UDC 537.52

DETERMINATION OF PARAMETERS OF AIR HIGH-FREQUENCY PLASMA BY MICROWAVE METHODS

I. A. Tikhomirov, V. V. Tikhomirov, A. A. Solov'ev, V. I. Shishkovskii,
V. N. Sergeev

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

Experimental results are presented for determining certain parameters of the plasma of h.f. discharges. Conditions have been found under which microwave methods give unambiguous measurement results. Satisfactory agreement between microwave and probe measurements has been obtained. Tables 2, references 6.

Low-temperature plasma of gas discharges is currently finding wide application in various fields of science and technology. At the same time, increasing attention is beginning to be attracted by the plasma of h.f. discharges, which is due to the high efficiency of these discharges, the particular purity of their gas-discharge space, and the simplicity of control and regulation of the plasma flows generated in them. Data on the physics and diagnostics of plasma make it possible to solve some problems of plasma chemistry and high-temperature technology with the greatest efficiency. The most suitable for diagnosing a high-frequency torch discharge (HFTD) are microwave diagnostic methods [1], namely the free-space method, in which the directly measured quantities are the phase shift and signal absorption.

To determine the two principal parameters—the electron concentration $n_e$ and the effective collision frequency $\nu_{\mathrm{eff}}$—it is necessary to measure two quantities characterizing the propagation of electromagnetic waves in the plasma. It is also necessary to know the effective diameter of the plasma formation, since in the course of the experiment parameters averaged over the length of the probing beam are obtained. Thus, to determine $n_e$ and $\nu_{\mathrm{eff}}$ a system of three equations is necessary.

As is known [2], in the general case the relation of the absorption coefficient $\gamma_i$ and the refractive index $N_i$ to the plasma parameters is given by the expressions:

\[ \gamma_i = \sqrt{ -\frac{1}{2}\left(1-\frac{v_i}{1+S_i^2}\right) +\frac{1}{2} \sqrt{ \left(1-\frac{v_i}{1+S_i^2}\right)^2 +\left(\frac{v_i S_i}{1+S_i^2}\right)^2 } }; \]

\[ N_i = \sqrt{ \frac{1}{2}\left(1-\frac{v_i}{1+S_i^2}\right) +\frac{1}{2} \sqrt{ \left(1-\frac{v_i}{1+S_i^2}\right)^2 +\left(\frac{v_i S_i}{1+S_i^2}\right)^2 } }, \tag{1} \]

\[ \frac{v_{i+1}}{v_i}=\left(\frac{\omega_i}{\omega_{i+1}}\right)^2; \qquad \frac{S_{i+1}}{S_i}=\frac{\omega_i}{\omega_{i+1}} . \]

where

\[ v_i=\left(\frac{\omega_0}{\omega_i}\right)^2;\qquad s_i=\frac{\nu_{\mathrm{eff}}}{\omega_i}. \tag{2} \]

The quantities \(\gamma_i\) and \(N_i\) are calculated from the experimentally determined plasma absorption coefficients \(\xi_i\) and the phase-shift values of the probing signal \(\varphi_i\) according to the formulas:

\[ \gamma_i=\frac{\lambda_i \xi_i}{4\pi\cdot 4.35 d}; \tag{3} \]

\[ N_i=1-\frac{\varphi_i}{d\,\dfrac{\omega_i}{c}}, \tag{4} \]

where \(d\) is the diameter of the plasma formation,
\(\lambda_i\) is the wavelength of the probing microwave wave.

Processing the results by formulas (1) presents a certain difficulty; therefore, to determine the electron concentration \(n_e\) and \(\nu_{\mathrm{eff}}\) in high-pressure HF plasma, we calculated on a DNEPR-21 computer nomograms for the parameters \(N_i\) and \(\gamma_i\), taking into account values \(s>1\).

To carry out the measurements, an apparatus was developed that combines the scheme of the two-frequency method and a phase meter, which makes it possible to determine attenuations at three frequencies and the phase shift at one frequency [3]. Plasma probing was performed at \(\lambda_1=8\) mm, \(\lambda_2=12\) mm, and \(\lambda_3=16\) mm; at \(\lambda_1\), the phase shift was measured.

A major advantage and original feature of the apparatus is the extensive use of dielectric waveguides. All transmission lines, directional couplers, and the frequency divider were made with them. To localize the microwave radiation in the plasma, focusing horn-lens antennas were used, consisting of pyramidal horns and focusing dielectric lenses.

When probing plasma objects with dimensions of several wavelengths, the accuracy of the measurement decreases considerably because of diffraction, refraction, and multiple reflection of the microwave signal in the space between the probing antennas.

In order to determine the minimum diameter of the plasma formation at which an unambiguous determination of the electron concentration and their effective collision frequency is still possible, we carried out an analog experiment on the passage of microwave radiation through cylindrical specimens of fluoroplastic, polystyrene, and paraffin simulating plasma. The measurement results are presented in Table 1.

As can be seen from Table 1, diffraction begins to have an effect already at \(D_{\min}\approx 10\) mm. In processing the experimental data with the aid of the nomogram, the discharge diameter was determined, simultaneously with \(n_e\) and \(\nu_{\mathrm{eff}}\), from the measured values \(\Gamma_1\), \(\Gamma_2\), and \(\Delta\varphi\) by the selection method. In all measurements it remained significantly larger than \(D_{\min}\). Comparison of the values of the effective diameters obtained by microwave methods with the results of an experimental study of the radial distribution of the electron concentration by the two-probe method [4] showed satisfactory agreement.

Microwave probing of HF air plasma was carried out in a metallic plasmatron [5] at a distance \(h=40\) mm from the electrode to the axis of the horn-lens system. The HF discharge was powered from a ge

of the LD1-4 generator with an operating frequency of 40 MHz, with a power supplied to the discharge of about 8 kW.

Table 1

Attenuations \(\xi_i\) and phase shifts \(\varphi_i\) for different dielectrics

The results of microwave measurements of the parameters of the HF plasma are presented in Table 2.

Table 2

Values of the electron concentration \(n_e\) and the effective frequency of electron collisions with heavy particles \(\nu_{\mathrm{eff}}\) at various pressures

From Table 2 it can be seen that \(n_e\) and \(\nu_{\mathrm{eff}}\) increase with increasing pressure in the discharge chamber. A comparison of the obtained dependence \(n_e = f(P)\) with the results of measurements of the burning voltage and the total discharge current [5] and with data on the gas temperature [6] at various pressures makes it possible to conclude that the pressure range at wh-

in which the formation of the HFP channel occurs, corresponds to a sharp increase in the electron concentration.

The studies carried out showed that microwave methods are suitable for diagnosing a high-frequency torch discharge at reduced pressure. However, the use of radiation with \(\lambda = 8\) mm is possible when the diameter of the plasma formation is \(D \geq 10\) mm. For \(D < 10\) mm and with sufficiently large \(n_e\), it is necessary to switch to shorter-wavelength radiation in the microwave range, or else to diagnose high-frequency plasma by means of lasers.

REFERENCES

1. I. A. Tikhomirov, V. V. Tikhomirov, V. V. Marusin. In the collection: Problems of Low-Temperature Plasma Physics. Minsk, “Nauka i tekhnika,” 1971.

2. A. V. Chernetskii, O. A. Zinov'ev, O. V. Kozlov. Apparatus and Methods of Plasma Research. Edited by V. D. Rusanov. Moscow, Atomizdat, 1968.

3. I. A. Tikhomirov, V. V. Tikhomirov, V. Ya. Fedyanin, V. I. Shishkovskii, A. A. Solov'ev. First All-Union Symposium on Plasma Chemistry. Moscow, 1971.

4. I. A. Tikhomirov, V. V. Tikhomirov, V. I. Shishkovskii, A. A. Solov'ev, V. N. Sergeev. Present collection.

5. I. A. Tikhomirov, V. V. Tikhomirov, N. A. Moshnenko, V. Ya. Fedyanin. In the collection: Physics, Technology, and Applications of Low-Temperature Plasma. Alma-Ata, 1970, p. 702.

6. M. Z. Khokhlov. Optics and Spectroscopy, 4, 439 (1958).