Plasma diagnostics (practical works): educational-methodical manual 9786010445901

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

M. Dosbolayev A. Tazhen A. Utegenov

PLASMA DIAGNOSTICS (practical works) Educational-methodical manual

Almaty «Qazaq University» 2020

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UDC 544(075) LBC 24.5 я73 D 75 Recommended by the Academic Council of the Faculty of Physics and Technology and Editorial and Publishing Council of KazNU al-Farabi (Protocol №2 dated 15.01.2020)

Review PhD O.A. Kalykulov

D 75

Dosbolayev M. Plasma diagnostics (practical works): educational-methodical manual / M. Dosbolayev, A. Tazhen, A. Utegenov. – Almaty: Qazaq University, 2020. – 54 p. ISBN 978-601-04-4590-1 The educational-methodical manual is intended for students of higher educational institutions as an instruction for doing nine experimental works containing selected topics on the basic methods of studying the properties of the plasma state of matter. Each text of the work is interpreted in a simple language, which reveals the physical processes and patterns, which, in turn, contributes to deeper understanding of the topic.

UDC 544(075) LBC 24.5 я73 © Dosbolayev M., Tazhen A., Utegenov A., 2020 © Al-Farabi KazNU, 2020

ISBN 978-601-04-4590-1

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FOREWORD The educational-methodical manual "Plasma diagnostics" was developed for students of the Faculty of Physics and Technology with specialties 6В05304 – "Physics" and 6B05307 – "Nuclear Physics". The works included in the manual have been fully tested and published in the form of scientific articles, approved at various local and international conferences. The educational-methodical manual was developed in the form of a methodological version for laboratory works, consisting of selected topics on the basic methods for studying the plasma medium. Practical works include the following important topics of plasma research: determining the current and conductivity of a plasma using a Rogowski coil, determining the density and spatial distribution of the energy of a pulsed plasma flow using solid and wire type calorimeters, studying the parameters of a low-temperature plasma by the method of an electric probe (temperature and density of plasma charges, distribution of the velocities and energy of plasma electrons), determination of the distribution of pulsed plasma by time and space with a magnetic probe, study of temperature and plasma density by the method based on the comparison of the spectral line intensity, determination of energy and spatial distribution of charges using Faraday cup. The main goal of this educational-methodical manual for the Faculty of Physics and Technology students is to help in deepening theoretical knowledge gained in studying gas discharges and plasma physics based on specific experiments. Each work consists of a brief theoretical introduction, a brief technical description of the instruments and installations, the procedure for performing the work, questions for self-control, and a list of references necessary to obtain additional information.

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1. STUDY OF VOLTAGE DIVIDERS AND WHEATSTONE BRIDGE The goal of the work. To study the operation principle of the voltage dividers and the Wheatstone bridge. Brief theoretical introduction The methods for measuring voltages in plasma physics experiments can be divided into two main classes: 1) measurement of high DC voltages on capacitor batteries and 2) measurement of high AC voltages appearing in the discharge of a capacitor battery through plasma. For these cases, voltage dividers are used. Thus, the voltage divider (attenuator) can be used to register DC or AC voltage of large-size conventional low-voltage equipment: oscilloscopes, amplitude voltmeters, and analog-to-digital converters. To register a DC or slowly varying voltage, resistive dividers (Figure 1.1) with a nominal conversion factor of less than one are used: =

Figure 1.1. Ohmic voltage divider

=

.

(1.1)

Figure 1.2. Capacitive voltage divider

The ohmic voltage divider is used only for AC voltages, in other cases a capacitive voltage divider can be used (Figure 1.2). If we assume that the input resistance of the device , to which the voltage reduced by the divider is supplied, with almost infinite value 4

compared to the reactance , then we can say that the same charges pass through each half period through and . In this case it turns out that =(

) ,

−

where we get: =

=

.

(1.2)

Both expressions are correct for a purely theoretical situation where the branches of the divider can be represented as ideal resistors or capacitors. In real conditions, the resistors of the upper branch must provide sufficient electrical strength and may have large dimensions, respectively; the parasitic capacitances of the resistors must be taken into account. An example is the connection to an oscilloscope, which, in addition to the input resistance, has an input capacitance. The wires connecting the divider to the oscilloscope can also contribute some capacitance (Figure 1.3).

Figure 1.3. The appearance of parasitic capacitance in low-voltage lines

If the input resistance of the device can be corrected in the calculation of the divider, then the input capacitance and the capacitance of the line will introduce frequency dependence in the division ratio and lead to the distortion of the waveform. High-frequency 5

harmonics of the signal will be "overwhelmed", as when exposed to an integrating element. It is possible to reduce the influence of paravalue, thereby reducing the outsitic capacitances by reducing the put resistance of the divider, but this will reduce the level of the useful signal, and a proportional reduction in the upper arm, as already mentioned, will load the signal source. Distortions of the pulse shape can also have the opposite, "differentiating" character, if the capacitor enters the circuit of the upper arm of the divider. This can occur, for example, when measuring a high-voltage pulse with a high-impedance voltage divider placed near the massive part of the pulse generator (Figure 1.4). Capacitive guidance from a high-voltage pulse source to a divider through parasitic capacitances will be equivalent to the action of a differentiating element.

Figure 1.4. Appearance of parasitic capacitance in high-voltage lines

This problem of pulse measurements is solved as follows. In order for not to depend on the frequency, it is necessary to connect the capacitor parallel to the resistor , guided by the formula = . That is, a low-impedance capacitive voltage divider with the same division factor is connected in parallel with the re6

sistive high-resistance divider. The capacitance values are calculated in inverse proportion, since the capacitance resistance is inversely proportional to the capacitance, = . The resulting divider is called frequency-compensated, that is, the resistance does not depend on the frequency of the signal (Figure 1.5). The conversion factor of the compensated divider: =

=

=

=

.

(1.3)

The resistive part of the divider is responsible for the division ratio in the direct current and in the low-frequency region to the limiting frequency = , where τ is the time constant of the divider arm. From formula 1.3 it follows that the time constant is the same for the upper and lower shoulders. At frequencies > , the capacitive part of the divider operates. For the high-voltage divider in Figure 1.4, the capacitance is connected in parallel with each resistor of the upper arm. The magnitudes of the compensating capacitances are chosen so that they are much larger than the “parasitic” capacitances that distort the measurements.

Figure 1.5. Diagram of a compensated voltage divider with a bandwidth from DC to several MHz

Now we turn to the study of the principle of the Wheatstone bridge. The branches of the bridge (Figure 1.6) generally contain impedances − . Also there is the load in the output diagonal. 7

Figure 1.6. Wheatstone bridge diagram

= 0, i.e. at

The equilibrium of the bridge occurs at =

(1.4)

.

In the expanded form, the expression of the impedance of branches is: =

+

;

=

+ =

; +

=

+

; (1.5)

.

Substituting (1.5) into expression (1.4) we get: − +

= =

− +

(1.6)

The scheme of the DC bridge does not differ from the considered scheme. The branches of the bridge have active resistances − , and a galvanometer in the output diagonal. Let us consider the example of this bridge DC output equilibrium equation, omitted in the previous case. If the bridge is balanced = 0, i.e.: =

,



=

=

,

=

.

(1.7)

Dividing one equation by another term by term, we get: =

or

= 8

.

(1.8)

If by

we mean an object with unknown resistance =

, then we get (1.9)

.

This expression is called the equilibrium equation of a single DC bridge. Here and are the relationship shoulders, and is the comparison shoulder. The order of work performance: Assemble the electrical circuit according to Figure 1.7. Check the assembly with the teacher! The baseline data for the various options are presented in Table 1.1 and 1.2. It is required to calculate the resistor and for voltage dividers. Table 1.1 Baseline data for the experiment on the study of the attenuator №. 1 2 3 4 5 6 7

Uin, Uout, R1, №. Uin, Uout, V V V V k 20 6 5 8 27 4 25 15 14 9 25 10 40 25 2 10 30 8 32 20 4 11 38 30 35 15 5 12 22 13 21 5 7 13 26 12 30 25 8 14 24 20 Note: for all options R2 = 2 k, R3 = 4 k.

R1, k 10 7 4 13 12 10 5

№. 15 16 17 18 19 20 21

Uin, V 40 37 39 29 25 40 38

Figure 1.7. Schemes for the study of the voltage dividers

9

Uout, V 30 14 10 4 15 25 20

R1, k 2 6 3 8 15 2 1

Table 1.2 The source data for the experiment on the study of capacitive voltage divider №. 1 2 3 4 5 6 7

Uin, V

Uout, V

С1, №. Uin, Uout, V V F 20 6 5 8 27 4 25 15 14 9 25 10 40 25 2 10 30 8 32 20 4 11 38 30 35 15 5 12 22 13 21 5 7 13 26 12 30 25 8 14 24 20 Note: for all options С2 = 2 F, С3 = 4 F.

С1, F 10 7 4 13 12 10 5

№.

Uin, V

Uout, V

15 16 17 18 19 20 21

40 37 39 29 25 40 38

30 14 10 4 15 25 20

С1, F 2 6 3 8 15 2 1

Verify the calculated data by the experiment. Assemble the electrical circuit according to Figure 1.8. Check the assembly with the teacher!

Figure 1.8. Diagram of the bridge under study

The baseline data for various options are provided in Table 1.3. Determine the resistance of R4 for a balanced bridge. Table 1.3 Baseline data for the Wheatstone bridge experiment №. 1 1

R3, k 2 2

R2, k 3 6

R1, k 4 5

№. 5 8

R3, k 6 7

R2, k 7 14

10

R1, k 8 13

№. 9 15

R3, k 10 7

R2, k 11 7

R1, k 12 5

1 2 3 4 5 6 7

2 5 14 13 1 8 7

3 12 3 2 23 8 12

4 10 15 4 14 17 6

5 9 10 11 12 13 14

6 6 16 15 2 7 14

7 9 8 8 13 3 5

8 7 4 13 12 9 8

9 16 17 18 19 20 21

10 9 6 4 5 12 17

11 6 7 16 14 6 6

12 8 8 7 3 8 4

Verify the calculated data by the experiment. Test questions: 1. What is the purpose of the voltage divider and the Wheatstone bridge? , how does change, if = , 2. With increasing resistance = (Figure 1.1)? Make a proof of the conclusion. 3. The current through the resistor was reduced, what were the reasons (Figure 1.1)? 4. Make a sensor based on a bridge circuit.

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2. MEASUREMENT OF PULSED DISCHARGE CURRENT BY THE ROGOWSKI COIL The goal of the work. Measurement of pulsed discharge and plasma current using a Rogowski coil. Brief theoretical introduction One of the basic methods of measuring fast discharge current that is rapidly changing and short-lived is Rogowski coil (current transformer) [1]. The convenience of this method is that it does not have a direct impact on the investigated environment, and the measurement is indirect. As it is shown in Figure 2.1, the construction of the Rogowski coil consists long, solely wound, ring-shaped solenoid.

Figure 2.1. A simple scheme of the Rogowski coil

The principle of the coil operation based on the electromagnetic induction law as it registers the magnetic field generated by the measured current ( ). If the ends of the Rogowski coil winding are closed by the resistor , then the current on the belt is characterized by the following equation: ) = ( )≡

+( +

∙

,

(2.1)

here , are belt inductance and resistance, is the number of turns, is the measured current. In this equation, the effect of parasite capacitance between turns is not taken into account because it is sui12

table for measured low frequency current ( ). The equation (2.1) corresponds to the equivalent scheme in Figure 2.2, where the interrupted line represents the parasite capacitance. Its effect can be taken into account in the following cases: ≪

(2.2)

.

Figure 2.2. Equivalent scheme of the Rogowski coil

The common solution of equation (1) above is: ( )=

/

/

( )

is the integration constant. If the duration of the current pulse solution of equation (2.3) is as follows:

, =

,

(2.3)

here

( )=

( )

=−

is smaller than τ, then the ( )

, ≫

,

(2.4)

therefore, the Rogowski coil operates in a current transformer mode, respectively, the voltage at the ends of the load is: ∙ ( ).

=

(2.5)

In such a working mode of the coil, in its own inductance and resistance, + is widely used in practice. However, the belt sensitivity, / ( ), is relatively low in this mode; the main error in the measured current is based on the threshold value of the time constant τ of the belt ( ≫ ). 13

When the load resistance is greater than ( ≫ , ), the coil operates in the shock-excited circuit mode. In this mode the sensitivity of the measuring device is much higher, but the output voltage does not correspond to the shape of the current pulse being measured. A special integrated circuit is used to prevent this drawback (Figure 2.3). When measuring high frequency currents, the condition ≫ is the limitation condition, therefore, a smaller resistor can be connected to the output of the Rogowski coil.

Figure 2.3. The electrical scheme of the Rogowski coil with an integration circuit

In this case, the turns of the coil in conjunction with the elements R and C of the integration circuit form a damped oscillation circuit, which is connected to an external ε (t) EMF (defined in equation 2.1) and its equation is written as follows: +( +

) +

= ( ).

(2.6)

If the value of the current characterization time is , then the components on the left side of equation (2.6) are equal to: ,( +

) ,

(2.7)

.

Selecting the parameters of the integrated circuit is as follows: ) ,√

≪( +

,

(2.8)

it is possible not to take into account the first and the third additions in equation (2.6), in which case the current is determined by (2.9): 14

( )

( )=

(2.9)

,

and the voltage on the capacitance (the voltage at the output of the integrated circuit) is equal to: ( )=

( )

=−

(

)

∙

( )

.

(2.10)

We put the inductance of the coil to (2.10), and we obtain the expression (2.11): ( )=−

)

(

∙

( ).

(2.11)

Thus, knowing the parameters of the coil and the integrated circuits, the current ( ) can be determined by the voltage on the capacitance. It should be noted that in such a case, it is sufficient that the measured current is punctured to the coil winding contour, regardless of the spatial distribution of the charged particle concentration inside the belt conductor or belt measured at the output of the belt (2.5) and the output of the integral circuit (2.10), (2.11). Things to consider while conducting the experiment. The low frequency boundary of the Rogowski coil method is determined by the following condition: + ≪ . The upper boundary depends on the resonant frequency of the coil. The wavelength that corresponds to the core self-frequency, as a rule, should be equal to the length of the conductor that forms the coil. The Rogowski coil uses a ferrite core to increase the ability to operate at low frequencies, which increases its inductance by retaining its turn quantity, but reduces the high frequency band. An electrostatic screen (magnetic stripe) to reduce the dependence on the external circuit and capacitance and to avoid large, rapidly changing voltage fluctuations covers the coil. Rogowski coils can be integrated into separate integrated devices, expand the range of operation, and can operate in coils as well as current transformers, the main advantage of which is the simplicity of the device and the convenience of processing the results. With low resistivity coaxial cables, the output voltage of the current transformer must be small enough to be distant. 15

It is important to note that in real plasma experiments, the flow generated by currents apart from measured one can cause the appearance of a large number of errors while it flows through the coil. The main reason of that is the absence of reverse directed wires in the coil; in addition the area of larger coil is much bigger than the area of individual coils. The main disadvantage of the Rogowski coil is the uneven excitation of the individual turns, which can add strong noise to the output voltage. The order of work performance Experimental setup and measuring instruments In this work, pulsed plasma accelerator experimental setup is used (see Appendix A). Preparation of the experimental setup for operation The order of work for the preparation of the pulsed plasma acelerator experimental setup is shown in Appendix A. Measurement and analysis of the results Determine the current of the plasma accelerator with coaxial electrodes. For this purpose, Rogowski belt with 400 turns is used in practice. The coil is wounded to fit the conductor wires of the plasma accelerator (Figure 2.4).

Figure 2.4. The Rogowski coil position on the experimental installation

For the purpose of recording the voltage generated by the Rogowski coil, it is connected to an electronic memory oscilloscope by the resistor = 12 Ом Ohms. In this regard, the current is calculated using the formula (2.12): 16

=

,

(2.12)

here

− the voltage at the ends of the resistor. Repeat the experiment for different parameters (voltage, pressure) of pulsed plasma accelerator. Make the conclusion of the work. You can also determine the plasma flow current by placing the Rogowski coil inside the vacuum chamber. If plasma flow velocity is set at two distances from one another, it is possible to detect the velocity of the plasma flow. Do these experiments together with the teacher. Test questions: 1. What methods of detecting a rapidly changing current that pass in a short period of time do you know? 2. What is the operation of Rogowski coil? 3. What is Rogowski coil construction? 4. What kinds of Rogowski coils are available? 5. In what cases the Rogowski coil operates in a current transformer mode? 6. In what cases the Rogowski coil operates in an oscillation contour mode? 7. How does parasitic capacitance come about? 8. How can you integrate the signal from Rogowski coil? 9. What are the advantages and disadvantages of Rogowski coil? 10. How can you determine the velocity of plasma flow using the Rogowski coil?

17

3. INVESTIGATION OF LOW TEMPERATURE PLASMA BY ELECTRIC PROBE METHOD The goal of the work. Obtain single-probe I-V characteristics. Determine the electron temperature and density in plasma. Brief theoretical introduction Plasma is a quasi-neutral system which consists of charged particles, i.e. electrons, ions and neutral atoms. Quasineutrality is the equality of the positive and negative space charge concentrations [2]. So, the term "plasma" means a semi-ionized (or fully ionized) gas in a quasi-neutral medium. |

−

|≪

=〈 〉=〈

(3.1)

〉,

where , are concentrations of ions and electrons of the plasma, is the mean value of the concentration. Plasma, itself, has the property of screening of electric field by charges. Screening is the process of collecting opposite charges around the charged body making a neutral system at a distance of the Debye radius: =(

/4

)

/

,

=

/

+

.

(3.2)

The potential of the isolated charge in a vacuum is equal to ⁄ , ⁄ also in a plasma and with the growth of the distance from the source in the charge field decreases rapidly. As usual, in plasma, charge carriers are electrons and ions. The ratio of the concentration of ions to the total concentration of particles is called the ionization degree. = where

=

(

)

,

, is the pressure in the volume. 18

(3.3)

If ≪ 1, then the probability of the multiple (double) ionization would be less, therefore the positive charge is transported by single-charged ions, and it leads to the equality of the electron concentration and the ion concentration taking into account the quasineutrality condition: ≈

.

(3.4)

In this case the ionization degree with high accuracy could be to the concentrafound by the ratio of the electron concentration tion of neutral atoms . If the kinetic energy of the thermal motion is comparable to the ionization energy of the atom (over ten thousand Kelvin), the ionization causes collisions of particles at their thermal motion. Such a plasma is called high-temperature plasma. The sun and other stars belong to a low-temperature plasma. The plasma in controlled thermonuclear fusion also refers to this type. The temperature in that case is equal to 100-150 million degrees Celsius. Plasma can be obtained at different gas discharge facilities. Usually in laboratories low ionized plasma is investigated. In such a plasma, the ionization process occurs due to the elastic collision of neutral atoms and molecules with drift electrons in an external electric field. In this case, Joule thermal energy is transferred to the chamber wall or gas surrounding the plasma. In the process of elastic collision, the particles similar in mass exchange energy. The mass of ions and neutral particles is approxymately equal, and the mass of electrons is much smaller compared to them. Consequently, the Maxwellian velocity distribution of the same type of particles is established faster in comparison with heterogeneous particles. The kinetic energy of electrons will be higher than that of the ions, while the average kinetic energy of the ions is higher than the average kinetic energy of the neutral atoms. It should also be taken into account that the mean-free pass distance of electrons is higher in comparison with ions, and therefore the external electric field will always act on the electrons. As a result of such conditions, the temperature of the plasma of the gas discharge will consist of the temperatures of three different particles: electrons – , ions – and neutral particles – ;

19

≫

>

(3.5)

.

Under such conditions, the gas discharge plasma is called nonuniform. The beginning of the investigation of the plasma properties using an electric probe was put by Langmuir in 1923 [3-5]. An electric probe is a small-sized electrode placed in plasma and, owing to the Debye screening, it does not substantially affect the plasma (see Figure 3.1).

Figure 3.1. The photo of the single cylinder type electric probe

The electric probe has a different design: cylindrical, spherical and plate (Figure 3.2).

а)

b)

c)

а) cylindrical, b) spherical c) plate. 1 – probe, 2 – insulation Figure 3.2. Types of electric probe

Usually, the electric probe is connected with one of the electrodes by an additional voltage source. As electrode, an anode or a cathode could be chosen [3]. 20

The potential of the probe is given by means of a power source and is measured by a voltmeter. The current flowing through the probe is measured by an ammeter. If the potential of the unperturbed plasma around the probe is , then the potential of the probe in comparison with the potential of the plasma will be: =

−

.

(3.6)

The current of the electrical probe consists of electrons and ions. If the probe has a negative potential in comparison with the environment, then we will see the ion current, and the electron current flows when the potential of the probe is positive. The generalized probe theory is based on the following conditions. 1. The velocity distribution of electrons in the plasma is Maxwellian. 2. Near the probe placed in the plasma, a layer of space charge with a thickness of several is formed thus, after screening, the perturbation of the probe in the plasma is not taken into account. 3. The size of the probe will be much larger than the thickness of the space charge: ≫ . So the surface area of the space charge is considered equal to the area of the probe and the charges falling into this region are attracted or repelled depending on the potential of the probe. 4. In the space charge layer there are no collisions of electrons and ions with heavy particles, that is , ≫ ( , − the mean free path of electrons and ions). 5. If < , then the penetration of electrons into the retarding region and the distribution of the electron concentration in the space = e , charge layer is determined by the Boltzmann law: where Φ = − , − electron concentration in plasma. When the potential of the probe is negative, plasma electrons cannot reach the probe and the current will consist of ions. This current is not so great, because in the discharge plasma the mobility of ions is much less than the mobility of electrons.

21

а) general form and b) the electron region on a semi-logarithmic scale Figure 3.3. I-V characteristics of the Langmuir probe

Thus, ions create a layer of the positive space charge around the probe and the I-V characteristic (read with Figure 3.3a) approaches saturation (point А in Figure 3.3а). With increasing voltage , the number of electrons moving toward the probe increases. The resultant probe current: =

+ ,

(3.7)

decreases in absolute value and at point B equals to 0. The potential at a given point is called "floating". If the is reduced further (in < 0 region), the electron current in the space charge layer becomes larger (BC region). At positive electrons are accelerated under the influence of a large field, and the ions slow down. In this case, a layer of the negative space charge is formed around the probe. In this region, the I-V characteristic of the probe approaches saturation (DE region). At the point D, when З = , the probe current is only determined by the flow of thermal motion of particles. In accordance with the molecular-kinetic theory (under the above conditions): =

(〈 〉 − 〈 〉), 22

(3.8)

where 〈 〉, 〈 〉 is the average velocity of thermal motion of electrons and ions, is the area of the collecting surface of the probe, is the electron charge. For electrons, the average velocity is: 〈 〉=

(3.9)

,

is the Boltzmann's constant, is the mass of the electron. However, the mass of electrons is much smaller than the ion mass ≪ , (〈 〉 ≫ 〈 〉) , and ≫ , therefore at = 0 (i.e. = ) the current flowing through the probe will largely be electron current: (3.10)

〈 〉.

=

The electron current of the probe in CD region of the I-V characteristic is determined by the Maxwellian velocity distribution of electrons: =

exp

.

(3.11)

If we find the logarithm of formula (3.10), the following formula can be taken: = where

=

−

+

,

(3.12)

.

Thus, on a semi-logarithmic scale, at < 0 the linear dependence of | | from can be obtained (Figure 3.3b). Angular coefficient of the linear dependence: =

| |

=

.

(3.13)

At > 0 the I-V characteristic of the probe approaches saturation, and therefore a curvature appears in the I-V line. Thus using the angle of inclination of the line we can find electron temperature: 23

=

(3.14)

,

where is the angle of rotation of a straight line around axis . Finding the saturation current in the I-V characteristic, it is possible to calculate the electron concentration by the following formula: =

(3.15)

.

However, usually during the experiment because of the large difference between the electron and ion currents, it is difficult to achieve saturation of the electron current (beyond point E in I-V characteristic), so to determine the concentration of ions will have to use the ionic saturation current. This satisfies the quasi-neutrality condition for the plasma. =

,

(3.16)

,

where is the ionic saturation current, is the mass of ions of the plasma-forming gas. An experimental look at the probe method and the accompanying difficulties. At first glance, the determination of the plasma parameters by the probe method seems easy: only to measure the current flowing in the wire. However, this case is slightly different and difficult. The probe characteristic in collisionless plasma from the theoretical point of view is sufficiently and qualitatively predetermined. But in the case of collisions and magnetic fields, many difficulties arise, however, with the addition of corrections, probe measurements can be made. Surface layer. The work function of electrons from the probe surface depends on its surface structure. If the value is reduced to a few eV, then the difference in the work function of different areas of the probe surface and its temporal variation affect the probe characteristics. These layers can be formed due to the adsorption of gas from metal films (Hg or Cs) or from the connection of high-resistan24

ce wires. Therefore, after placing the probe in a vacuum, it must be degassed. For this, the probe should be held for a few seconds in the regime of saturation of the electron current before reddening. Secondary emission and arc. If the ions contribute to the exit of secondary electrons from the surface of the probe, then a stream of ions will tend to the negatively charged probe. Thus, as a result of a positive bias, electrons cannot leave the probe and will not play any role. It is difficult to consider the effect of secondary emissions, so it must be prevented. To do this, when manufacturing the probe, a material with the lowest secondary emission coefficient and with the ability to work at low voltages is selected. However, when performing works with high power, it is not always possible to get rid of this effect. Moreover, in such cases a "unipolar" arc can arise. In this case, the role of the cathode will be played by a probe, and the anode will be the boundary layer of the space charge. Also, the circuit will be closed through the metal wall of the discharge chamber. Such an arc can lead to burning and inoperability of the probe. In platinum, in comparison with tungsten the probability of arc appearance is less. Effect on plasma. In a weakly ionized plasma, a decrease in the charge density can occur near the probe, this phenomenon is considered in the collision theory. However, in a fully ionized plasma, the effect of the probe is different. The most influential is the appearance of atom impurities from the probe and insulating material. Due to inelastic collisions, these atoms are excited and release energy, thus leading to a decrease in the temperature of the electron gas and to a decrease in its conductivity. For instance, in a thermal ionized cesium plasma trapped in a magnetic field, the probe can lead to plasma quenching. The role of the screen insulating the probe. Despite the screen plays the role of isolation, it can attract electrons and ions. During the collision, the plasma density decreases. Taking into account the effect of the insulator, the density can be measured in a differential form. To do this, the probe must move in the plasma volume without an insulator. Change the collecting area of the probe. The current that the probe collects depends on the area bordering the plasma. In discharges with high powers, such a region can change due to sputtering or evaporation. Thus, a conductive layer appears on the surface of the insulator. 25

If the surface of the probe has the electric connection with this layer, then effective collecting surface could be significantly changed (the area will increase). To prevent this, probes with special constructions are used (dash line in Figure 3.4).

Figure 3.4. Construction of the probe

Electron scattering. If the surface of the probe is not an ideal receiver for particles and the scattering coefficient is known, then this effect can be taken into account theoretically. However, scattering will not affect the value of . In fact, in a homogeneous gas, the velocity distribution of electrons arriving at the probe will be the same for all values of the voltage at the probe, and therefore the scattering coefficient will be constant. Experimental setup and measuring instruments. In this work, an experimental setup of DC glow gas discharge is used, laboratory work [see APPENDIX B]. Preparation of the experimental setup for operation. The order of work for preparation of the DC glow discharge is shown in reference [APPENDIX B]. Measurement and analysis of the results. Let's find the plasma parameters at the positive column of the glow discharge. A schematic diagram of the electrical probe is shown in reference [6]. The electrical circuit of the discharge system consists of the two power sources of the electrodes of the discharge tube and the probe. The anode is selected as the reference electrode for the probe. The discharge current is measured by an ammeter, and voltages by a voltmeter. Due to the high resistance of the circuit, the current is determined by measuring the difference in the potential at the output of the resistor with a previously known value (r). 26

Tasks: What is the thickness of the space charge layer at the surface of a flat and = 12000° К? probe immersed in a plasma with = 5 ∙ 10 The potential of the probe relative to the plasma is ± 10 V. Will the probe measurements be correct if the gas pressure is p = 0.1 torr? The gas is argon. Find the expression for the Debye screening radius in the cases of in a nonisothermal isothermal and nonisothermal plasma. Estimate plasma at = 3 ∙ 10 К and charge concentrations = 1 ∙ 10 . How many charged particles are contained in the volume of the Debye sphere? Take ≪ and the plasma density distributed by Boltzmann law. Creative engineering tasks: Make a model of an electric single probe from a nichrome wire with a diameter of 150-200 microns. To straighten the wire, pass the electric current through it in a tensioned position. The quality of the insulator uses a plastic rod from a ballpoint pen. To fix the wire to the rod, use hot glue. Observe all the conditions (geometric parameters) specified in the description. The order of work performance Attention! Experiments are carried out only under the supervision of the teacher. 1. Before ignition of the gas discharge, it is necessary to switch off the probe from the electrical circuit. If the probe is turned on when the discharge is ignited, the probe may be damaged due to the appearance of a strong arc. 2. Turn on the probe, voltmeter and ammeter in the gas discharge circuit. Slowly changing the voltage on the probe, record the voltage and current values in the table. 3. Translate the values in the table from the SI system to the CGS (Gauss) system. 4. Using the obtained data, construct the I-V characteristic of the probe, it should be like in Figure 4а. 5. Find the ion saturation current on I-V characteristic. 6. For positive current values, construct the I-V characteristic ion a semi-logarithmic scale and find the angular coefficient. 27

7. Using formulas (3.14) and (3.16), determine the electron temperature and concentration, respectively. 8. Using formula (3.3) obtain the degree of plasma ionization. 9. Calculate the potential of the plasma based on the above Figure 3.3. 10. Calculate the error for one of the obtained I-V characteristics. 11. Summarize the work. An electric probe can also be used to measure the plasma parameters of a radio-frequency (RF) gas discharge, suggest to the teacher. In this case, a radio-frequency gas discharge installation is used [7]. The order of work for the preparation of the RF gas discharge is shown in reference [see APPENDIX C]. The operating procedure for the measurement corresponds to the above points. To reduce parasite capacitances and inductance when working with RF voltage, the electrical probe is connected to the circuit through a resonant circuit (Figure 3.5).

1 – part of the probe which contacts with the plasma, 2 – insulator, 3 – compensating electrode, 4 – capacitor, 5,6 – resonant circuits, 7 – probe support Figure 3.5. The probe connected through a resonant circuit.

The location of the electrical probe in the plasma volume of the RF discharge is shown in Figure 3.6.

Figure 3.6. The location of the electrical probe in the plasma of the RF discharge

28

Test questions: 1. What is a plasma and what are its main parameters? 2. Explain the appearance of the screening phenomenon in plasma. 3. Explain the physical meaning of the ratio of ion concentration to total particle concentration. 4. How does the energy of particles comparable in mass change with their elastic collision? 5. Give the basic conditions of the probe theory. 6. Analyze the I-V characteristic of a probe. 7. Explain the relationship between plasma particles and pressure. 8. Explain the structure and work principle of the single probe. 9. What are the warnings when measuring with an electric probe?

29

4. INVESTIGATION OF THE PROPERTIES OF PULSED PLASMA BY A MAGNETIC PROBE The goal of the work. Investigation of the spatial distribution of the magnetic induction and its temporary change in pulsed plasma by a magnetic probe (measuring coil). Brief theoretical introduction There are many different ways of contactless investigation of plasma parameters, however, in all these methods it is impossible to determine the magnetic field of plasma systems. Of course, there are some methods, for example, by introducing a fast charged beam of particles into a plasma, one can obtain information about the internal magnetic field, but in this case it is not very convenient to interpret the beam change from a practical point of view (especially with rapidly changing beams, not including the simplest stationary systems). Because of this, to measure the distribution of force lines of magnetic field, a magnetic probe is inserted into the plasma. The method of measuring the magnetic field by the probe is accompanied by direct interaction with the plasma, so, this method is convenient for investigating low-temperature plasma. The plasma medium always interacts with its own magnetic fields or with the fields of external wires. So, if there is no spatial distribution of the magnetic field and a temporal change, then it means that there is no information about plasma characteristics. In addition, another reason for studying the magnetic flux in the plasma is that the spatial distribution of the plasma depends on its source and restraining forces. And these data play an important role in many practical applications of ionized media. Plasma confinement and magnetic hydrodynamic stability depend on the relative location of the plasma and the magnetic field. It means that, at some relations of impulse balance, in the general case, by the distribution of magnetic field a spatial position of the plasma, its thermal energy density, and the stability of the configuration can be found. However, in the system under consideration, the plasma must interact substantially with the magnetic field. Of course, the study of the spatial distribution of electrons 30

and ions at several thousand Ørsted (1 Ørsted = 80 А/m) using a magnetic probe will not yield any fruitful information. However, when the magnetic field is fully coupled to the plasma current (for instance, self-expanding discharges, pulsed plasma flow), the use of a magnetic probe is an excellent solution and can yield fruitful results [8-13]. The design of the magnetic probe includes a measuring coil with a diameter of 1-2 mm, if the frequency of the studied signal is not high the coil with more windings can be used. The coil inserted into the discharge is insulated with a refractory dielectric material (for example, quartz, ceramics), in some cases, to prevent electrical noise, it is packed with an electrostatic screen. Measuring a high-frequency magnetic field from a practical point of view is very difficult, to do that a coil with a few windings is used (2-5 windings, 100 МHz). If high-frequency vibrations are excited in a plasma in a magnetic field, then an alternating magnetic field will be induced at any point in the space where the magnetic probe head is located, and accordingly an alternating electric field. Thus, depending on the location of the probe and the spatial distribution of field lines, different results will be obtained. That is why, in order to register the necessary fields on the site where the coil is located, there will be a cutout on the electrostatic screen (Figure 4.1). In addition, an electric field can appear in the gap between the coil head and the plasma, hence the capacitive currents. To prevent this phenomenon, the probe must be made very small, usually its diameter including the screen does not exceed several millimeters.

1 – magnetic coil, 2 – cutout of the screen, 3 – coaxial wire, 4 – electrostatic screen Figure 4.1. Design of RF magnetic probe

To reduce the signal-to-noise ratio (in general it shouldn't exceed 0,1), the signal from the coil is transmitted through a coaxial 31

wire located inside the outer screen. In this case, the probe parameters will be such: diameter of the coil – 1 mm, number of windings – 3-5, coaxial network diameter – 1,8 mm, outer diameter of the screen – 2,5 mm. The magnetic probe must satisfy the following conditions: – The measured signals (clear) must exceed the electric noise produced by the pulsed discharge, that is, it must have a high sensitivity; – Must have the ability to register fast-changing fields, that is, sensitivity to the frequency; – The influence on the medium (plasma) should be minimal, that is, a probe should have a minimal size. Some conditions in this list may contradict each other, if so let us consider them. Sensitivity of the probe is determined as follows ,

=

(4.1)

where is the number of windings, is the area, is the rate of the change of magnetic field. Consequently, by keeping the area of the probe (in order not to increase the size of the probe) and rising the number of windings it is possible to increase the sensitivity. However, the upper limit of the frequency can be obtained by the following constant time (contradicttion to the second condition): = , i.e., the period of flucis the tuation of the rapidly changing field recorded by the probe. load of the probe, it usually equals to the oscillatory resistance of the is the inductance of the coil (single-layer solenetwork. = = 2 → = 0,029 . is noid). is the geometric coefficient the length of the soil, is the radius of the coil. The maximum output signal at the minimal inductance of the coil can be obtained by: ~ .

(4.2)

This means that for a small inductance, the diameter of the coil should be large, which contradicts the third condition. 32

Electrostatic screening. Magnetic probe should have only sensitivity to the magnetic field, and must not register electric fields. But, in plasma with rapidly changeable magnetic field an electric field also exists. It means, in many cases due to the appearance of parasite capacitance the potential difference is formed between the grounded probe and plasma. Afterwards, spurious signals pass into the measuring circuit, to prevent this, an electrostatic screen is used. The electrostatic screen is made from a grid or from a mold with a hole for the passage of the magnetic field. The time constant, determining the rate of penetration of the external magnetic field on the cylindrical screen, is obtained as follows, = . Where is the permeability, is the wall thickness, is the conductivity of the material. If is much more than the time of the process in the medium, then the signal passing through the screen does not change. Moreover, to decrease the influence of spurious electrostatic signals on the output of the probe a resistor with a small resistance is connected. At small value of inductance , an amplitude produced by magnetic field at the output of the probe does not depend on . In this case, an electrostatic field until its passing to the measuring circuit is reduced by the voltage divider consisting of capacitor (in the system coil-plasma) and resistor . The ratio signal/noise in this case will be proportional to , so the electrostatic spurious signals with frequency less than

are greatly weakened.

Another way to get rid of spurious signals is to use a ballast coil in the probe. Its two ends are connected to a differential amplifier, and the middle end is grounded. At the ends of the coil, two sign signals with the ability to increase the magnetic field are created, and single-valued spurious signals compensate each other. If the coil is located with a high accuracy perpendicularly to the axis of the probe, then using the following not difficult method it is possible to determine the presence of spurious signals. In a certain position of the coil, an oscillogram is obtained ( ), then the probe is turned 180 degrees and the oscillogram is taken again, and in this case the sign of the magnetic component in the oscillogram changes 33

( ). Such a movement in the oscillogram does not lead to a change in the electrostatic component of the signal, i.e. if there are no spurious signals, then two signals will give a mirror image. Output probe resistor, . A condition of the small value of the ratio is equivalent to the free motion of the current induced in the coil in a magnetic field. If we consider the reverse case, when tends to zero, the magnetic flux will not penetrate the coil. The circulating current in the coil will be proportional not to the time derivative of the external magnetic field , but to itself ( ), it means it is not necessary to integrate the signal (Rogowski coil). Nevertheless, in experiments where small-sizes coils are used, this method does not fit, because the value will decrease. Perturbations from the probe (errors). The limitation in the application of magnetic probes is caused by their direct interaction with the plasma, because when the probe penetrates into the plasma it leads to the local changes in the medium. Below, 4 possible types of this phenomenon are showed. 1. The probe embedded in the plasma lowers its temperature (based on the elastic collisions of the plasma particles with the probe surface). 2. Pollution of plasma by probe material (due to heating and melting of the probe in a high-temperature plasma). 3. The change in the current distribution near the probe (the appearance of the non-conductive area – the probe covered with a dielectric in the plasma medium). 4. Effect of plasma on probe sensitivity (force lines of the magnetic field which penetrating the coil, pass through the plasma surrounding it, i.e. coil-field connection associated with transient processses in this place). Connection of the magnetic probe to the electric circuit and its methodology When a plasma appears between the electrodes of a gas discharge, an azimuthally magnetic field arises. In this case, magnetic measurements are based on obtaining a "pinch" degree or self-expansion of the discharge. The axis of the coil can be placed perpendicular or 34

parallel to the tube axis, it depends on the magnetic field component. The probe penetrates into the plasma chamber through a special sealant and this makes it possible to measure several points in the space of the plasma medium. Pinch is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it. The signal inducted in the coil is proportional to the value , it means that on the oscilloscope screen a temporary change of the magnetic field will be obtained. To do that, a RC integrating circuit should be used (Figure 4.2). Thus, if the plasma system is symmetric, then the curve of the distribution of the magnetic field along its radius will be obtained ( ). Furthermore, using this curve a spatial distribution of the current (on the basis of Maxwell's equations), plasma pressure and pulse (based on the pulse balance equation) can be determined. Integration of the probe signal. Since the signal from the coil of the magnetic probe is proportional to the change in the magnetic field velocity , to measure the value ( ) directly, special integrating electric circuit should be connected between probe and oscilloscope.

Figure 4.2. Passive RC circuit

In this case usage of a simple passive RC circuit will give good results, thus, the output voltage of the integrator will be as follows: =

=

=

35

(

−

)

,

(4.3)

where is the input voltage. When the constant is more than the integrating time, a voltage will be less than the value and the will give the same value of the integral . value The error of the integral can be found by the following simple way. Let's consider the instant change in the voltage which at the time = 0 was unchanged. In this case =

1−

−

=

+⋯ .

(4.4)

The first member on the right side is the actual value of the integral and the second one is a first-order error, which for = 0.1 is equal to 0.5 %. The result in this case: the time constant should exceed the time of the observed process 10 times. / , the output signal Thus, since the coil voltage is = on the integrator: =

.

(4.5)

As seen, to ensure that the amplitude of the signal does not decrease, the value of the constant should be a small value. It is necessary to pay much attention to the choice of the elements of the integrating circuit. As known, composite resistances with low power and high resistances at high frequencies can change their values, and have bypass capacitance. The limiting capacitors with a simple structure have in series connected spurious inductances, and this, in turn, does not allow us to integrate accurately (in this case, the electric characteristics of single elements are not considered, however the experimenter should pay attention to this). Tasks: Ionization manometer represents a triode type flat system. The distance between the grid and the cathode is 0.3 cm, the grid-collector distance is 1 cm. The grid potential is Ug = 250 V, the potential of the collector is equal to Ua = -20 V. The geometric transparency of the grid is q = 0.8. The residual gas is nitrogen. What is the gas pressure in the tube if the ion current at the collector is 5 ∙ 10 А? The electron current emitted by the cathode is 10 A. 36

Calculate the direct velocity of mercury ions moving in a field = 20 В⁄м, in mercury vapor. The temperature of mercury vapors is 48 °С. Creative engineering tasks: Make a model of a frameless magnetic probe (coil) made of copper wire with a diameter of 200 μm. To retain the shape of the coil, use "super glue". To make an insulator use transparent plastic straws for drinking (straw) with a diameter of 5-6 mm. To fix the copper coil to the tube, use hot glue. Observe all the conditions (geometric parameters) specified in the description. The order of work performance Let's consider the investigation of the current sheet structure separating the plasma and the "repulsive" magnetic field in the plasma accelerator, the electrodes of which are coaxial (Figure 4.3). This phenomenon occurs in systems as a dynamic pinch. As shown in Figure 4.3, the magnetic probe is placed between electrodes and it is possible to move it along the axis of the chamber. Full information about the accelerator is given in reference [APPENDIX A].

Figure 4.3. The location of the magnetic field in the setup.

= 14 kV

Let's assume that the maximum value of the magnetic field strength created by the plasma current layer is 10 Gs. At this condition, from the edges of the electrode a plate current layer appears, which is compressed more slowly than the motion along the electrode (the shaded area in Figure 4.3). The middle electrode is the anode, i.e. the current directed to the cathode. 37

During the experiments a magnetic probe with the following parameters was used: a coil has 30 windings with wires in diameter ~ 0.08 mm wound on a base with a diameter of 1.5 mm, and all are placed in the quartz tube with the outer diameter 3 mm. The probe is connected to the oscilloscope by the integrating RC circuit with a coaxial wire with resistance 93 (50) ohm. Equivalent area of the coil is equal , and inductance is =2 ( = 3 ∙ 10 ). In to = 0.5 these cases , i.e., which is rather short for this experi≈ 2 ∙ 10 ment. The changes of the magnetic field registered by the probe are approximately equal to 1 , that's why a passive integrating circuit with constant time = 20 can be used. Thus, sensitivity can be found as [1]: =

= 2.5 ∙ 10

В

(4.6)

.

In Figure 4.4, the image of the signal formed on the oscilloscope screen by the magnetic probe is presented.

Figure-4.4. The oscillograms of the magnetic probe voltage. ( ) [

.

]

Test questions: 1. How can we get the flow of impulse plasma? What are its main parameters? 2. What is the work principle of the magnetic probe, explain from the physical point of view. 3. Draw the structure of the magnetic probe and the scheme of its connection to the electrical circuit. 4. What are the main conditions when measuring with a magnetic probe? 5. What is the purpose of the electrostatic screening of a magnetic probe? 6. What are the main errors in measuring with a magnetic probe? 7. What is the passive RC circuit? How does the process of integration of the signal occur in it?

38

5. DETERMINATION OF ENERGY AND CONCENTRATION OF IONS IN PULSED PLASMA FLOW USING A FARADAY CUP The goal of the work. Learn to use Faraday cup and to determine of energy and concentration of ions in pulsed plasma flow. Brief theoretical introduction Faraday cup (FC) is a measuring device consisting of two coaxially arranged electrode systems. Usually it is used to record the electron and ion current. Depending on which particle we observe on the internal electrode of the FC, either a negative or a positive potential is applied. To prevent the effect of additional charges on the operation of the device, the internal electrode of FC is made of a material with the lowest degree of secondary emission. To isolate the gap between the two electrodes, a fluoroplastic is used. To equalize the impedance by 50 ohms, the dimensions of the inner and outer electrodes are determined by the following formula, the impedance itself reduces the scattering of the RF signal during the flow in the circuit: =

. √

,

(5.1)

where is the inner diameter of the external electrode, is the internal electrode diameter, is the dielectric constant of the insulating material. In order for the particle beam (electrons or ions) to hit the surface of the internal electrode of the device, a gap of 100-300 in diameter is made on the surface of the outer electrode. Principle of operation of the device. Depending on the sign of the bias potential on the inner electrode, the charges penetrate into the FC and collide with the surface of the inner electrode. In this connection, a current appears on the electrical circuit and it is recorded with an oscilloscope [14-15]. The use of FC in the determination of the energy properties of a pulsed plasma flow and its methodology. The FC makes it possible to determine the parameters of a pulsed plasma, such as electron and ion energies, concentration and velocity. Because the plasma ions are 39

much heavier than electrons, the energy of the plasma is concentrated mainly from these scattered particles. Therefore, in this work, ionic particles are given special attention. Let us consider two methods for determining the concentration and energy of ions using FC. In the first case, the FC operates as a probe, that is, it is based on the equations in the probe theory. In the second case, the above parameters are found from the time of ions in the path from the source to the FC. 1st method. We assume that a local thermodynamic equilibrium is established in the plasma. Then, in accordance with this approximation, the velocity distribution of the particles in the plasma will be Boltzmann's: ( )

=

=

.

(5.2)

The ion flow density at the boundary with the space charge around the cylindrical probe is determined from their velocity and concentration: =

( ) ( ),

(5.3)

where is the radius of the space charge layer. From the boundary of the space charge with the approach to the probe, the concentration of electrodes decreases. In this connection, the form of the potential at the boundary of the space charge will be as follows: ≈ The velocity of ions ( ( ))

≈

(5.4)

.

( ) is determined by the potential:

, i.e.: ( )≈

.

(5.5)

Using the ratios (5.3) and (5.5), we get the equation for the ion current in the probe: 40

≈

exp −

,

(5.6)

where is the area of the space charge layer. Taking into account the equation (5.4), the equation (5.6) can be changed as: ≈

(5.7)

.

As FC works like a probe the equation (46) for the cylindrical probe will change as follows: ≈ 0.4

.

(5.8)

2nd method. When the electrons accelerated in a strong field of a pulsed plasma accelerator decelerate on the anode, the x-rays appear. X-rays are the first to reach the Faraday cylinder in comparison with plasma particles. As a result, a weak signal appears in the electrical circuit (Figure 5.1). ion current 0 -2

x-ray currents

I

-4 -6 -8 -10

Up=6 kV; р=2 torr Up=6 kV; р=2,1 torr electronic current

-12 -0,00015 -0,00010 -0,00005 0,00000 0,00005 0,00010

t Figure 5.1. Oscillogram of currents obtained with FC

41

This case makes it possible to determine the velocity of plasma ions. Knowing the distance passed by ions, their velocity is determined as follows: (5.9)

≈ ,

where is the distance from the electrode system (source) to the FC, is the time of passage of ions from the electrodes of the plasma accelerator to the FC, which is equal to the time difference between the appearance of x-ray signals and the ion flow and it determines from oscillograms obtained in an oscilloscope. Knowing the ion velocities obtained by this method, we find the energy and concentration by the following formulas: =

(5.10)

.

is the amplitude of then ion signal on the oscilloscope, where is the load resistance in the electrical circuit, is the ion charge, is the area of the gap on the outer electrode of the FC. = where

,

(5.11)

is the mass of the gas ion.

Tasks: Resistor R, uncharged capacitor C, switch K and constant voltage generator ε are connected in series. Determine the voltage dependence on the capacitor as a function of the time after closing the key. In a cylindrical vessel of length = 0.6 and diameter = 0.4 , a pulsed discharge of capacitance C energizes a powerful linear discharge to produce a "hot" plasma. The initial gas pressure in the vessel is p = 0.01 torr. What values should the capacity of the capacitor bank C, the inductance of the inputs L and the average value of the current in the pulse I have, that the plasma particles can acquire the temperature = 5 ∙ 10 К? The pulse is duration = 10 sec, the initial voltage, up to which the capacitors are charged is equal to U = 30 kV. 42

Creative engineering tasks: Assemble the integrating and differentiating electrical circuits. To do this, determine the temporal characteristics of the pulsed plasma (check with the teacher) and on the basis of the data obtained select the nominal parameters, the brands of resistors and capacitors. The electrical circuit should be compact and installed in an electrostatic screen. Observe all conditions stated in the description. Experimental setup and measuring instruments In this work, an experimental setup of pulsed plasma accelerator is used, laboratory work [see APPENDIX A]. Faraday cup The FC used in this work consists of two coaxial electrodes. The inner electrode is made of carbon, and the outer one is made of copper. The insulation between the two electrodes is made of a cylindrical fluoroplastic. An aperture on the surface of the outer electrode has a diameter ~150 μm. The order of work performance Preparation of the FC for operation: 1) Attach the cylinder to the linear electric motor to move it along the axis of the vacuum chamber. 2) Using connecting coaxial wires connect the measuring instrument to the electrical circuit and to the electronic oscilloscope as shown in the Figure 5.2.

1 – collector, 2 – insulator, 3 – screen, 4 – aperture Figure 5.2. Connection of the FC to electric circuit

43

Preparation of the experimental setup for operation: 1) The order of work for preparation of the pulsed plasma accelerator is shown in reference [see APPENDIX A]. Measurement and analysis of the results 1st method: 1. After connecting the FC to the oscilloscope, set the scale of the axes by time (50 / .) and voltage (500 / .) on the oscilloscope panel. 2. Reduce the pressure in the chamber to 2 torr. Charge the capacitor to 6 kV, ignite the pulsed plasma. Save this parameter until the end of the experiment. 3. Keeping the parameters on the 2nd point, step by step, change the voltage offset on the cylinder from -10 to -100 V in steps of 10 V. For each point, the pressure and voltage values must be the same. 4. Using the data of the oscillogram, determine the currents of electrons and ions. 5. Construct an I-V characteristic using the logarithm scale for the electron current. From the electron region of this curve, determine the temperature of the electrons according to Figure 5.3. 6. Using the electron temperatures and the Bohm criterion [2], calculate the ion velocity by the 1st method: =

.

Figure 5.3. I-V characteristic of FC in logarithmic scale

44

(5.12)

7. Using the values of the saturation current and ion velocity, respectively, with the equations (5.11) and (5.12), find the concentration and energy of the ions. 2nd method: 1. After connecting the FC to the oscilloscope, set the scale of the axes by time (50 / .) and voltage (500 / .) on the oscilloscope panel. 2. Apply -40 V voltage bias to the FC. Save this value of the voltage until the end of the experiment. 3. Keeping the parameters on the 2nd point, reduce the pressure in the chamber to 2 torr. Charge the capacitor to 3 kV, ignite the pulsed plasma. 4. Repeat the 3rd point for the values of the voltage at 4 kV, 5 kV, 6 kV. 5. Calculate the ionic current knowing the amplitude of the appeared signal in oscillogram and load resistance in electric circuit = 50 Ом. 6. Obtain the flight time of the ions from the oscillogram, and using equations (5.9), (5.10), (5.11) calculate the ion velocities, concentrations and energies. 7. Summarize the work. Test questions: 1. What is the Faraday Cup? 2. What is the principle of FC work? 3. What parameters of the pulsed plasma could be obtained by using FC? 4. For what distribution is the particle motion based at established local thermodynamic equilibrium in the plasma? 5. Obtain the electron temperature from I-V characteristic of the FC in the logarithmic scale. 6. What methods to determine the ion energy and concentration by FC do you know? Explain in details. 7. Explain Bohm criterion.

45

6. DETERMINATION OF PLAZMA ENERGY BY THE CALORIMETRIC METHOD The goal of the work. Determinion of the energy density of pulsed plasma flow using cone-type calorimeter. Brief theoretical introduction The calorimeter determines the energy of the plasma flow for per unit area. It is convenient to use it to determine the distribution and quantity of heat flux in plasma when investigating the parameters of plasma in different installations. The spatial distribution of the energy density of the plasma flow is one of the main parameters of the pulsed plasma accelerator. The principle of calorimeter operation is as follows: the investigated plasma flow collides with the calorimeter, giving its energy as thermal energy. The temperature change of the calorimeter at that time is registered by the "thermocouple" and recorded by an electronic oscilloscope. The energy density of the plasma flow is determined by the following formula [16-18]: =

(

)

,

(6.1)

here − the initial temperature of the calorimeter, − the temperature of the calorimeter after the interaction with the plasma flow, − specific heat of the material of the calorimeter, − mass of the calorimeter, − the cross section area of the cone. The calorimeter is made of materials such as copper, nickel, molybdenum (Cu, Ni, Mo), that have higher heat and melting temperature. The calorimeter's shape can be a cone, cylinder or disc as shown in Figure 6.1.

Figure 6.1. a) Cone, b) cylinder, and c) disk types of calorimeter

46

The heat ΔQ from the plasma increases the temperature of the calorimeter, and some of its heat is lost as a result of heat transfer and radiation. If the temperature of the calorimeter surface is not very high and the calorimeter is in contact with the less holding area, it is possible not to take into account the energy lost in the heat exchanger. The cylindrical calorimeters completely absorb the energy coming from the surface, and the calorimeter in the form of the disc absorbs about 20% of the energy consumed. The sensitivity of the calorimeter depends on the thermal equivalent of the calorimeter system (calorimeter, support, contacts). By taking into account thermal equivalents, the accuracy of the calorimeter increases and the value of the error in practice decreases. Thermal equivalents are defined as the sum of the specific heats of parts of the calorimeter system involved in the heat transfer. You can define the specific heats from the table or the experiment. There is the following method of determining thermal equivalence. Here, the thermal equivalent of the calorimeter is defined by its enthalpy. =

,

(6.2)

here − the effective specific heat of the calorimeter (the calorimeter, the stand holding it, the contacts connected to it). In order to calculate this amount in practice, you need a calorimeter heater. As shown in Figure 6.2, the experimental installation can be used:

Figure 6.2. A simple scheme of the experimental installation for detecting the sensitivity of the calorimeter 47

The installiation consists of a vacuum chamber, a source of thermal emission of electrons, a tungsten wire and an electric field-generating electrode. 100 μm tungsten wire is continuously heated at = 10 voltage and current 1,5 A and additional = −80 reverse discharge voltage is provided. It is specially designed to accelerate the electrons to the calorimeter. The calorimeter is in the vacuum chamber and the pressure inside the chamber is low for the electrons to reach the surface of the calorimeter, without any hindrance to their path, about 10 . Thus, the enthalpy change of the heated calorimeter with the electron beam is written as follows: ,

=

(6.3)

( ),

−

and the enthalpy change of the calorimeter after cooling is expressed as follows: ,

(6.4)

( ).

=−

given to the calorimeter is constant at heating If the energy ( ) is a calorimeter temperature function, can and the lost heat be found from the differences of formulas (6.3) and (6.4): ,

( )=

,

−

=

∙ ( ).

(6.5)

The function ( ) in the equation (6.5) above is defined as the difference in the curvature of the dependence curves derived from the calorimetry for different temperatures (heated and calorimeter). By knowing this function, you can calculate the effective capacity by using (6.5). To do this, you need to know the amount of power coming to the surface of the calorimeter . Since the calorimeter is heated by electrons (returning to practice), the input power is equal to: =

=

− 48

+

∙ ,

(6.6)

here − the value of the current passing through the calorimeter. In the cooling phase the calorimeter is given a negative displacement voltage, which, when cooled to calorimeter, prevents the electrons from entering the surface as a result of = 0. Thus, when using the calorimeter, it is possible to create a "calibration" with the above-mentioned method to reduce the error in practice and to ensure that the calorimeter research is correct. Experimental setup and measuring instruments In this work, the pulsed plasma accelerator experimental setup is used (see Appendix A). The order of work performance Preparation of calorimeter to work: 1. Move the calorimeter along the vacuum chamber axis, attach it to the linear electric motor (Z). 2. Connect the calorimeter to the electronic oscilloscope by using conductor wires. 3. Set the scale of the time (2 sec/div) and voltage (2V/div) on the oscilloscope panel. 4. Install the pressure in the chamber and the charging voltage of the capacitors as required by the teacher's instructions. 5. Repeat steps 4 for different types of gas discharges. 6. Using the obtained oscillograms, determine the energy density of the plasma flow using the formula (6.1). 7. Make conclusions of work. Test questions: 1. Describe the method of determining the energy of plasma flow based on a conical calorimeter. 2. What is the operation principle of a conical calorimeter? 3. What is the special feature of the calorimeter material and its size? 4. Thermocouple and its types. 5. What is the difference between disc, cylinder, and conical calorimeters? 6. What is the experience of calibration calorimeter? 7. Explain the progress in the calorimeter calibration experiment. 8. What is the thermal equivalent of the calorimeter?

49

7. DETERMINATION OF THE ENERGY DENSITY OF A PULSED PLASMA BY WIRE CALORIMETER The goal of the work. Acquaintance with the principle of operation of a wire calorimeter and determination of the energy density of a pulsed plasma with its help. Brief theoretical introduction Compared to a conventional calorimeter, the wire calorimeter has a high sensitivity and does not have a significant effect on the plasma flow. Its design consists of tungsten wires with a diameter at a distance of ∆ from each other. Knowing the resistance on the wires, the energy spent on heating the calorimeter can be found [19]. The resistivity of the metal upon its heating is determined as follows: (7.1)

(1 + ∆ ),

=

is the resistivity before heating, is the temperature coeffiwhere cient of resistance, ∆ is the temperature change on heating. Thus, according to the equation (7.1), the change in resistance of one wire is recorded as follows: =

()

=

∙(

∆ ( ))

=

+∆ ,

(7.2)

where is the unit length along the wire, and are the lengths of and the wire and the cross-section of the wire, respectively, also ∆ are the resistances of the wire before its heating and after heating, respectively. The value of heat supplied to one wire is determined on the basis of the change in resistance: =

∙

∙∆ ( )

=

∆ ()

=

∆ , (7.3)

where is the unit wire mass, is its density and is the heat capacity. This means that to find the value of the energy applied to the wire, it is sufficient to measure the resistance before and after 50

heating. The calorimeter absorbs only a part of the energy, its value is determined by the ratio of the area of the wire and the frame. Taking this into account, all the energy absorbed by all the wires is found from the formula (7.4): =

∆

∙∑

с

=

∆

∙

∙∑

∆ .

(7.4)

This formula, in comparison with equation (7.3), differs in the sum of the resistance ∑ ∆ . Since all the wires in the calorimeter are connected in series, it is sufficient to find the sum. The use of wire calorimeter in the determination of the energy density of a pulsed plasma and its methodology. The wire calorimeter is placed in the path of the plasma flow. Passage of the plasma flow through the calorimeter is accompanied by its heating. As a result, the resistance of the calorimeter increases. In order to find the resistance changes, the calorimeter is connected to the oscilloscope as the electric circuit, shown in Figure 7.1.

Figure 7.1. Connecting the calorimeter to the electrical circuit

Before the measurement, a current is passed through the calorimeter. Before heating, the temperature of the calorimeter will be comparable to room temperature. The change in the resistance of the 51

calorimeter when heated is determined by the decrease in the voltage in the electrical circuit. To do this, we first find the current flowing in the circuit according to the formula (7.5): =

=

(7.5)

.

Given that the resistance (calorimeter resistance) in the circuit is connected in series, the impedance is in their sum. Since the calorimeter is heated by the plasma flow, its resistance rises, so the value of ∆ appears: =

+∆ +

,

(7.6)

is the initial value of the calorimeter resistance before heawhere ting in accordance with room temperature. The total voltage in the circuit remains unchanged in the experiments; therefore, the impedance is found by subtracting the primary resistance of the calorimeter and finding the difference ∆ . Tasks: Make a model of a wire calorimeter (bolometer) made of copper wire with a diameter of 40-100 microns. To make a frame (frame) use solid wooden plywood with a thickness of 5-7 mm. Observe all conditions stated in the description. Creative engineering tasks: When the conductor with cross section S is heated its resistance increases by ∆ . Knowing the density of the substance , the resistivity ρ of the conductor and the specific heat , find the change in the internal energy ΔW of the conductor. The temperature coefficient of the conductor material is α. In a linear pulsed discharge the plasma is a long column of cylindrical shape. The temperature of electrons and ions is = 10 К, and N is the total number of particles of the same sign per 1 m of the length of the plasma column is 10 . What is the magnitude of the discharge current needed to hold the plasma?

52

Experimental setup and measuring instruments In this work, the pulsed plasma accelerator experimental setup is used (see Appendix A). The order of work performance Preparation of the calorimeter for operation: In this work, the wire calorimeter is placed on a ceramic frame, at a distance ∆ = 5 mm from each other, and consists of 20 tungsten wires with diameters of = 40 μm. Lengths of wires are = 10 сm. 1. Attach the calorimeter to the linear electric motor to move it along the axis of the vacuum chamber. 2. Using the connecting wires, connect the calorimeter to the oscilloscope and the power supply (battery AAA with voltage 1.5 V). 3. Set the scale of the axes by time (2 sec/div.) and voltage (0.5 V/div.) on the oscilloscope panel. 4. Set the pressure in the chamber and the charge voltage in capacitor to the value suggested by the teacher. 5. Repeat first 4 points for different values of the gas discharge voltages. 6. Determine the voltage at the shunt terminals from the oscillograms obtained during the experiment, and using the equation (7.5) calculate the circuit current. 7. Taking into account that the main voltage (1.5 V) doesn't change during the passage of the plasma flow, calculate the impedance of the circuit, and the resistance of the calorimeter after passage of the plasma flow. 8. Using the change in resistance which was found in point 7, using the equation (7.4) calculate the plasma flow energy. , = 4,8 ∙ 10 , = ( = 0,15 ∙ 10 ∙

= 19,6 ∙ 10

,

= 5,6 ∙ 10

ℎ

∙

).

9. Find the energy density per unit area / ( = 0,8 10. Summarize the work.

).

Test questions: 1. What is the physical meaning of resistivity? What is the dependence of resistivity on temperature?

53

2. Explain the physical meaning of Ohm's law for a part of the circuit, give the formula. 3. Explain the law of Joule-Lentz. 4. What is the structure of the wire calorimeter and its work principle? 5. What material should be used to make the calorimeter wires and why? 6. Does the calorimeter absorb all of the energy, what is it related to? 7. Use a calorimeter to determine the energy density of the plasma flow. 8. Obtain the plasma flow on a pulsed plasma accelerator. 9. Explain the mechanism of plasma acceleration in a pulsed plasma accelerator.

54

8. DETERMINATION OF THE PLASMA ELECTRON TEMPERATURE USING RELATIVE INTENSITIES OF THE SPECTRAL LINES METHOD The goal of the work. Acquaintance with the operation principle of the Solar S100 spectrometer in obtaining of the plasma spectrum. Determination of electron temperature of high-frequency gas discharge plasma based on relative intensities of spectral lines. Brief theoretical introduction The sum of wavelengths of electromagnetic radiation emitted (absorbed) when any body deviates from a steady state, for example, when heated at high temperatures, is called the emission (absorption) spectrum. Spectral lines are divided into three types depending on their nature: continuous, absorption, and emission [20-22]. Heated solids, liquids, and dense gases emit a continuous spectrum. Molecules emit absorption spectrum. Free, non-interacting atoms emit emission spectrum. Generally, quantum of light is radiated by changes in the energy state of the electrons in atoms.The radiation spectrum of the atoms consists of individual spectral lines or so called multiplets – groups of adjacent lines. These are called emission spectrum. Each element has its own emission spectrum as the handprints of human fingers, i.e. it can be found by radiation spectrum, as well as emission spectrum doesn't depends on the way of atom excitation. All stars are in plasma state, thereby atoms and molecules emit quantum light during excitation and ion-electron recombination. Spectroscopic method is widely used in astrophysics because radiation is the only way to obtain distant (indirect) information about the radiation source. Thus, the temperature and density of electrons in plasma, as well as the chemical composition and other important parameters can be measured on the basis of the spectroscopic method. Different plasma models that take into account the most important processes of different types of plasma are used for theoretical description of any radiation emission. In practice, the analysis of the radiation measured by such models allows us to carry out observation of the processes occurring in the plasma. 55

In this work, the method of measuring the electron temperature in a pulsed plasma is presented, which is based on the state of local thermodynamic equilibrium (LTE). The main parameter in the LTE model is the particles collision in the plasma. By collisions between particles and energy exchange after such processes, the static energy distribution of plasma particles is evaluated. However, in LTE model by the reason of the frequent collision of plasma particles, the distribution of particles by energy is rapidly equilibrated when plasma parameters change. Electrons can easily exchange energy with each other, at first free electrons are spread by speeds, which are determined by the Maxwell formula: ( )=

4

−

,

(8.1)

where − the density of electrons and − their temperature. Excitation of bound electrons in atoms or ions occurs as a result of collision between particles. Besides, there are contradictory processses in all plasma processes. For example, excitation and returning to the equilibrium state, ionization and recombination, and so on. Thus, since these contradictory processes in LTE plasma take place at the same time, the energy distribution of particles can be regarded as a complete thermodynamic equilibrium. In this case, the number of excited atoms which is located at the (from the ground state) is deenergy of an external electron level termined by the Boltzmann Law: ∗

~

−

.

(8.2)

In this equation only the temperature of electrons is determined in the experiment, and other quantities are constants. At this point, it is possible to calculate the electron temperature by measuring the number of excited atoms. At the same time, the number of excited atoms can be determined by the number of photons radiated from the plasma. 56

When an atomic electron makes a transition from an к excited state to the i lower state (see figure 8.1) the light intensity of the spectral lines in unit volumes and at the unit solid angle are as follows: =

ℎ

=

h

exp −

,

(8.3)

− the transition probability; , − the density of the here excited atoms and atoms in the ground state; ℎ − Planck's constant; = ( − )/ℎ − the emission frequency; , are the energies of the levels.

Figure 8.1. Emission of a quantum of light at excitation

is Instead of the transition probability, the oscillator 's force usually used and they are linked to each other by atomic constants: =

ω

.

(8.4)

Measuring the intensity of spectral lines and knowing the strength or probability of transition of the oscillator, we use the formula (8.3) to determine the electron temperature. However, measurement of the 57

absolute intensity of the spectral lines is one of the most difficult tasks. In addition, it is possible to obtain the electron temperature by comparing the intensity of two or more spectral lines of the plasma in the state of LTE, so that: =

−

⧍Ɛ

.

(8.5)

Summarizing the above formula, the electron temperature can be calculated by the following formula: =

( ( (

) )

)

,

(8.6)

where, , − the wavelengths of the spectral lines, , − the excitation energy,( ) and ( ) − the statistical weight of the excited states and the probability of transition by radiation, , − the intensity of the spectral lines. Experimental setup and measuring instruments In this work, the experimental setup of pulsed plasma accelerator is used (see Appendix А). Preparation of the experimental setup for operation The order of work for the preparation of the pulsed plasma accelerator is shown in Appendix A. Measurement and analysis of the results In the experiment, argon is used as a working gas. The plasma spectrum is derived from the quartz window of the gas discharge vacuum chamber. The plasma’s light is supplied by the optical fiber to the spectrometer input. Usually, the argon spectral lines corresponding to the wavelength of 750.38 nm and 751.4 nm are used. The main condition here is that the difference in excitation energies corresponding to the spectral lines must be greater than 2 eV. The transition probability of the argon plasma for a spectral line of 750.38 nm is 4.45·107 s-1, the spontaneous transition is 2p1 → 1s2 [23]. The order of work performance 1. Connect a linear spectrometer to the PC and run ссdtool software. 58

2. Adjust the exposure time to the desired value by pressing the Exposure button, typically 100-1000 ms. 3. By pressing the background button and closing the spectrometer hole take a background spectrum, and remove these values from the values used in the calculation. It will run automatically. 4. Without changing any data in the interface of cсdtool software program, obtain the spectrum of the plasma at different parameters of the plasma accelerator by pressing the button start (gas pressure 0.1-5 torr, discharge voltage between 2-10 kV). 5. Analyze the obtained spectral lines and determine the electron temperature of the plasma using the formula (8.6). 6. Make a conclusion about the work. Test questions: 1. Explain the operation principle of the spectrometer Solar S100. 2. Explain the nature of spectral lines. 3. What are the absorption and emission spectra? 4. Give a description of emission, adsorption and Raman spectrometers. 5. What is the local thermodynamic equilibrium state model (LTE)? 6. What kinds of optical diagnostics methods do you know? 7. Give a detailed description of the relative intensities of the spectral lines method. 8. Explain the determination of the electron temperature and density of the plasma on the basis of the spectroscopic method.

59

9. INVESTIGATION OF OPTICAL PROPERTIES OF DUSTY PLASMA IN RADIO-FREQUENCY GAS DISCHARGE The goal of the work. To investigate properties of buffer and dusty plasma in radio frequency discharge of argon and helium gases based on optical spectroscopic methods. Brief theoretical introduction At the end of the last century, the negative effects of dusty plasma in preparation of thin films in semiconductor elements production attracted attention to studying this environment. In order to prevent these negative effects, it was necessary to understand the appearance and growth of nanoparticles in plasma, their transport mechanisms and influence on the discharge properties. The laboratory dusty plasma was first observed in 1920s by Langmuir. However, intensive dusty plasma research has been carried out only in the last twenty years. As known, dusty plasma refers to the ionized gas medium, which consists of electrons, ions, neutral particles, and positively or negatively charged particles of small solid body [24-25]. Investigation of optical properties of dusty plasma allows us to obtain clear information about the parameters of the system and to give a deeper understanding of the physical processes of the system. In this work, the electron temperature of plasma is determined by the method of their absolute intensity on the basis of the analysis of plasma spectrum. Investigated dusty plasma of the radio-frequency discharge isn't in the local thermodynamic equilibrium system, it is a weak ionized ≠ , ( ≈ 10 м ). plasma at low pressure, that is In this case, a large number of neutral Ar atoms are in the ground state and the total number of electrons in the level of 2p1 decreases by the spontaneous transition 2p1-1s2, see Fig. 9.1. It should be noted that the source of self-sufficiency excitation is minimal, as well as excitation of Ar atoms is only possible by electron-atomic collisions. This condition corresponds to the "corona balance" model. 60

Figure 9.1. Atomic excitation, corona balance model

Based on this method, the electron temperature is calculated by comparing the light intensity of spectral lines of argon and helium plasma with the light intensity of the spectral lines of the tungsten lamp. The tungsten lamp is used as a model of the solar corona, hence the name the "corona balance model". The light temperature of the tungsten lamp is determined by the electronic pyrometer. The electrons temperature of the lamp is calculated as follows: = here

( )

,

(9.1)

− the light temperature, = 1,44 ∙ , = 0,5, = 6,69 ∙ 10 . The intensity of the plasma light is determined as follows: =

ℎ

∆ ∆Ω ,

(9.2)

here − a quantum number, transition probability from level to level , − the density of excited atoms, ℎ − Planck's constant, − the light speed, − a wavenumber; ∆Ω − the angle of observation, ∆ − the volume of plasma, − a calibration factor (tungsten lamp); 61

The light intensity of the tungsten lamp is: = here

( , ) ( , )∆ ∆ ∆Ω ,

(9.3)

( , ) = 0,5 − tungsten excitation coefficient, ∆k = 30 cm-1. Light spectrum density: ( , )=

.

(9.4)

By relative intensities of two spectral lines we obtain the following relation: =

[

] ( , )

∆

,

(9.5)

From this relation, we obtain the formula that defines the electron density N at the excited level: =

( , ) [

]

.

(9.6)

In the experiment, for argon at 750,38 nm and for helium at 388,86 nm spectral lines are used. The probability of transition of the argon plasma in a spectral line of 750,38 nm is 4,45·107 s-1, as well as the spontaneous transition is 2p1 → 1s2, and the probability of the helium transition in the spectral line of 388,86 nm, 9,47·106, spontaneous transition 3p → 3s1. The equation corresponding to the Corona Balance Model is written as follows: ( )= ,

(9.7)

− the neutral atoms density in here − the excitation coefficient, – the electron density, − the time of the equilibrium state, staying at level 2p1 (3p), − the density at level 2p1(3p). 62

By comparing intensities of the argon and helium spectral lines with the spectral lines of the tungsten lamp, the density of electrons at the excited level 2p1 (3p) is obtained. After plasma appearance up to 20 sec it will be in duration 1 ∙ 10 м − 4 ∙ 10 м . The relationship between the excitation coefficient and the electron temperature for argon is as follows: ( ) ≈ 2,78 ∙ 10

exp − ,

=−

,

,

(9.8)

,

(9.9)

.

So for helium: ( ) ≈ 3,97 ∙ 10 =−

exp − , ,

.

,

,

(9.10) (9.11)

Experimental setup and measuring instruments In this work, radio frequency gas discharge experimental setup is used (see Appendix C). Preparation of the experimental setup for operation The order of work for preparation of the radio frequency gas discharge experimental setup is shown in Appendix C. Measurement and analysis of the results In the experiment, argon or helium is used as a working gas. The plasma spectrum is registered from the quartz window of the gas discharge chamber. The plasma light is supplied to the spectrometer input by optical fiber. Description of the experimental setup: For optical spectral analysis, the Solar S100 linear (with a large range of measurement, 190 – 1100 nm) and SDH-1 two-dimensional (with high resolution) spectrometers are used. 63

The order of work performance Task 1: Investigation of the effect of dust particles on the light intensity of buffer plasma. 1. Use the SDH-1 spectrometer to study the effect of dust particles on the light intensity of the plasma, to which the full-fledged (inter-electrode area) image of the radio-frequency discharge is focused on the spectrometer input. 2. Connect the spectrometer to the PC, set up a special program and place it in the spectral line coverage area corresponding to the 700-800 nm wavelength. 3. Turn on the gas discharge by the order as given in Appendix C. 4. Capture the spectral lines of the plasma before and after ejecting of dust particles into a gas discharge, and then split the video files into frames as shown in Figure 24 with a software Virtual Dub.

wavelength Figure 9.2. Plasma spectrum

5. Compare the results and make a conclusion from the work. Task 2: Determination of electron temperature of buffer and dusty plasma. 1. Connect the tungsten lamp TPR3020H to the power supply (19.5A and 6.5V), determine the temperature of the wire cord by the pyrometer. Use light filters if needed. 2. Connect the linear spectrometer to the PC and run ссdtool software. 3. Adjust exposure time to the desired value by pressing the Exposure button, typically 100-1000 ms. 64

4. By pressing the background button and closing the spectrometer hole take a background spectrum, and remove these values from the values used in the calculation. It will run automatically. 5. Without changing any data in the interface of cсdtool software program, obtain the spectrum of the plasma in different parameters of the HF gas discharge by pressing the button start (gas pressure 0,1-5 torr and power 20-80 W). 6. Analyze the obtained spectral lines and determine the electron temperature of the plasma using the formulas (9.9) and (9.11) in accordance with the type of gas. 7. Make a conclusion from the work. Test questions: 1. What is dusty plasma? 2. Give a description of a Local thermodynamic equilibrium model. 3. What is the meaning of corona balance model? 4. How can be the electron temperature of the plasma be determined? 5. What is the difference of the spectral method in the study of plasma from the method of electric probe? 6. Optical properties of dusty plasma. 7. What spectrum lines of gases are used in the study of optical properties of dusty plasma in this experimental work?

65

REFERENCES 1. Methods of plasma research. Ed. V. Lochte – Holtgrevena. Moscow: Publishing house «Mir», 1971. – P. 552. 2. Raizer Yu.P. Physics of the gas discharge. Academic publication. Moscow: Publishing House: "Intellect", 2009. – P. 734. 3. Kozlov O.V. Electric probe in the plasma. – M.: Atomizdat, 1969. – P. 290. 4. Huddlestone R. and. Leonard S. Plasma diagnostics. Chapter 3. – Moscow: Publishing house «Mir», 1967. – P. 515. 5. Hansioahim Bloom. Circuit design and the use of high-power pulse devices. – M.: Dodeka-XXI, 2008. – P. 352. 6. Ramazanov T.S., Dosbolayev M.K., Dzhumabekov A.N., Petrov O.F., Antipov S.N. Experimental setup for investigation of the properties of dusty plasma structures // Vestnik KazNU, Physical Series. – 2006. – No.1,(21). – Pp. 41-49. 7. Utegenov A.U., Ussenov Y.A., Dosbolayev M.K., Ramazanov T.S., Probe diagnostics of high-frequency discharge plasma additionally perturbed by an electrostatic field // PEOS. Iss.18. – 2016. – T2. – Pp. 22-26. 8. Hutchinson I.H. Principles of Plasma Diagnostics. – 2nd ed. – Cambridge: Cambridge University Press, 2005. – P. 460. 9. Everson E.T., Pribyl P., Constantin C.G., Zylstra A., Schaeffer D., Kugland N.L., and C. Niemann Design, construction, and calibration of a three-axis, high-frequency magnetic probe ( B -dot probe) as a diagnostic for exploding plasmas // REVIEW OF SCIENTIFIC INSTRUMENTS. –2009. – Vol. 80. Pp 0-8 (113505). 10. Voronin A.V., Gusev V.K., Gerasimenko, Ya.A. and Sudienkov Yu.V., Measurement of Plasma Jet Parameters in the Process of Irradiation of Materials // TECHNICAL PHYSICS. –2013. – Vol. 58. – No. 8. Pp. 1122-1128. 11. Sharif Al-Hawat. Axial Velocity Measurement of Current Sheath in a Plasma Focus Device Using a Magnetic Probe // IEEE TRANSACTIONS ON PLASMA SCIENCE. – 2004. – Vol. 32. – No. 2. – Pp. 764-769. 12. Saw S.H., Akel M., Lee P.C.K., Ong S.T., Mohamad S.N., Ismail F.D., Nawi N.D., Devi K., Sabri R.M., Baijan A.H., Ali J., Lee S. Magnetic Probe Measurements in INTI Plasma Focus to Determine Dependence of Axial Speed with Pressure in Neon // J Fusion Energy. – 2012. – Vol. 31. – No 5. – Pp. 411-417. 13. Zhukeshov A.M. Determination of the volume of magnetic field and the flow speed in a coaxial accelerator // Vestnik KazNU. al-Farabi. Physical series. – Almaty, 2011. – No. 3 (38). – Pp. 22-26. 14. Mohanty S.R., Bhuyan H., Neog N.K., Rout R.K. and Hotta E. Development of multi Faraday cup assembly for ion beam measurements for a low energy plasma focus device // Japanese Journal of applied Physics. – 2005. – Vol. 44. – No. 7A. – Pp. 5199-5205.

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15. Tazhen A.B., Utegenov A.U., Dosbolayev M.K., Ramazanov T.S., Kaykhanov M.I., Tikhonov A.V. Investigation of parameters of pulsed plasma using a Faraday cup // PEOS. – 2016. Iss.18. – T. 2. – P. 40-44. 16. Miskinova N.A., Shvilkin B.N. Physical electronics in tasks. – M.: Publishing house "Librikom", 2013. – P. 256. 17. Dosbolayev M.K., Kasen A., Niyazymbetov A., Ramazanov T.S., Experimental investigation of the electric and energy properties of pulsed plasma accelerator IP-5 // Vestnik KazNU. Physical series. – No. 4 (51). – Almaty. – Pp. 24-29. – 2014. 18. Dosbolayev M.K., Utegenov A.U., Tazhen A.B., Ramazanov T.S., Gabdullin M.T. Dynamic properties of a pulsed plasma flow and dust formation in an IPU // News of the NAS RK. Physics and Mathematics series. – 2016. – No. 6 (310). – Pp. 59-66. 19. Tazhen A.B., Suleimenova A.Kh., Dosbolayev M.K., Ramazanov T.S. Determination of the energy density of a pulsed plasma flow using a wire calorimeter // PEOS. – 2017. – Iss. 19. – T. 2. – Pp. 5-10. 20. Zhumanov K.B., Atomic Physics. Almaty: Publishing house: "Kazakh University". – 2003. – P. 420. 21. Devia D.M., Rodriguez-Restrepo L.V. and Restrepo-Parra E. Methods Employed in Optical Emission Spectroscopy Analysis: a Review. ing. cienc. – 2015. – Vol. 11. – No. 21. – Pp. 239–267. 22. Zaydel A.N., Ostrovskaya G.V., Ostrovskiy Yu.N. Technique and Practice of spectroscopy. – M.: Nauka. – 1976. – P. 375. 23. Orazbayev S.A., Slamiya M., Dzhumagulov M.N., Kabylkhak M., Zhumabekov A.N., Dosbolayev M.K., Ramazanov T.S., Optical-spectroscopic diagnostics of dusty plasma in the high-frequency discharge // News of the NAS RK, Physics and Mathematics series. – 2011. – No. 3 (277). – Pp. 47-51. 24. Encyclopedia of Low-Temperature Plasma. Dusty plasma. V.E. Fortov. – M.: Nauka. 2000. – P. 754. 25. Dosbolayev M.K., Experimental investigation of the properties of dusty plasma as an open system // Problem of the evolution of an open system. – 2007. – Vol. 9. – T. 1. – Pp. 65-68.

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APPENDIX A PULSED PLASMA ACCELERATOR Pulsed plasma accelerators are installations for producing a high-temperature plasma flow with a velocity of 10 − 10 / . For some processes, the plasma flow can be regarded as a quasi-stationary. Compared with other accelerators, in pulsed plasma accelerators electrons and ions are accelerated simultaneously. The principle scheme of the plasma accelerator is shown in Fig. 1, which consists of the following main parts: a high voltage capacitor bank (C) for storage of the electric field energy, a gas discharge commuter (VC), a system of coaxial electrodes (CE), vacuum pumps (DP and FP), the source (HVS) and control (Con.) systems.

Figure 1. A simple scheme of a pulsed plasma accelerator The electric field energy is accumulated in parallel and in series connected pulsed capacitors; by adjusting the connection type, the total voltage and capacity can be selected. By changing the capacitance it is possible to change the time of pulsed plasma formation. Capacitors are charged with power source "HVS-3". Coaxial electrodes, made from copper material, are located inside a vacuum chamber with length 1200 mm and diameters of 200 mm (VCh.). Also, there are seven quartz windows (QW) on the vacuum chamber located on sides, including one opposite to the ES, which are required for spectroscopic diagnostics of plasma and making a video and photos of pulsed plasma flow. Vacuum commuter is used to supply the electric field energy accumulated in the capacitors to the electrodes. It consists of two basic and one start-up electrodes separated by a cylindrical insulator. The operation principle is based on the formation of the spark discharge on the start-up electrode which leads of the plasma generation on the main electrodes. To understand the mechanism of plasma acceleration in pulsed plasma acelerators, it is necessary first to know the data about the current channel in the interelectrode space, the plasma density and its velocity distribution. In this regard, there

68

are several models that describe the mechanism of plasma acceleration, including a commonly used magnetic hydrodynamic approximation model, which we will consider in two ways. At first, plasma can be considered as a one-component electroconductive system. In consequence of this, the plasma accelerates due to the total (ionic and electronic) pressure differences and the Ampere force, which appears after interaction of magnetic field with current of the plasma. This approximation is convenient for uniform, two-dimensional plasma flows, where the difference between the mobility of electrons and ions is taken as minimal. In the second case, the plasma is considered as a conducting substance, which includes charged particles (ions and electrons). Here, based on the solution of the motion equations for electrons and ions, three components of EMF can be found. – EMF associated with the gradient pe = nkT in the electron pressure. A decrease in the concentration n and temperature of electrons Te appears during the electron gas flow and plasma expansion in vacuum. – The Hall EMF of charge separation is formed as a result of interaction of the azimuthally ring current with the longitudinal component of the magnetic field. The azimuthally motion of electrons in the plasma is particularly remarkable for the Hall Effect that occurs in the magnetic and electric fields. – The Ohm EMF arises as a result of electron-ion friction (the electron wind effect). The friction of electrons with ions causes a decrease in the energy of their directional movement, appearance of the resistance accelerates ions and generates the electric field in the direction of current lines. Preparing the plasma accelerator for the experiment. Experiments are performed in a clean gas medium or in a vacuum state. For this reason, the installation chamber is equipped with a vacuum system (DP and FP) that permits us to achieve the vacuum to 10-6 torr. Since the accelerator operates at high voltage, for safety reasons control system and plasma diagnostics devices are located in the next room. All equipment is galvanically connected with the accelerator, which is achieved by using transformers. Devices for diagnostics are connected by the optical fiber. The wall that separates the rooms is preserved by an electrostatic screen. Warning! When working in the accelerator room it is necessary to deliver the accumulator charges in the capacitors to the ground, where their potential will be zero. The order of work on the accelerator. 1. Before switching the accelerator, make sure that the required detector is set inside the working chamber (J) and it is completely closed. 2. Open the water pipe system of the cooling systems. 3. Switch on the fore vacuum pump (FP). 4. When the pressure in the chamber reaches 10-2 torr (if the pressure exceeds this value, it means that the air flows from the outside into the vacuum chamber, in which case we will return to item 1 and perform it again), switch on the diffusion pump (DP). It takes about 30 minutes to reach the stable working mode of the diffusion pump. Each time you open the vacuum chamber, the air molecules fall into its inner wall, so it takes a few hours to get a relatively clean vacuum. If you do not open the vacuum chamber along the experiments, it takes 30-60 minutes to get a high vacuum.

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5. Close the valve between the vacuum chamber and the diffusion pump. 6. If we work with pure gas, we will add gas to the chamber till the required pressure. 7. Start to charge the capacitors by switching on the power source "HVS-3". 8. When the required voltage is reached, switch off the power source "HVS-3". 9. Supply the voltage to the start-up electrode of the vacuum discharge switch. In this case, the electric field energy accumulated in the capacitors transmits to the electrodes in the vacuum chamber and pulsed plasma flow appears and rapidly accelerates along the working chamber. 10. Each experiment is carried out in this order. At the end of the work, switch off the diffusion pump for 30 minutes, whereas the fore vacuum pump remains in a working condition. Then we switch off the fore vacuum pump and let air fall into it at the atmospheric pressure. Otherwise, there is a possibility of oil leak from fore vacuum pump to the outside. 11. Close-up water pipes intended for the cooling systems.

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APPENDIX B DIRECT CURRENT GLOW DISCHARGE The glow discharge forms at a definite value of the current passing through the glass tube, which is consequently filled with gas, where two metal electrodes are located on both ends and connected in the electrical circuit as shown in Fig. 2, which conand the ballast resistor б . The major mechasists of the source of high dc voltage nism of the appearance of the glow discharge in the tube is the emission of electrons (secondary emission) caused by the collision with positive ions and the appearance of volumetric electron flow. The glow discharge has a complicated structure, consisting of frequent dark and light spaces. According to Paschen’s law, a spark discharge forms corresponding to any (pressure and electrode distance) when the breakdown voltage is known (Fig. 2a), and, if the pressure is gradually decreased, the increase in the speed of the electrons causes the expansion of the discharge "channel" (Fig. 2b). Approximately at a critical pressure 5 torr the distribution of discharge light brightness will be uniform and the charged particles extend almost entirely along the volume of the tube. Moreover, near the cathode, dark light bands will appear and when the pressure is 0.1 torr, they begin to be clearly separated from each other (see Fig. 2 c,d,e).

Figure 2. The mechanisms of formation of the glow discharge. ADS – Aston dark space, CG – first cathode glow, CDS – Crookes dark space, GL – cathodic glow light, FDS – Faraday dark space, PC – positive column of the discharge, AnDS – anode dark space

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To describe the electrical properties of the glow discharge, one should separately consider the three main spaces in the discharge: the cathode region, the anode region, and the positive column of the discharge. The processes near the cathode occur as a result of strong electric field. Further from the cathode region, there is a positive column of the discharge (weak ionized non-uniform plasma), which is uniformly distributed along the length. Here, the field is relatively weak but it has high electrical conductivity. Keeping stationary discharge depends on the processes occurred in that space, so that the length of the positive column can be adjusted by increasing the distance between the electrodes and, of course, enough voltage must be supplied to the electrodes. In a classic glow discharge, the heat balance is established by the energy transmission in the volume to the tube wall (diffusion cooling). This type of cooling is only effective at low pressure, so the pressure of the glow discharge does not exceed 10 torr. The anode region is located near the anode and is characterized by negative charges that are overwhelmed by a strong field in the positive column (non-compensated charges). As we've seen, the field in this region is stronger than in the positive column, since additional weak ionization is needed to compensate the reduced ion current, so the anode brightness is formed. The voltage drop in the anode is mostly distributed several millimeters from the anode, approximately equal to the ionization potential of the gas and is much lower than the cathode voltage drop. From the physical point of view, the anode region in the glow discharge causes much less interest than the cathode region or positive columns, so we do not consider it in detail. In the positive column of the glow discharge, dark bands are observed frequently with glow bands. They are stratifications. In some cases, the stratum is motionless, in general, it is always moving, usually from anode to cathode. The formation of stratification depends on the ionization instability in the glow discharge. Their size depends on the pressure in the tube and gas composition. The principle scheme of the glow discharge installation is shown in Fig. 3 and consists of the following jointly functioning parts: gas discharge tube with electrodes inside (GDT), power supply (PS), vacuum pumps (DP and FP), electric measuring equipment (V), GI-2 gas inlet. Additionally, the figure shows the circuit used for the study of the glow discharge by the electric probe (P). (PPS) of the probe’s voltage source.

Figure 3. Principle scheme of the experimental setup for formation of the direct current glow discharge

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The voltage is supplied to the electrodes by high voltage power supply. By changing the voltage, it is possible to change the current flowing through the discharge. The main unit of the installation is the cone-shaped electrodes with diameter 2.5 cm: they are settled on the both side of the molybdenum vertical cylindrical glass tube (GDT) 5 cm in diameter, 90 cm in height. Cone shape of the electrodes enlarges the collecting surface, which in turn promotes a steady discharge. The distance between the electrodes is 60 cm. Warning! When working in a room with the experimental installation, first ground one of the electrodes and the power supply, since they can accumulate excessive charges. The order of work on the glow discharge installation: 1. Before starting work on the setup, make sure that the required detector is set inside the discharge tube (GDT) and it is completely closed. 2. Open the water pipe system of the cooling systems. 3. Switch on the fore vacuum pump. 4. When the pressure in the chamber reaches 10-2 torr, switch on the diffusion pump. It takes about 30 minutes to reach the stable working mode of the diffusion pump. Each time you open the discharge tube, the air molecules fall into its inner wall, so it takes a few hours to get a relatively clean vacuum. If you do not open the discharge tube along the experiments, it takes 30-60 minutes to get a high vacuum. 5. Close the valve between the discharge tube and the diffusion pump. 6. If we work with pure gas, we will add gas to the discharge tube for the required pressure. 7. Switch on the high voltage power source (PS) to supply the voltage to the electrodes. 8. During the experiment, the high voltage power supply is switched on. 9. A glow discharge occurs in the discharge tube at some point in the voltage supplied to the electrodes. 10. Each experiment is carried out in this order. At the end of the work, switch off the diffusion pump for 30 minutes, whereas the fore vacuum pump remains in a working condition. Then we switch off the fore pump and let the air into. Otherwise, there is a possibility of an oil leak from fore vacuum pump to the outside. 11. Close-up water pipes intended for the cooling systems.

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APPENDIX C HIGH-FREQUENCY CAPACITIVE GAS DISCHARGE High-frequency gas discharges occur in a frequency range of 105-109 Hz. In high-frequency capacitive gas discharge, high frequency voltages are mostly supplied on flat, parallel electrodes (similar to condenser), the principle scheme of this installation is shown in Figure 4.

Figure 4. Principle scheme of high-frequency capacitve gas discharge installation Electrodes can be in contact with the discharge (electrode discharges) or can be insulated (without electrode discharges). Overall, the high frequency discharge formation parameters are in the following range: frequency f = 13,56 MHz, pressure p = 10 − 100 torr (for creating an active medium excitation in high-power gas-discharge molecular lasers), p = 10 − 10 torr (in plasma technology, at the laboratory). When the gas pressure in the volume is 10-100 torr, the electron collision frequency is higher than that of the oscillating field, so the electromagnetic oscillation amplitude is less than the discharge distance (d ~ 1-10 cm). High-frequency gas-discharge plasma is low-temperature plasma, and its parameters are as follows: density ≈ 10 − 10 см , shielding Debye radius ≪ , therefore the high-frequency capacity discharge is electro neutral. High-frequency voltage supplied on flat parallel electrodes generates an oscillatory electromagnetic field and drives periodic type oscillating motions along with chaos motion caused by collision of charged particles. The equation of movement , − an impressive frequency of elechere is as follows: = − sin − trons colliding with gas atoms and molecules. The last member of the equation determines the average change in the number of electrons due to collision effect (the change in each electron collision varies between 0 − 2 ).

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When electrons accumulate energy in the electric field and have an influence on the transmission during collisions, the ionization process occurs and can generate a discharge in the high-frequency electromagnetic field. During a rapidly changing electric field, charged particles cannot follow the field changes, so the phase difference between the electric field and the velocity vector of the particle is generated. The motion of particles is slowed down by the field as their mass grows. It is known that the drift velocity and oscillation amplitude of ~10 smaller, so the oscillation of ions can be overlooked in many the ions are cases. Firstly they merged with alternating or variable field; secondly, they can produce a spatial field of charge which detects the place of discharge. The amplitude of the electron oscillation in the electromagnetic field is determined as follows: =

=

=

here

=

др

,

= 2 − angular velocity. For example, the amplitude of oscillations of the electrons in the field strength of 100 W/cm2 at gas pressure p ~ 10 torr, frequency f = 13,56 MHz is ~ 0,1 cm. It is clear from this that the amplitude of the electron oscillations in the high-frequency field is smaller than the size of the discharge space, so the processes around the discharge chamber and electrodes do not affect the discharge, and there is no need to place the electrodes in the environment where the discharge occurs (discharge without electrodes). The high-frequency capacitive discharge installation consists of three functionnal parts: a vacuum system, a power supply (high frequency generator) and a parallel electrode system. The gas discharge occurs between the electrodes (E) with diameter 100-150 mm parallel to each other at a distance of approximately 30 mm, see Figura 28. Electrodes are located inside the cylindrical vacuum chamber with a number of quartz windows (QW) on the heads and walls. The windows are needed for spectroscopic diagnostics of plasma and for plasma structure photography and video shooting. Additionally, the chamber is equipped with electrical pluggings that are used to supply voltage to the electrodes, to provide probe research, and other operations. Preparation of a high-frequency capacitive discharge installation for the experiment. Experiments are made in a clean gas medium (typically used in inert gases) or in mixtures of various gases. For this reason, the installation chamberis are equipped with a vacuum system (DP and FP) that provides the pressure level (10-6) torr. Due to the fact that the installation works with high frequency voltage, all its parts are covered with an electrostatic screen for safety. Warning! Follow the safety instructions strictly. The order of working on the high-frequency capacitive discharge installation. 1. Before starting work on the installation, make sure that the required detector is set inside the working chamber and it is completely closed. 2. Open the water pipe system for vacuum systems cooling.

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3. Switch on the fore vacuum pump. 4. When the pressure in the chamber reaches 10-2 torr, switch on the diffuseon pump. It takes about 30 minutes to reach the stable working mode of the diffusion pump. Each time you open the working chamber, the air molecules fall into its inner wall, so it takes a few hours to get a relatively clean vacuum. If you do not open the working chamber along the experiments, it takes 30-60 minutes to get a high vacuum. 5. Close the valve between the discharge tube and the diffusion pump. 6. Fill the working chamber with gas for the required pressure. 7. Swith on the high frequency generator. At this point, a gas discharge occurs between the electrodes. The discharge power is usually high, so adjust the generator power after discharge. 8. Do the planned measurements. 9. Each experiment is carried out in this order. At the end of the work, disconnect the diffusion pump from the power line for 30 minutes, whereas the fore vacuum pump remains in a working condition. Then we disconnect the fore vacuum pump and let air fall into it at the atmospheric pressure. Otherwise, there is a possibility of oil leak fore vacuum pump to the outside. 10. Close-up water pipes intended for the vacuum systems cooling.

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CONTENT Foreword ................................................................................................... 3 1. Study of voltage dividers and Wheatstone bridge ................................. 4 2. Measurement of pulsed discharge current by the Rogowski coil .................................................................... 12 3. Investigation of low temperature plasma by electric probe method ........................................................................... 18 4. Investigation of the properties of pulsed plasma by a magnetic probe ...................................................................... 30 5. Determination of energy and concentration of ions in pulsed plasma flow using a Faraday cup ............................................... 39 6. Determination of plazma energy by the calorimetric method .................................................................................. 46 7. Determination of the energy density of a pulsed plasma by wire calorimeter ..................................................... 50 8. Determination of the electron temperature in plasma using relative intensities of the spectral lines method ......................................... 55 9. Investigation of optical properties of dusty plasma in radio-frequency gas discharge ............................................................... 60 References ................................................................................................. 66 Appendix A ............................................................................................... 68 Appendix B ............................................................................................... 71 Appendix C ............................................................................................... 74

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Еducational issue

Dosbolayev Merlan Tazhen Aigerim Utegenov Almasbek

PLASMA DIAGNOSTICS (practical works) Educational-methodical manual Editor L. Strautman Typesetting U. Moldasheva Cover design Y. Gorbunov Cover design photos were used from sites www.background-2672597_960_720.com

IB No. 13598

Signed for publishing 15.05.2020. Format 60x84 1/16. Offset paper. Digital printing. Volume 13 printer’s sheet. 100 copies. Order No. 4042. Publishing house "Qazaq University" Al-Farabi Kazakh National University KazNU, 71 Al-Farabi, 050040, Almaty Printed in the printing office of the "Qazaq University" Publishing House.

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