Control of the delay in spark appearance by the potential of an auxiliary electrode in the gap
Abstract Generated abstract
This paper examines regulation of spark breakdown delay in high-voltage nanosecond pulse gaps using the potential of an auxiliary middle electrode, rather than changing gas pressure or electrode spacing. The authors derive conditions relating the static breakdown voltages and gap lengths for controlling delay at fixed pulse amplitude and for maintaining constant delay when pulse amplitude varies, then test the scheme in nitrogen-filled discharge gaps with optical preionization. Experiments show that the auxiliary electrode can tune the delay and can extend the usable amplitude range of a pulse-front sharpener, producing subnanosecond output fronts over a substantially wider range than a comparable two-electrode gap.
Full Text
Control of Spark Delay by the Potential of an Auxiliary Electrode in the Gap
G. S. KORSHUNOV, G. A. MESYATS
(Presented by the scientific seminar of the Research Institute of Nuclear Physics, Electronics, and Automation at TPI)
In high-voltage nanosecond pulse devices it is necessary to have an adjustable delay time for the appearance of the spark, \(t_z\), in the gap relative to the moment of arrival of the voltage pulse (for example, chopping devices [1]), or to keep this time constant when the pulse amplitude changes (peaking devices [2]). If the magnitude of the photocurrent from the cathode is sufficient to eliminate the statistical component of the time \(t_z\), then, in a uniform field in the gap, for a rectangular voltage pulse under streamer breakdown [3, 4],
\[ t_z = \frac{1}{p} f\left(\frac{U_a}{p\delta}\right), \tag{1} \]
and for a linear front of duration \(t_\phi\) with a slow rise, when the pulse coefficient is close to 1,
\[ t_z = \frac{t_\phi}{U_a} U_{\mathrm{pr}}(p\delta). \tag{2} \]
Here \(f\) is a function that depends on the type of gas; \(p\) is the pressure; \(\delta\) is the gap length; \(U_a\) is the pulse amplitude; \(U_{\mathrm{pr}}(p\delta)\) is the static breakdown voltage, which depends on the product \(p\delta\) (Paschen curve).
It follows from (1) and (2) that, with unchanged pulse parameters, the time \(t_z\) can be regulated by the quantities \(p\) and \(\delta\). For sealed devices these methods are unsuitable for regulating \(t_z\). In the present work a method is considered for regulating the quantity \(t_z\), at unchanged \(p\) and \(\delta\), by the potential of an additional middle electrode in the gap.
The schematic diagram of the device is given in Fig. 1,a. When the pulse \(U(t)\) arrives, the potential difference across the first gap is \(U(t) - U_0\). If \(R_0 \gg R_1 + R_2\), then after breakdown of the gap \(\delta_1\) the middle electrode is charged to the potential \(U(t)\), which ensures breakdown of the gap \(\delta_2\). Let us denote the static breakdown voltages of the gaps by \(U_{\mathrm{pr},1}\) and \(U_{\mathrm{pr},2}\). The quantity \(U_0\) must not exceed the static breakdown voltage of the shortest gap, so as not to cause its spontaneous breakdown.
Let us consider, by examples, how the ratio between \(\delta_1\) and \(\delta_2\) is chosen as a function of the regulation conditions. Since, at a given pressure, the relation between \(U_{\mathrm{pr}}\) and \(\delta\) is single-valued (Paschen curve), then for
To determine the relation between \(\delta_1\) and \(\delta_2\), it is sufficient to establish the relation between \(U_{\mathrm{br}.1}\) and \(U_{\mathrm{br}.2}\). Let, at an unchanged amplitude of the rectangular pulse \(U_a\), a certain delay interval be provided.
Fig. 1. \(a\)—schematic diagram, \(b\)—experimental setup.
The overvoltages in gaps \(\delta_1\) and \(\delta_2\) are written as follows:
\[ \beta_1=\frac{U_a+U_0}{U_{\mathrm{br}.1}},\qquad \beta'_1=\frac{U_a-U_0}{U_{\mathrm{br}.1}},\qquad \beta_2=\frac{U_a}{U_{\mathrm{br}.2}}, \tag{3} \]
where \(U_0\) is the greatest value of the potential of the auxiliary electrode; \(\beta_1\), \(\beta'_1\), and \(\beta_2\) are the overvoltages, respectively, in \(\delta_1\) at the smallest \(t_z\), in \(\delta_1\) at the greatest \(t_z\), and in \(\delta_2\). Let us choose \(\beta_2\) so that the breakdown delay of the gap \(\delta_2\) is much less than the smallest value of \(t_z\). In this case \(\beta_1\) will be approximately equal to the overvoltage in \(\delta_1\) at the smallest value of \(t_z\). Moreover, it is obvious that \(\beta'_1 \simeq 1\), since in this case \(t_z\) can be made arbitrarily large. Then
\[ U_{\mathrm{br}.1}=\frac{2U_a}{\beta_1+1},\qquad U_{\mathrm{br}.2}=\frac{U_a}{\beta_2}. \tag{3'} \]
Let us consider another example. Suppose it is necessary to have \(t_z=\mathrm{const}\) when the pulse amplitude changes in the interval \(U_{a.\max}\div U_{a.\min}\). If, as in the preceding case, the influence of the breakdown delay of the gap \(\delta_2\) on \(t_z\) is neglected, then it is necessary to have a constant overvoltage in the gap \(\delta_1\). In this case, from (3) and (3′) it follows:
\[ U_{\mathrm{br}.1}=\frac{U_{a.\max}+U_{a.\min}}{2\beta_1},\qquad U_{\mathrm{br}.2}=\frac{U_{a.\min}}{\beta_2}. \tag{4} \]
The value \(\beta_1\) is chosen from the condition of obtaining the specified delay \(t_z\). Since in both cases \(\beta_2>\beta_1\), it follows that \(U_{\mathrm{br}.2}<U_{\mathrm{br}.1}\) and \(U_0 \simeq U_{\mathrm{br}.2}\).
Let us also determine the relation between \(U_{\mathrm{br}.1}\) and \(U_{\mathrm{br}.2}\) under satisfaction of (2), equality of the time \(t_z\), the duration of the pulse front \(t_f\), and the condition of obtaining the greatest ratio
\[ \frac{U_{a.\max}}{U_{a.\min}}. \]
The breakdown condition for the first gap is written as follows:
\[ U_a-U_0=U_{\mathrm{br}.1}. \tag{5} \]
Since it is necessary to have
\[ U_{\mathrm{br}.2}\leqslant U_{a.\min},\qquad U_{\mathrm{br}.1}\leqslant U_{a.\min}+U_0, \tag{ } \]
then
\[ \frac{U_{\mathrm{br}.2}}{U_{\mathrm{br}.1}}<1,\qquad U_0 \simeq U_{\mathrm{br}.2}. \]
Determining from (5) \(U_{a.\max}\) for \(U_0\simeq U_{\mathrm{br}.2}\) and combining this expression with (6), we find:
\[ \frac{U_{\mathrm{br}.1}}{U_{\mathrm{br}.2}}=2,\qquad \frac{U_{a.\max}}{U_{a.\min}}=3. \tag{7} \]
Consequently, with a long pulse front, when the development time of the discharge in the gap is much less than the duration of the pulse front \(t_f\), with an unchanged gap length one can have a threefold change in amplitude with a delay of the appearance of the spark \(t_z\simeq t_f\).
The experimental arrangement is shown in Fig. 1, b.
The studies were carried out with a discharger filled with nitrogen. Steel electrodes 8 mm in diameter had rounded edges. The lengths of gaps \(\delta_1\) and \(\delta_2\) were adjustable and could be illuminated by a spark. The illumination was carried out in the same way as in [5], approximately \(70\ \mathrm{ns}\) before the arrival of the pulse at the discharger under study. The voltage of the triggering pulse was distributed over the triggering gaps (with point–point electrodes) and caused breakdown of one of them, after which the other was automatically broken down.
For fixed values of \(\delta_1\) and \(\delta_2\), the pulses under study had positive polarity, a duration of \(300\ \mathrm{ns}\), and a duration
front of 0.7 nsec. S1-14 and OK-19M oscillographs were used, with resolutions of \(10^{-10}\) sec and \(10^{-9}\) sec, respectively.
Fig. 2. Dependences \(t_3(U_0)\) for \(U_a=20\) kV, ■—\(p=6\) atm, ×—\(p=11\) atm; dependences \(U_a(U_0)\) for \(t_3=5, 7, 10, 14\) nsec.
In Fig. 2 the dependences \(t_3(U_0)\) are presented for an amplitude \(U_a=20\) kV at nitrogen pressures of 6 and 11 atm and \(U_{\mathrm{br}.1}=14\) kV, \(U_{\mathrm{br}.2}=7\) kV. Because of the small magnitudes of the gaps \(\delta_1\) and \(\delta_2\), it was not possible to eliminate completely the statistical component of the time \(t_3\). At \(p=1\) atm it is eliminated completely. In Fig. 2 the curves are drawn through the points corresponding to the smallest of the observed \(t_3\) values (from 15 readings). Figure 2 also gives the dependences \(U_a(U_0)\) at different \(t_3\) for a nitrogen pressure of 6 atm. Since the breakdown delay of \(\delta_2\) is much smaller than that of \(\delta_1\), in accordance with (1) the experimental points lie on straight lines. At large negative values of the potential of the middle electrode, the time \(t_3\) decreases only slightly with increasing value of this potential. This is explained by the fact that the component of \(t_3\) due to breakdown of \(\delta_2\) remains unchanged and makes a substantial contribution to \(t_3\) when the component—
Fig. 3. Oscillograms of pulses: \(a\)—primary (period of calibration oscillations \(T=10\) nsec); \(b, c\)—converted, at \(U_a=10\) and 36 kV, respectively, \((T_k=2\) nsec). The pulse at \(U_a=36\) kV was recorded with a 15-dB attenuator.
...of \(t_z\), caused by breakdown \(\delta_1\). Therefore, the linear course of the dependences \(U_a\) on \(U_0\) at \(t_z = 5\ \mu\text{sec}\) is disrupted.
A discharge gap with an additional electrode under a nitrogen pressure of \(11\ \text{atm}\) was used as a pulse-front sharpener. It is known that in a sharpener, when the pulse amplitude is varied, it is necessary to keep \(t_z\) unchanged [2]. In two-electrode sharpeners this is achieved by adjusting the length of the gap. At \(U_{\text{pr}.1} = 14\ \text{kV}\), \(U_{\text{pr}.2} = 7\ \text{kV}\), and a primary-pulse front duration of \(30\ \mu\text{sec}\), the minimum amplitude of the transformed pulse was \(10\ \text{kV}\), and the maximum was \(36\ \text{kV}\). Consequently, the ratio
\[ \frac{U_{a\max}}{U_{a\min}} = 3.6, \]
whereas for a two-electrode sharpener at \(\delta = \text{Const}\) this ratio is slightly greater than 1 [2]. The front duration of the transformed pulse did not exceed \(8 \cdot 10^{-10}\ \text{sec}\) over the entire amplitude interval of the pulses. Oscillograms of the primary and transformed pulses are shown in Fig. 3, a, b, c.
It is not difficult to show that the discharge gap considered can be used as a valve device, i.e., it can operate under the action of pulses of one polarity and not operate for the other.
REFERENCES
- G. A. Mesyats, Proceedings of the Third Interuniversity Conference on Electron Accelerators. TSU Publishing House, 1961.
- G. A. Mesyats, ZhTF, vol. 35, No. 3, 1965.
- S. Brown, Elementary Processes in Gas-Discharge Plasma. Gosatomizdat, p. 249, 1961.
- D. Meek and D. Craggs, Electrical Breakdown of Gases. IL, 1961.
- G. A. Mesyats, Yu. P. Usov, G. S. Korshunov, Radio Engineering and Electronics, No. 5, 1964.