oxygen, and the liquid droplets produced did not last long due to the heat leak from the environment. Zygmunt Wroblewski and Karol Olszewski, working in Krakow, Poland, liquefied oxygen in 1883 using Cailetet’s approach with one significant change: by reducing the pressure of the liquid ethylene to below atmospheric pressure, they reduced the temperature of the liquid ethylene bath to 137 K. At this temperature, the compressed oxygen gas starts to liquefy without any reduction of its pressure, and the resulting liquid (surrounded by the cold 137 K bath rather than a room temperature of 300 K) would remain longer than in Caillett’s case. The technique of reducing the boiling temperature of a liquid by reducing its pressure is well understood, and as we will see, it is the approach taken to get to He II temperatures.3 Note that Wroblewski and Olszewski improved both the ability to make things colder but also the ability to keep them cold. This dual improvement in both producing cold temperatures and maintaining cold temperatures is seen throughout the early days of cryogenics. Using similar techniques, Wroblewski and Olszewski also liquefied nitrogen (77 K) in 1883. In 1895, Olszewski, working alone liquified argon (87 K) and by reducing the pressure on the liquid, was able to freeze argon at 84 K. Argon brings up an interesting problem. To liquefy a gas, you had to a) know that it exists and b) have a reliable source of it. In the case of argon, the Scottish chemist William Ramsey discovered argon by extracting it from air in 1894 and provided it to Olszewski. In 1898, Ramsey working with Morris Travers also discovered the elements neon, xenon and krypton in air. William Ramsey also played an important role with helium. First though, let’s turn to hydrogen. Hydrogen was first liquefied (20 K) by James Dewar at the Royal Institution in London in 1898. However, prior to this, Dewar made a major innovation in cryogenics. He realized that if you placed one vessel inside another and removed all the air in the space between the vessels, thus creating a vacuum, you would greatly reduce the heat transfer  This effect is seen in everyday life. Water boils at lower temperature when at less than sea level atmospheric pressure. This is why many cooking recipes have to be adjusted in Denver, CO. 3

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Heat exchanger

Spaceframe support

Magnetic shielding

Vacuum valve

Thermal Alignement fiducial shielding

Diphasic He pipe

Proton Beam

Cold to warm transition

Intercavities belows

Power coupler

Cavity with Helium tank

Fig. 2.2  Cutaway view of superconducting radiofrequency cavity Cryostat used in the European Spallation Source Accelerator. The cryomodule is approximately 1 m in diameter and 8 m long. The accelerator contains forty-two of these and similar cryostats. Dewar’s innovation in vacuum insulation is a fundamental part of the design of these cryostats. (Courtesy of CNRS & CEA, France)

between the outer and inner vessels. Furthermore, if you silvered the glass inner vessel, you would also reduce the heat transferred by thermal radiation. The result was that you could store cryogenic liquids such as liquid nitrogen or liquid hydrogen for days to weeks. Such vacuum insulated containers are known as dewars or cryostats and are a fundamental building block of cryogenic engineering today (Fig. 2.2). Dewar displayed the first of his vacuum insulated flasks (Fig. 2.3) in January 1893. With these devices, Dewar was able to collect and study the liquid hydrogen he made. Once hydrogen was liquefied, the next goal for everyone was helium. Competitors here included Olszewski, Dewar, and Heike Kamerlingh Onnes of Leiden University in the Netherlands. The element helium was first discovered as a distinct line in the Sun’s spectrum observed during an eclipse. The element takes its name from the Greek god of the sun Helios. The first helium seen on Earth was found by Luigi Palmieri, who, when studying lava from Mount Vesuvius, saw the same spectral line in his data in 1882. Twelve years later and much more significantly, William Ramsey extracted helium gas from Cleveite (a mineral of uranium). Terrestrial helium comes from the radioactive decay of uranium, thorium and some other elements. The principal supply of helium today is found in some, but not all, natural gas fields. However, this source wasn’t discovered until 1905. Ramsey sent some helium to Olszewski, who was unable to

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Fig. 2.3  Dewar’s “dewar” in the Museum of the Royal Institution. A vacuum space between the outer wall and inner container greatly reduces the heat leak into the inner container, allowing storage of cryogenic fluids

liquefy it. Another source of helium was found in the sands (which contained thorium) of the mineral springs in Bath, England. Kamerlingh Onnes suggested to Dewar that they share this helium and work together to liquefy it. However, Dewar refused, wanting to work alone. Kamerlingh Onnes was able to find another helium source from monzanite sands (also containing thorium) from the USA. It turned out that the helium from Bath contained many other gases that had to be removed, which delayed Dewar’s efforts, and in 1908, Kamerlingh Onnes became the first person to liquefy helium. What happened next is both illustrative and seen frequently in the history of science. Once he liquefied helium, Kamerlingh Onnes now had access to temperatures of 4.2  K (the room pressure boiling point of helium) and started to conduct research on the properties of materials at these lower temperatures. One property he investigated was the electrical resistivity of metals. In 1911, when making these measurements with mercury, he observed that near 4.2 K, the electrical resistance of mercury vanished. Kamerlingh Onnes discovered superconductivity: the ability of some materials to carry electrical current

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without any resistance or loss. The practical applications of superconductivity, developed since then, include powerful magnets for particle accelerators, MRI systems, fusion energy research and superconducting radiofrequency cavities for particle acceleration. Today, the principal use of liquid helium (including He II) is the cooling of superconducting components. In effect, Kamerlingh Onnes not only liquefied helium but also discovered the main practical application of liquid helium. The discovery of superconductivity is a prime example of what frequently occurs in science whenever a new capability, such as a more powerful telescope or particle accelerator or a more precise measurement technique, is developed. New and unexpected scientific discoveries, sometimes along with new practical applications, arise. The field of cryogenics continued to develop and grow after 1911, but this is outside the scope of this book. In the specific case of liquid helium, developments were slower. Liquid helium and superconductivity were of academic interest in a number of universities, but by the early 1930s, only four institutes—one in Leiden, one in Toronto and two in Berlin—could reach liquid helium temperatures. Our story now moves to England.

3 Discovery

Professor Lindemann really wanted to beat Cambridge University. In 1933, Frederick Lindemann was the head of Clarendon Laboratory and thus was responsible for physics research at the University of Oxford. Lindemann had trained under Prof. Walther Nernst at the University of Berlin. Nernst proposed what we now call the Third Law of Thermodynamics. It is this law that shows that we can never actually reach absolute 0 K (see Chap. 1). The Third Law also predicts that the specific heat (a property that describes how much a material’s temperature changes upon absorbing or losing heat) will approach zero as the temperature approaches zero. In order to provide experimental evidence of the Third Law, Nernst and his students, including Lindemann and Francis Simon, along with Simon’s student, Kurt Mendelssohn, started making precision measurements of the specific heat of materials at cryogenic temperatures, including at liquid hydrogen temperatures. Based on his experiences in Berlin, when Lindemann took up his position as head of the Clarendon Laboratory in 1919, one of the areas of research that he started was in cryogenics with the goal of working at liquid helium temperatures. In 1930, Lindemann purchased a hydrogen liquefier designed by Francis Simon and started work at liquid hydrogen temperatures (20  K). Simon also developed a series of miniature helium liquefiers, and Lindemann was also interested in these devices. At about the same time (late 1932), Cambridge University was building a new laboratory to conduct research in cryogenics and superconductivity funded by the Royal Society using money from a donation by Dr. Ludwig Mond. The Mond lab was led by the Russian physicist Peter Kapitza, and if all went to plan, it would be the first lab in the UK to liquefy helium. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_3

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Lindemann, however, had a different plan. He purchased a helium liquefier from Simon and had Kurt Mendelssohn come to Oxford in January 1933 to install and commission it. This was successfully accomplished, and the first helium in the UK was liquefied on January 13, 1933, beating the Mond lab at Cambridge. This anecdote illustrates competition in science, a theme that we will see repeatedly in the story of superfluid helium. However, it is important to realize that such competition is accompanied by collaboration. Competing labs frequently share data, experiences, equipment and people both formally and informally. Open communication is both a prerequisite for and a hallmark of scientific progress. We will also see this in the superfluid helium story. Another reason to tell the story of the first liquefaction of helium in the UK is that Kapitza, Mendelssohn, Simon and the cryogenics groups at Oxford and Cambridge played a major role in our understanding of superfluid helium. Soon after the liquefaction of helium in Oxford, Kurt Mendelssohn fled Germany as the Nazis came to power and he went to Oxford. Professor Lindemann found Mendelssohn a position at the Clarendon Laboratory. Working together, Mendelssohn and Lindemann recruited Francis Simon, Nicholas Kurti and Heinz London from Germany to Oxford in the fall of 1933. Heinz London moved to the University of Bristol in 1936, but the team of Simon, Mendelssohn and Kurti formed the basis of the very productive Oxford cryogenics program. In 1934, Peter Kapitza made what was supposed to be a short visit back to the Soviet Union from Cambridge. However, once there, his passport was confiscated, and the Russian government forced him to remain in the Soviet Union. The reasoning behind this was that the government wanted Kapitza to start and lead a laboratory in the USSR similar to the Mond Laboratory. Funding was provided, and the Institute for Physical Problems (IPP) was established in Moscow with Kapitza as leader in 1935. Like the Mond laboratory, IPP had a strong emphasis on research in cryogenics and superconductivity. The discovery of superfluid helium actually occurred in two steps. First was the discovery that a second liquid phase of helium existed, and later was the discovery that this second liquid phase was a superfluid under certain conditions and thus represented an entirely new type of fluid. The observation that a second liquid phase of helium existed was made at Leiden University, where helium was first liquefied in 1908. In addition to discovering superconductivity, Kamerlingh Onnes and his team investigated the physical properties of liquid helium and continued to reach lower temperatures. One observation was that the density of the liquid peaked value at

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2.2  K, decreasing again as the temperature of the liquid was reduced to 1.5 K. This was very unusual, as most fluids would be expected to uniformly increase in density as they become colder. For a fluid to first increase and then decrease in density as the temperature is reduced, was a hint that something else was happening. The measurement that really showed there were two liquid phases of helium was done by Willem Keesom and his postdoctoral researcher Klaus Clusius (whom we will see in an entirely different context later) at Leiden University in 1932. Keesom and Clusius discovered that there was a very sharp peak in the specific heat of liquid helium at a temperature of approximately 2.2 K (see Fig. 3.1). The shape of the curve in Fig. 3.1 resembles the Greek letter lambda, and thus, this peak became known as the lambda point and the temperature at which it occurs as the lambda temperature (Tλ). Through careful measurements, Keesom and Clusius showed that the lambda temperature varied with pressure from 2.17 K at 0.0497 atmospheres of pressure to 1.75 K at 30 atmospheres. The line formed by this variation in temperature and pressure is known as the lambda line and is the border between the two liquid phases of helium (He I and He II). See Fig. 2.1 in the previous chapter. An immediately observed and unusual feature of these two phases is the lack of a latent heat in the transition between the two phases. To understand

Fig. 3.1  Specific heat of helium as a function of temperature. The peak in the curve shows the He I to He II transition. From C. Gorter Progress in Low Temperature Physics Vol. 1 (1955)

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this, consider the boiling of water. Liquid water boils at 100 °C at 1 atmosphere of pressure. When you boil water on your stove, the temperature of the boiling water remains at 100 °C no matter how much heat you apply. The temperature will only rise once all the water has been converted to steam. This is because energy is required to convert the water to steam once the water has reached its boiling temperature. This energy is known as the latent heat. In the case of the He I/He II transition, no latent heat is required. Once helium reaches the lambda line, it instantaneously and completely converts between He I and He II. Other unusual behaviors started to be observed in the He II phase. In 1936, Keesom, working with his daughter Ania, found that He II transferred heat very efficiently, more than 1000 times better than copper.1 Additionally, in 1936, B.V. Rollin at the University of Leiden observed that a thin film of helium covered the inside of vessels that contained He II. Such a film did not exist upon transition to He I. Clearly, something was different about He II. Viscosity is a fundamental property of fluids that in effect describes the ease with which a fluid will flow when subjected to a force. Fluids with high viscosity, such as molasses, do not flow easily, while those with lower viscosities, such as water, flow more easily. Measurements of the viscosity of liquid helium were made at the University of Toronto in 1935 by E. Burton, J. Wilhelm, A. D. Misener and A. Clark. They found that the viscosity of He II was more than 1000 times smaller than that of He I. However, the measured viscosity was still above zero, and they did not take this result to mean that He II was fundamentally different kind of fluid. The technique used for these measurements was to observe the slowing down of a solid cylinder rotating in He II. This is a classical approach to measuring viscosity. In the fall of 1935, Jack Allen, who earned his doctorate in physics from the University of Toronto, arrived in Cambridge to conduct research in liquid helium. In 1937, he recruited A.  D. (Don) Misener from Toronto to Cambridge and together they continued measurements of the viscosity of He II. This time, however, a different measuring technique was used. Allen and Misener determined the He II viscosity by measuring the pressure drop of He II as it moved through very small diameter capillary tubes. Now, they observed that the viscosity was vanishingly small (less than 10−5 Poise) and that the relationship between pressure and helium velocity was inconsistent with commonly understood laws of fluid behavior.

 This was reported as a measurement of the thermal conductivity but as we will see, this result is explained by an entirely new method of transferring heat. 1

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Simultaneously, and independently, Peter Kapitza was measuring the viscosity of He II in his laboratory in Moscow and was getting similar results by looking at the flow of He II through a very narrow slit. In the January 8, 1938 issue of the journal Nature, two articles, one by Kapitza and one by Allen and Misener, described the vanishingly small viscosity off He II. In his article, Kapitza used the term “superfluid”. This was not only the first time this term was used for He II but also the first time it was applied to ANY fluid. He II was clearly something very different. However, what was it? Why did it appear to have near zero viscosity and a very efficient heat transfer mechanism? Why, for that matter, did the measured viscosity appear to be small but nonzero when measured via the damping of a rotating cylinder but apparently zero when measured via flow through capillaries or narrow slits? Before we answer some of these questions in the next chapter, there are two interesting asides about some of the people in the story thus far. Jack Allen continued to perform ground breaking work in He II and cryogenics. He eventually moved to the University of St Andrews in Scotland. He was greatly interested in using visual media to explain scientific concepts. As part of this effort, he created a film demonstrating and describing the behavior of He II. The film, narrated by Allen, can be found at https://www.youtube.com/watch?v=lEPc-­rBMAuU. This film is meant for the general public and nicely illustrates many of the features of He II described in this book. It is highly recommended viewing. During the Second World War, Francis Simon worked on the project to build the atomic bomb, first in England and then in the USA. He made significant contributions to the technique of gaseous diffusion that was used for uranium enrichment. Among his contributions, which earned him a knighthood after the war, was the conceptual design of the large gaseous diffusion plant built in Oak Ridge, Tennessee. Klaus Clusius, the German physicist who assisted Willem Keesom in mapping the boundary between the He I and He II liquid states, returned to Germany after his work with Keesom and started a university career. During the Second World War, he also worked on the problem of uranium enrichment but on the German side. Thus, we have two scientists, both of whom made important contributions to the study of He II, working on the same (noncryogenic) problem on opposing sides of the war.

4 Explaining He II: Quantum Mechanics and the Two-Fluid Model

Quantum mechanics is the physics of the microscopic. It explains the behavior of atoms, atomic nuclei and subatomic particles such as electrons, neutrons, protons and quarks. You don’t need quantum mechanics to build bridges, trains or airplanes, or to predict planetary motion. However, quantum mechanics is needed to understand and build lasers, particle accelerators, semiconductors or nuclear reactors. It’s not a coincidence that the theory of quantum mechanics was developed in the early twentieth century just as experimental studies of atoms, nuclei and subatomic particles started. The observations from these experiments frequently cannot be explained by classical physics. Generally, the effects of quantum mechanics are only observed on a microscopic level, although the technology based on these effects, such as computers or lasers, is certainly macroscopic. He II is a rare example where we can directly observe the effects of quantum mechanics using only our eyes. To understand the behavior of He II and its resulting technological value, we must understand something of quantum mechanics. The good news is that while quantum mechanics is a complicated theory explaining the behavior of all known matter at microscopic sizes, we only need to know a few concepts to tell the story of He II. The first is quantization. This means that for particles—atoms, nuclei, electrons, protons, neutrons and so on—physical parameters such as energy or momentum are not continuous. As an example, the electrons in an atom cannot possess any amount of energy but instead can only occupy certain distinct (quantized) energy levels. More generally, we speak of quantum states, which are a set of physical parameters that describe the condition of the particle at a given moment. It is the existence of these quantized states and the transition © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_4

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of particles such as electrons between these states that underlies technology such as semiconductors.1 The next concept is the distinction between fermions and bosons, which is related to the quantum property of spin – a description of angular momentum. Fermions are particles whose spin is quantized in half integers (1/2, 3/2…) while the spins of bosons are quantized in full integers (0,1,2,3…). Examples of fermions include electrons, protons and nuclei with odd mass numbers, and examples of bosons include the Higgs boson and nuclei with even mass numbers. Significantly, the most common isotope of helium, 4He, is a boson. A key difference between fermions and bosons is that a single energy level (or quantum state) of a quantum system can contain only one fermion—this is known as the Pauli exclusion principle—while there is no restriction to how many bosons you can have at a given quantum energy level. Einstein and others recognized that it was, in theory, possible for a large number of bosons in a system to drop into the lowest energy (or ground) quantum state. This effect is known as Bose–Einstein condensation and prior to the discovery of He II had never been observed experimentally. With this background, we now go to Fritz London and Laszlo Tisza in Paris in 1937. Both London and Tisza were refugees. Laszlo Tisza was a Hungarian physicist who had previously been working at the Ukrainian Physico-Technical Institute with Lev Landau, about whom we will hear more later. Tisza was a member of the Communist Party, but Stalin’s purges had made him lose faith in the party, and he left the USSR for Paris. Before leaving the USSR, however, Tisza had begun to develop a theory of liquid helium. Fritz London, also a theoretical physicist, was the brother of Heinz London (Chap. 3) and, along with him, moved to the Clarendon Laboratory at Oxford University in 1933. In 1935, Fritz London moved to the Institut Poincaré in Paris, where he met Tisza. When the discovery of superfluidity in He II was announced in January 1938, London proposed that this effect could be explained if one assumed that a fraction of He II had undergone Bose–Einstein condensation. Tisza realized that if London’s proposal was true, one could then model He II as two separate fluids. One of these fluids known today, as the normal fluid component, has its own density (mass divided by volume), its own velocity and a small but finite viscosity. The normal fluid component represents the fraction of helium atoms that are in the higher energy quantum states (or levels). The  In a very real sense, it is quantum mechanics that allows you to post cute pictures of your dog on the internet. 1

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Fig. 4.1  Relative densities of superfluid and normal fluid components in He II as a function of temperature. Note that He II approaches 100% normal fluid near Tλ and 100% superfluid below 1 K. (From Helium Cryogenics – Van Sciver)

superfluid component with its own density and velocity but zero viscosity represents the fraction of helium atoms that have condensed into the ground quantum state. The total density of He II at any time is the sum of the normal component density and the superfluid component density. These densities change with temperature, and more importantly, the ratio of the superfluid and normal fluid densities varies with temperature, as shown in Fig. 4.1. Note that this shows that near the lambda point, almost all the He II is in the normal fluid component, while below 1 K, almost all the He II is in the superfluid component. This reflects the fact that as the temperature of He II is lowered, an increasing number of helium atoms condense into the ground state. The two components can interact with each other under certain conditions. It’s useful to pause and point out the two-fluid model is just that; a model that explains physical behavior. While there is a real distribution of the atoms in He II between the ground and higher energy (or excited) quantum states, there aren’t actually two kinds of fluid. For example, we cannot directly measure the normal fluid density. Nor does the two-fluid model directly use the fundamental equations of quantum mechanics. The test of such a model in physics and engineering is whether it can be used to explain observed behavior and properly predict behavior yet to be observed. In this regard, the two-fluid model of He II is very powerful. Using it, one can write the equations of conservation of mass, momentum and energy for each component, including terms that describe the interaction between components under certain conditions. Experiments have shown that these

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equations accurately predict the behavior measured in He II.  While not a complete model (more on this later), the two-fluid model is still used today to predict and explain much of the behavior of He II. There were a few early victories for the two-fluid model. Recall from Chap. 3 that when the viscosity of He II was measured by the slowing down of a rotating cylinder, it was found to be smaller than that of He I but nonzero, while measurements made by flowing He II through capillary tubes showed a zero viscosity. The two-fluid model explains this discrepancy. In the case of the rotating cylinder, both the normal fluid and superfluid components are in contact with the cylinder, and the cylinder is slowed down by the viscosity of the normal fluid component. However, in the case of the capillary technique, only the nonviscous superfluid component is able to flow through the small openings, and thus, the technique only measures the zero viscosity of the superfluid component. The two-fluid model also explained the observed fountain effect and predicted the yet-to-be-observed phenomena of second sound. Both of these effects are described in more detail in Chap. 7. A distinction is frequently made between the transport properties and the state properties of a material. Transport properties are those that are associated with the transport of heat, mass and electricity. Examples include viscosity, thermal conductivity and electrical resistivity. State properties are not directly associated with the movement of mass or heat and are independent of the volume or mass of the material. Examples of these properties include specific heat, internal energy and the special thermodynamic properties of entropy and enthalpy. The two-fluid model explained the transport behavior of He II but was less useful in describing the state properties of He II. In addition, as mentioned earlier, the two-fluid model was only loosely linked to the fundamental equations of quantum mechanics. Both of these deficiencies were addressed by a complimentary model developed by Lev Landau, but he first had to get out of prison. Lev Landau was a brilliant and productive theoretical physicist. He made significant contributions in a wide range of subjects, including cryogenics, fluid mechanics and plasma physics. His ten-book series on theoretical physics, written with Evgeny Lifshitz, remains one of the standard works of the field. During his leadership of the theory department of the Ukrainian Physico-Technical Institute, Landau recruited a number of talented colleagues, including as seen above, Tizsa. In 1938, however, Landau, now working in Moscow, was accused of subversion during the Stalin era purges and locked up in Lubyanka Prison. Recall that it was these purges that dismayed Tisza and caused him to leave the USSR for Paris.

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With the discovery of He II, Peter Kapitza in Moscow wanted Landau to come and develop a fundamental explanation for He II. Kapitza wrote a letter to the Soviet authorities, vouching for Landau and explaining that he needed him for important work. Such was both Kapitza’s and Landau’s reputations that this came to pass, and Landau was released to come and work on the He II problem. Fully describing Landau’s He II model requires an understanding of quantum mechanics that is beyond the scope of this book; a few key points can, however, be discussed. Recall that in quantum mechanics, there are only a certain number of allowed excited states. Landau defined, based partly on experimental data, some fundamental excited states that the He II atoms that were not condensed into the ground state could occupy. Based on these definitions and existing quantum physics, Landau was then able to correctly calculate state properties such as specific heat and entropy for He II. As in the case of the Tizsa’a model, Landau divided the helium atoms into a ground state and excited states. Today, Landau’s more fundamental model published in 1941 is recognized as the correct microscopic model of He II. Landau was awarded the Nobel Prize in physics in 1962 principally for this work. While Landau’s model is more fundamental, it’s complicated and not terribly useful for predicting the transport properties of He II. It is these properties that in many cases make He II so useful in engineering applications, and for the remainder of this book, Tizsa’s two-fluid model will be used to explain He II behavior. Paris at the start of the Second World War was not a good place for people fleeing totalitarian governments, and thus, both Fritz London and Lazlo Tisza moved again, this time to the United States. Both had long and productive academic careers, Tisza at the Massachusetts Institute of Technology and London at Duke University. Both Kapitza and Landau remained in the Soviet Union and continued to do important work in a number of fields, including cryogenics. Thus, by the end of the 1930s, He II had been discovered, a basic understanding of why it existed was reached, and two models of its behavior, one more fundamental than the other, had been developed. There were significant research programs on He II underway in Leiden, Oxford, Cambridge and Moscow. In the next chapters, we will see that He II has other fascinating behaviors, including those that make it so valuable for big science projects.

5 What If You Had a Bucket?

Suppose you had a bucket of He II. Suppose further that He II was at a temperature of 1 K, where the vast majority of He II was in the superfluid component (see Fig. 4.1). What would happen if you rotated the bucket? Since the superfluid component has no viscosity and it’s viscosity that in effect makes a fluid interact with a solid surface, you could reasonably expect that He II composed mostly of the superfluid component would stay still while the bucket rotated.1 However, an experiment performed by D.V. Osborne in 1950 at Cambridge University showed this not to be the case. His observations showed that a rotating bucket of He II at 1 K behaved very much as if He II were a regular fluid with normal viscosity. While rotating a bucket of liquid helium at 1 K sounds like the kind of thing you might do after a few beers on a Friday evening, Osborne’s experiment had a very real and serious motivation. Researchers had observed cases in heat transfer (Chap. 6), film flow (Chap. 7) and even in measurements of viscosity where the superfluid component starts to interact with the normal fluid component. These interactions began to occur at a certain velocity of the superfluid component, now known as the critical velocity. Osborne’s experiment was an attempt to create a situation in which He II would act as an ideal, i.e., nonviscous fluid. Understanding the results of the rotating bucket experiment brings up two additional features of He II (quantized vortices and mutual friction). These features are not only important to understanding He II but also play (as we  This is me thinking like an engineer. The more fundamental physics explanation for the superfluid component being irrotational (i.e., not able to rotate) comes from the quantum mechanical properties of the Bose–Einstein condensation and was first predicted by Landau. 1

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will see in the next chapter) an important role in making He II useful in big science projects. Circulation or vorticity in the superfluid component of He II is quantized. Just as electrons in atoms can only occupy discrete energy levels, so too can the circulation of the superfluid component only occupy discrete levels of angular momentum. This was mentioned as a brief footnote in a paper by L. Onsager of Yale in 1949, but the theory was really worked out by Richard Feynman in 1955. Feynman showed that not only was the circulation of the superfluid component quantized but that it would be possible for these quantized vortices to arrange themselves in a regular array within a rotating bucket, as shown in Fig. 5.1. The quantized vortices are microscopic, and in this case, all rotate in the same direction as the bucket. Looking carefully at Fig. 5.1, one can see that the rotations of adjacent vortices in the body of the fluid cancel each other out, but at the wall of the container, this cancellation does not occur; thus, while the bulk of the superfluid is irrotational, at the wall of the container, the superfluid component rotates with the container. Recall, however, that Osborne’s experiment implied that all the helium in the bucket was rotating. The answer to this is mutual friction. As mentioned before, researchers had observed that at a certain superfluid component velocity, the normal fluid component and the superfluid component started to interact with each other. In 1949, C.  Gorter and J.  Mellink of Leiden University developed a mathematical expression for this force between the superfluid and normal fluid components. They based this on experimental

Fig. 5.1  Schematic of an array of quantized vortices in a container of He II rotating at a constant speed. From W.F. Vinen, Advances in Cryogenic Engineering, Vol. 35, 1990

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data and the two-fluid model. They coined the term mutual friction for this force. We now know that mutual friction occurs when the normal fluid component starts to interact with the quantized vortices of the superfluid component. So, in the rotating bucket experiment, the superfluid component against the wall rotates with the wall, while mutual friction ties together all the quantized vortices with the normal fluid component and thus with each other. The result is that almost all the He II rotates with the bucket, as seen in the experiment. Feynman’s theory was published in 1955. In 1956, William (Joe) Vinen, a student of Osbourne working together with H.E.  Hall indirectly detected quantized vortices by using their interaction with second sound (Chap. 7). In 1961, Vinen used a very clever experiment that involved a vibrating wire in a rotating container of He II to directly capture and measure quantized vortices. His results showed that Feynman’s theory was correct. If quantized vortices and mutual friction were only important for rotating buckets, they would not be very interesting. However, it turns out that these phenomena have a much larger role in He II. Quantized vortices will form whenever the velocity of the superfluid component exceeds its critical velocity, and once formed, these vortices will interact with the normal fluid component via mutual friction. This critical velocity can be reached in a number of ways, say during the forced flow of He II by a pump, or importantly, as we will see in the next chapter, during the transfer of heat in He II. vortices formed outside of the carefully controlled rotating bucket experiment do not line up in a regular array but rather form a twisted clump or “ball of string”, as shown in Fig. 5.2. Quantized vortices are turbulence in the superfluid component. Significant efforts, including much research by Joe Vinen, have been carried out using He II to conduct fundamental studies of turbulence in fluids.2 Experiments over the years have shown that the critical velocity is proportional to the inverse of the typical diameter of the system being studied. Practically speaking, this means that for almost all the large scale applications of He II that we will discuss later, both quantized vortices and mutual friction will be present. Figure 5.3 shows another version of a rotating bucket experiment. Here, electrons from a radioactive source have been passed through the helium, and some of them have been captured by the cores of quantized vortices. Figure 5.3  Turbulence in fluids is one of the last great mysteries in classical physics. We can create turbulence models based on experimental data sufficient for many engineering applications, but describing turbulence from fundamental physical laws has yet to be done. There are still many mysteries in so called “modern physics” involving topics such as relativity, quantum mechanics, and fundamental particles. 2

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Fig. 5.2  Computer simulation of a tangle of vortices in He II at 1.6 K. Reproduced from William F. Vinen, Russell J.  Donnelly; “Quantum turbulence”. Physics Today 1 April 2007; 60 (4): 43–48. https://doi.org/10.1063/1.2731972; with the permission of the American Institute of Physics

shows the detection of these electrons (and thus the quantized vortices) looking down into the rotating bucket. Note that as the speed of rotation increases, so does the number of vortices. The vortices in this figure are not seen in a regular array, as they are moving through the helium. With this background of quantized vortices and mutual friction, we can now turn to the transfer of heat in He II.

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Fig. 5.3  Direct observation via an electron trapping technique of quantized vorticies in a rotating bucket of He II. The speed of rotation increases from a – c. (From “Photographs of Quantized Vortex Lines in rotating He II”, G.A. Williams, R.E. Packard, Physical Review Letters, Vo. 33, Number 2 (1974)

6 Moving Heat

We are all familiar in everyday life with the three most common ways that heat is transferred from a warm location to a cold one. Conduction: heat transfer through a solid material explains why the metal handle of a pot on a stove becomes hot. Convection: heat transfer via a moving fluid explains why you feel cool when the wind is blowing. Lastly, radiation: heat transfer via electromagnetic waves explains why wearing a hat helps keep you comfortable on a sunny day. These three mechanisms along with some variations in them (boiling heat transfer, for example, is a variation in convection) explain almost all heat transfer in the universe. However, there is a fourth mechanism that is not only unique to He II and a macroscopic manifestation of quantum mechanics but is also one of the main reasons that He II is so useful to us. This is known as internal convection. Figure 6.1 shows a tube of He II at 1.8 K. One end of the tube has a heater on it, and the other end is connected to a bath that is maintained at the saturation pressure corresponding to 1.8 K helium. An aside is necessary here about saturation (or boiling) temperature and pressure. Not only is this needed to understand Fig. 6.1 but it is also useful in understanding applications of He II. Look again at Fig. 2.1 which shows the helium phase diagram. Note that there is a line that separates the vapor phase from the liquid He I phase and from the liquid He II phase. This is the boiling or saturation curve, and it represents where the liquid and vapor phases are in equilibrium, that is, where the liquid boils into vapor. Notice that for each point on this curve, there is a unique temperature, known as the saturation temperature, and a corresponding pressure known as the saturation pressure. A liquid at its saturation temperature and pressure is said to be a saturated liquid. A liquid whose temperature is lower than the saturation temperature © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_6

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Fig. 6.1  A schematic representation of internal convection. The normal fluid component (Vn) moves away from the heat source and is replaced by the superfluid component (Vs) moving toward the heat source

of its current pressure is said to be subcooled, while a vapor whose temperature is higher than the saturation temperature of its current pressure is said to be superheated. The saturation temperature of helium at 1 atmosphere pressure is 4.2 K. Thus, He II at 1 atmosphere and 1.8 K is a subcooled liquid.1 The saturation pressure of He II at 1.8 K is 0.016 atmospheres, and in a cryogenic system, this subatmospheric pressure is maintained by pumping on the vapor above the liquid. Note that throughout this book, we will use atmosphere as the unit of pressure. An atmosphere equals 14.7 pounds per square inch and is the nominal air pressure at sea level. While an atmosphere is not a metric unit, for our purposes, it is the most intuitive. Returning to Fig. 6.1, if we add heat via the heater, it will convert some of the superfluid component into a normal fluid component (the heat moves the helium from the ground state to excited states). This normal fluid component moves away from the heater to the bath, while the additional superfluid component helium moves from the bath to the heater to replace the normal fluid component moving away. The heat transferred from the heater to the bath causes vapor to evaporate at the surface of the bath, and the vapor is then pumped away. As long as we apply heat, we have set up a continuous flow of the normal fluid component away from the heater and the superfluid component toward the heater. This new heat transfer mechanism, only found in He II, is called internal convection. Since the flow of the normal component is compensated by the flow of the superfluid component, there is no net mass flow in this process. A flowmeter installed into the tube in Fig. 6.1 will show no movement of the helium. There are two types of internal convection described by different mathematical equations. The difference comes from quantized vortices. The velocity of the normal and superfluid components in internal convection increases  This is true of more common fluids as well, the saturation temperature of water (i.e., the boiling point) is 100 °C at sea level. Water at room temperature and sea level is a subcooled liquid. 1

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Fig. 6.2  Heat conductivity function for the mutual friction regime of internal convection in He II as a function of temperature. Note that the heat conductivity function, and by extension, the effectiveness of the internal convection process peaks at approximately 1.95  K.  From Helium Cryogenics, S.W. Van Sciver, Springer (2012)

with the amount of heat applied. Once the velocity of the superfluid component exceeds the critical velocity at which quantized vortices form, the resulting quantized vortices will interact with the normal fluid component via mutual friction. This type of internal convection heat transfer is known as the mutual friction regime. Recall from Chap. 5 that the critical velocity at which the quantized vortices form is inversely related to the typical size of the system. Thus, in most large-scale applications of He II, internal convection occurs in the mutual friction regime. Figure  6.2 shows the property that describes this mutual friction heat transfer regime as a function of temperature and pressure. Note that this heat transfer mechanism is highest at approximately 1.95  K.  This fact will be reflected in many practical applications of He II. Internal convection heat transfer is amazingly efficient. When engineers speak of efficient heat transfer, they mean that a large amount of heat can be removed from the heat source without a large temperature difference between the heat source and the coolant. This means that significant heat can be removed without the heated surface becoming too hot; generally, the point of cooling it in the first place.

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How efficient is internal convection? IF Fig. 6.1 represented a tube of He II 12 cm long and 0.25 cm in diameter with the heated end at 2 K and the cold end at 1.8 K, internal convection would transfer 133 milliwatts of heat. While that may not seem like a lot, conduction through a copper rod of the same size with the same temperatures would only transfer 163 microwatts of heat or almost a thousand times less than internal convection in He II. The efficiency of internal convection is one of the reasons He II is so useful as a coolant at cryogenic temperatures. The efficiency of internal convection results in another practical feature of He II. For bubbles to form in a liquid, there must be a slight temperature difference between the vapor inside the bubble and the liquid surrounding it. Internal convection in He II will not permit the required temperature difference, and thus, we do not see boiling within the body of He II. Instead, heat is transferred through He II via internal convection to the surface of the He II, where the heat evaporates the liquid into vapor. As we will see, this lack of boiling is very valuable in applications of He II, particularly when cooling superconducting radiofrequency cavities. There are limits to how much heat we can transfer via internal convection. If the high temperature in Fig. 6.1 exceeds the transition temperature between He II and He I or exceeds the saturation temperature of He II (see Fig. 2.1), then the internal convection mechanism stops, and the heat transfer is dominated by less efficient, conventional mechanisms such as convection or boiling. Despite these limits, internal convection is, as we will see, at the heart of most practical applications of He II. There is one final aspect of heat transfer related to He II. There is a fundamental inefficiency in all cases of moving heat from a solid into a fluid. However, this inefficiency is very temperature dependent and can generally be ignored in most cases. In fact, typically when we calculate heat transfer from a solid to a liquid, we assume that the temperature of the solid and the temperature of the liquid immediately on the solid surface are the same. This is not strictly true, but this effect only becomes important at cryogenic temperatures, particularly in the case of He II. In a He II-cooled system, due to the efficiency of internal convection, the temperature difference between the solid and the He II immediately on it may be the largest temperature difference in the system. This effect was first discovered and described by Peter Kapitza in Moscow and is known as Kapitza conductance. Kapitza conductance is affected by temperature, the amount of heat being transferred, the type of solid material, e.g., it is different in copper than in aluminum, and even the cleanliness of the solid surface. There are no truly useful theories for predicting Kaptiza conductance, and practical applications

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require experimental measurements of the materials being used. As will be seen in Chap. 10, such measurements were an important part of developing large-scale applications of He II. Therefore, in summary: • Heat is transferred in He II via a unique and highly efficient process known as internal convection. • This mechanism results, in almost all circumstances, in a lack of boiling within He II. • The amount of heat that can be transferred by internal convection has limits. • The transfer of heat from a solid surface to He II is limited by Kapitza conductance, the understanding of which is based on experimental data. The next chapter describes a few of the remaining unique behaviors of He II. Once that is done, the growth of applications of He II can be addressed.

7 General Weirdness: Fountains, Porous Plugs, Second Sound and Films

In addition to quantized vortices and an extremely effective heat transfer mechanism, the macroscopic quantum nature of He II results in behavior not seen in other fluids. These behaviors were for the most part observed and explained in the 1930s and 1940s. They may seem just to be laboratory curiosities, but as we will see later, they have important technical applications. The first of these behaviors is the fountain effect or thermomechanical effect. This effect was first observed by J. Allen and J. Jones in Cambridge in 1938 at about the same time that the Cambridge team codiscovered superfluidity in He II. Allen and Jones noted that with He II in narrow channels, a temperature difference will result in a strong pressure difference and that the size of the pressure difference is proportional to the size of the temperature difference. This is not the case with everyday fluids. If you place water in a horizontal narrow tube and heat one end of the tube, the pressure at the heated end does not increase, but this is what Allen and Jones observed with He II. Tisza’s two-fluid model of He II provides the explanation of this effect. Consider Fig. 7.1 below. In the figure, the blue color represents He II contained in a long tube also containing a heater and a porous plug. The porous plug is made of a material with very small holes and mimics the narrow channel used in Allen and Jones’ experiment. When the heater is turned on and the temperature near it rises, the superfluid component of He II passes through the narrow holes of the porous plug toward the heater. However, the normal fluid component cannot flow back through the porous plug, as the normal fluid component has a nonzero viscosity. The result is a pressure increase near the heater and a net mass flow of He II in the direction of the arrow. A fountain pump, as illustrated here, is a way to pump He II without the use of any moving parts. We will see © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. G. Weisend II, Superfluid, https://doi.org/10.1007/978-3-031-42652-0_7

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Porous Plug

Heater

Fig. 7.1  Schematic of a fountain pump. From He is for Helium, J. G. Weisend II Cryogenic Society of America (2018)

Fig. 7.2  A He II fountain. This is created by having a small vessel containing a heater with an opening on one end and a porous plug on the other, partially immersed in He II. When the heater is turned on, the fountain effect causes a pressure rise in He II, resulting in the fountain shown in the figure. Courtesy of J. Pfotenhauer – University of Wisconsin – Madison

an example of a practical use of this later in this story. The term fountain effect stems from a common laboratory demonstration of this behavior shown in Fig. 7.2 in which a helium fountain can be created. J. Allen’s previously mentioned movie on He II (Chap. 3) shows a nice version of a helium fountain. We will see in Chap. 9 that the behavior of He II and a specialized design of porous plugs can be used to create devices that separate He vapor from He

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II. These vapor liquid phase separators are particularly valuable in space applications of He II. Second sound in He II is best understood by first thinking about everyday sound. The sound that we are most familiar with consists of density changes in media such as air, water or even helium. High density is caused by high pressure, and lower densities are caused by lower pressures. In air, we perceive the higher pressure (higher density) as “loud” and the lower pressure (lower density) as “soft”. Recall that in He II, there are in fact two densities: a density associated with the normal fluid component and a density associated with the superfluid component. The total density of He II is the sum of these two component densities. Since the superfluid component does not carry any energy, regions with mostly superfluid component will be cooler than those rich in the normal fluid component. Creating regions of varying concentrations of normal and superfluid components will create regions of varying temperatures. These temperature variations are known as second sound. Instead of pressure changing the density as it does in “first sound”, heat pulses or oscillations cause sound in He II. Figure 7.3 compares first and sounds in He II. Note that in the case of first sound, the total density varies, while in second sound, the total density is approximately the same, while the relative densities of the normal and superfluid components vary. Just as in the case of first sound, the temperature variations in sound can take the form of traveling waves, standing waves or pulses. One of the triumphs of Tisza’s two-fluid model is that it predicted the existence of sound. However, sound was not seen in the laboratory until 1944 when it was first observed by V. P. Peshkov working in Kaptiza’s institute in Moscow. In 1947, C.T.  Lane at Yale working with his graduate students. W. M. Fairbank and H. A. Fairbank observed sound by detecting bursts of first sound that were caused when pulses of sound reached the surface of a He II bath releasing bursts of helium vapor, which were then detected by a microphone. The speed of the sound in He II is about 20 m/s, which can be compared to the speed of first sound in He II of ~200 m/s. Second sound is not just a laboratory curiosity. It can be used (Chap. 5) to make detailed measurements of the quantized vortices in He II and thus help investigate turbulence in He II. Detection of sound has also been used to find hot spots on the surface of superconducting radiofrequency cavities (Chap. 8), aiding in the optimization of such cavities. In 2020, sound came full circle back to first sound. Second sound and other properties of He II inspired the composer Michael Edward Edgerton of the Malmö Academy of Music, Lund University, to create a modern

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∆P

n s n s n s n s n s n s

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Fig. 7.3  A comparison of first sound (Top figure) and sound (Bottom figure) in He II. N and S represent the normal and superfluid components of He II. Reproduced from Russell J. Donnelly; “The two-fluid theory and sound in liquid helium”. Physics Today 1 October 2009; 62 (10): 34–39. https://doi.org/10.1063/1.3248499, with the permission of the American Institute of Physics

percussion composition called “Der Rufer” written for Olaf Tzschoppe, director of the Bremer Schlagzeugensemble and Professor of Music at the University of the Arts Bremen (Germany). In Der Rufer, a number of phenomena involved in ultracold physics influenced the composition, including anisotropy, which is the property of substances to exhibit variations in physical properties in different directions; isotropy, which is the property of substances to exhibit uniformity in all orientations; vortices, including their bending and twisting; quantum leaks (or jumps), the movement of particles between allowed quantum states in discontinuous steps; mutual friction; turbulence and sound. A sample of the musical score is shown in Fig. 7.4. This work, which can be heard here: https://soundcloud.com/ user-­5 22403162/edgerton_106_derrufer_bremerschlagzeugensemble _2021-­10-­08_perinimixwav, is part of an ongoing collaboration between the

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Fig. 7.4  A Section of the score for “Der Rufer”. Courtesy M.E. Edgerton, Malmo Academy of Music, Lund University

Malmö Academy of Music, Lund University and the European Spallation Source Laboratory. Two other types of “sound” have been identified in He II. Third sound is a surface wave on a He II film in which the superfluid component moves while the normal fluid component remains stationary. Fourth sound is similar in that again, only the superfluid component moves but only occurs in porous media or very small capillaries and causes larger changes in pressure and temperature than the third sound. The behavior of He II films was observed very early, with some preliminary indications seen by H. Kamerligh Onnes (Chap. 2) at his laboratory in Leiden in 1922. B. Rollin, working with F. Simon in Oxford, suggested in 1936 that the high heat leak into a container of He II they were using was a result of a thin film of He II that covered the wall of the tube connecting the He II surface to the outside environment. This suggestion has led these films to be called Rollin films. The phenomenon can be described as follows: In an open container of He II, a thin film will form on the walls above the liquid surface and creep up

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Fig. 7.5  Behavior of a He II film from the Quest for Absolute Zero, K. Mendelssohn

(against gravity) out of the container. Imagine that you have a container of He II and you partially dip into it a empty container (Fig. 7.5). What you will observe is that a film of He II will form that transfers (against gravity and without any pressure difference) liquid from the outer container into the inner container until the helium level of both containers is equal. If we were then to pull the inner container partially out of the outer container, He II will then move via a film from the inner to the outer container until the levels are again equal. If the inner container was pulled completely out of the liquid in the outer container. He II would flow via a film out of the inner container and drop into the outer container until the inner container was empty (Fig. 7.6). The film effect results from the superfluidity of He II. All fluids are attracted at an atomic level to solids. If you look carefully at a glass of water you will notice that the water at the walls of the glass is slightly higher than the surface of the water in the center of the glass. The viscosity of the water prevents the water from climbing any higher up the side of the glass. However, in He II, the superfluid component has no viscosity and thus continues to climb up the walls and out of the container. There are many subtle details associated with He II film flow, and in the 1930s and 1940s, Kurt Mendelssohn, working

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Fig. 7.6  He II film flow He II flows in a film up and out of the suspended container and into the He II bath below. From Alfred Leitner (Wikicommons/public domain)

with his student John Daunt at Oxford, carried out a very elegant set of experiments that described and explained this behavior. Just as in the case of the sound, He II film flow is not strictly a laboratory curiosity. Most He II vessels are sealed and not open topped, but they all have pipes for venting, instrumentation wires and so on, and He II films can creep up these lines, causing helium loss and additional heat leak. In most cases, these losses are not important, but there are situations, particularly in applications of He II in space (Chaps. 9 and 13), where any loss of He II will reduce the lifetime of the scientific mission. In such cases, clever techniques are used to reduce or prevent helium film flow. An example of this is shown in Fig. 7.7. in the XRS Helium Dewar”, P. J. Shirron and M. J. DiPirro advances in Cryogenic engineering (1998) The five concentric troughs, each 0.2 mm wide, surrounding a central vent line create knife edges that impede the He II Film flow. This device was developed for the He II dewar used on the X-ray Spectrometer instrument on the instrument on ASTRO-E satellite and its successors on ASTRO-E2, Hitomi, and currently, the X-Ray Imaging and Spectroscopy Mission (XRISM). This chapter concludes the description of the properties of He II.  From here on out, we will see how He II became so useful in science and technology.

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Fig. 7.7  An example of a device to limit He II film flow. From “Suppression of superfluid film flow

8 Early Applications

Why is He II not just a laboratory curiosity? So far, we have seen that He II is a macroscopic example of quantum mechanics with many interesting features. While this is important in understanding the universe, how does it translate into He II being vital for many Big Science projects? One way to understand this is to ask a different question: what practical value is there to cooling anything down to He II temperatures? There are a number of good answers to this question. The first is that certain materials have very useful properties when cooled to these temperatures. The second is that there are phenomena that occur at these temperatures, and we want to build systems to study them. Last, studies of He II itself may answer broader questions in science. Once the need to reach these temperatures is identified, the other useful properties of He II, namely, its high heat transfer ability, its lack of bulk boiling, and its behavior in porous media, become important. Many of the current applications of He II that we see today were not known at the time of its discovery. In addition, technological advances in both materials and refrigeration technology as well as a practical understanding of how to use He II as an industrial coolant had to occur for some of these applications to become possible. The most important material property made useful by liquid helium temperatures is superconductivity. Recall from Chap. 2 that H.  Kamerlingh Onnes discovered superconductivity shortly after being the first person to liquefy helium. A superconductor will carry a constant electrical current without any resistive losses. Thus, an electrical current will run forever in a closed loop of superconducting material. The details of superconductivity and the development of both an understanding of superconductivity and of practical

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superconducting materials are beyond the scope of this book. Many of the research groups investigating He II also studied superconductivity. For the story of He II, the following aspects of superconductors are important: 1. Most materials are not superconductors. Materials that are superconductors are only superconducting within an envelope of temperature, electrical current and magnetic field. These parameters are interconnected. For example, operating at a lower temperature will permit a material to remain superconducting at higher currents and magnet fields. 2. Practical low-temperature superconductors are superconducting only below 18 K (−427 °F). 3. High-temperature superconductors that operate between 50 K (−370 °F) and approximately 120 K (−244 °F) were discovered in 1985. While applications are being found for them, further development is needed before they will play a significant role in large-scale science projects. 4. The most important low-temperature superconductors, alloys of niobium and titanium and of niobium and tin, were not developed until the 1960s and were still being improved well into the 1980s. 5. While superconductors carrying constant currents do not experience resistive losses, those carrying alternating currents do experience resistive losses, although these losses are much smaller in size than those in nonsuperconductors. Superconductivity allows the construction of electromagnets that are smaller, produce higher magnetic fields and are cheaper to operate, even with the higher cost of cryogenic cooling, than magnets built with normal conductors such as copper. People started to build superconducting magnets immediately after the discovery of superconductivity, and the desire to build high-field superconducting magnets drove a significant amount of research into superconducting materials. Today, the cooling of superconducting magnets, particularly for MRI systems, is the main application of liquid helium cryogenics. Most of these applications occur at 4 K. He II cooling of superconducting magnets at large scales didn’t start until the 1980s, and the earliest large-scale application of He II cooling was in the area of superconducting radiofrequency (SRF) cavities. To understand the use of SRF cavities, a few words are needed on particle accelerators. These devices, somewhat obviously, accelerate particles, specifically tiny charged particles such as electrons (negatively charged), protons (positively charged) and ions (positive or negative depending on the ion). While particle accelerators sound esoteric, they are widely used in industry,

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for cancer therapy, and as a basic research tool. Particle accelerators will appear often in the story of He II as one of the major motivations for He II cooling. There are a number of different types of particle accelerators, but they all have two things in common: they can change the direction of the charged particles with magnets, and they can change the speed of the charged particle with electric fields. Imagine you have an electron and you have it move past an electric field with a one volt difference between the positive and negative side of the field. The electron will gain in energy by one electron volt. An electron volt is a unit of energy. Energy and the speed of the particles are usually directly related; by increasing the particle’s speed, we are increasing the particle’s kinetic energy. However, as we approach the speed of light, which happens in many accelerators, special relatively starts to become important and this clear link starts to break down. Thus, from now on, we will talk about the energy rather than the speed of particles in accelerators. The highest energy particle accelerator currently is the Large Hadron Collider at the CERN laboratory in Geneva, Switzerland. This machine, which does use He II and will be described later on, accelerates particles up to 7 Trillion electron volts. There are a variety of techniques for using electric fields to accelerate charged particles, but a very common one is the use of radiofrequency cavities. A radiofrequency (RF) cavity is a metal structure designed so that electrical energy in the form of radio waves oscillates inside the cavity. These waves are composed of both electric and magnetic fields, and the system is designed so that when a charged particle enters the cavity, the electric field points in the correct direction to accelerate the particle (see Fig.  8.1). RF energy has to continually be added to these cavities to compensate for the energy transferred to the particle and to compensate for the energy lost as resistive losses in the walls of the cavity. It’s this second loss can be greatly reduced by superconductivity.

Fig. 8.1  Schematic of an RF cavity. The system is designed so that the electrical field (E) is pointing in the correct direction to accelerate the charged particles entering from the left-hand side of the cavity. From: H. Padamsee et al. RF Superconductivity for Accelerators (Wiley)

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A superconducting radiofrequency (SRF) cavity is constructed of a superconducting material (typically niobium) cooled to a temperature at which it becomes superconducting. Since radio waves are an example of alternating currents, there are still resistive losses in the SRF cavity wall, but they are much, much smaller than in the case of a copper cavity. Moreover, the wall losses in the superconductor decrease as the temperature is decreased. As a result, an SRF cavity operating in the range of 1.8 K – 2 K (that is, in He II) will generally be more energy efficient than one operating at 4.2 K (the normal boiling point of helium, i.e., He I). In summary, a more energy efficient particle accelerator could be built using SRF cavities cooled by He II. The first significant one of these was built at Stanford University. In the mid-1960s, a group of researchers in the physics department of Stanford University investigated the possibility of basing a particle accelerator on SRF cavities. Their work resulted in the first accelerator to use SRF cavities and demonstrated that He II was the coolant of choice for such machines. This work at Stanford was the moment when He II started to move from laboratory curiosity to an industrial-scale coolant for big science projects. This group, which included W. Fairbank, T. Smith, P. Wilson, H. Schwettman and M.  McAshan, described the advantages of using superconducting RF cavities to accelerate particles. Using SRF cavities would result in the ability to use smaller and lower cost RF power supplies, a greater fraction of the RF energy going into the beam and a greater acceleration of the beam per unit length (known as the accelerating gradient). All this meant that an SRF-based accelerator had the potential to be cheaper, smaller and more powerful than accelerators using copper or other nonsuperconducting materials. From the very beginning of their studies, it was clear to the Stanford team that cooling with He II was the proper approach. In addition to the much lower wall resistance at He II temperatures, the higher specific heat (see Fig. 3.1) and efficient heat transfer in He II meant that the temperature rise in the He II bath surrounding the SRF cavity was minimal. This kept the temperature of the cavity at its desired value and minimized the change in temperature of the cavity. This is important for the stable operation of the cavity. All the designs and actual accelerators built by the Stanford team used between 1.8 and 2 K as the operating temperature. Why not go colder? While it is true that reducing the temperature below 1.8 K would continue to reduce the wall losses, it would also make refrigeration more difficult. The laws of thermodynamics show that the efficiency of removing heat decreases as the temperature drops. This means that the colder you go, the more work has to be done to remove the heat, resulting in

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refrigeration systems requiring more electrical power. Over the years, experience has shown that the range of 1.8–2.0 K is the best compromise between the advantages of He II and the difficulties of building refrigeration systems for those temperatures. Recall from Fig. 6.1 that this range is also the peak of heat transfer in the mutual friction regime. Scientists at Stanford demonstrated the first acceleration (of a single electron) by an SRF cavity in 1964. This was followed in 1965 by the construction of a 4-inch long SRF cavity-based electron accelerator. From there work scaled up quickly with a 10 foot long test accelerator built in 1966 (see Fig. 8.2). In describing this figure, the researchers note “the essential features of nearly any superconducting accelerator are included. Looking at this figure more than 50 years later, that remains a true statement. Comparing this figure to a modern accelerator cryomodule such as that of the European Spallation Source (Fig. 2.2) shows many similarities, chief among them the saturated He II bath that surrounds the SRF cavities. The real difference between now and the 1960s in SRF accelerators is the huge improvement in performance (accelerating gradient and losses) in the SRF cavities. The Stanford effort culminated in the Stanford Superconducting Accelerator (SCA, also known as the Recyclotron), which consisted of a set of 4 superconducting accelerator sections, each approximately 5.6 m long and all operating at 1.9  K.  The accelerating gradient of each section was approximately 2.6 MV/m, meaning that an electron traveling through the accelerator and its

Fig. 8.2  Ten Foot long test accelerator built at Stanford University. From: “Stanford’s Superconducting Accelerator Program”, T.I. Smith et al., Proceedings of the 1966 Linear Accelerator Conference

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preaccelerator section would gain an energy of approximately 50 MeV (or 50 million electron volts). One of the four superconducting sections in this machine suffered a technical failure and did not add any energy to the beam. All the Stanford machines were linear accelerators (or linacs) in which the beam passed in a straight line through the accelerating section. To further increase the energy, the designers recirculated the beam several times through the accelerating structure with the beam gaining additional energy during each pass. At the end, the beam energy could be greater than 200 MeV. This design, known as a recirculating linac, was later used in the much larger CEBAF machine (Chap. 9). Cooling for this machine was provided by a cryogenic refrigerator built by the Arthur D. Little Corporation. This refrigerator provided up to 300 watts of cooling at 1.85 K and was the first commercial refrigerator built specifically for He II cooling. The success of the recyclotron led to similar machines being built (some by the Stanford team) at other institutions such as the University of Illinois and the Karlsruhe Center for Nuclear Research in Germany during the first half of the 1970s. However, larger applications of SRF cavities didn’t really start until the mid- to late 1980s. As we will see, larger applications required significant improvement in SRF cavities and He II refrigerators. Two numbers to keep in mind regarding the Stanford machines are an accelerating gradient of 2.6 MV/m in the SRF cavities and 300 W of cooling at 1.85 K; both of these numbers grew substantially during the 1980s. The Stanford superconducting accelerators were built at Stanford University. Adjacent to and operated by Stanford University for the US Department of Energy was the much larger Stanford Linear Accelerator Center (SLAC). While SLAC used cryogenics,1 first for liquid hydrogen bubble chambers and targets and then for superconducting magnets, its 2 mile long linear accelerator is based on room temperature copper RF structures. SLAC would not have an SRF-based accelerator until the twenty-first century with the construction of LCLS II (see Chap. 12).

 I led the SLAC Cryogenics Group from 1999–2007

1

9 The Fabulous 80s: Tore Supra, IRAS and CEBAF

By the end of the 1980s, the use of He II as a coolant in large-scale scientific projects had been fully demonstrated. Three projects in different scientific fields along with innovations in refrigeration technology and basic studies in the engineering aspects of He II (Chap. 10) made this possible. The success of these projects enabled scientists, engineers and funding agencies to feel comfortable with the use of He II in even larger projects to come. These projects also resulted in the establishment of new laboratories and the strengthening of existing cryogenic research groups. Most importantly, the Tore Supra, IRAS and CEBAF projects resulted in new scientific capabilities and even a new way to look at the universe. An electric current creates a magnetic field; the larger the current is, the larger the field. This is the basis of the electromagnets that we see in everyday life. Electromagnets can produce much higher magnetic fields than permanent magnetic materials such as iron or cobalt and have the added advantage of having their magnetic field be adjustable by changing the electric current. However, in a normal conducting material such as copper, the current experiences resistive losses, losing energy and heating the conductor. While it is entirely possible to create high field magnets using normal conductors, the amount of energy that must be used to drive the current and to drive the water cooling systems that cool the conductor and keep it from melting is problematic. In a superconducting magnet, as long as the electrical current is constant, there are no electrical losses, and above a certain magnetic field size, it is more energy efficient and ultimately easier to use superconducting rather than normal conducting electromagnets even with the need for cryogenic cooling.

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Generally, superconducting magnets become the best solution at fields of around 1 Tesla (T). For comparison, the Earth’s magnetic field varies between 0.00003 T and 0.00007 T, while a refrigerator magnet is approximately 0.01 T. Figure 9.1 shows the typical relationship between the magnetic field, critical current and temperature in a superconductor. If the current, magnetic field or temperature in a superconductor exceeds certain values, then the material stops being a superconductor. Since superconducting magnets have a critical magnet field above which they are no longer superconducting, for very high field research facilities (typically 45  T or above; Chap. 14), a hybrid approach is used. Here, a superconducting magnet (frequently cooled by He II) provides a background field of 10–15 T, while a copper-based electromagnet provides the remaining magnetic field. Notice also in Fig. 9.1 the effect of temperature on the critical field and critical current of superconductors: at lower temperatures, superconducting magnets can carry higher currents and generate higher magnetic fields. This effect frequently makes magnet operation at the lower temperatures of He II advantageous, and the first large-scale application of He II cooled magnets was in Tore Supra. Tora Supra was a fusion energy experiment. In fusion energy, light elements such as hydrogen are fused together, producing energy. This is the same Current density [A/cm2] 107 critical J-H-T surface

106 Nb3Sn

105

Nb-Ti

104 5 10 15 20

temperature [K]

103 5 10 15 20 magnetic field [T]

Fig. 9.1  Variation in superconductivity with temperature, current and magnetic field for the two principal low-temperature superconductors (NbTi and Nb3Tn). Note that as the temperature is decreased, the superconductor can reach higher magnetic fields and remain in the superconducting state. Courtesy of CERN

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process that produces energy in stars, including in our sun. In contrast to fission, in which heavy elements such as uranium are split to produce energy, and fusion energy offers the possibility of essentially limitless fuel (there are two hydrogen atoms in every water molecule) and less long-lasting radioactive waste. The problem is that creating fusion energy on Earth is very difficult. Research on fusion energy has been underway around the world since the 1950s, and work continues to this day. One of the principal approaches to creating fusion energy is to use magnetic fields to contain and heat plasmas of hydrogen and its isotopes. A plasma is an ionized (or charged) gas. For example, an electrically neutral hydrogen atom contains a positively charged proton and a negatively charged electron; removing the electron results in a positively charged hydrogen plasma containing only protons. Strong magnet fields are required for the confinement of plasmas in fusion energy experiments, and until Tore Supra, these fields were provided mostly by normal (or nonsuperconducting) electromagnets. In the 1980s, a scientific goal in fusion energy research was to move to plasma experiments that were longer in time. This implied the need to move to superconducting magnet systems that could be run for long periods of time with lower energy consumption than normal conducting magnets. Recognizing this need, in the early 1980s, the European Atomic Energy Community (EURATOM) and the French Atomic Energy Commission (Commissariat à l’Énergie Atomique, CEA) joined together to design and build the Tore Supra Tokamak1 at a CEA laboratory in Caderache, France. Two of the stated goals of the Tore Supra project were to develop the world’s first large-scale tokamak that uses superconducting magnets and to fully integrate a cryogenic system into the other tokamak systems. Tore Supra is an example of something that will be seen again during the development of He II. Big Science projects frequently have both scientific goals and technology demonstration goals. The later goals demonstrate, or in many cases, force the development of, technologies thought to be needed in future projects. The scientific goals associated with the plasma physics of Tore Supra required the superconducting magnets to have a field at the superconductor of 9 T. The only way to achieve a field that size with the niobium-titanium alloy superconductor available was to operate the magnets in the He II temperature range. Thus, Tore Supra would not only be the first large-scale application of superconducting magnets in tokamaks; it would also be the first  A Tokamak is a toroidal shaped magnetic fusion device originally developed in Russia. Most of the magnetic fusion devices today use this design. 1

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large-scale use of He II.  Before that could happen, several innovations were needed. The earlier application of He II to SRF cavity cooling (Chap. 8) used saturated helium at 1.8 K and 0.016 atmosphere pressure. This approach did not work well for magnet cooling. The complicated geometry of the magnets frequently results in low-pressure helium vapor being trapped against the superconducting coils. Low-pressure helium vapor is a very poor electrical insulator, and its presence would result in electrical short circuits in the magnets. The solution to this problem was to use pressurized He II at 1.8 K and 1 atmosphere pressure. Helium under these conditions would not have any vapor present, and only liquid helium, which performed much better as an electrical insulator, would be in contact with the magnet. Pressurized He II has two additional advantages. Operating at 1 atmosphere or above greatly reduces the risk of outside air leaking into the helium space, which can cause blockages in the cryogenic system as the air freezes in the cold helium. Additionally, as mentioned in Chap. 6, there are limits to the amount of heat that can be transferred by internal convection. This limit is highest in pressurized He II, where the maximum allowed helium temperature is the lambda temperature (2.17) rather than the lower saturation temperature that applies with saturated He II. This approach was mainly developed by G. Claudet and G. Bon Mardion based on some early work done by P. Roubeau. Claudet and Bon Mardion worked at the CEA Centre d’études Nucléaires in Grenoble, France (CENG), whose cryogenics group was tasked with the design of the Tore Supra cryogenic system. A simple version of this approach, known as a Claudet bath, is shown in Fig. 9.2. Patm 4.2 K He I T–

He II T