Nanosecond Discharge Plasma and Its Application in Assisting Oxidation Influence of electrode spacing and gas pressure on parameters of a runaway electron beam generating during the nanosecond breakdown in SF 6 and nitrogen

This study deals with experimental and theoretical simulation data showing the influence of electrode spacing and gas pressure on parameters of a supershort avalanche electron beam (SAEB) formed in SF6 and nitrogen at different rise times and amplitudes of a voltage pulse. Using GIN-55-01, VPG-30-200, and SLEP-150M pulsers, tubular cathodes with a diameter of 6 mm, as well as gaps of 3, 5, and 8 mm, it was shown that the SAEB current amplitude can both increase and decrease depending on an electrode spacing, a waveform and a rise time of the voltage pulse, as well as the pressure of SF6 and nitrogen. It was established as a result of simulation that maximal voltage across the gap during the process of generation of runaway electrons and the thickness of an anode foil have a major effect on the SAEB current pulse amplitude.


Introduction
By now, many research papers have reported on the generation of X-rays and runaway electron (RAE) beams during the nanosecond breakdown in high-pressure gases, including atmospheric-pressure air, at the voltage pulse amplitude of ∼100 kV and higher (see, e.g.related studies [1][2][3][4][5][6][7][8][9][10], reviews [11,12], and monographs [13,14]).The study of this phenomenon allowed us to understand what basic requirements should be met for detection with collectors of runaway electron beams in gas diodes and gave us the idea of how the amplitude and duration of the beam's current pulse are influenced by the gas kind and pressure as well as by the rise time and the amplitude of the voltage pulse.However, very few comprehensive data on parameters of RAEs in heavy gases such as sulphur hexafluoride (SF 6 ) are available.As far as RAEs at the breakdown in SF 6 are concerned, only three scientific teams have reported their detection.
In [15], the information about generation of RAEs behind the anode foil at the breakdown in SF 6 was first presented.Quantity of RAEs measured by darkening the X-ray film was ∼10 8 per pulse.This amount was approximately one order of magnitude lower than that in atmospheric-pressure air.Time behaviour of the RAEs was measured with the detector consisted of a scintillator and a photomultiplier and having the temporal resolution no better than 3.5 ns.It was reported that energy of RAEs in SF 6 was higher than that in air, as well as the possibility of generation in both SF 6 and air a monoenergetic RAEs beam with anomalous energy [15][16][17].The term 'anomalous' electrons with energy higher than eU m (eelectron charge, U m -maximum voltage across the discharge gap during the generation of RAEs).In [15,16], it was proposed that the electron beam current in SF 6 is less than that in air due to the process of electron attachment to SF 6 molecules.
It should be said that important experimental results on RAEs in different gases were obtained by the scientific team headed by V.F.Tarasenko (IHCE SB RAS, Russia).It was found that the energy spectrum of electrons registered behind the anode foil consists of at least three groups [18][19][20].Moreover, under optimal conditions, the number of electrons with anomalous energy was not >10% of the total number of RAEs.In papers of this team, a beam of RAEs registered behind the anode foil was named a supershort avalanche electron beam (SAEB).Registration of a SAEB with a collector having subnanosecond temporal resolution was firstly carried out in [21], where the nanosecond-pulse discharge was formed with a RADAN-220 pulser.A SAEB was obtained in six different gases, including ones with a high atomic mass (e.g.Kr, Xe etc.).It was shown that the full-width at half-maximum (FWHM) of the SAEB current pulse in SF 6 and other gases at atmospheric pressure was about 100 ps.Furthermore, energies of electrons of the SAEB in air and SF 6 were compared.It was shown that at 0.5-ns rise time of the voltage pulse, all other things being equal, energy of electrons of the SAEB in air was higher than that in SF 6 [20].An increase in the voltage pulse rise time to 2 ns led to a decrease in the difference in the electron energy of the SAEB in air and SF 6 [3].Thus, the differences in energy of electrons in [3,[15][16][17]20] and can be explained not by the electronegativity of the SF 6 gas, but by the error in measuring the duration of the voltage pulse rise time in the last.
According to the research in [6] all energies of RAEs in atmospheric-pressure air are not higher than eU m .There, it was pointed that RAEs with anomalous energy were not detected in atmospheric-pressure air when voltage pulses with a subnanosecond rise time were applied across the discharge gap, indicating no RAEs with anomalous energy in atmospheric air existed.In [22], an attempt to measure SAEB parameters during the discharge in atmospheric-pressure SF 6 was unsuccessful.This can be explained by the use in [6] a RADAN-303 pulser having the voltage pulse rise time of ∼1.5 ns, which is slower than that for RADAN-220 pulser (∼0.5 ns).However, because the amplitude of SAEB current pulse in air was higher than that in SF 6 , one in air was obtained.
In 2014, detailed investigation on the parameters of the SAEB in SF 6 with temporal resolution of up to 90 ps were carried out jointly by the scientific group from Institute of Electrical Engineering (China) and Tarasenko's team [3,9].It was found that the SAEB in SF 6 can be obtained at pressures up to 0.2 MPa, as well as its FWHM depended on SF 6 pressure and the voltage pulse amplitude.In addition, it was shown that the main effect on the SAEB current pulse amplitude was not due to the electronegativity of gases, but their atomic weight [9].
From all the statements about the RAEs at the breakdown in SF 6 , air and nitrogen mentioned above, it is easy to understand that there is no consensus of opinions regarding the characteristics of RAEs in air and heavy gases and their generation mechanism among scientific teams .Therefore, it is necessary to carry out new research to eliminate misunderstandings.Note that the study of discharge in SF 6 has not only scientific importance, but also great practical importance, because SF 6 is widely used as insulating gas in high-voltage devices [28,29] and a component of the chemical gas lasers [30,31].
Here we study the amplitude and the duration of the runaway electron beam current in SF 6 and nitrogen at a pressure of 1-100 kPa, the electrode spacing of 3, 5, and 8 mm, and applied voltage pulses differing in a rise time, a duration, and a shape.
Our study was inspired by the results obtained earlier in [32,33].It was found that the amplitude of a runway electron beam current realised in SF 6 with a tubular cathode of 6 mm in diameter at the voltage rise time of ∼2 ns increased considerably as the gap width was decreased from 12 to 8 mm [32].Reasoning that the beam amplitude is determined by the voltage across the gap, all other things being equal, at the instant of generation of runaway electrons , it can be assumed that a decrease in the electrode spacing increased the gap voltage [32].The assumption is indirectly supported by research data on a runaway electron beam produced in nitrogen with the gap of 12 mm and tubular cathode with the diameter of 6 mm at the voltage rise time of 0.3 ns [33], showing a considerable increase in the voltage across the gap and the beam current amplitude with a decrease in the pressure.The electron beam produced in a gas diode and measured behind the anode foil is hereinafter referred to as a supershort avalanche electron beam or SAEB [34].
In this paper, we also simulate the main processes occurring in a gas diode and determine the beam parameters for gaps of 3, 5, and 8 mm.

Experimental setup
The SAEB parameters were studied on three experimental setups with three different pulsers forming voltage pulses of negative polarity and three gas diodes.Each setup consisted of a pulser and the gas diode designed for this pulser, as well as a measuring system.The setup No. 1 included a GIN-55-01 pulser (FID Technology [35]) which produced triangular voltage pulses with the FWHM of ∼1 ns, the rise time of ∼0.7 ns, the fall time of ∼5 ns, and the amplitude in idle mode of ∼110 kV.The gap was formed by a sharp-ended cathode (with a small radius of curvature) and a flat anode.The cathode was made of aluminium or stainless steel and was shaped as a tube with the diameter of 6 mm, the wall thickness of 1 mm and the thickness of its edge facing the anode of 100 μm.The flat anode, through which electrons were extracted, was a 10-μm-thickness aluminium foil.More detailed design of a similar gas diode is in [36].
The setup No. 2 was based on VPG-30-200 pulser [37] which produced trapezoidal voltage pulses with the FWHM of ∼4 ns, the rise time of ∼2 ns, and the amplitude in the incident wave of 15-100 kV.The voltage amplitude in idle mode could range from 30 to 200 kV, and its value in our experiments was 160 kV.The gap was formed by a sharp-ended cathode and a flat anode.The cathode was a stainless steel tube with the inner diameter of 6 mm and the edge thickness of ∼100 µm.The flat anode, through which electrons were extracted, was a 10-μm-thickness aluminium foil.More detailed design of a similar gas diode is in [32].
In the setup No. 3, a SLEP-150M pulser [37] which produced trapezoidal voltage pulses with the FWHM of ∼1 ns, the rise time of ∼0.3 ns, and amplitude of ∼120 kV in its transmission line was used.The cathode was a stainless steel tube with the inner diameter of 6 mm and the thickness of 100 μm.The anode, through which electrons were extracted, was a 15-μm-thickness flat aluminium foil.More detailed design of a similar gas diode is in [11].
The distances between electrodes were 3, 5, and 8 mm.The diode was pumped with a fore-vacuum pump and filled with SF 6 or nitrogen via metal pipe system.The gas pressure in the diode was varied from 1 to 100 kPa.The pulse repetition frequency was no >1 Hz.Use the above setups allowed to carry out research in a wide range of experimental conditions.
The measuring devices were capacitive voltage dividers and aluminium collectors.On setups Nos. 1 and 3, the diameters of the collector's receiving parts were 20 and 13 mm, respectively.Temporal resolutions of ones were 80 and 50 ps, respectively, [38].The signals from these sensors were transmitted to a DSO-X6004A digital real-time oscilloscope (6 GHz, 20 GS/s) (Keysight Technologies, USA) via RG58-A/U high-frequency cables (Antenna Network Lab Inc., USA) having a length of 1.5 m with N-type connectors Suhner 11 N-50-3-28/133 NE (HUBER + SUHNER, Switzerland) and SMA connectors Radiall R125.075.000(Radiall, France).Under the experimental conditions, the temporal resolution of the oscilloscope was 100 ps.The waveforms were recorded in a single pulse mode, as well as averaged (normally over 16 pulses).For signal attenuation, 142-NM high-frequency attenuators (Barth Electronics, USA) with a bandwidth of up to 30 GHz were used.
On setup No. 2, the collector's receiving part was 30 mm in diameter.Its temporal resolution was 150 ps [38].The signals from the detectors were transmitted via RF cables with length of 4 m to a LeCroy WaveMaster 808Zi-A digital real-time oscilloscope (8 GHz, 40 GS/s), having a temporal resolution better than 80 ps.Nevertheless, the collector used in this setup restricted its temporal resolution.

Setup No. 1
Since the parameters of the voltage pulses of the setups were different, the measurement results are given for each of the ones.Fig. 1 shows the maximum and minimum SAEB current amplitudes and the SAEB current amplitude averaged over 16 pulses at different SF 6 pressures for the electrode spacing d of 3 and 8 mm.
Due to this setup, the amplitude of triangular voltage pulses with a FWHM of ∼1 ns in idle mode was no >110 kV, the beam current in SF 6 at 100 kPa was low and it was difficult to distinguish it against the background of electromagnetic noise.Therefore, SAEB current amplitudes are presented from 50 kPa.
On setup No. 1 at the voltage rise time of 0.7 ns, decrease in the SF 6 pressure led to an increase in the SAEB current amplitude for all three gaps (Fig. 2a).
The highest SAEB current pulse amplitudes under these conditions were registered for the electrode spacing of 8 mm.The breakdown voltage U br for the 8 mm gap was also maximal and varied slightly with decreasing pressure.Reducing the electrode spacing led to a decrease in the breakdown voltage and the SAEB current amplitude.The pressure dependencies for three gaps were similar, as evidenced by the SAEB current amplitudes averaged over 16 pulses in Fig. 2. The highest SAEB current pulse amplitudes on setup No. 1 were registered for the electrode spacing of 8 mm and low SF 6 pressure.
The SAEB current in nitrogen on this setup was also highest for the largest electrode spacing.However, the pressure dependences of the SAEB current were different (Fig. 3).
For the gaps of 5 and 8 mm, decrease in the pressure below 100 kPa first led to an increase in the beam current, and then, the current decreased.For the 3 mm gap, the SAEB current began to decrease at 100 kPa.The SAEB current in nitrogen, like in SF 6 , was maximal for the 8 mm gap but at a higher pressure compared to SF 6 .When the electrode spacing was of 3 and 5 mm, the breakdown voltage decreased and so did the SAEB current pulse amplitude I b .
The FWHM of the beam current pulse in SF 6 was weakly dependent on pressure in the range of 10-50 kPa and in nitrogen at 10-100 kPa.Fig. 3b shows its maximum, minimum, and averaged (over 16 pulses) values as a function of SF 6 pressure for d = 3 mm.An average value of the FWHM in this pressure range was ∼110 ps for the both SF 6 and nitrogen.

Setup No. 2
Fig. 4 shows the breakdown voltage U br and average SAEB current pulse amplitude as a function of nitrogen pressure for the gaps of 5 and 8 mm.Fig. 5 presents waveforms of the voltage and the beam current for the same pressures and electrode spacing 5 mm.
The voltage rise time on setup No. 2 was ∼2 ns.The values of U br for the gaps of 5 and 8 mm differed slightly and decreased with decreasing pressure.However, the SAEB current amplitudes in both cases varied differently with decreasing pressure.As the pressure was decreased, the beam current for the 8 mm gap decreased, whereas that for the 5 mm gap it increased.Unlike the data obtained on setup No. 1, the SAEB current pulse amplitude was highest for the smallest electrode spacing d = 3 mm.It should be noted that the duration of the SAEB current pulse measured with collector having 30-mm-diameter receiving part was ∼150 ps (Fig. 5b) and corresponded to the temporal resolution of this detector.
In SF 6 , like nitrogen, the beam current had the highest value at d = 3 mm.Fig. 6 shows the breakdown voltage U br and SAEB current pulse amplitude I b in SF 6 as a function of pressure for the gaps of 3, 5, and 8 mm.
The U br for all d changed slightly with decreasing p.The pressure dependencies of the beam current amplitude in Fig. 6b reveal a portion on which the beam current first decreases with decreasing pressure and then begin to increase.For the 8 mm gap, the pressure at which the SAEB current pulse amplitude in SF 6 begins to increase is lower than that for the 5 mm gap.Such dependencies are observed under slight changes in the breakdown voltage.The experiments on setup No. 2 demonstrate that at comparatively long voltage pulse rise times (∼2 ns), the SAEB current pulse amplitude in SF 6 and nitrogen increases with decreasing d and that its behaviour in response to the decrease in pressure from 100 to 5 kPa differs for different d.These data are distinct from the results obtained on setup No. 1.Note that the amplitudes of the SAEB current pulse on the setup No. 2 at higher voltage pulse amplitudes were less than those on setup No. 1.This is due to longer voltage pulse rise time.

Setup No. 3
On setup No. 3, the voltage pulse rise time was ∼0.3 ns.As the SF 6 pressure was decreased, the breakdown voltage changed slightly, and as the nitrogen pressure was decreased below 50 kPa, the breakdown voltage increased (Fig. 7a), as was observed earlier [33].
The SAEB current pulse amplitude on setup No. 3 increased with decreasing pressure of both gases.Fig. 7b shows the SAEB current pulse amplitude as a function of nitrogen pressure for d = 8 mm.The beam current was the highest at d = 12 mm in nitrogen and at d = 8 mm in SF 6 .The optimal electrode spacing in nitrogen for the tubular cathode having a diameter of 6 mm and thickness of 100 μm was the same as that found earlier [39].At pressures of 10-100 kPa, the FWHM of the beam current pulse in both gases was almost unchanged and was ∼100 ps.Thus, the value of U br in nitrogen at the subnanosecond voltage pulse rise time increases with decreasing pressure, and in SF 6 , it varies slightly, allowing an increase in the SAEB current pulse amplitude.
At this setup, the maximal SAEB current pulse amplitudes were obtained.This is due to a shorter rise time duration and the higher amplitude of a voltage pulse in comparison with setups Nos. 1 and 2.

Theoretical model
The experiments revealed at least one unexpected fact: in some cases, the SAEB current in nitrogen decreased rather than increased with decreasing the pressure, all other things being equal, which is unexpected from general considerations.Such a behaviour of the beam current in nitrogen can readily be seen in Fig. 3а.Sometimes, the same situation was observed in SF 6 , as evidenced in Fig. 6b.
For elucidating the causes of this behaviour, the discharge current in nitrogen was simulated with using a hybrid model [25,39].Basically, assuming the fraction of high-energy electrons to be negligible and not affecting the discharge, the dynamics of different components of low-temperature discharge plasma was described in a drift-diffusion approximation and solved the Boltzmann equation for runaway electrons using data on the electric field distribution and particle generation [25].
Reasoning that the theoretical model in its current version is applicable only to one-dimensional (1D) spatial problems and that the discharge inhomogeneity in our experiments was high, the diode geometry in the simulation was coaxial.A detailed description of the model, simulation results for a coaxial diode filled with SF 6 , and comparison with experimental data can be found elsewhere [39].
Thus, we simulated the discharge in a coaxial diode filled with nitrogen in an inhomogeneous electric field roughly typical for the gap between a sharp-ended 0.5-mm-radius inner electrode and an outer electrode made of 10-µm-thickness Al foil.In the simulation the diode length was 1 cm.The voltage pulse applied to the diode was bell-shaped and had the amplitude of 90 kV and the FWHM of 1 ns.The operation of the transmission line was modelled by an equivalent resistance of 75 Ω connected in the series circuit between the voltage source and the discharge gap, allowing us to adequately simulate the voltage across the gap at rapidly varying discharge resistance.The range of nitrogen pressure was the same as that used in the experiments (Fig. 3а).Fig. 8 presents calculated time dependences of the voltage across the gap and the current of fast electrons behind the 10-μmthickness Al foil at different nitrogen pressures.
As can be seen from the figures, the current of runaway electrons tends to increase with decreasing the pressure and drops at <20 kPa, though the reduced field strength E/p grows.The simulation shows that a decrease in the pressure speeds up the ionisation processes in the gap compared to their rate at high pressure.As a result, the current switches earlier and the maximum voltage across the gap is lower than its value at high pressure.Thus, the average energy of runaway electrons arriving at the anode decreases, their attenuation factor through the anode foil rises steeply, and the amplitude of the beam current behind the foil decays [40].Calculated spectra of the electron beam behind the anode foil are presented in Fig. 9.It is notable that the maximum energies in the spectra in Fig. 9 are slightly higher than eU max (U max is the discharge voltage amplitude in Fig. 8a).This fact suggests the presence of runaway electrons with so-called anomalous energy in the discharge.Their generation and nature are considered in detail elsewhere [11, 15-20, 39, 41].
The advantage of the theoretical modelling was that we could 'see' all electrons in the discharge.As the pressure was decreased, the number of runaway electrons arriving at the anode always increased with a decrease in their average energy (at constant parameters of the voltage pulse produced by the pulser), and because the attenuation factor through the foil at low energies of incident electrons increased steeply, the low-energy spectrum of runaway electrons was highly filtered and we observed a decrease in the total number of fast electrons passed through the foil.

Discussion
The experimental data suggest that varying the voltage pulse parameters can greatly change the pressure dependence of the SAEB current amplitude.A decrease in the gas pressure in the case of an unchanged breakdown voltage or its increase leads to an increase in the parameter U m /pd, and, accordingly, increases efficiency of the generation of RAEs.In this case, the amplitude of the SAEB current increases.When the breakdown voltage and gas pressure decrease, the parameter U m /pd can both decrease and increase.This leads to different dependencies of the SAEB current amplitude on the gas pressure.It should be noted that the SAEB current is also influenced by the cathode material and design.All these factors primarily influence the voltage across the gap at the instant at which runaway electrons are produced.
First of all, it should be said that it would be unreasonable to expect any strict quantitative coincidence between the experiments and simulation.In the simulation, the discharge was ID, whereas its actual structure was 3D along both its axis and azimuth.Nevertheless, the simulation properly reflects the main trends of the response of the system parameters to varying external conditions and gives the proper order of magnitude for the number of fast electrons, thus showing a good agreement with the experiments.Thus, calculations of the pressure dependencies of runaway electron current correlate well with experimental data in nitrogen.The non-monotonic pressure dependence of the beam current is due to a decrease in the mean electron energy and, as a result, a decrease in their number behind the Al foil.
In particular, the pressure at which the beam current changes its ascending tendency and drops is much lower in SF 6 (∼2.5 kPa at d = 3 mm) than in nitrogen.This is because the discharge voltage in SF 6 remains high (above 30 kV) up to very low pressures and the thin foil is almost transparent for electrons.The pressure at which the beam current changes its ascending tendency and drops is much lower in SF 6 (∼2.5 kPa at d = 3 mm) than in nitrogen.This is because the discharge voltage in SF 6 already remains high (above 30 kV) up to very low pressures and the thin foil is almost transparent for electrons.
The experiments show that the breakdown voltage depends on many factors and in an intricate manner.It is known that decreasing the gas pressure at relatively long voltage pulse rise time leads to decrease in U br .It should be said that in this case a slight increase in SAEB current amplitude is observed.However, the largest increase in the SAEB current amplitude is occurred when due to subsequent decrease in gas pressure the value of U br begins to increase.In particular, the use of cathodes with a less radius of curvature stabilises the breakdown processes but reduces the maximum voltage across the gap.The use of cathodes with a high work function increases the breakdown voltage, and if the voltage amplitude is sufficiently high, the beam current increases.In our experiments, such an increase was observed on setup No. 3 when the Al cathode was replaced by the stainless steel one.However, on setup No. 1 with a short triangular excitation pulse of limited amplitude (110 kV), the electron beam current in nitrogen was highest for the Al cathode.

Conclusion
Our research results allow us to conclude that parameters of a SAEB detectable behind the anode of a gas diode depends intricately on the electrode spacing, kind of working gas, pressure, and the amplitude and the rise time of an applied voltage.Decreasing the pressure of nitrogen and SF 6 in the range of 100-10 kPa can both decrease and increase the SAEB current amplitude depending on the electrode spacing.The experiments and the simulation at duration of the voltage pulse rise time of 1 ns agree and suggest that the SAEB current amplitude is strongly affected by the voltage across the gap during the generation of the beam and by the gas pressure in the diode.Increasing voltage across the gap or decreasing pressure of nitrogen and SF 6 from 100 to 10 kPa with the voltage across the gap kept constant leads, as a rule, to an increase in SAEB current amplitude.However, if we change the cathode design, e.g. the curvature radius, or the shape and the amplitude of applied voltage with a simultaneous decrease in pressure and voltage across the gap during the generation of runaway electrons, we can obtain a decrease in SAEB current.Such dependences were observed in nitrogen at d = 8 mm on setup No. 2.
At small values of electrode spacing, the response of SAEB current to the decrease in pressure from 100 to 10 kPa depends strongly on the kind of gas.In SF 6 , decreasing the gas pressure increases the SAEB current amplitude at all d studied (3, 5, and 8 mm) and on all three setups.In nitrogen, the SAEB current amplitude on setup No. 1 at d = 3 mm decreases with decreasing the pressure.
At the 2-ns voltage pulse rise time, the SAEB current in SF 6 reaches its maximum amplitudes when d is 3 mm, and at the 0.7-ns voltage pulse rise time, when d is 8 mm.
Based on the experimental and simulation results obtained, it is possible to draw an unambiguous conclusion about the effect of RAEs on the breakdown process during the nanosecond-pulse discharges.However, this influence has complex dependencies and requires further research.
The results of this work will be useful for gases used as insulating media and fillers [28] of spark gap switches [29], as well as non-chain HF and DF lasers [30,31].

Fig. 7 Fig. 8 Fig. 9
Fig. 7 Setup No. 3, tubular stainless steel cathode with the diameter of 6 mm (a) Breakdown voltage U br (averaging over ten pulses) versus nitrogen pressure, (b) SAEB current I b aver behind Al foil of thickness 15 μm, collector receiving part 13 mm, (averaging over ten pulses) versus nitrogen pressure