INVESTIGATION OF THE ACOUSTIC EFFECT OF A TORCH DISCHARGE UNDER AMPLITUDE MODULATION OF A HIGH-FREQUENCY FIELD

V. V. MARUSIN, I. A. TIKHOMIROV, Yu. G. YUR’EV

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

In the continuous generation regime and with sufficient power supplied to the discharge, the plasma of the torch throughout its volume, except for the near-electrode region, at atmospheric pressure may be approximately regarded as thermodynamically equilibrium, and the Boltzmann and Saha equations [1], [2], [3] may be used for calculations. When the external conditions change (an increase in the gas pumping rate, a decrease in the power supplied to the discharge, a decrease in pressure, etc.), the role of electron ionization increases, and when it predominates over thermal ionization the torch passes into a high-frequency corona [4]; in this case the directed velocity of the electrons exceeds the thermal velocity [5].

Under certain conditions the torch may serve as a source of acoustic waves [6], [7]. In [6], however, “subacoustic” oscillations of the torch were investigated, while the acoustic effect of a torch discharge studied in [7] can be explained by near-electrode processes and the noise properties of the discharge plasma itself [8], [9]. The acoustic effect of a gas discharge in direct current at high pressures, with and without amplitude modulation of the feeding field, was studied in a number of works [10], [11], [13]. In the investigation of a point corona in direct current, a “mechanical-electrical efficiency” of about 1% was obtained [10], [11]. In a number of works the acoustic effect of a high-frequency corona under amplitude modulation of the feeding field with a modulation coefficient \(m < 0.2\) was studied [12], [14], [15]. With an electronic excitation mechanism and with the corona approximated as a point source, the independence of the acoustic effect of the corona from the high frequency and the modulating frequency \(f_{\text{mod}}\) was obtained; at a maximum modulation frequency of up to 40 kHz the “acoustic efficiency” was 2.5% and the radiation intensity level was 132 dB.

Mechanism of the acoustic effect of a “modulated” torch

If the field feeding the discharge is amplitude-modulated with modulation frequency \(f_{\text{mod}} \ll f_{\text{h}}\), where \(f_{\text{h}}\) is the field frequency, then the amplitude of the wave at the plasma boundary near the electrode may be written as

\[ E = E_0 \left(1 + \cos \omega_0 t\right), \tag{1} \]

where \(\omega_0\) is the angular modulation frequency. If the maximum coeffi-

modulation coefficient \(m = 0.4\), the distortion of the modulation depth (provided that the relation \(\nu^2 \gg \omega^2\) is satisfied, where \(\nu\) is the electron-collision frequency and \(\omega\) is the field frequency; modulation amplification [16] occurs in the discharge channel) will nevertheless take place owing to self-action; however, to a first approximation one may take the law of variation of the field in the discharge channel according to equation (1). For \(m < 0.4\) and \(E_{\min} \gg E_{\mathrm{cr}}\), where \(E_{\mathrm{cr}}\) is the critical voltage of the torch [17], the temperature difference in the torch is \(\Delta T_{\mathrm{av}} \ll T\), where \(T\) is the mean temperature of the torch channel; therefore one may assume a thermal character of the acoustic effect of the discharge, i.e., [15]

\[ \frac{p}{P_0} \simeq \frac{\Delta T_{\mathrm{av}}}{T}, \tag{2} \]

where \(p\) is the amplitude of the sound pressure developed by the discharge, and \(p_0\) is the gas pressure in the chamber. Consequently, the acoustic effect of the discharge increases with increasing \(\Delta T_{\mathrm{av}}\), i.e., with increasing \(m\). The dependence of the acoustic effect of the discharge on \(f_{\mathrm{mod}}\) is determined by the time for establishment of equilibrium in the discharge plasma, \(t_c\). At high pressure and in an air discharge, \(t_c\) is determined by the time for establishment of the stationary state over the vibrational levels of the molecules [18]; therefore, at modulation frequencies of several tens of kHz, owing to the commensurability of \(t_c\) and

\[ \frac{1}{\omega_0} \]

(thus, in air and at a pressure \(P_0 = 1\) atm, \(t_c = 20\ \mu\text{sec}\) [19]), an inverse proportionality of \(p\) to \(\omega_0\) takes place.

Acoustic effect of a “modulated” discharge in air

To obtain a “modulated” torch discharge, an apparatus was assembled, the block diagram of which is shown in Fig. 1. Here \(KV\) is a cathode voltmeter, \(D\) a sensor, \(BP\) a power-supply unit, \(ZGNCh\) a low-frequency master oscillator, \(GVCh\) a high-frequency generator, \(SM\) a mixing unit, \(OE\) an electronic oscilloscope, \(G\) a frequency meter, \(R\) a flowmeter, \(N\) a pump, \(K\) a reaction chamber, and \(FB\) a forbalon.

Fig. 1. Block diagram of the apparatus.

The high-frequency voltage was measured with a cathode voltmeter using a special voltage divider; the modulation coefficient was recorded with an oscilloscope. The autogene-

The high-frequency generator was assembled using a GU-80 tube; its operating frequency was 30 MHz. The operating frequency of the modulator could be varied within the range from 50 Hz to 100 kHz.

The torch 7 burned vertically upward in a copper cylindrical chamber 1 (Fig. 2) on a nickel electrode 5 mounted on a Teflon insulator 4. The discharge was ignited by the ignition electrode 3 with the aid of a Sylphon 2. The electrode had the shape of a truncated cone with a tip in the form of a hemisphere of radius 1 mm and a through hole along the electrode axis, 1 mm in diameter, for pumping gas through the discharge zone. The electrode was cooled with water. The relative intensity of the ultrasonic radiation of the discharge was measured using piezoelectric sensors (barium titanate and ADP). After amplification, the signal from the sensor was recorded by a cathode voltmeter and an oscilloscope. The measurements were complicated by high-frequency pickups; therefore the sensor 6 and the amplifier were carefully shielded, and the high-frequency background was taken into account in the measurements.

Fig. 2. Diagram of the working chamber

The distribution of the intensity of oscillations \(I\) over the height \(h\) of the torch discharge in air at \(f_{\text{mod}} = 25\ \text{kHz}\) and \(m = 0.4\) is shown in Fig. 3. The point \(h = 0\) corresponds to the point where the torch issues from the electrode. Curves 1, 2, 3, 4 were taken at distances of the sensor from the discharge axis \(R = 30\ \text{cm}\), \(R = 20\ \text{cm}\), \(R = 12\ \text{cm}\), and \(R = 8\ \text{cm}\), respectively. The similarity of the obtained dependence to the distribution of ions around the torch over the height [20] is noteworthy. As the distance from the torch axis to the sensor is increased, the nonuniformity of the radiation is smoothed out. The form of the dependence makes it possible to conclude that the principal radiator is the discharge channel, while the sheath of the discharge takes no direct part in the conversion of electrical energy into acoustic energy.

The change in the intensity of oscillations of the “modulated” torch as a function of the distance to the discharge in air at \(f_{\text{mod}} = 25\ \text{kHz}\) and \(m = 0.4\) is shown in Fig. 4. The distance \(h\) was varied along a straight line perpendicular to the torch axis and passing 3 cm above the point at which it issued. In all measurements the condition \(D \gg \lambda\) was satisfied, where \(D\) is the chamber diameter and \(\lambda\) is the wavelength of the ultrasound. When the condition \(l \gg d\) is fulfilled, where \(l\) is the length of the discharge channel and \(d\) its diameter, the “modulated” torch may be regarded as a radiator of cylindrical waves; the solution of the wave equation for them is

\[ a = \frac{A_0}{\sqrt{h}} \sin \omega_0 \left( t - \frac{h}{c} \right), \tag{3} \]

where \(A_0\) is the oscillation amplitude of the radiator, \(a\) is the displacement amplitude of the particle, and \(h\) is its distance from the radiator.

Fig. 3. Distribution of the oscillation intensity over the height of the torch (discharge height 10 cm)

From the Newtonian equation we have [21]

\[ dp=\int \frac{\omega_0^2 \rho A}{\sqrt{h}} \sin \omega_0\left(t-\frac{h}{c}\right)\,dh , \tag{4} \]

where \(p\) is the pressure developed in the wave. For \(h \gg \lambda\), the cylindrical wave surfaces become plane [21], and the hyperbola becomes a straight line.

As the modulation coefficient and the discharge power are increased, the intensity of the oscillations increases; as the pressure is decreased, it diminishes. Measurements above the torch showed that the intensity of the oscillations was independent of the distance to the discharge (the maximum distance was \(30\ \text{cm}\)) at a low radiation level. Calculations by graphical

Fig. 4. Dependence of the oscillation intensity on the distance to the torch.

integration of the dependence of the distribution of the oscillation intensity over the height of the discharge, and neglecting absorption losses, give from the experiments a value of the acoustic efficiency of the discharge—defined as the ratio of the radiated acoustic power to the electrical power consumed by the discharge—of the order of \(1.5 \div 2\%\). The electrical power of the discharge was measured by a calorimetric method. When the modulation frequency is lowered below \(1\ \text{kHz}\), the acoustic efficiency decreases sharply; when \(f_{\text{mod}}\) is increased above \(30\ \text{kHz}\), the acoustic efficiency also decreases.

The torch discharge can serve as an effective activator for carrying out many chemical reactions in the gas phase [22]. The sharp increase in the “nonthermality” of the plasma of the “modulated” discharge, with a comparatively small change in the mean gas temperature of the torch plasma, as well as the formation of acoustic waves in the discharge zone and in the reaction chamber, can be used to intensify chemical reactions occurring in the torch discharge.

Conclusions

The mechanism of the acoustic effect of a “modulated” torch discharge has been considered. The acoustic effect of a modulated discharge in air at high pressure has been investigated, and the possibilities of applying it for practical purposes have been considered.

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