Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Volume 162　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1967

Investigation of the Temporal Characteristics of Electrical Breakdown in Short Gas Gaps in the Nanosecond Time Range

Yu. I. Bychkov, G. S. Korshunov

(Presented by the scientific seminar of the Research Institute of Nuclear Physics)

Few works have been devoted to the study of the temporal characteristics of electrical breakdown of short gas gaps in the nanosecond time range, although the investigation of these characteristics is important for clarifying the physics of the process and for practical application in high-voltage nanosecond pulse technology. In connection with the development in recent years at the Tomsk Polytechnic Institute of a large number of high-voltage nanosecond pulse generators [1--3], which have found broad application in research in nuclear physics, quantum electronics, dielectric physics, etc., and in connection with the need for continual improvement of generator parameters in the direction of increasing the steepness of the pulse front and the stability of triggering upon startup, there arose the need to investigate the temporal characteristics of short gas gaps in the nanosecond time region.

The present work gives the results of a statistical study of the delay and commutation time under static and pulsed breakdown of short gas gaps in the nanosecond time range. In this case, the range of investigated gap lengths was determined by the actual magnitudes of gaps used in high-voltage nanosecond pulse generators, and was 0.05--2.2 mm.

Investigation of the Statistical Discharge Delay Time

As is known, the operating time of a spark gap consists of two components:

\[ t_z = \sigma_{\mathrm{st}} + \tau_{\mathrm{f}}, \tag{1} \]

where \(\sigma_{\mathrm{st}}\) is the statistical delay time, caused by the appearance of an effective electron, and \(\tau_{\mathrm{f}}\) is the discharge formation time. Since \(\sigma_{\mathrm{st}}\) is associated with waiting for an effective electron, it is a statistical quantity and has a scatter over wide limits. Irradiation of the cathode with ultraviolet light (quartz lamp, spark discharge) creates a photocurrent from the cathode surface, owing to which the scatter of \(\sigma_{\mathrm{st}}\) can be reduced. In work [4] it was shown that, under irradiation

spark gap by the spark of a nearby discharge gap, \(\sigma_{\mathrm{st}}=0.01\ \mathrm{nsec}\), while \(\tau_{\phi}\) has no scatter and depends only on the applied field \(E\). In [5] it is shown that the irradiation effect is manifested fully in the case when the irradiation precedes the arrival of the pulse by \(70\ \mathrm{nsec}\).

The use of irradiation is not always desirable for design reasons.

We investigated the statistical delay time of the discharge at fields \(E=300 \div 1400\ \mathrm{kV/cm}\), i.e., when effective electrons are provided by autoemission from the cathode surface.

The experimental procedure is described in [6]. The pass band of the recording channel was not less than \(3\cdot 10^{9}\ \mathrm{Hz}\). An S1-14 oscilloscope was used. An automatic photographic device made it possible to oscillograph a large number of breakdowns, up to 600 for each case. Such a number of oscillograms gives reliable statistics for the distribution of the delay time.

In Fig. 1,a the distribution \(\Delta \dfrac{n_t}{n_0}\) is shown as a function of time, where \(n_t\) is the number of pulses with a given delay time, and \(n_0\) is the total number of pulses.

Fig. 1.

\(a\) — dependence \(\Delta \dfrac{n_t}{n_0}(t_z)\),

\[ E=1400\ \frac{\mathrm{kV}}{\mathrm{cm}}, \qquad \delta=0.01\ \mathrm{cm}; \]

\(b\) — dependence

\[ \ln\left|\frac{n_t}{n_0}(t_z)\right|, \qquad E=1400\ \frac{\mathrm{kV}}{\mathrm{cm}}, \qquad \delta=0.01\ \mathrm{cm}. \]

Fig. 2.

\(a\) — dependence \(t_z\) mean stat. \((p)\)

\[ E=300\ \frac{\mathrm{kV}}{\mathrm{cm}}, \qquad \delta=0.05\ \mathrm{cm}; \]

\(b\) — dependence \(t_z\) mean stat. \((\delta)\),

\[ E=300\ \frac{\mathrm{kV}}{\mathrm{cm}}, \qquad p=1\ \mathrm{atm}. \]

Thus, \(\Delta \dfrac{n_t}{n_0}\) is the relative number of breakdowns having a given delay time. For example, 0.25 of the breakdowns have a delay time in the interval \(1.8\text{–}2\ \mathrm{nsec}\).

In Fig. 1,b the same distribution is shown in the axes \(\left|\ln \dfrac{n_t}{n_0}\right|\) and \(t_z\), where \(n_t\) is the number of pulses having this delay time or greater, and \(n_0\) is the total number of pulses. The \(t_{z\,\mathrm{av.\,st.}}\) shown in Fig. 1,b is the mean-statistical delay time, which can characterize the degree of scatter of the delay times. The greater the scatter in the delay times, the flatter the dependence of \(\left|\ln \dfrac{n_t}{n_0}\right|\) on \(t_z\) will be, and the larger \(t_{z\,\mathrm{av.\,st.}}\) will be. As the scatter decreases, \(t_{z\,\mathrm{av.\,st.}}\) decreases. In Fig. 1,a,b the distributions of delay times are shown for a gap of length \(\delta = 0.01\ \mathrm{cm}\) and \(E = 1400\ \mathrm{kV/cm}\); the electrodes are made of copper and carefully polished.

In Fig. 2,a,b the dependences of \(t_{z\,\mathrm{av.\,st.}}\) are given, respectively, on pressure and on the gap length at a constant field strength \(E = 300\ \mathrm{kV/cm}\). The electrodes are made of aluminum and carefully polished. From the dependence in Fig. 2,a it is seen that \(t_{z\,\mathrm{av.\,st.}}\) decreases sharply with decreasing pressure and at \(p = 20\ \mathrm{mm}\) Hg is \(0.7\ \mathrm{nsec}\). According to (1), \(\sigma_{\mathrm{st}} < 0.7\ \mathrm{nsec}\). In our case \(\sigma_{\mathrm{st}}\) is determined by the autoemission current, which depends only on the field strength \(E\). With an increase in pressure at \(E=\mathrm{const}\), \(\sigma_{\mathrm{st}}\) must remain less than \(0.7\ \mathrm{nsec}\), and, consequently, the delay-time scatters observed by us with increasing pressure are scatters of the time \(\tau_{\mathrm{f}}\). Fig. 2,b shows the dependence of \(t_{z\,\mathrm{av.\,st.}}\) on the length of the discharge gap at \(E=300\ \mathrm{kV/cm}\), atmospheric pressure. In this case we have a decrease in \(t_{z\,\mathrm{av.\,st.}}\) from \(1400\ \mathrm{nsec}\) to \(28\ \mathrm{nsec}\) when \(\delta\) is increased from \(0.02\ \mathrm{cm}\) to \(0.08\ \mathrm{cm}\). In small gaps, a decrease in the scatter of delay times can be achieved by means of superhigh overvoltages. In Fig. 1 it is seen that only at a 14-fold overvoltage was it possible to reduce \(t_{z\,\mathrm{av.\,st.}}\) to \(1\ \mathrm{nsec}\).

It should be noted that irradiation of the gap by a spark from a nearby arrester sharply reduces \(t_{z\,\mathrm{av.\,st.}}\); thus, for gaps of \(0.01 \div 0.02\ \mathrm{cm}\), under irradiation \(t_{z\,\mathrm{av.\,st.}}\) decreases by more than a factor of 100. Consequently, irradiation of the gap reduces not only the component \(\sigma_{\mathrm{st}}\), but also \(\tau_{\mathrm{f}}\).

Investigation of switching times

During the switching period of the spark gap, the initial voltage on the electrodes \(U_0\) decreases to a value \(U \ll U_0\). It is known [1] that, with an increase in the field strength \(E\) in the gap—which can be achieved by increasing the pressure \(P\) or by creating an overvoltage \(\beta\)—the switching time decreases. There are, however, very few experimental data on the investigation of switching in the nanosecond range of times during static and overvoltage breakdown of short gaps. In connection with this, we carried out an investigation of the switching time during static breakdown of gaps of length \(\delta = 0.05 \div 2.2\ \mathrm{mm}\) in various gases at pressures \(P = 1—7\ \mathrm{atm}\), and of overvolted gaps of length \(0.1\) and \(2\ \mathrm{mm}\) in air at atmospheric pressure. In these experiments the gaps were illuminated both with a PRK-5 lamp and without it.

The experimental procedure is set forth in [7]. The electrode diameters \(d\) were chosen from the condition of excluding the influence of the interelectrode capacitance on the switching time, described in [8], and were made ...

Fig. 3. a—dependence \(t_m(p)\): \(1\)—\(\delta = 2.2\ \mathrm{mm}\), \(2\)—\(\delta = 0.98\ \mathrm{mm}\), \(3\)—\(\delta = 0.7\ \mathrm{mm}\), \(4\)—\(\delta = 0.4\ \mathrm{mm}\), \(5\)—\(\delta = 0.2\ \mathrm{mm}\), \(6\)—\(\delta = 0.05\ \mathrm{mm}\), \(7\)—\(\delta = 0.085\ \mathrm{mm}\), \(8\)—\(\delta = 0.13\ \mathrm{mm}\);
b—dependence \(t_m(E)\) for different gases; for air, \(N_2\), \(H_2\), \(U_0 = 15\ \mathrm{kV}\); for Ar at \(E = 9.3\ \mathrm{kV/cm}\), \(U_0 = 7.2\ \mathrm{kV}\), and for the remaining points \(U_0 = 11.5\ \mathrm{kV}\).

for \(\delta = 0.05 \div 0.2\) mm, \(d = 1.2\) mm; for \(\delta = 0.4—1\) cm, \(d = 6\) mm; for \(\delta = 2.2\) mm, \(d = 20\) mm.

The characteristic of the switching time is the time \(t_m\) [1]

\[ t_m=\frac{i_0}{(di/dt)_m}=\frac{9.5\cdot p}{a\cdot E^2}, \tag{2} \]

where \(i_0\) is the current amplitude; \((di/dt)_m\) is the maximum steepness of the current rise in time; \(a\) is a constant depending on the type of gas.

When measuring the values \(t_m\), fluctuations were observed. Therefore each value of \(t_m\) was taken as the arithmetic mean of 20 or more measurements.

The static breakdown of gaps was investigated with discharge of the line into a line (wave impedance \(z_B = 75\) ohms). In Fig. 3,a the dependences of \(t_m\) on the pressure \(P\) and the gap length \(\delta\) are presented. As \(\delta\) decreases, the time \(t_m\) decreases, as it does when \(P\) increases, since the field strength increases in both cases. At \(E > 150\) kV/cm the time \(t_m\) practically no longer depends on \(P\) and \(\delta\). Using formula (2), an estimate of the coefficient \(a\) was carried out for the data of Fig. 3,a. In this case satisfactory agreement with the Rompe—Weizel theory [9] was obtained. The maximum in the dependences for \(\delta = 0.05,\ 0.085,\ 0.13\) mm is also consistent with this theory.

The results presented above for the investigation of the switching time were obtained in the absence of illumination of the gaps. When gaps of length \(\delta = 0.1—0.5\) mm were illuminated with a PRK-5 lamp, no noticeable differences in the time \(t_m\) were found.

It should be noted that for \(\delta = 0.05;\ 0.2;\ 0.5\) mm the electrode material (Cu, Al, W, steel) and the number of shots (\(\sim 1000\)) did not affect \(t_m\) or the character of the oscillograms \(U_R(t)\). This indicates that electrode effects have no substantial influence on the switching process during static breakdown of short gaps.

In Fig. 3,b the dependences of \(t_m\) on \(E\) for different gases during line discharge are presented. Here, for air, \(\mathrm{N_2}\), \(\mathrm{H_2}\), \(U_0 = 15\) kV; for Ar at \(E = 9.3\) kV/cm, \(U_0 = 7.2\) kV, and for the remaining points \(U_0 = 11.5\) kV. For air, nitrogen, and hydrogen there is a tendency toward convergence of the times \(t_m\) as \(E\) increases. It is interesting to note that in Ar at atmospheric pressure (which in our case corresponds to \(E = 9.3\) kV/cm, \(\delta = 7.8\) mm) the time \(t_m\) is much smaller than in the other gases. This fact has not previously been noted anywhere.

Table 1

The impulse breakdown of gaps was carried out by applying pulses with a steep front and of various amplitudes to the gap under investigation. The pulse-front time was chosen such that breakdown of the gap occurred on the flat part of the pulse. Two were investigated

gap. At \(\delta=0.1\) mm the gap was illuminated by a PRK-5 lamp; at \(\delta=2\) mm there was no illumination. The data on the time \(t_{\mathrm{m}}\) and the overvoltage \(\beta=\dfrac{U_{\mathrm{br}}}{U_{\mathrm{st}}}\), where \(U_{\mathrm{br}}\) is the voltage at which breakdown occurs and \(U_{\mathrm{st}}\) is the static breakdown voltage of the gap, are given in Table 1.

It follows from Table 1 that the same value of \(t_{\mathrm{m}}\) for the gap \(\delta=2\) mm is obtained at a much smaller overvoltage than for \(\delta=0.1\) mm. It is interesting to note that for the gap \(\delta=2\) mm, at \(\beta=1.25\), the time \(t_{\mathrm{m}}\) is already several times less than the time \(t_{\mathrm{m}}\) obtained in static breakdown of the gap \(\delta=2.0\) mm, \(p=1\) atm.

The authors thank G. A. Mesyats for formulating the problem.

REFERENCES

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