PROCEEDINGS
OF THE TOMSK ORDER OF THE OCTOBER REVOLUTION AND ORDER OF THE RED BANNER OF LABOR
POLYTECHNIC INSTITUTE named after S. M. KIROV

Vol. 293 1977

UDC 537.52

SOME FEATURES OF THE PRACTICAL APPLICATION OF PLASMA OF HIGH-FREQUENCY TORCH DISCHARGES

I. A. TIKHOMIROV, V. V. TIKHOMIROV, V. Ya. FEDYANIN, A. A. SOLOV'EV,
V. N. SERGEEV, V. I. SHISHKOVSKII

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

The implementation of modern high-productivity processes in gas-discharge plasma, and especially in the plasma of high-frequency (h.f.) discharges, requires a detailed study of the principal physical parameters of the latter, with the aim of taking them into account in designing plasma-chemical apparatus and developing technological processes.

We have investigated, in particular, a torch discharge, which, while possessing all the advantages of high-frequency discharges, is at the same time free of such shortcomings of the induction discharge as the impossibility of using the latter in fully metallic structures.

The h.f. torch discharge was obtained in 1928 by Zilitinkevich. Work on studying the physics and kinetics of the processes occurring in the presence of this type of discharge, with the aim of using it effectively for solving a number of applied problems, began to be carried out only recently.

The h.f. torch discharge exists over a wide interval of frequencies of the feeding h.f. field and over a wide range of pressures. The main external features that distinguish it from other types of discharges are that at \(P > 250\) mm Hg the discharge consists of a near-electrode spot, a thin channel, and a diffuse sheath. The field lines are not closed, and therefore the discharge can be excited from a single electrode.

Ionization processes predominate in the gas volume, while secondary processes at the electrodes and on the walls of the discharge chamber are less important. A change in the velocity of axial blowing up to certain values does not affect the gas temperature in the discharge channel, but does affect the gas temperature in the sheath. This fact makes it possible, at certain flow rates of the plasma-forming gas, to form plasma flows with a uniform radial distribution of gas temperature and electron density.

The temperature of the torch discharge depends to a significant degree on the nature of the plasma-forming gas. Data on the temperature of the h.f. torch discharge at atmospheric pressure are presented in Table 1.

At pressures \(P > 250\) mm Hg, the gas temperature of the h.f. torch discharge depends only weakly on the pressure and on the power supplied to the discharge. The electron temperature in the discharge channel in practically all cases exceeds the gas temperature by an order of magnitude or more. The electron concentration also depends on the nature of the plasma-forming gas and ranges from \(10^{11}\) to \(10^{15}\ \mathrm{cm}^{-3}\).

The equivalent electrical circuit of an RF torch discharge at high powers supplied to the discharge can be represented as a line with distributed parameters. Such an equivalent circuit makes it possible to calculate the effective electrical parameters of the discharge: resistance, capacitance, and inductance. These discharge parameters at \(f = 40\) MHz are presented in Table 2.

Table 1

The studies we carried out [2] showed that, in designing RF plasmatrons, it is necessary to take into account the intrinsic electrical parameters of the discharge. There exist several models of the torch discharge; of greatest interest among them, in our view, is the electrodynamic model of the discharge proposed by A. V. Kachanov and G. S. Trekhov [3]. According to it, the discharge channel is a column of plasma with an electromagnetic wave propagating along it. The power released in this process in the form of ohmic losses is dissipated through radial thermal conductivity.

Existing theoretical models at present do not describe the observed experimental facts sufficiently completely; there even exist certain contradictions between theoretical and experimental data. In addition, the process of formation of the torch-discharge channel, which is interesting from the theoretical point of view, remains unexplained. Therefore theoretical experimental work cannot be regarded as completed, and further investigations in this field are necessary.

Table 2

A considerable increase in the effectiveness of the application of RF plasma for technological purposes can be achieved by using a modulated RF discharge.

The production of modulated plasma is accomplished by amplitude modulation (AM) of the field feeding the discharge. If the RF field supplied to the plasma of the torch discharge is amplitude-modulated with modulation frequency \(\Omega \ll \omega\), where \(\omega\) is the frequency of the RF field, then the wave amplitude at the plasma boundary near the electrode can be written as

\[ E = E_0(1 + m \cos \Omega t)\cos \omega t, \tag{1} \]

where \(\Omega\) is the modulation frequency;
\(\omega\) is the carrier frequency;
\(m\) is the modulation-depth coefficient.

For the case when the modulation coefficient is small \((m \geq 0.4)\), distortion of the modulation depth in the discharge channel may be neglected, although the latter will occur as a result of the self-action of the wave. Proceeding from this, for approximate estimates it may be assumed that the field in the discharge channel varies harmonically according to equation (1). In accord—

In accordance with the law of variation of the field, the energy spectrum of the electrons changes. This makes AM plasma, in a number of cases, even more nonequilibrium than plasma in h.f. discharges without modulation.

The indicated fact can be used to carry out reactions with high threshold energies, initiated by electrons, and to achieve a general intensification of chemical processes occurring in the plasma. The rate of processes initiated by electrons, as is known [4], is proportional to the total concentration of excited particles with the excitation level that determines the process.

The studies we have carried out have made it possible to establish that in amplitude-modulated plasma, at one and the same discharge power but at different modulation depths, together with an increase in \(T_e\) and an enhancement of its nonequilibrium, the rates of chemical processes increase noticeably, with an increase in product yield and an improvement in its quality. Let us also note one more very important property of high-frequency AM plasma. At pressures of \(100\) mm Hg and higher, AM plasma becomes a source of acoustic fields [5] (sound or ultrasonic, depending on the modulation frequency), whose power may reach up to \(2\%\) of the total discharge power.

The modulators [6] developed by us for h.f. generators of various types produced by our industry make it possible to obtain AM plasma with a modulation frequency of \(50\)—\(10^5\) Hz and an adjustable modulation depth from \(0\) to \(1.0\), with a carrier field frequency from \(10\) to \(70\) MHz.

It is of interest to dwell on the features of the electron energy distribution function in a h.f. torch discharge.

Nonequilibrium plasma is a single system of interacting components (atoms, ions, electrons, etc.), and the departure from equilibrium of one of the components in practice leads to an analogous effect for the others. In accordance with this, a complete mathematical description of nonequilibrium plasma reduces to a system of equations determining the distribution of atoms, molecules, and electrons over energies.

The first attempt to estimate the electron energy distribution in the channel of a torch discharge burning in molecular gases was made in the work of Ecker and Kessler [8], who used the results of Margenau [9]. In doing so, only inelastic collisions were taken into account, leading to an almost complete loss of electron energy. But, as is known, in molecular gases such as \(N_2\), \(O_2\), or \(H_2\), even electrons possessing energies of fractions of an electronvolt can readily excite rotational levels of molecules (\(\sim 10^{-3}\) eV). In this case it may turn out that collisions with excitation of rotational levels of molecules will be decisive for the electron distribution function. As experimental results [10] and theoretical calculations [11] show, in the plasma of an h.f. torch channel only those electron collisions are significant in which the latter, on average, lose only a small fraction of their initial energy. We considered the solution of the gas-kinetic Boltzmann equation under the plasma conditions of a torch discharge. It was assumed that the velocity distribution of ions and molecules is Maxwellian. The influence of the space charge on the electron energy distribution function was considered negligibly small. All collisions with a small relative fraction of transferred energy were taken into account with the aid of the generalized parameter

\[ \delta(v)\equiv \frac{ \sum \frac{2m\nu_m}{M-m} + \sum \frac{\Delta E}{mv^2}\frac{\Delta E}{kT_g}\nu_1 }{ \sum \nu_m }, \tag{2} \]

where \(\nu_m\) is the collision frequency for momentum transfer;

\(\nu_1\) is the frequency of inelastic collisions of the first kind.

In expression (2) summation over all scattering components and over all transitions is assumed. The expression we obtained for the symmetric part of the distribution function can be represented in the following form:

\[ f_0 = c \exp - \int_0^v \frac{m v\,dv} {kT + \dfrac{2e^2E^2}{3m\delta(v)(\omega^2+\nu^2)}} , \tag{3} \]

where the constant \(c\) is found from the normalization condition

\[ n_e = \int_0^\infty f(\varepsilon)\,d\varepsilon . \tag{4} \]

Figure 1 shows the electron energy distribution function (curve 2), obtained by us for a discharge channel in air at \(T_2 \sim 4\cdot 10^3\,^\circ\mathrm{K}\), \(P \sim 760\) mm Hg, \(|E| \sim 300\) V/cm. For comparison, the Maxwellian distribution function for \(T = 4\cdot 10^3\,^\circ\mathrm{K}\) (curve 1) and the Margenau distribution function (curve 3) are also plotted here.

The studies carried out on the diagnostics and physics of h.f. discharges enabled us to create a number of torch-type plasmatrons [1, 6, 7]. All plasmatrons in metal construction possess chemical and mechanical durability, a long service life under continuous operation (hundreds of hours), and a fairly high efficiency (over 50–60%). The long-term tests of the plasmatrons that were carried out showed that they satisfy technological requirements and can be recommended for industrial introduction.

Fig. 1. Electron energy distribution function by energies

The problems of studying chemical reactions carried out in plasma and plasma jets require, first of all, knowledge of the basic parameters of the plasma being used—“effective” temperatures and concentrations of the various particles and their spatiotemporal distribution. The methods for determining these parameters used in the study of “pure” plasma can also be applied to the study of plasma with reagents of some chemical reaction introduced into it.

These considerations served as the basis for the creation of research plasmatrons, one of which is presented in Fig. 2. In such a plasmatron, when carrying out plasmochemical reactions, it is possible to determine all the basic parameters of the plasma of an h.f. discharge: the gas temperature \(T_2\), the mean electron energy \(T_e\), the electron concentration \(n_e\), the effective collision frequency of electrons with heavy particles—\(\nu_{\mathrm{eff}}\), and the electron velocity distribution function.

As is known, optimization of plasmochemical processes is possible only when detailed information about the discharge is available. In principle, a research plasmatron can be made both in the form of a stra-

Fig. 2. High-frequency torch plasmatron for studies of plasma technological processes

both in the form of a high-frequency torch plasmatron and in the form of a suspended-layer plasmatron. The design features of such a plasmatron include vacuum-tight dielectric windows-lenses 11, intended for measurements by microwave methods; a fitting 7 with windows made of \(LiF\) for conducting spectral studies; chambers for placing a solid-phase sample 3; and chambers for gas-dynamic formation of a plasma layer of constant geometry. In the plasmatron a water-cooled electrode 2 of original design is used, combined with a device for admitting the plasma-forming gas.

To power such a plasmatron, high-frequency generators with a power of \(2—12\) kW and an operating frequency of \(5—60\) MHz are used. The efficiency of gas heating in the plasmatron is \(40—65\%\) at pressures in the range \(0.001—1\) atm and plasma-forming-gas flow rates of \(0.1—100\) l/min.

The generated plasma flows, with electron concentration \(10^{11}—10^{17}\ \mathrm{ohm}^{-3}\) and electron temperature \(1000—200000^\circ\mathrm{K}\), have a gas temperature on the order of \(1000—5000^\circ\mathrm{K}\).

Simultaneous measurement of a set of plasma-physical parameters together with electrical measurements makes it possible to obtain information on the mechanisms and direction of plasma-chemical processes.

Thus, the studies we have carried out have shown the great promise of using a high-frequency torch discharge in plasma-chemical technology. Plasmatrons based on this type of discharge are durable, simple to manufacture and operate, economical, have high efficiency, and possess a number of other advantages.

REFERENCES

1. I. A. Tikhomirov, V. V. Tikhomirov, V. Ya. Fetianin. Izvestiya TPI, vol. 225, 1972.

2. I. A. Tikhomirov, V. V. Tikhomirov, V. S. Levashov. Izvestiya TPI, vol. 276, in press.

3. A. V. Kachanov, E. S. Trekhov, E. P. Fetisov. In: Physics of Gas-Discharge Plasma, issue 1. Moscow, Atomizdat, 1968.

4. Essays on the Physics of Low-Temperature Plasma, ed. L. S. Polak. Moscow, “Nauka,” 1971.

5. I. A. Tikhomirov, V. V. Tikhomirov, V. N. Sergeev. In: Questions of the Methods and Technique of Ultrasonic Spectroscopy. Kaunas, 1973.

6. V. V. Marusin, I. A. Tikhomirov. In: Generators of Low-Temperature Plasma. Moscow, “Energiya,” 1969.

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8. U. Jecht, W. Kessler. Phys. Rev., 178, 133 (1964).

9. H. Margenau. Phys. Rev., 73, 297 (1948).

10. R. Grigorovich, D. Kristecki. Optics and Spectroscopy, 6, 129 (1959).

11. I. Janca. Phys. Letters, A25, 165 (1967).