On the Contraction of a Low-Pressure High-Frequency Discharge
Abstract Generated abstract
This paper examines constriction in low-pressure high-frequency air discharges, focusing on the radial distributions of electron concentration, effective electron temperature, and electric-field strength in a cylindrical quartz discharge chamber. Using two-probe measurements at different pressures and discharge currents, the authors compare low-pressure behavior with Schottky’s theory and analyze contraction mechanisms by analogy with models for the positive column of a glow discharge. The results indicate that at very low pressure the discharge resembles a diffusion-controlled positive column, while above about 1 mm Hg it becomes constricted. The proposed interpretation distinguishes a diffusion mechanism near 1 mm Hg from a higher-pressure mechanism in which radial gas-temperature nonuniformity enhances axial ionization and promotes formation of a narrower current-conducting cord.
Full Text
UDC 537.521.1
ON THE CONSTRICTION OF A LOW-PRESSURE HIGH-FREQUENCY DISCHARGE
V. I. Shishkovskii, A. A. Solov’ev, V. N. Sergeev
(Presented by the scientific seminar of the Faculty of Physics and Technology)
The problems of constriction of a low-pressure high-frequency discharge are considered. Results of experiments in air plasma are presented. It is shown that, depending on the pressure and the discharge current, a high-frequency discharge has different mechanisms of contraction.
Table 1, bibliography 7.
A number of experimental and theoretical studies [1–6] are known which establish that the positive column of a glow discharge at \(P > 1\) mm Hg and in certain current regimes can contract, i.e., a sharply bounded luminous cord is formed, running along the axis of the discharge chamber.
It is of interest to study the radial distribution of charged particles in high-frequency (h.f.) discharges. The distribution of these particles over the radius of a cylindrical discharge chamber can be obtained from the solution of the equation
\[ \frac{1}{r}\frac{\partial}{\partial r}\left[D_a r \frac{\partial n}{\partial r}\right] + I - R = 0, \]
where \(n\) is the concentration of charged particles, \(D_a\) is the coefficient of ambipolar diffusion, \(I\) is the ionization rate, and \(R\) is the rate of recombination and electron attachment.
Determination of \(I\) and \(R\) for h.f. air plasma is at present very difficult, while the radial distribution of plasma parameters gives answers to a number of questions of interest both scientifically and in applications. We have carried out experimental studies of the radial distribution of the electron concentration—\(n_e\), the effective electron temperature—\(T_e\), and the electric-field strength—\(E\).
Measurements by the two-probe method were carried out in a quartz discharge chamber at different pressures and discharge currents. The measurement results are presented in Table 1.
We have established that at a pressure \(P = 0.1\) mm Hg the experimental values agree well with those calculated according to Schottky’s theory [7], which once again indicates the similarity of a low-pressure h.f. discharge to the positive column of a glow discharge. At a pressure \(P > 1\) mm Hg the h.f. discharge is constricted.
We do not yet have a theory of constriction of an h.f. discharge; therefore, we shall estimate the mechanism of contraction on the basis of those models,
Table 1
Radial distribution of the electron concentration
| \(p\), mm Hg | No. | \(x=\dfrac{r}{R_0}\) | \multicolumn{3}{c}{\(l_p=170\) mm} | \multicolumn{3}{c}{\(l_p=190\) mm} | \multicolumn{3}{c}{\(l_p=210\) mm} |
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| | | | \(\dfrac{n_r}{n_0}\) | \(T_e\), eV | \(E\), \(V_{\mathrm{eff}}/\mathrm{cm}\) | \(\dfrac{n_r}{n_0}\) | \(T_e\), eV | \(E\), \(V_{\mathrm{eff}}/\mathrm{cm}\) | \(\dfrac{n_r}{n_0}\) | \(T_e\), eV | \(E\), \(V_{\mathrm{eff}}/\mathrm{cm}\) |
| \(p=1\) mm Hg | 1 | 0 | 1.00±0.08 | 10.3±0.8 | 22±2 | 1.00±0.08 | 9.9±0.7 | 20±2 | 1.00±0.08 | 9.5±0.7 | 19±2 |
| \(p=1\) mm Hg | 2 | 0.12 | 0.76±0.07 | 10.1±0.8 | 24±2 | 0.81±0.07 | 9.7±0.7 | 22±2 | 0.94±0.08 | 9.4±0.7 | 21±2 |
| \(p=1\) mm Hg | 3 | 0.24 | 0.45±0.04 | 10.2±0.8 | 21±2 | 0.5±0.05 | 10.1±0.8 | 21±2 | 0.60±0.06 | 10.1±0.8 | 20±2 |
| \(p=1\) mm Hg | 4 | 0.36 | 0.26±0.03 | 11.2±0.8 | 23±2 | 0.37±0.04 | 10.0±0.8 | 20±2 | 0.40±0.04 | 9.4±0.7 | 19±2 |
| \(p=1\) mm Hg | 5 | 0.48 | 0.24±0.02 | 10.1±0.8 | 20±2 | 0.26±0.02 | 10.0±0.8 | 20±2 | 0.32±0.03 | 9.7±0.7 | 20±2 |
| \(p=1\) mm Hg | 6 | 0.64 | 0.20±0.02 | 9.7±0.8 | 21±2 | 0.20±0.02 | 9.6±0.7 | 21±2 | 0.22±0.02 | 9.7±0.7 | 19±2 |
| \(p=1\) mm Hg | 7 | 0.80 | 0.23±0.02 | 10.0±0.8 | 23±2 | 0.30±0.04 | 9.7±0.7 | 19±2 | 0.32±0.03 | 9.8±0.8 | 19±2 |
| \(p=3\) mm Hg | 1 | 0 | 1.00±0.08 | 11.0±0.8 | 24±2 | 1.00±0.08 | 10.3±0.8 | 24±2 | 1.00±0.08 | 9.7±0.7 | 23±2 |
| \(p=3\) mm Hg | 2 | 0.12 | 0.94±0.08 | 10.7±0.8 | 25±2 | 0.73±0.07 | 10.3±0.8 | 20±2 | 0.68±0.07 | 9.5±0.7 | 18±2 |
| \(p=3\) mm Hg | 3 | 0.24 | 0.64±0.07 | 10.2±0.8 | 24±2 | 0.50±0.05 | 10.0±0.8 | 21±2 | 0.45±0.04 | 9.9±0.7 | 18±2 |
| \(p=3\) mm Hg | 4 | 0.36 | 0.38±0.04 | 10.0±0.8 | 24±2 | 0.41±0.04 | 9.8±0.7 | 21±2 | 0.42±0.04 | 9.0±0.7 | 18±2 |
| \(p=3\) mm Hg | 5 | 0.48 | 0.20±0.02 | 9.6±0.7 | 24±2 | 0.22±0.02 | 9.3±0.7 | 20±2 | 0.23±0.02 | 9.4±0.7 | 18±2 |
| \(p=3\) mm Hg | 6 | 0.64 | 0.13±0.01 | 10.0±0.8 | 22±2 | 0.13±0.01 | 9.8±0.7 | 21±2 | 0.12±0.03 | 9.5±0.7 | 18±2 |
| \(p=3\) mm Hg | 7 | 0.80 | 0.21±0.02 | 9.7±0.7 | 17±2 | 0.21±0.02 | 9.7±0.7 | 19±2 | 0.22±0.02 | 9.6±0.7 | 18±2 |
which are now known for the positive column [4–6].
As can be seen from Table 1, at \(P = 1\) mm Hg, with an increase in the discharge current, the constriction increases. At \(P = 1\) mm Hg we have a purely diffusion regime, i.e., \(T_e\) and \(E\) are constant, within the accuracy of the experimental error, over the entire cross section of the discharge chamber; \(n_{e(r)}\) changes because the electrons are lost only at the walls, and recombination in the volume may be neglected. Owing to the diffusion of electrons to the wall, the form of the electron energy distribution function evidently changes as a function of distance from the axis. With increasing distance from the axis, the number of fast electrons in the distribution decreases and, consequently, the number of ionizations and excitations falls substantially. Visually, the discharge appears as a luminous cord located along the axis of the discharge chamber. With such a mechanism of contraction, an increase in the discharge current and the associated decrease of \(T_e\) on the axis should correspond to an increase in constriction, as is observed experimentally.
On going to higher pressures, for example \(P > 3\) mm Hg, we observed a change in the mechanism of contraction, which confirmed the assumption stated earlier [6]. The nonuniformity of the gas-temperature distribution along the radius begins to play an essential role. When the discharge current passes, heating of the gas occurs nonuniformly: the gas temperature at the walls is lower than on the axis, and, correspondingly, the density is higher; therefore \(T_e\) at the walls will be somewhat lower than on the axis. This leads to ionization on the axis occurring more intensely, and \(n_e\) being higher than in the peripheral parts of the discharge chamber. This, in turn, will cause a further decrease in the density of the neutral gas; i.e., an avalanche-like process develops, as a result of which a current-conducting cord is formed whose effective diameter is smaller than the diameter of the discharge tube. In this case, recombination in the volume likewise does not play a noticeable role. Measurements of \(T_e\) showed that the value of \(T_e\) at the center is somewhat higher than all the others. Owing to electron thermal conductivity, the gradient \(T_r\) decreases and the cord increases in diameter, as is also evident from Table 1. It follows from this as well that, at an unchanged discharge current, with increasing pressure the constriction increases.
REFERENCES
- S. D. Vagner, A. I. Zubov, A. D. Khakhaev, ZhTF, 31, 336 (1951).
- V. Yu. Baranov, Yu. N. Ulyanov, ZhTF, 39, 249 (1965).
- Yu. M. Kagan, R. I. Lyagushenko, Optics and Spectroscopy, 15, 13 (1963).
- A. T. Rakhimov, F. R. Ulinich, DAN SSSR, 187, 72 (1969).
- V. Yu. Baranov, K. N. Ulyanov, ZhTF, 39, 259 (1969).
- Yu. G. Kozlov, Optics and Spectroscopy, 38, 654 (1970).
- Schottky, I. Issendorf, Phys. Zs., 25, 342, 635 (1924).