UDC 537.52

ESTIMATION OF SOME PARAMETERS OF AN RF TORCH DISCHARGE IN AIR IN THE PRESSURE RANGE FROM 400 TO 760 mm Hg

V. Ya. Fedyanin, V. V. Tikhomirov, A. I. Kuzminykh, M. M. Pugovkin

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

A simple formula is proposed that relates the total current and the power released per unit length of an RF torch discharge to the average parameters characterizing the state of the gas-discharge plasma. The quantities of the total current, the thermal power, and the gas temperature of an RF torch discharge in air in the pressure range from 400 to 760 mm Hg have been measured.

From the experimental results, the effective electron temperature has been estimated.

Illustrations 1, tables 1, bibliography 8.

A simple formula is proposed that relates the total current and the power released per unit length of an RF torch discharge to the average parameters characterizing the state of the gas-discharge plasma. The quantities of the total current, the thermal power, and the gas temperature of an RF torch discharge in air in the pressure range from 400 to 760 mm Hg have been measured. From the experimental results, the effective electron temperature has been estimated.

1. A high-frequency torch discharge in gases is a plasma formation with a clearly defined channel and envelope. In this case, the length of the discharge is much greater than its transverse dimensions.

High-frequency plasmatrons of the torch type, owing to certain of their properties (sterile purity of the plasma, uncontaminated by products of electrode erosion; ease of creating metallic structures; practically unlimited operating time), are finding ever broader application in plasma-chemical technology [1–3], as a light source in emission spectral analysis, and for thermophysical testing of certain materials.

In the present work an attempt is made, using the energy-balance equation for electrons and molecules, to relate the parameters characterizing the state of the gas-discharge plasma to the macroscopic parameters of the discharge: the power released per unit length and the total current.

1. Let us write the energy-balance equation for the electron gas and neutral molecules for the stationary case:

\[ \frac{dW_{eE}}{dt} - \frac{dW_{em}}{dt} = 0, \tag{1} \]

\[ \frac{dW_{em}}{dt} + \vec{\nabla} \varkappa \vec{\nabla} T_m = 0. \tag{2} \]

Here \(\dfrac{dW_{eF}}{dt}\), \(\dfrac{dW_{em}}{dt}\) are the mean rates of energy transfer from the high-frequency electromagnetic field to the electrons and from the electrons to the molecules; \(\chi\) is the coefficient of thermal conductivity. Moreover,

\[ \frac{dW_{em}}{dt} = \left(\frac{dW_{em}}{dt}\right)_{\mathrm{col}} + \left(\frac{dW_{em}}{dt}\right)_{\mathrm{vib}} + \left(\frac{dW_{em}}{dt}\right)_{\mathrm{el}} + \left(\frac{dW_{em}}{dt}\right)_{\mathrm{diss}} = \]

\[ = \frac{3}{2} k n_e \nu_{em}\,\delta\,(T_e-T_{\mathrm{g}}), \tag{3} \]

where \(\left(\dfrac{dW_{em}}{dt}\right)_{\mathrm{col}}\), \(\left(\dfrac{dW_{em}}{dt}\right)_{\mathrm{vib}}\), \(\left(\dfrac{dW_{em}}{dt}\right)_{\mathrm{el}}\), \(\left(\dfrac{dW_{em}}{dt}\right)_{\mathrm{diss}}\) are the mean rates of energy transfer from the electron gas to vibrational and rotational levels, to the translational degree of freedom, and to molecular dissociation; \(n_e\) is the density of the electron gas; \(\nu_{em}\) is the effective frequency of collisions of an electron with molecules; \(\delta\) is the mean relative fraction of energy transferred by an electron to a molecule in a collision; \(T_e\), \(T_{\mathrm{g}}\) are the temperatures of the electrons and heavy particles, respectively. Substituting (3) into (1) and (2) and averaging all quantities over the volume, we obtain

\[ \frac{3}{2} k n_e \nu_{em}\,\delta\,(T_e-T_{\mathrm{g}})=P_e, \tag{4} \]

\[ P_e \bar n\, a^2 = Q. \tag{5} \]

Here \(P_e\) is the density of heat sources in the discharge, \(Q\) is the heat flux per unit length of the wall of the plasmatron, and \(a\) is the radius of the discharge channel. Combining (4), (5) and using Ohm’s law, we obtain

\[ \frac{Q^2}{I^2} = \frac{1}{2} E_p^2 \frac{T_e(T_e-T_{\mathrm{g}})}{T_{\mathrm{g}}^2}, \tag{6} \]

where

\[ E_p=\sqrt{\frac{3kT_{\mathrm{g}}\,m\delta\nu_{em}^2(T_{\mathrm{g}})}{e^2}} \]

is the characteristic “plasma field” [4], and \(I\) is the rms value of the total discharge current.

1. Experimental studies were carried out in a high-frequency torch discharge in air. The discharge was excited in a specially made quartz plasmatron–calorimeter connected to the anode circuit of the LD1-4 high-frequency installation. The pressure was varied from 400 to 760 mm Hg. The total discharge current was measured by means of a Rogowski belt operating in current-transformer mode. The Rogowski belt and the water calorimeter were calibrated by the substitution method.

The gas temperature was determined spectroscopically—by the relative-intensity method [5]. The intensity distribution of rotational lines in the \(Q\)-branch of the hydroxyl band \(OH\) with the band head at 3064 Å \(({}^2\Pi-{}^2\Sigma)\) was investigated. In [6] it was shown that the rotational temperature of hydroxyl in a torch discharge at pressures greater than 100 mm Hg coincides with the gas temperature.

The spectrum was photographed on aerophotographic film with a sensitivity of 1100 GOST units using an ISP-28 quartz spectrograph (reciprocal dispersion in the region of 3000 Å—16 Å/mm). The investigations showed that in the pressure range from 400 to 760 mm Hg the gas temperature from

pressure and increases only slightly with an increase in the power released in the discharge. The experimental results are presented in Table 1.

From the experimentally obtained values of \(Q, I, T_{\mathrm{g}}\), \(T_e\) was determined from equation (6). Figure 1 shows the dependence of

\[ \frac{T_e - T_{\mathrm{g}}}{T_{\mathrm{g}}} \]

on pressure for two values of

\[ \frac{Q}{I}. \]

Table 1

In the calculations it was assumed that the collision cross section of electrons with molecules does not depend on the electron velocity and is equal, for air, to \(4.4 \cdot 10^{-16}\ \mathrm{cm}^{-2}\) [4]; the mean relative fraction of energy transferred by an electron to a molecule in a single collision was calculated from the data of [7].

From the graphs in Fig. 1 it is seen that, as the pressure increases, \(T_e \to T_{\mathrm{g}}\), and the nonisothermality of the plasma of the RF torch discharge decreases. The absolute values of \(T_e\) at \(T_{\mathrm{g}} = 3500^\circ\mathrm{K}\) are, for example, at \(P = 760\) mm Hg, \(7000^\circ\mathrm{K}\), which also agrees with the literature data [8]. Thus, formula (6), in our opinion, describes with satisfactory accuracy the relation between the macroscopic parameters of the discharge and the parameters of the gaseous plasma.

1. In conclusion, it should be noted that, in deriving formula (6), two assumptions were made:

2. The plasma of the channel is nonisothermal \((T_e > T_{\mathrm{g}})\).

3. The mechanism of RF energy transfer into the discharge is described by the following scheme: the energy of the RF electromagnetic field is transferred mainly to the electrons; then, in elastic and inelastic collisions, it is transferred to the molecules and, through the mechanism of molecular thermal conductivity, is removed from the discharge zone (the thermal conductivity of the electron gas and energy transfer by radiation may be neglected).

Fig. 1. Dependence of

\[ \frac{T_e - T_{\mathrm{g}}}{T_{\mathrm{g}}} \]

on pressure: \(1 — \dfrac{Q}{I} = 62\ \dfrac{\mathrm{W}}{\mathrm{cm}}\); \(2 — \dfrac{Q}{I} = 60\ \dfrac{\mathrm{W}}{\mathrm{cm}}\).

Thus, equation (6) is applicable not only to the torch discharge, but also to discharges of other types for which conditions 1 and 2 are satisfied (for example, to glow discharges and dc arcs at medium pressures).

References

1. I. A. Tikhomirov et al. In: Physics, Technology, and Application of Low-Temperature Plasma. Alma-Ata, KazGU Publishing House, 1970.

2. West C. D., Hume D. N. “Analyt. Chem.,” 36, No. 2, 412 (1964).

3. V. K. Zakharov. In: Problems of General and Applied Physics. Alma-Ata, KazGU Publishing House, 1969.

4. V. L. Ginzburg. Propagation of Electromagnetic Waves in Plasma. Moscow, “Nauka,” 1967.

5. Optical Pyrometry of Plasma. Collection of articles edited by N. I. Sobolev. Moscow, IL, 1960.

6. M. Z. Khokhlov. “Optics and Spectroscopy,” 4, issue 4 (1958).

7. Farsky V., Janca J. “Beitr. Plasmaphys.,” 8, No. 2 (1968).

8. Mollwo L. “Ann. Phys.,” 7, vol. 2 (1958).