ON ENERGY RELEASE IN THE CHANNEL OF A PULSED DISCHARGE DURING BREAKDOWN OF SOLID DIELECTRICS

Yu. N. Leont’ev

(Presented by the scientific seminar of the Department of High-Voltage Engineering)

Introduction

In connection with the broad technical use of shock waves arising during a pulsed electric discharge in a dielectric medium, it is of interest to study certain energy characteristics of the channel of a pulsed discharge in solid dielectrics. The electrophysical parameters of the pulsed-discharge channel in gases have been studied rather fully [1–4]. There are a number of works devoted to the study of the discharge channel during pulsed breakdown in a liquid dielectric medium [5, 6, 7]. The energy characteristics of the pulsed-discharge channel in solid dielectrics have been little studied [8].

The shock waves arising during a pulsed discharge lead to explosive destruction of the dielectric medium both at the site of breakdown and at some distance from the discharge channel. The overall destructive action of the shock wave is characterized by the total energy released in the discharge channel. The present work gives the results of a study of the channel parameters and of the process of energy release during pulsed electric breakdown. On the basis of oscillographic recording of the change in voltage on the specimen and of the current in the post-breakdown period, some data have been obtained on the release of energy in the channel of the pulsed discharge and on its parameters.

Experimental setup and procedure

As the high-voltage source in the work, a pulse-voltage generator (PVG) was used. The capacitance of the generator in the discharge was \(C = 1660\) pF. The inductance of the circuit was \(L = 8.5 \cdot 10^{-6}\) H. The pulse-voltage generator was discharged into an ohmic divider with resistance \(R_g = 6000\ \Omega\). The specimens were placed between “point”—“point” grounded electrodes and “point”—“plane” grounded electrodes. A positive-polarity pulse with amplitude up to \(U_m = 300\) kV and a pulse-front duration of the order of \(\tau_f = 0.2 \cdot 10^{-6}\) s was applied to the “point” electrode. To eliminate surface flashover of the specimens, they were placed in a tank with transformer oil. For oscillographic recording of the voltage curve on the specimen, the voltage drop across a resistance \(r = 35\ \Omega\) of the voltage divider was applied to the plates of the oscillograph tube.

graph OK-19M. The current in the channel was recorded by means of a strip shunt with an active resistance \(R_{\mathrm{sh}} = 0.285\ \Omega\). The voltage drop across the active resistance of the shunt was fed to the plates of the deflection system of the second tube of the OK-19M oscilloscope. Simultaneous oscillography of the voltage and current made it possible to determine the energy released in the channel of the pulsed discharge,

\[ W_{\mathrm{k}}=\int_{0}^{\infty} U(t)\cdot I(t)\cdot dt, \]

as well as the instantaneous powers and the resistance of the discharge channel. The energy stored in the electric field of the capacitors was determined as

\[ W_{0}=\frac{C_{\mathrm{p}}U_{0}^{2}}{2}, \]

where \(C_{\mathrm{p}}\) is the capacitance in the discharge,
\(U_{0}\) is the amplitude voltage of the pulse.

Experimental Results

From the data obtained by processing the current and voltage oscillograms it was established that, during the first half-period of the current oscillation in the channel, from 30% to 60% of the pulse energy is released; this once again confirms the data of [8]. Some other data on the process of energy release in the channel of a pulsed discharge were also obtained. Figure 1 presents the dependence of the energy release in the discharge channel in a solid dielectric on time. From Fig. 1 it is seen that during the first half-period, equal to \(t = 0.745 \cdot 10^{-6}\ \mathrm{s}\), 70–80% of all the energy released in the channel over the entire discharge period is released in the discharge channel. As is seen from Fig. 1, beginning from the time \(t = 3.725 \cdot 10^{-6}\ \mathrm{s}\), no more than 0.1 J, i.e., 2% of the pulse energy, is released in the channel during each subsequent half-period of current oscillation. Moreover, the energy release subsequently decreases sharply, and it may be considered that all the energy is released in the channel by the time \(t = 3.725 \cdot 10^{-6}\ \mathrm{s}\). Thus

Fig. 1. Change in the amount of energy released in the spark channel with time.

Thus, the determining factor may be considered the time of the first half-period, i.e., the explosive destructive action is influenced by the energy released in the channel during the first half-period of current oscillation.

The change in the minimum resistance of the discharge channel is shown in Fig. 2. From this figure it is evident that, as the overvoltage decreases, the channel resistance increases, and consequently the fraction of energy released in the channel increases.

Fig. 2. Change in the minimum resistance of the spark channel as a function of specimen thickness.
1—organic glass, 2—paraffin.

released in the channel. Estimates of the channel resistance give a value \(R_k = 1.8 \div 2.2\ \Omega\) for specimen thickness \(d = 10\) mm. Estimates from the damping decrement show that the channel resistance in the post-breakdown period decreases to a certain minimum value and remains almost unchanged for several half-periods.

Figure 3 shows the change in the amount of energy released in the spark channel as a function of voltage during the first half-period. Curves 1 and 2 were obtained for the circuit parameters:
\(L = 8.5 \cdot 10^{-6}\ \mathrm{H}\), \(C_p = 1660\ \mathrm{pF}\), and “point—plane” electrodes. Curves 3, 4, and 5 were obtained for the circuit parameters:
\(L = 18 \cdot 10^{-6}\ \mathrm{H}\), \(C_p = 0.01 \cdot 10^{-6}\ \mathrm{F}\), and “point—point” electrodes.

In the breakdown of specimens through an air capillary (capillary diameter \(0.25\) mm), the energy released in the channel during the first half-period (curve 2) is less than in the breakdown of solid specimens. This is probably explained by the fact that the channel resistance in breakdown through an air capillary is less than the channel resistance in breakdown of solid specimens. This is also evident from curves 4 and 5.

In electrical breakdown of paraffin specimens through an exploding wire (curve 3), better energy release in the channel is observed than in breakdown of solid specimens (curve 4) and specimens with an air capillary (curve 5).

Nichrome of diameter \(0.1\) mm and resistance \(130\ \Omega/\mathrm{m}\) was used as the exploding wire. The maximum instantaneous powers developed in the channel during breakdown of specimens through an exploding wire are 2–3 times greater than in breakdown of solid specimens, and almost an order of magnitude greater than in breakdown of specimens with an air capillary. Thus, the maximum power in

when samples were broken down through an air capillary it was \(N_m = 8 \cdot 10^6\) W, whereas for breakdown of solid samples it was \(N_m = (15 \div 20)\cdot 10^6\) W, and for breakdown through an exploding wire it was of the order of \(N_m = (50 \div 60)\cdot 10^6\) W at \(U = 200\) kV, \(L = 18 \cdot 10^{-6}\) H, and \(C_p = 0.01 \cdot 10^{-6}\) F.

Fig. 3. Change in the amount of energy released in the spark channel with voltage. Paraffin \(d = 10\) mm.
1—solid samples, \(L = 8.5\) μH, \(C_p = 1660\) pF;
2—samples with an air capillary, \(L = 8.5\) μH,
\(\qquad C_p = 1660\) pF.
3—samples with an exploding nichrome wire of diameter 0.1 mm, \(L = 18\) μH,
\(\qquad C_p = 0.01\) μF.
4—solid samples, \(L = 18\) μH, \(C_p = 0.01\) μF.
5—samples with an air capillary, \(L = 18\) μH,
\(\qquad C_p = 0.01\) μF.

Conclusions

1. It was established that during the first half-period of current oscillation, up to \(70 \div 80\%\) of the energy released over the entire period of the pulsed discharge is released in the channel.

2. The instantaneous maximum powers developed in the discharge channel during pulsed breakdown of solid dielectrics through an exploding wire are \(2 \div 3\) times higher than during breakdown of solid samples, and almost an order of magnitude higher than during breakdown of samples with an air capillary.

3. The experiments showed that the resistance of the pulsed-discharge channel, upon reaching its minimum value, remains almost unchanged during the time of the first and several subsequent half-periods of current oscillation.

References

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