UDC 537.52

SOME ELECTROPHYSICAL CHARACTERISTICS OF A HIGH-FREQUENCY TORCH DISCHARGE

P. A. TIKHOMIROV, V. L. TEPLOUKHOV, V. A. VERNYAEV,
Vik. L. TEPLOUKHOV, A. G. KARENGIN, S. M. GOGLEV

(Presented by the scientific seminar of the Faculty of Physics and Technology)

The distribution of powers in the system consisting of a high-frequency generator and a medium-power high-frequency torch discharge at atmospheric pressure has been studied experimentally. Values of efficiency and of \(\cos \varphi\) in the discharge have been obtained. The active resistance and capacitance of the high-frequency torch discharge have been determined. The number of effective collisions of electrons with heavy particles in the channel of the high-frequency torch discharge has been calculated. It is shown that the electrophysical parameters of the torch discharge depend strongly on the magnitude of the power supplied to the discharge.
Illustrations 6, tables 4, references 5.

Recently, much attention has been devoted to the study of low-temperature plasma of gas discharges and, in particular, the plasma of a high-frequency torch discharge. A number of features of this discharge make it highly promising for various fields of chemical technology. Hence the importance of a thorough study of the peculiarities of the behavior of this discharge, its characteristics and properties, and the processes determining its occurrence and stable existence becomes clear. The present work is devoted to clarifying certain experimental characteristics and physical properties of a high-frequency torch discharge.

Fig. 1. Schematic of the experimental setup.
1 — high-frequency generator LGD-12; 2 — Rogowski belt; 3 — electrode; 4 — plasmatron; 5 — cathode voltmeter of the “Orion” type; 6 — DNE-6 voltage divider; 7 — cathode voltmeter of the “Orion” type; 8 — temperature sensor; 9 — water-flow sensor.

The literature available on this question, as a rule, covers studies carried out with a low-power high-frequency torch discharge [1, 2]. In this case the thermal power of the discharge ranged from several tens to one or two hundred watts, and the geometrical length of the torch was on the order of several centimeters [1, 2, 3]. However, industrial applications require discharges of considerably higher powers. In this connection, our interest in studying discharges of increased power, from 1 to several tens of kilowatts, is understandable.

The schematic of the experimental setup for carrying out the investigations is shown in Fig. 1. As the source of high-frequency energy, an industrial high-frequency generator LGD-12 (1) was used, with an oscillatory power of 12 kW and an operating frequency of 20–25 MHz. The high-frequency torch discharge was excited in a copper plasmatron with water cooling of the walls. In the experiment, the amount of energy released in the plasmatron and at the anode of the generator tube was measured. The voltage on the electrode was measured using an “Orion” cathode voltmeter connected through a standard DNE-6 voltage divider. The current in the discharge was measured using a high-frequency current transformer. The voltage at the anode of the generator tube was measured with a type S-96 electrostatic voltmeter. The results obtained are presented in Table 1.

Table 1

The measurement results make it possible to calculate important energy and electrophysical characteristics of the discharge and to trace their change with changing discharge power. Using a number of known formulas, we can estimate the thermal power \(P_T = Q \cdot c \cdot \Delta_\tau\) released in the discharge; the total power

\[ P_\phi = \frac{I_{\sim} U_{\sim}}{2}, \]

supplied to the discharge; and also the oscillatory power of the h.f. generator \(P_k = P_v - P_A\). Here \(P_v\) is the power of the rectifier of the high-frequency generator, and \(P_A\) is the power of losses at the anode. The calculation results are presented in Table 2.

Table 2

on the basis of which curves have been constructed showing the change in the distribution of powers with increasing generator load (Fig. 2). The shaded part in the graph shows the magnitude of the oscillatory power.

Fig. 2. Power distribution in the high-frequency generator—discharge system. \(P_{\mathrm{t}}\) is the thermal power in the discharge; \(P_{\mathrm{v}}\) is the rectifier power; \(P_{\mathrm{a}}\) is the power of losses at the tube anode.

Figure 3 presents the current-voltage characteristic of the high-frequency torch discharge. Using known formulas, the values of the efficiency \(\eta\) and \(\cos\varphi\) of the discharge power coefficient were calculated. The results are presented in Table 2 and in Fig. 4.

Fig. 3. Current-voltage characteristic of the high-frequency torch discharge.

Fig. 4. Dependence of the discharge power coefficient and generator efficiency on the power released in the discharge.

Of interest is the calculation of the active and reactive resistances in the load of the torch discharge. It is known that the thermal power released in the discharge can be represented in the form

\[ P_{\mathrm{t}} = \frac{1}{2} \cdot I_{\sim}^{2} \cdot r_{\mathrm{f}}, \tag{1} \]

where \(I_{\sim}\) is the value of the discharge current.

Hence the magnitude of the active resistance is

\[ r_{\mathrm{f}} = \frac{2P_{\mathrm{t}}}{I_{\sim}^{2}} . \tag{2} \]

and the value of the reactance

\[ X=\frac{1}{\omega C}=r_{\phi}\cdot \operatorname{tg}\varphi =\frac{2P_{\mathrm{T}}\sqrt{1-\cos^{2}\varphi}}{I_{\sim}^{2}\cdot \cos\varphi}. \tag{3} \]

The capacitance of the torch discharge is equal to

\[ C_{\phi}=\frac{I_{\sim}^{2}\cdot \cos\varphi} {2\cdot \omega \cdot P_{\mathrm{T}}\sqrt{1-\cos^{2}\varphi}} . \tag{4} \]

The results of the calculation are presented in Table 3 and in the graph of Fig. 5. The maximum value of the active resistance \(r_{\phi}\) coincides with the maxi-

Table 3

mum of the efficiency \(\eta\): at the maximum value of the capacitance \(C_{\phi}\), a maximum of the discharge power factor is observed. It is known that the resistance of the channel of a torch discharge can be written as

\[ r_{\phi}=\frac{l}{\gamma\cdot S}, \tag{5} \]

where \(\gamma\) is the specific conductivity of the plasma, averaged over the volume. On the other hand, if the channel of the torch discharge is considered as a solitary conductor, then the capacitance of such a conductor is written as

\[ C_{\phi}=\varepsilon\cdot l. \tag{6} \]

Fig. 5. Dependence of the capacitance and active resistance of the discharge on the released power.

If the usual expressions for \(\varepsilon\) and \(\gamma\) of the plasma are written down [5]:

\[ \varepsilon=1-\kappa_{\varepsilon}\cdot \frac{\omega_{Le}^{2}}{\left(\omega^{2}+\nu_{\mathrm{eff}}^{2}\right)}, \tag{7} \]

\[ \gamma=\kappa_{\delta}\cdot \frac{\omega_{Le}^{2}\cdot \nu_{\mathrm{eff}}} {\left(\omega^{2}+\nu_{\mathrm{eff}}^{2}\right)\cdot 4\pi}, \tag{8} \]

(\(\kappa_\varepsilon\) and \(\kappa_\sigma\) are factors whose numerical values are known) and substituting them into expressions (5) and (6), we obtain:

\[ C_{\phi}=(\varepsilon-1)\cdot l=-\kappa_\varepsilon \frac{\omega^{2}L_e\cdot l}{(\omega^{2}+\nu_{\mathrm{eff}}^{2})}, \tag{9} \]

\[ \frac{1}{r_{\phi}}=\gamma\frac{S}{l}=\kappa_\sigma \frac{\omega^{2}L_e\cdot \nu_{\mathrm{eff}}\cdot S} {(\omega^{2}+\nu_{\mathrm{eff}}^{2})\cdot 4\pi\cdot l}. \tag{10} \]

Combining expressions (9) and (10), we obtain

\[ C_{\phi}\cdot r_{\phi} = \frac{\kappa_\varepsilon\cdot 16\cdot l^{2}} {\kappa_\sigma\cdot d^{2}\cdot \nu_{\mathrm{eff}}} \]

or

\[ \nu_{\mathrm{eff}}= 16\frac{\kappa_\varepsilon\cdot l^{2}} {\kappa_\sigma\cdot d^{2}\cdot C_{\phi}\cdot r_{\phi}}, \tag{11} \]

This expression makes it possible to calculate the effective collision frequency of electrons with heavy particles. In our case \(\nu_{\mathrm{eff}}^{2}\gg \omega^{2}\), and, following [5], \(\kappa_\varepsilon=1.51\) and \(\kappa_\sigma=1.13\). The results of the calculation are presented in Table 4 and in the graph of Fig. 6.

Table 4

In the calculation it was assumed that the diameter of the torch-discharge channel remains approximately constant.

The inflection points present in the curves of Fig. 6 apparently arise because, in the real case, the thickness of the torch-discharge channel does not remain constant. On segment AB of the curves, the comparatively small increase in \(\nu_{\mathrm{eff}}\) is explained by the fact that, in this interval, the volume of the torch increases rapidly owing to the sharp increase in the torch length: when the power changes by 140 W, the torch length increases by 12 cm. For comparison, note that on segment CD, when the power increases by 110 W, the torch length increases by only 5–6 cm. On segment BC there is a significant increase in the torch diameter with a small increase in length. On segment CD

the growth of the geometrical dimensions of the torch slows down, while an accelerated increase in the temperature in it occurs. According to the work of the authors [1], measurements of \(r_{\phi}\) and \(C_{\phi}\) carried out for a torch discharge of low power (\(\sim 70\) W) gave the values \(r_{\phi}=10000\ \Omega\) and \(C_{\phi}=1\) pF. Comparing the values obtained by us (for example, at a power of 700 W, \(r_{\phi}=1060\ \Omega\), \(C_{\phi}=11\) pF), we see that the physical parameters of the high-frequency torch discharge depend to a considerable degree on the power supplied to the discharge.

Fig. 6. Dependence of the effective collision frequency on the discharge power

It is also interesting to note that the product \(C_{\phi}r_{\phi}\) in both cases has, in order of magnitude, an equal value:

\[ C_{\phi}r_{\phi}=10^{4}\cdot 10^{-12}\approx 10^{3}\cdot 10^{-11}\approx 10^{-8}. \]

It is known that \(C_{\phi}r_{\phi}=\tau\), where \(\tau\) is the time constant of the circuit, which determines the periodicity of the processes occurring in it.

In our case \(\tau\approx 10^{-8}\) corresponds to the frequency of the high-frequency power feeding the discharge. Similar estimates carried out for a high-frequency torch discharge excited by industrial generators of the LD1-4, LD4-10, and LD1-40 types show that the relation

\[ C_{\phi}r_{\phi}\approx \frac{1}{f} \]

is satisfied within the measurement error in all these cases.

REFERENCES

1. A. A. Kuzovnikov. Scientific Reports of Higher Educational Institutions. Physics and Mathematics, 1958, No. 4, 191.
2. J. Kristek, R. Grigorovich, Optics and Spectroscopy, 1959, No. 6, issue 2, 129.
3. A. V. Kachanov, E. S. Trekhov, E. P. Fetisov. In: Physics of Gas-Discharge Plasma, 1968, issue 1.
4. B. M. Betin. Radio Transmitting Devices. Moscow, Vysshaya Shkola, 1972.
5. V. L. Ginzburg. Propagation of Electromagnetic Waves in Plasma. Moscow, Nauka, 1967.