Table Of ContentAL-FARABI KAZAKH NATIONAL UNIVERSITY
M. Dosbolayev
A. Tazhen
A. Utegenov
PLASMA DIAGNOSTICS
(practical works)
Educational-methodical manual
Almaty
«Qazaq University»
2020
1
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
Dosbolayev M.
D 75 Plasma diagnostics (practical works): educational-metho-
dical manual / M. Dosbolayev, A. Tazhen, A. Utegenov. – Al-
maty: 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
ISBN 978-601-04-4590-1 © Dosbolayev M., Tazhen A.,
Utegenov A., 2020
© Al-Farabi KazNU, 2020
2
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 se-
lected topics on the basic methods for studying the plasma medium.
Practical works include the following important topics of plasma re-
search: 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 calorime-
ters, studying the parameters of a low-temperature plasma by the
method of an electric probe (temperature and density of plasma char-
ges, 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, de-
termination of energy and spatial distribution of charges using Fara-
day cup.
The main goal of this educational-methodical manual for the Fa-
culty of Physics and Technology students is to help in deepening the-
oretical knowledge gained in studying gas discharges and plasma
physics based on specific experiments.
Each work consists of a brief theoretical introduction, a brief tech-
nical description of the instruments and installations, the procedure
for performing the work, questions for self-control, and a list of refe-
rences necessary to obtain additional information.
3
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 experi-
ments 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: os-
cilloscopes, amplitude voltmeters, and analog-to-digital converters.
To register a DC or slowly varying voltage, resistive dividers (Figu-
re 1.1) with a nominal conversion factor of less than one are used:
(cid:1863) = (cid:3022)(cid:3290)(cid:3296)(cid:3295) = (cid:3019)(cid:3118) . (1.1)
(cid:3005)
(cid:3022)(cid:3284)(cid:3289) (cid:3019)(cid:3117)(cid:2878)(cid:3019)(cid:3118)
Figure 1.1. Ohmic voltage divider 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 as-
sume that the input resistance of the device (cid:1844) , to which the voltage
(cid:3036)(cid:3041)
(cid:1847) reduced by the divider is supplied, with almost infinite value
(cid:3042)(cid:3048)(cid:3047)
4
compared to the reactance (cid:1829) , then we can say that the same charges
(cid:2870)
pass through each half period through (cid:1829) and (cid:1829) . In this case it turns
(cid:2869) (cid:2870)
out that
(cid:1847) (cid:1829) = ((cid:1847) −(cid:1847) )(cid:1829) ,
(cid:3042)(cid:3048)(cid:3047) (cid:2870) (cid:3036)(cid:3041) (cid:3042)(cid:3048)(cid:3047) (cid:2869)
where we get:
(cid:1863) = (cid:3022)(cid:3290)(cid:3296)(cid:3295) = (cid:3004)(cid:3117) . (1.2)
(cid:3005)
(cid:3022)(cid:3284)(cid:3289) (cid:3004)(cid:3117)(cid:2878)(cid:3004)(cid:3118)
Both expressions are correct for a purely theoretical situation where
the branches of the divider can be represented as ideal resistors or capa-
citors. In real conditions, the resistors of the upper branch must pro-
vide 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 cal-
culation of the divider, then the input capacitance and the capacitan-
ce of the line will introduce frequency dependence in the division ra-
tio 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 para-
sitic capacitances by reducing the (cid:1844) value, thereby reducing the out-
(cid:2870)
put resistance of the divider, but this will reduce the level of the use-
ful 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 capaci-
tor enters the circuit of the upper arm of the divider. This can occur,
for example, when measuring a high-voltage pulse with a high-impe-
dance voltage divider placed near the massive part of the pulse gene-
rator (Figure 1.4). Capacitive guidance from a high-voltage pulse
source to a divider through parasitic capacitances (cid:1829) will be equiva-
(cid:3043)
lent 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 or-
der for (cid:1847) not to depend on the frequency, it is necessary to con-
(cid:3042)(cid:3048)(cid:3047)
nect the capacitor (cid:1829) parallel to the resistor (cid:1844) , guided by the formula
(cid:2869) (cid:2869)
(cid:1844) (cid:1829) = (cid:1844) (cid:1829) . That is, a low-impedance capacitive voltage divider
(cid:2869) (cid:2869) (cid:2870) (cid:2870)
with the same division factor is connected in parallel with the re-
6
sistive high-resistance divider. The capacitance values are calculated
in inverse proportion, since the capacitance resistance is inversely
(cid:2869)
proportional to the capacitance, (cid:1850) = .
(cid:3004)
(cid:3037)(cid:3104)(cid:3004)
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:
(cid:3117)
(cid:1863) = (cid:3022)(cid:3290)(cid:3296)(cid:3295) = (cid:3019)(cid:3118) = (cid:3285)(cid:3352)(cid:3252)(cid:3118) = (cid:3004)(cid:3117) . (1.3)
(cid:3005) (cid:3022)(cid:3284)(cid:3289) (cid:3019)(cid:3117)(cid:2878)(cid:3019)(cid:3118) (cid:3117) (cid:2878) (cid:3117) (cid:3004)(cid:3117)(cid:2878)(cid:3004)(cid:3118)
(cid:3285)(cid:3352)(cid:3252)(cid:3117) (cid:3285)(cid:3352)(cid:3252)(cid:3118)
The resistive part of the divider is responsible for the division ra-
tio in the direct current and in the low-frequency region to the limiting
(cid:2869)
frequency (cid:2033) = , where τ is the time constant of the divider arm.
(cid:3039)
(cid:3099)
From formula 1.3 it follows that the time constant is the same for the
upper and lower shoulders. At frequencies (cid:2033) > (cid:2033) , the capacitive
(cid:3039)
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 up-
per arm. The magnitudes of the compensating capacitances are cho-
sen 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 im-
pedances (cid:1852) −(cid:1852) . Also there is the load (cid:1852) in the output diagonal.
(cid:2869) (cid:2872) (cid:2868)
7
Figure1.6. Wheatstone bridge diagram
The equilibrium of the bridge occurs at (cid:1835) = 0, i.e. at
(cid:2868)
(cid:1852) (cid:1852) = (cid:1852) (cid:1852) . (1.4)
(cid:2869) (cid:2872) (cid:2870) (cid:2871)
In the expanded form, the expression of the impedance of branches
is:
(cid:1852) = (cid:1844) +(cid:1862)(cid:1850) ; (cid:1852) = (cid:1844) +(cid:1862)(cid:1850) ; (cid:1852) = (cid:1844) +(cid:1862)(cid:1850) ;
(cid:2869) (cid:2869) (cid:2869) (cid:2870) (cid:2870) (cid:2870) (cid:2871) (cid:2871) (cid:2871)
(cid:1852) = (cid:1844) +(cid:1862)(cid:1850) . (1.5)
(cid:2871) (cid:2871) (cid:2871)
Substituting (1.5) into expression (1.4) we get:
(cid:1844) (cid:1844) −(cid:1850) (cid:1850) = (cid:1844) (cid:1844) −(cid:1850) (cid:1850)
(cid:3420) (cid:2869) (cid:2872) (cid:2869) (cid:2872) (cid:2870) (cid:2871) (cid:2870) (cid:2871) (1.6)
(cid:1844) (cid:1850) +(cid:1844) (cid:1850) = (cid:1844) (cid:1850) +(cid:1844) (cid:1850)
(cid:2869) (cid:2872) (cid:2872) (cid:2869) (cid:2870) (cid:2871) (cid:2871) (cid:2870)
The scheme of the DC bridge does not differ from the conside-
red scheme. The branches of the bridge have active resistances
(cid:1844) − (cid:1844) , and a galvanometer in the output diagonal. Let us consider
(cid:2869) (cid:2872)
the example of this bridge DC output equilibrium equation, omitted
in the previous case. If the bridge is balanced (cid:1835) = 0, i.e.:
(cid:2868)
(cid:1835) = (cid:1835) ,(cid:1835) = (cid:1835) (cid:1844) (cid:1835) = (cid:1844) (cid:1835) ,(cid:1844) (cid:1835) = (cid:1844) (cid:1835) . (1.7)
(cid:2869) (cid:2870) (cid:2871) (cid:2872) (cid:2869) (cid:2869) (cid:2871) (cid:2871) (cid:2870) (cid:2870) (cid:2872) (cid:2872)
Dividing one equation by another term by term, we get:
(cid:3019)(cid:3117) = (cid:3019)(cid:3119) or (cid:1844) (cid:1844) = (cid:1844) (cid:1844) . (1.8)
(cid:2869) (cid:2872) (cid:2870) (cid:2871)
(cid:3019)(cid:3118) (cid:3019)(cid:3120)
8
If by (cid:1844) we mean an object with unknown resistance (cid:1844) , then we get
(cid:2869) (cid:3051)
(cid:1844) = (cid:3019)(cid:3118)(cid:3019)(cid:3119). (1.9)
(cid:3051)
(cid:3019)(cid:3120)
This expression is called the equilibrium equation of a single DC
bridge. Here (cid:1844) and (cid:1844) are the relationship shoulders, and (cid:1844) is the
(cid:2872) (cid:2870) (cid:2871)
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 (cid:1844) and (cid:1829)
(cid:2872) (cid:2872)
for voltage dividers.
Table 1.1
Baseline data for the experiment on the study of the attenuator
№. Uin, Uout, R1, №. Uin, Uout, R1, №. Uin, Uout, R1,
V V k V V k V V k
1 20 6 5 8 27 4 10 15 40 30 2
2 25 15 14 9 25 10 7 16 37 14 6
3 40 25 2 10 30 8 4 17 39 10 3
4 32 20 4 11 38 30 13 18 29 4 8
5 35 15 5 12 22 13 12 19 25 15 15
6 21 5 7 13 26 12 10 20 40 25 2
7 30 25 8 14 24 20 5 21 38 20 1
Note: for all options R2 = 2 k, R3 = 4 k.
Figure1.7. Schemes for the study of the voltage dividers
9
Table 1.2
The source data for the experiment on the study of capacitive voltage divider
№. Uin, Uout, С1, №. Uin, Uout, С1, №. Uin, Uout, С1,
V V F V V F V V F
1 20 6 5 8 27 4 10 15 40 30 2
2 25 15 14 9 25 10 7 16 37 14 6
3 40 25 2 10 30 8 4 17 39 10 3
4 32 20 4 11 38 30 13 18 29 4 8
5 35 15 5 12 22 13 12 19 25 15 15
6 21 5 7 13 26 12 10 20 40 25 2
7 30 25 8 14 24 20 5 21 38 20 1
Note: for all options С2 = 2 F, С3 = 4 F.
Verify the calculated data by the experiment.
Assemble the electrical circuit according to Figure 1.8. Check
the assembly with the teacher!
Figure1.8. Diagram of the bridge under study
The baseline data for various options are provided in Table 1.3.
Determine the resistance of R for a balanced bridge.
4
Table 1.3
Baseline data for the Wheatstone bridge experiment
№. R3, R2, R1, №. R3, R2, R1, №. R3, R2, R1,
k k k k k k k k k
1 2 3 4 5 6 7 8 9 10 11 12
1 2 6 5 8 7 14 13 15 7 7 5
10
