Amplitude-time characteristics of runaway electron beams during the breakdown phase in high-pressure gases

Results of experimental studies of the amplitude-temporal characteristics of a supershort avalanche electron beam (SAEB) with a picosecond time resolution are presented. It is shown that the maximum SAEB current and the voltage drop in the gap are timed to tens of picoseconds and that the use of sharp-ended cathode improves the stability of SAEB generation.


Introduction
The generation of runaway electrons in high-pressure gases is a fundamental physical phenomenon. Now, many papers dealing with the runaway electron beams and X-rays, which are produced at 1 atm pressure and higher are available. In the last ten years, the greatest progress was reached in this field due to the development of high-voltage pulses and optimum gas diode designs, subnanosecond and picosecond current sensors, and high-resolution real-time oscilloscopes. There are also theoretical models of the processes occurring in gas diodes within several and split picoseconds. The latest results of experimental and theoretical research in runaway electrons and in diffuse discharges are summarized elsewhere [1,2]. Analysis of these results shows that the parameters of runaway electron beams obtained by researchers differ greatly. It seems to be a consequence of different experimental and measurement conditions, as well as due to the limited number of studies, in which the oscilloscopes operating at 30 GHz and 100 GS/s are used. We know about only several studies, in which the time resolution was close to the maximum one of those available today. They are applied by the Institute of High Current Electronics, Tomsk [3,4], and the Institute of Electrophysics, Ekaterinburg [5].
Here, we report the experimental study of a picosecond resolution allowing further researches in the field of runaway electron beams generated in subnanosecond breakdowns in the air of an atmospheric pressure. In the study, we measured the amplitude-time characteristics of runaway electron beams and the breakdown voltage, as well as followed the time correlation between the maximum supershort avalanche electron beam current and the voltage drop across the gap.

Experimental setup
The setup shown in figure 1 was used in our experiments. It assembled a SLEP-150 pulser, a gas diode, and a measuring system. The collector receiving part was 3 mm in diameter. One of the electrodes of high-voltage line 1 was the peaking switch 2, allowing us to decrease the line length and  The parameters of a SAEB were measured with two cathodes, one of which was a stainless steel foil tube of 6 mm diameter and 100 m thickness (cathode 1). Another one was a stainless steel ball of 9.5 mm diameter (cathode 2). The anode of gas diode was an aluminum foil 8 of 10 m thickness, which was reinforced with a grid or a collimator 9 from the collector side. In a series of experiments, the foil was removed, and the collimator served as the anode. Thus, the SAEB was measured through 1-mm collimator hole without any attenuation by aluminum foil. The time resolution of collector reached 20 ps [4].
The measuring equipment also included a capacitive voltage divider and a current shunt. The signals from the divider, shunt, and collector were transmitted to a LeCroy WaveMaster 830Zi-A realtime digital oscilloscope (the bandwidth 30 GHz, the sampling increment 12.5 ps) via RG58-A/U high-frequency cables (Radiolab) of 1 m length with N-type (Suhner 11 N-50-3-28/133 NE) and SMA-type connectors (Radiall R125.075.000). To register the signal of voltage attenuation, we used 142-NM high-frequency attenuators (Barth Electronics) with a bandwidth of up to 30 GHz. The signal from the collector was transmitted to the oscilloscope without attenuators, either with or without anode foil. The voltage and the SAEB current were measured simultaneously in each pulse. The timing accuracy of SAEB and voltage pulses were not worse than 10 ps. The SAEB generation time with respect to the voltage pulse was determined from the capacitive current fed to the collector. For this purpose, the collimator was removed, and the foil was replaced by a grid of 64 % transparency. This procedure is described in details elsewhere [6]; the voltage timing accuracy and SAEB pulses were not worse than 50 ps. The SAEB and X-rays were detected using the blackening of RF-3 film, in a black paper envelope of 120 m thickness placed downstream to Al foil anode. The discharge plasma glow in the gap was photographed using Sony A100 camera.

Results and discussion
The nanosecond voltage pulse applied to the gap with the sharp-ended cathode, in an inhomogeneous electric field, gives rise to a discharge, in which runaway electrons are generated [1,2] This discharge mode is termed a runaway electron preionized diffuse discharge or REP DD [7] and is described in detail elsewhere [1]. The glow of diffuse discharge is much brighter than that of the corona. As far as d is further decreasing, we observed the sequence of three discharge forms in the gap: a corona discharge (detected by high-resolution CCD camera), a REP DD, and a spark, into which the REP DD was transformed during the voltage pulse. The duration of diffuse and spark discharges as well as the energy deposited in the gas by every discharge depends on the gap width, cathode design, air pressure, and voltage pulse parameters. In the course of the REP DD formation, an ionization wave starts from the sharp-ended electrode. When the wave front reaches the opposite electrode, the runaway electron beam of the highest amplitude is detected downstream of the thin foil anode.
In our experiments, the SAEB parameters were studied when the cathode 1 was at an interelectrode gap of 4-35 mm and when the cathode 2 was at the gap of 4. 6 and 8.5 mm. The imprint left on the film by the electron beam downstream to the anode foil without the collimator was 54 mm in diameter, i.e. covering the entire foil surface. The maximum film exposure was observed when we pplied the tubular cathode 1 at a gap of 12 mm or less, near the sharp end of the cathode. Near the central axis the exposure decreased. The decrease of film exposure was more noticeable at small interelectrode gaps and when the distance from the central region of the foil increased.
Waveforms of the voltage and SAEB current for the cathode 1 at d = 12 mm are presented in figure  2. Figure 2. Waveforms of the voltage (a,c) and the SAEB current (b,d) pulses. The SAEB was registered by a collector with the 3-mm-diameter receiving area, which was located behind a collimator with 1-mm-diameter hole and 10-μm-thick aluminium foil (a,b) and behind a collimator without a foil (c,d). The gap width is d = 12 mm. The cathode is a tube of 6-mm-diameter.
The runaway electron current was measured through the collimator hole (1 mm diameter) with and without anode foil of 10 m thickness. The FWHM and the amplitude of the SAEB without foil changed insignificantly, which indicated that the collector did not detect electrons of an energy higher than 32 keV. However, the SAEB pulse rise times in these two cases differed. With no anode foil, there was a prepulse (figure 2(d), symbol P), whereas the beam current measured with the anode foil rose steeper ( figure 2(b)). Hence, the energy of runaway electrons that contribute to the prepulse is no greater than 32 keV. It is seen from the figures for the timed SAEB pulse and the voltage drop.
Waveforms  The runaway electron current was measured through the collimator hole (1 mm diameter). A decrease of the gap width d decreased the voltage amplitude, as well as the SAEB amplitude and FWHM. The interelectrode gap d = 12 mm was optimal for the cathode 1. At d = 18 mm, the voltage amplitude increased but the SAEB amplitude decreased. An increase of the interelectrode gap increased the FWHM of SAEB, which can be explained by the longer time of ionization wave transition through the gap at large d. As the distance to the anode foil increased, the prepulse was detected (figure 3(d), symbol P). Figure 3 shows that the SAEB pulses and the voltage drop are timed, similar to the case when the gap was equal to 12 mm. Figure 4 shows waveforms of the voltage and SAEB for the cathode 2 at d = 6 mm.  The average electric field strength at the surface of cathode 2 was lower than that at the sharp end of the cathode 1, and the breakdown voltage increased. The spread of breakdown delay times and breakdown voltage amplitudes became larger. The beam current measured through the collimator hole decreased. However, the SAEB generation and the voltage drop in the gap were timed as before (figures 2 and 3). The increase of breakdown delay time proportionally increased with delay time of the SAEB generation.
Analyzing the oscilloscope traces obtained with high time resolution, we can distinguish the following features. First, the maximum of the SAEB current and the voltage drop in the gap are timed to high accuracy for both cathodes. At the moment when the collector records the maximum SAEB current, the voltage across the small and optimal gaps decreases steeply. In air of an atmospheric pressure, when the voltage amplitude is of hundred kilovolts, the FWHM of SAEB current measured through the collimator holes of small diameters, with the cathode 2 and d = 4 mm can be ≈25 ps. Downstream to the entire anode foil surface, the FWHM of SAEB is 100 ps.

Conclusion
Thus, the experimental research of the amplitude-time characteristics of runaway electron beams with picosecond resolution and the discharge characteristics in air of an atmospheric pressure allows the following conclusions. 1. The maximum SAEB current and the voltage drop in the gap are timed to an accuracy of tens of picoseconds. 2. As far as the gap with cathode foil tube of 6 mm diameter and 100 m thickness increases, we detect electrons, the energy of which was less than 32 keV before the main beam current pulse. 3. The use of sharp-ended cathode 1 stabilizes the breakdown delay time and voltage, ensuring better stability of SAEB generation.
The amplitude-time characteristics of runaway electron can be caclulated using new hybrid mathematical model [8]. Detailed results will be given in the nearest future.