3.1. Observed Forms of Discharge in Atmospheric-Pressure Air and Nitrogen

The form of the discharge excited after applying a nanosecond voltage pulse to a gap with a non-uniform distribution of the electric field depends on the gap length d (Tarasova et al., Reference Tarasova, Khudyakova, Loiko and Tsukerman1974; Babich, Reference Babich2003; Yakovlenko, Reference Yakovlenko2007; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a ; Levko et al., Reference Levko, Krasik and Tarasenko2012; Tarasenko, Reference Tarasenko2014). At large values of d, a diffuse corona discharge forms near the cathode. As d decreases, the diffuse discharge fills the entire gap and the brightness of its glow increases. In (Tarasenko et al., Reference Tarasenko, Orlovskii and Shunailov2003a ), this discharge mode was proposed to be called a volume discharge initiated by an avalanche electron beam (VDIAEB). In the English-language papers, we use more short term REP DD – Runaway Electrons Preionized Diffuse Discharges. The REP DD was discussed in detail in (Tarasenko, Reference Tarasenko2014). Figure 3a and 3b shows photographs of the plasma glow of REP DDs in nitrogen and air obtained on the setup with the RADAN-220 pulser (see Fig. 1).

Fig. 3. Time-integrated images of the discharge plasma glow in atmospheric-pressure nitrogen (a) and air (b, c), as well as SAEB print on an RF-3 film (d), obtained on the setups with the RADAN-220 pulser (a, b) and the SLEP-150 pulser (c, d) per one pulse. Gap lengths is 14 mm (a, b) and 11 mm (c, d). The diameter of the tubular cathode located on the left in frames (a) and (b) is 6 mm, and that of the tubular cathode located in the centers of frames (c) and (d) is 7 mm.

An atmospheric-pressure diffuse discharge forms in both nitrogen and air. Bright spots appear only on the cathode with a small curvature radius. Short anode-directed spark leaders growing from the cathode spots are also seen. In the gas-filled diode filled with nitrogen, the diffuse discharge is visually more uniform and contacts the side surface of the tubular cathode (Fig. 3a). It is seen in the photograph of the REP DD in air that the diffuse discharge consists of separate jets (Fig. 3b).

Figure 3c shows a photograph of the integral REP DD plasma glow taken from the side of the grid anode on the setup with the SLEP-150 pulser. A bright glow consisting of diffuse jets, which are closed on the grid, is observed near the annular cathode. At observation of the REP DD plasma glow in atmospheric-pressure nitrogen or air through the side window (Fig. 3a, 3b), the glows of separate jets in the integral photographs overlap and, they become almost indistinguishable. As the gas pressure increases, the diameters of separate diffuse jets decrease and they become visible when being observed through the side window (Tarasenko, Reference Tarasenko2014). At pressures below the atmospheric one, the diffuse jets overlap and they are usually not seen in the integral photographs. Bright spots from which diffuse jets emerge are seen at the cathode edge (Fig. 3c) as in Figure 3a and 3b. Short small-diameter diffuse jets that do not reach the grid are also observed. In Figure 3c, a low-intensity air glow is also observed in the region of the gas-filed diode remote from the cathode. It is seen from Figure 3c that the axial region of the gap with diameter nearly equal to the diameter of the tubular cathode has the lowest glow intensity. However, at d = 12 mm, no decrease in the blackening of the RF-3 film near the axis of the gas-filed diode with the 6-mm-diameter tubular cathode was observed in the print of the RE beam (Fig. 3d). The difference between the regions of the REP DD plasma glow and the print of the electron beam is due to the fact that the SAEB is generated about 300 ps after applying the voltage pulse to the gap and has a duration of about 100 ps, whereas the plasma glow lasts for several tens of nanoseconds and reaches its maximum intensity about 500 ps after SAEB generation (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a ; Levko et al., Reference Levko, Krasik and Tarasenko2012; Tarasenko, Reference Tarasenko2014). In addition, the SAEB electrons are emitted into a wide angle, due to which the size of the beam print increases substantially (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a ). As the diameter of the tubular cathode increases, both the film blackening and the SAEB current density near the diode axis decrease (Tarasenko, Reference Tarasenko2011).

At d ≤ 10 mm, a cathode-directed spark leader formed on the background of the diffuse discharge on the setups with the SLEP-150, SLEP-150М, and RADAN-220 generators. As the gap length decreased, the spark leader transformed into a spark channel (Lomaev et al., Reference Lomaev, Rybka, Sorokin, Tarasenko and Krivonogova2009; Shao et al., Reference Shao, Tarasenko, Zhang, Baksht, Yan and Shut'ko2012; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko and Erofeev2013b ; Beloplotov et al., Reference Beloplotov, Lomaev, Sorokin and Tarasenko2014b ). As d decreased further, the brightness of the spark channel increased and the diffuse discharge became almost invisible. However, our studies have shown that, at a nanosecond rise time of the high-voltage pulse, the discharge in a gap with a non-uniform electric field first operates in the diffuse mode and, then, constricts (Lomaev et al., Reference Lomaev, Rybka, Sorokin, Tarasenko and Krivonogova2009; Shao et al., Reference Shao, Tarasenko, Zhang, Baksht, Yan and Shut'ko2012; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko and Erofeev2013b ; Beloplotov et al., Reference Beloplotov, Lomaev, Sorokin and Tarasenko2014b ; Tarasenko, Reference Tarasenko2014). As will be shown below, the SAEB is generated in the initial stage of the discharge, thereby providing REP DD formation.

3.2. Waveforms of the Voltage and Discharge Current Pulses

Figure 4 shows waveforms of the voltage pulses and the current through the gap for three values of d. When the REP DD forms on the setups with the RADAN-220 and SLEP-150 pulsers, the resistance of the diffuse discharge plasma is usually lower than the wave impedance of the pulsers. As a result, an oscillatory discharge mode takes place. At d = 12 and 18 mm, no more than five half-periods are observed in the waveform of the discharge current (Fig. 4b). As the gas pressure and/or the gap length d the increase, as well as when the gas-filed diode is filled with electronegative gas SF₆, the resistance of the discharge plasma increases and an aperiodic discharge mode takes place.

Fig. 4. Waveforms of the voltage (a) and discharge current (b) pulses at different gap lengths. The cathode is a 6-mm-diameter tube. The waveforms were obtained on the setup with the SLEP-150 pulser.

At d = 6 mm (Fig. 4), the amplitude of the gap voltage, as was expected, decreased and both the amplitude of the discharge current and the number of current half-periods increased. The results obtained using an HSFC PRO high-speed four-channel CCD camera with the minimal exposure of 3 ns (Shao et al., Reference Shao, Tarasenko, Zhang, Baksht, Yan and Shut'ko2012; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko and Erofeev2013b ) show that, at small values of d, the gap is bridged by the spark channel in several nanoseconds or less. This leads to an even larger decrease in the plasma resistance in the discharge gap and an increase in the number of oscillations of the discharge current. However, under these conditions, even at small d, the SAEB is observed in the beginning of the diffuse discharge stage before the formation of the spark channel.

Figure 5 demonstrates the initial segments of the voltage and current waveforms shown in Figure 4.

Fig. 5. Waveforms of the voltage (a) and discharge current (b) pulses registered in the initial stage of the discharge on the setup with the SLEP-150 pulser at different gap length. The cathode is a 6-mm-diameter tube. Time intervals А, B, and C correspond to the current of the “cold” diode (displacement current), dynamic displacement current, and conduction current, respectively.

In these waveforms, obtained with a high time resolution, one can distinguish three typical discharge stages that were described for the first time in our works (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c ). When the voltage pulse is applied to the gap, the well-known displacement current of a “cold” diode, that equal С(dU/dt) (where C is the capacitance of the “cold” diode and U is the gap voltage), is first registered (time interval A in Fig. 5). By the “cold” diode we mean a diode in which there is still no dense plasma that “pushes out” the electric field. Note that Figure 5 shows the voltage pulses detected by the capacitive divider located at a distance of 22 mm from the anode of the SLEP-150 pulser. First, the divider detects the front of the incident wave. About 100 ps later, the front of the reflected wave reaches the divider, after which the divider detects the sum of these two waves. As a result, the waveform of the discharge current pulse in Figure 5 is shifted with respect to the front of the voltage pulse by about 100 ps. At d = 6 mm, the displacement current continues to increase ≅250 ps after the voltage pulse has arrived at the capacitive divider, while dU/dt begins to decrease. The decrease in the dU/dt can be seen on the waveforms of the discharge current at d > 10 mm. At d = 12 and 18 mm, the decrease in the displacement current is observed ≅250 ps after the arrival of the voltage pulse at the capacitive divider, while at d = 6 mm, the current through the gap continues to increase. Within time interval B (Fig. 5b), the current through the gap (curve 1) slightly decreases and then increases. This is due to the contribution of the dynamic displacement current U(dC*/dt), caused by the charging of “compressing capacitor” C*, formed by the edge of the dense plasma crossing the gap and the flat anode (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2010a , Reference Tarasenko, Baksht, Burachenko, Lomaev, Sorokin and Shut'ko b , Reference Tarasenko, Beloplotov and Lomaev2015). As was shown in (Tarasenko et al., Reference Tarasenko, Beloplotov and Lomaev2015), after the edge of the dense plasma reaches the anode, the second ionization wave with a higher velocity passes through the gap in the opposite direction. In this case, the current through the gap is determined by the conduction current (time interval C in Fig. 5b). At d = 12 and 18 mm, the discharge current (Fig. 5b; curves 2, 3) reaches its peak value later than at d = 6 mm (Fig. 5b, curve 1). The time delays are about 50 and 100 ps, respectively. This is because, at larger values of d, a longer time is required for the ionization wave to traverse the gap.

Thus, the time evolution of the discharge current in the REP DD includes three stages: the displacement current of the “cold” diode, the dynamic displacement current, and the conduction current. As will be shown below, the SAEB is generated mainly in the stage of the dynamic displacement current. It should also be kept in mind that, within time interval B, the current between the plasma edge and the anode is determined by the dynamic displacement current and the SAEB current, while that between the cathode and the edge of the dense plasma is determined by the conduction current. The current shunt records the sum of the dynamic displacement current and the SAEB current. These currents are difficult to separate, because the amplitude of the dynamic displacement current is, as a rule, much higher. For example, with the grid cathode, the amplitude of the dynamic displacement current reaches 2 kA (Shao et al., Reference Shao, Tarasenko, Zhang, Burachenko, Rybka, Kostyrya, Lomaev, Baksht and Yan2013).

3.3. Waveforms of the SAEB Current Pulses and Their Shift Relative to Those of the Voltage and Discharge Current Pulses

There are only two research groups in which the waveforms of the SAEB current behind the anode foil were registered with a time resolution of several tens of picoseconds (Kostyrya et al., Reference Kostyrya, Rybka and Tarasenko2012; Mesyats et al., Reference Mesyats, Yalandin, Reutova, Sharypov, Shpak and Shunailov2012, Reference Mesyats, Sadykova, Shunailov, Shpak and Yalandin2013; Rybka et al., Reference Rybka, Tarasenko, Burachenko and Balzovskii2012; Sharypov et al., Reference Sharypov, Ul'masculov, Shpak, Shunailov, Yalandin, Mesyats and Kolomiets2014; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya and Rybka2013a , Reference Tarasenko, Baksht, Burachenko and Erofeev b ). However, only in our works (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c ; Burachenko & Tarasenko, Reference Burachenko and Tarasenko2010; Tarasenko, Reference Tarasenko2011), the waveforms of the SAEB current were synchronized with those of the voltage and discharge current pulses. Than a time resolution of the registration system is ~100 ps, it is not difficult to synchronize voltage in the idle mode and discharge current pulses. The displacement current of the “cold” diode and the front of the voltage pulses on the gap are synchronous in time, hence the peak of the displacement current corresponds to the maximum of dU/dt. To provide a more accurate synchronization of the waveforms of the voltage pulses with the ones of the discharge current, it is necessary to reconstruct the voltage on the gap from the waveforms of an incident and reflected voltage pulses. To this end, the SLEP-150М pulser was equipped with an additional transmission line with built-in capacitive voltage dividers allowing one to register the incident and reflected voltage pulses separately.

In these experiments, the waveforms of the SAEB current registered with the collector were synchronized with the waveforms of the voltage pulse on the gap and discharge current in the same way as in (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c ; Burachenko & Tarasenko, Reference Burachenko and Tarasenko2010; Tarasenko, Reference Tarasenko2011), that is, by means of the displacement current of the “cold” diode. To this end, a grid anode was used, which made it possible to record the displacement current by the collector. Varying the size of the grid cell while keeping its transparency, it was possible to control the amplitude of the displacement current of the “cold” gas-filed diode that are recorded by the collector while keeping the amplitude of the SAEB current unchanged. In this way, it was possible to make the amplitude of the displacement current sufficient for synchronization with the front of the voltage pulse and, thereby, to synchronize the waveforms of the discharge current and the SAEB current pulses with that of the voltage pulse. Note that the effect of the grid cell size on the value of the displacement current was not taken into account in (Babich & Loiko, Reference Babich and Loiko2010), which, along with the low resolution of the registration system [in (Babich & Loiko, Reference Babich and Loiko2010), a TDS 3052B oscilloscope with a transmission band of 500 MHz was used], led the authors of (Babich & Loiko, Reference Babich and Loiko2010) to the erroneous conclusion on the registration of an “electromagnetic” pickup in our works. The dynamic displacement current in (Tarasova & Khudyakova, Reference Tarasova and Khudyakova1969; Tarasova et al., Reference Tarasova, Khudyakova, Loiko and Tsukerman1974; Babich, Reference Babich2003, Babich & Loiko, Reference Babich and Loiko2010, Reference Babich and Loiko2015) could not be registered because of the insufficient time resolution of the oscilloscope, the Faraday cup, and the shunt made of TVO resistors.

In the present work, as in (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c , Reference Tarasenko, Beloplotov and Lomaev2015; Burachenko & Tarasenko Reference Burachenko and Tarasenko2010), the amplitude of the dynamic displacement current was comparable with that of the SAEB current registered with the collector when a specially selected grid was used as an anode. To determine the moment of SAEB generation, the signals from the collector behind the foil anode and the grid anode were recorded at the same voltage pulses and/or discharge current pulses. This allowed us to determine the position of the SAEB current pulses with respect to other pulses with an accuracy of several tens of picoseconds. Figure 6 presents an example of synchronization of waveforms of the SAEB current pulses with that of the voltage pulses when using the grid (Fig. 6; curves 1, 3) and foil (Fig. 6; curves 2, 4) anodes.

Fig. 6. Waveforms of the voltage (a) and the SAEB current (b) pulses. The SAEB was registered by collector with the 20-mm-diameter receiving area: 1, 3 – the anode is a grid with a transparency of 64%; 2, 4 – the anode is a 10-μm-thick aluminum foil. The cathode is a 6-mm-diameter tube. The gap length is d = 12 mm. The waveforms were obtained on the setup with the SLEP-150 pulser. Time intervals А, B, and C correspond to the current of the “cold” diode (displacement current), dynamic displacement current, and conduction current, respectively.

In Figure 6 (as in Fig. 5), signals from the capacitive voltage divider of the SAEB-150 generator located at a distance of 10 mm from the cathode edge are shown. In this case, the front of the incident voltage wave was registered ≅60 ps earlier. Due to the special choice of the grid transparency and the grid cell size, the amplitudes and trailing edges of the collector signals obtained with the grid and foil anodes are determined by the SAEB current. A large-amplitude positive spike in the waveform of the collector signals (Fig. 6b, curve 3) after the SAEB pulse in the case of the grid anode is associated with the effect of the positive charge of ions, which remain near the anode after REs escape through the grid. In the case of the grid anode, the initial segment of the collector signal (Fig. 6b, time interval A) is related to the displacement current of the “cold” diode. Then, the collector detects the dynamic capacitive current and the SAEB current (Fig. 6b, time interval B). As in the case of registration of the discharge current with the shunt (Fig. 5a), the dynamic displacement current at a gap length of 6 mm begins to be registered about 250 ps after the arrival of the voltage pulse at the capacitive divider. This means that, by this time, the first electrons have already been emitted from the cathode and the plasma begins to form in the gap and propagate toward the anode. It is assumed that, at gap lengths of 12 and 16 mm, the first REs also appear with a time delay of about 250 ps after the arrival of the voltage pulse at the capacitive divider and 200 ps after the appearance of the displacement current of the “cold” diode. However, as the gap length d increases, the formation rate of the dense plasma near the cathode decreases due to a decrease in the electric field strength with distance from the cathode. As a result, within time interval B, the current signal from the collector and shunt decreases (see Figs 5 and 6).

At d = 12 mm and atmospheric-pressure air, the peak of the SAEB current nearly coincides with the maximum of the voltage pulse (Fig. 6). It should be taken into account that the receiving area of the collector is located at a distance of 5 mm from the anode. Electrons with energies of ≅150 keV travel this distance over 30 ps. Thus, electrons in the peak of the SAEB current come from the foil anode only 30 ps earlier. In (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c ), the energy of electrons of the main SAEB group for d = 12 mm, a tubular cathode, and the voltage amplitude of ≅170 kV was found to be ≅150 keV. Under the conditions of Figure 6, the voltage amplitude was ≅220 kV, that is, it was lower than that in idle mode (which under these conditions exceeded 350 kV), but higher than in (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008b , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun c ). The increase in the voltage amplitude leads to an increase in the electron energy and, accordingly, a faster arrival of SAEB electrons at the collector.

Figure 7 shows waveforms of the voltage and SAEB current pulses for different gap lengths d.

Fig. 7. Waveforms of the voltage (a) and the SAEB current (b) pulses. The SAEB was registered by collector with the 3-mm-diameter receiving area, located behind a 5-mm-thick collimator with a 1-mm-diameter hole and a 10-μm-thick aluminum foil at different gap length. The cathode is a 6-mm-diameter tube. The waveforms were obtained on the setup with the SLEP-150 pulser.

The collector with the 3-mm-diameter receiving area and a 5-mm-thick collimator with a 1-mm-diameter hole were used during registration of SAEB. As was shown in (Rybka et al., Reference Rybka, Tarasenko, Burachenko and Balzovskii2012; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya and Rybka2013a , Reference Tarasenko, Baksht, Burachenko and Erofeev b ), this allowed us to correctly register the SAEB current pulse, the FWHM of which was ≥25 ps. As d was reduced, the maximum gap voltage decreased and the time delay of the SAEB current pulse registered with the collector behind the foil anode with respect to the front of the voltage pulse reached its minimal value. In these experiments, the synchronization accuracy of different SAEB current pulses to each other as well as the one of different voltage pulses was better than 10 ps. Furthermore, the synchronization accuracy of the SAEB current pulses to the voltage pulses was no worse than several tens of picoseconds.

An increase in the time delay of the SAEB current from the collector with increasing gap length can be associated with a slower formation of the dense plasma near the cathode and a slower passage of the front of the first ionization wave through the discharge gap. In addition, as the gap length increases, a longer time is required for the ionization wave to traverse the gap. Furthermore, the distance between the peaking spark gap and the anode plane was fixed, the gap length was varied by moving the tubular cathode in the gas-filled diode along the cathode holder (the inner conductor of the transmission line, see Fig. 2). As a result, at the large gap length d the incident voltage pulse arrived to the cathode edge earlier than at the small one. The voltage amplitude increases at the gap length increase. The increase in the breakdown voltage indicates that the formation rate of the dense plasma near the cathode and in the gap decreases with increasing gap length. In long gaps, the dynamic displacement current increases slower and a maximum is observed in the waveform of the displacement current of the “cold” diode (Figs 5 and 6). Under these conditions, the ionization wave bridges the discharge gap over a longer time. Accordingly, the voltage begins to decay later and the SAEB duration somewhat increases. In Figure 7, the duration of the SAEB current pulse is the highest at d = 16 mm. It is seen from Figure 7 that, for the 6-mm-diameter tubular cathode, a 12-mm-long gap is optimal for obtaining the largest SAEB amplitude. Measurements performed with the collector with a 20-mm-diameter receiving area also show that the SAEB currents is maximum at d = 12 mm. An increase in the length of the sharp cathode edge (using of a grid cathode, an increase in the diameter of the tubular cathode) leads to a decrease in both the optimal gap length and the gap voltage. It is of interest to examine how the SAEB parameters depend on the propagation time of the voltage wave with a rise time of ~300 ps over the working surface of the grid cathode, with which the largest number of SAEB electrons was obtained (Kostyrya et al., Reference Kostyrya, Rybka and Tarasenko2012). Figure 8 shows waveforms of the SAEB current pulses passed through a 1-mm-diameter hole of the collimator that was located on the axis of the gas-filled diode or displaced from the axis by 19 mm in the radial direction. A 30-mm-diameter grid cathode was used.

Fig. 8. Waveforms of the voltage (a) and the SAEB current (b) pulses. The SAEB was registered by a collector with the 3-mm-diameter receiving area, located behind a collimator with a 1-mm-diameter hole and a 10-μm-thick aluminum foil: 1 – per one pulse; 2, 3 – averaged over 25 pulses. The collimator hole is located on the axis of the gas-filed diode (1, 3), and at a distance of 19 mm from the axis (2). The gap length is 6 mm. The cathode is a grid fixed on a 30-mm-diameter ring. The waveforms were obtained on the setup with the SLEP-150 pulser.

Waveform 1, obtained per one shot, demonstrates the time resolution of the registration system. Among 50 waveforms, this is the waveform with the minimal (under these conditions) SAEB duration. Waveforms 2 and 3 are averaged over 25 pulses. Comparison of waveforms 1, 2, and 3 shows that the electron beams from center of the cathode (waveform 3) and from a peripheral area (waveform 2) are generated simultaneously (to within 20 ps). The generation of SAEB is more stable in the peripheral areas of the cathode. In waveform 2, the FWHM of the SAEB current pulse is smaller than in waveform 3 and is close to that in waveform 1, registered per one pulse.

3.4. Effect of the Collector, Collimator, and Cathode on the Amplitude and Duration of the SAEB Current

Direct detection of an SAEB pulse with an FWHM of ~100 ps, which corresponded to the actual SAEB duration, was reported for the first time in (Tarasenko et al., Reference Tarasenko, Shpak, Shunailov and Kostyrya2005). The SAEB duration was measured using a collector with a time resolution of ~50 ps and corresponded to the limiting time resolution of the TDS-6604 oscilloscope (6 GHz, sampling time of 50 ps) used in (Tarasenko et al., Reference Tarasenko, Shpak, Shunailov and Kostyrya2005). To resolve the leading and trailing edges of the SAEB current pulse, it is necessary to have at least three sampling points within them. For the sampling time of 50 ps, the minimal resolvable durations of the leading and trailing edges of the pulse are 100 ps. For a triangular SAEB pulse, this corresponds to the 100-ps-long FWHM. As was shown later in (Tarasenko, Reference Tarasenko2011; Kostyrya et al., Reference Kostyrya, Rybka and Tarasenko2012), this duration was nearly equal to the durations of SAEB pulses registered behind the gas-filled diode foil under similar conditions. Figure 9 shows waveforms of SAEB current pulses obtained with different collectors and cathodes and different collimators.

Fig. 9. Waveforms of the SAEB current pulses registered by a collector with diameter receiving area of 3 (a−c, f) and 20 mm (d, e). The collector was located behind a collimator with a hole diameter of 1 (a, b, f), 4 (c), and 18 mm (d, e). The cathode is a sphere (a) and a tube (b−f). The gap length is 6 (a) and 12 mm (b–f).

The SAEB current pulse shown in Figure 9a was registered by the collector with the 3-mm-diameter receiving area behind a 5-mm-thick collimator with a 1-mm-diameter hole. For a spherical cathode and a gap length of 6 mm, the FWHM of the SAEB was ≅25 ps. The minimal durations of the SAEB current pulses were achieved with spherical and conic cathodes for gap lengths as short as 2–6 mm. The SAEB duration increases with increasing gap length and when using a tubular cathode with the length of the emitting edge of 19 mm. The FWHM of the SAEB current pulse shown in Figure 9b is ≅40 ps. The duration of the SAEB pulse became even longer when the diameter of the collimator hole increased, while the collimator thickness decreased (Fig. 9c–9e). The FWHM of the SAEB pulse was ≅45 ps when using a 250-μm-thick copper collimator with a 4-mm-diameter hole (Fig. 9c).

The SAEB current pulse with the FWHM of ≅80 ps shown in Figure 9d demonstrates the resolution capability of the collector with a 20-mm-diameter receiving area. The pulse registered from a considerable part of the anode foil by the collector behind a copper collimator with an 18-mm-diameter hole (Fig. 9e) has a typical SAEB pulse duration of ~100 ps. SAEB pulses with similar durations were also registered when using cathodes of different design, as well as in discharges in atmospheric-pressure nitrogen and other gases. This unambiguously indicates that the duration of SAEB pulses behind the anode foil of a gas-filed diode is ~100 ps, rather than less than 50 ps, as was stated in (Mesyats et al., Reference Mesyats, Shpak, Shunailov and Yalandin2008; Babich & Loiko, Reference Babich and Loiko2015). For the first time, a decrease in the SAEB duration with decreasing collector dimensions was observed in (Tarasenko et al., Reference Tarasenko, Yakovlenko, Orlovskii, Tkachev and Shunailov2003b ). As the thickness of the anode foil increased, the duration of the SAEB pulse changed insignificantly when using collectors with both 3- and 20-mm-diameter receiving areas.

Note that, under certain conditions, a decrease in the parameter U/pd (where p is the gas pressure) (Baksht et al., Reference Baksht, Tarasenko, Lomaev and Rybka2007, Reference Baksht, Burachenko, Lomaev, Rybka and Tarasenko2008a ; Tarasenko et al., Reference Tarasenko, Erofeev, Lomaev, Sorokin and Rybka2012a ) or the screening of the sharp cathode edge lead to the generation of an SAEB consisting of two pulses (Mesyats et al., Reference Mesyats, Sadykova, Shunailov, Shpak and Yalandin2013). The time interval between the maxima of these pulses exceeded 100 ps, due to which they could be registered using the collector with the 20-mm-diameter receiving area. The formation of two pulses can be explained by a relatively small (~20%) decay of the gap voltage during the generation of the first pulse and the passage of the second ionization wave from the cathode (Baksht et al., Reference Baksht, Tarasenko, Lomaev and Rybka2007, Reference Baksht, Burachenko, Lomaev, Rybka and Tarasenko2008a ) during the secondary voltage decay. It is assumed that the second pulse is generated due to electron emission from the front of the second ionization wave, which propagates from the cathode. Due to a decrease in the gap voltage, the electron energy in the second pulse is lower than in the first one and the FWHM of the second pulse is larger. When an SAEB consisting of two pulses is generated, its amplitude decreases.

As was noted in the Introduction, the parameters (amplitude and duration) of the SAEB current can vary from pulse to pulse. The strongest variations are observed under non-optimal conditions and also when using a freshly manufactured cathode. Therefore, before experiments, the cathode was trained over several tens of pulses. Note that, here, for illustration, we present SAEB pulses obtained at identical voltage pulses and, when using a collimator with a 1-mm-diameter aperture, SAEB pulses of the same shape. In our previous works (Rybka et al., Reference Rybka, Tarasenko, Burachenko and Balzovskii2012; Tarasenko et al., Reference Tarasenko, Erofeev, Lomaev, Sorokin and Rybka2012a , Reference Tarasenko, Rybka, Burachenko, Lomaev and Balzovsky2012b ; Levko et al., Reference Levko, Krasik, Tarasenko, Rybka and Burachenko2013; Balzovsky et al., Reference Balzovsky, Rybka and Tarasenko2015), SAEB pulses having two to three peaks with a time interval between peaks of ~30 ps were recorded with a picosecond time resolution. The reliability of registration of the SAEB pulses with an FWHM of ~25 ps as well as the picosecond resolution of the registration system consisted of the collector, cables, and connectors are confirmed by measurements of amplitude, phase, and frequency characteristics of the one by using an Agilent Technologies E8363B vector network analyzer in the frequency range of 0.01–40 GHz (Balzovsky et al., Reference Balzovsky, Rybka and Tarasenko2015). An example of a double-peak SAEB pulse is given in Figure 9f. Such waveforms were most often registered with a tubular cathode at gap lengths shorter and longer than the optimal one. Double-peak pulses were also registered behind thick foils. We consider that two and more peaks are generated due to picosecond time delays between the formation of separate diffuse jets near the cathode and their subsequent propagation (see Fig. 3c). Since the gap voltage in this case changes insignificantly, double-peak pulses are registered behind thick foils. As the collimator hole diameter increases, the RE fluxes from separate jets are mixed and the double-peak structure of the SAEB current becomes unobservable. Furthermore, due to mixing of electrons from separate jets and an insufficient time resolution, the double-peak structure is difficult to register by the collector with the 20-mm-diameter receiving area even with the use of a collimator.

The largest SAEB current amplitudes in atmospheric-pressure air were recently obtained with the SLEP-150 pulser at an amplitude of the incident voltage wave of 200 kV and a cathode made of wires stretched in parallel on a 40-mm-diameter ring (Kostyrya et al., Reference Kostyrya, Rybka and Tarasenko2012). The number of electrons in the beam reached 6.2 × 10¹⁰, which corresponds to the SAEB current amplitude of 100 A at an FWHM of ~100 ps. In those experiments, a gas-filed diode similar to that shown in Figure 2 was used. Specific features of this diode are that it has the minimal inductance of the junction between the transmission line and the diode and that the entire side surface of the gas-filled diode is covered with an insulator. When the side surface of the gas-filled diode is partially open, the SAEB amplitude decreases. This is achieved by decreasing the insulator length or applying a gas-filled diode the side surface of which is not covered with an insulator (Fig. 1). The decrease in the SAEB current amplitude can be caused by the escape of a substantial fraction of REs onto the open part of the side surface of the gas-filled diode. The application of an internal conical insulator (Fig. 2) results in the arrival of REs generated in the lateral direction (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b ) at its inner wall and the charging of its surface. Apparently, this additional electric field of the negative surface charge of the insulator increases the number of REs arriving at the anode. At a voltage pulse rise time of 1 ns and shorter, the SAEB amplitude depends on the cathode material (Zhang et al., Reference Zhang, Tarasenko, Shao, Baksht, Burachenko, Yan and Kostyray2013). On the setup with the SLEP-150 M generator, it is shown that the amplitude of the voltage across the gap during the generation of the SAEB depends on the cathode material and reaches the highest value with a stainless steel cathode. When all other factors are equal, the highest maximal amplitudes of the SAEB current are attained with cathodes that ensure the existence of the maximal voltages across the gap.

3.5. Energy of SAEB Electrons

The RE energy spectra were previously studied in our works (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun2008c , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b ; Baksht et al., Reference Baksht, Burachenko, Kozhevnikov, Kozyrev, Kostyrya and Tarasenko2010; Kozyrev et al., Reference Kozyrev, Kozhevnikov, Vorobyev, Baksht, Burachenko, Koval and Tarasenko2015). Those studies, as well as results obtained with a high time resolution (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya and Rybka2013a ), unambiguously indicate the presence of two to three groups of electrons with different energies in SAEB generated under conditions close to the optimal ones. The energy distribution of the main (the second according to our classification) group of electrons usually has a maximum at an energy that is lower by several tens of keV than eU _m. Note that, in most experiments with a subnanosecond rise time of the voltage pulse, electrons of the main group are mainly registered. The electrons of the first group have relatively low energies, as a rule, a few tens of keV and less. To register the electrons of this group, one should use thin (≤20 µm) aluminum anode foils. In our experiments with the SLEP-150М pulser (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a , Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka b ) and the RADAN-220 generator (Tarasenko et al., Reference Tarasenko, Shpak, Shunailov and Kostyrya2005), a considerable increase in the SAEB current amplitude was observed with decreasing foil thickness. An example of such a dependence is presented in Figure 10, which along with the experimental absorption curve, shows the calculated attenuations of monoenergetic electron beams in aluminum foils of different thicknesses.

Fig. 10. Calculated numbers of electrons behind aluminum foils of different thickness for monoenergetic beams with different electron energies and experimental SAEB attenuation curve obtained for d = 12 mm on the setup with the SLEP-150М pulser with the tubular cathode at U _m = 170 kV: 1–50, 2–100, 3–150, 4–200, and 5–250 keV.

The calculations were performed by the formula taken from (Tabata & Ito, Reference Tabata and Ito1975). The experimental curve has two characteristic bends at energies of 30 and 140 keV, which confirm the presence of three groups of electrons with different energies. The electrons of the third group have energies higher than eU _m. However, these electrons are small in number. In experiments with a spherical cathode (which, among all cathodes under study, was optimal for the generation of electrons with energies higher than eU _m), the number of such electrons was no more 10% of the total number of SAEB electrons. This result is confirmed by experiments with the use of a time-of-flight spectrometer (Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev, Petin, Rybka and Shlyakhtun2008c ). Note that, with the use of a spherical cathode, the breakdown gap voltage increased and varied substantially from pulse to pulse.

Experiments with different gap lengths and anode foils of different thickness have shown that, as the gap length (and, accordingly, the gap voltage) increases, the fraction of electrons with elevated energies in the main group increases. However, the number of these electrons is less than the number of electrons in the SAEB at the optimal gap length. For example, it follows from the dependence of the number of electrons in the beam on the gap length d that, for the SAEB-150 pulser with a 20-mm-diameter tubular cathode and a 15-μm-think Al foil anode, the optimal value of d is 6 mm. For a 20-μm-thick Cu foil anode under the same conditions, the largest number of REs was obtained at d = 14 mm. Due to an increase in electron energy losses in the anode, it is necessary to rise the gap voltage in order to increase the SAEB current amplitude behind the foil. This was achieved by increasing d without varying the pulser voltage pulse. Similar results were also obtained with the RADAN-220 pulser with the 6-mm-diameter tubular cathode. So, for example, as the anode Al foil thickness increased from 10 to 100 µm, the SAEB current amplitude decreased 24-fold at d = 8 mm, sixfold at d = 12 mm, and only 2.8-fold at d = 16 mm, that is, the fraction of electrons with elevated energies increased with increasing gap length. It is seen from Figure 7 that the breakdown voltage under these conditions increases.

3.6. REs and X-rays downstream of anode foil at pressure more than 0.1 MPa

Until our earliest studies (Alekseev et al., Reference Alekseev, Orlovskii and Tarasenko2003, Reference Alekseev, Orlovskii, Tarasenko, Tkachev and Yakovlenko2005; Tarasenko et al., Reference Tarasenko, Orlovskii and Shunailov2003a , Reference Tarasenko, Yakovlenko, Orlovskii, Tkachev and Shunailov b ; Kostyrya & Tarasenko, Reference Kostyrya and Tarasenko2004), only one scientific group managed to detect a RE beam downstream of an anode foil in atmospheric-pressure air using a Faraday cup (Tarasova et al., Reference Tarasova, Khudyakova, Loiko and Tsukerman1974; Babich, Reference Babich2003). By now we are aware of two more groups who succeeded in this using a collector (Mesyats et al., Reference Mesyats, Korovin, Sharypov, Shpak, Shunailov and Yalandin2006, Reference Mesyats, Reutova, Sharypov, Shpak, Shunailov and Yalandin2011; Yalandin et al., Reference Yalandin, Reutova, Sharupov, Shpak, Shunailov, Ul'maculov, Rostov and Mesyats2010; Zhang et al., Reference Zhang, Tarasenko, Gu, Baksht, Wang, Yan and Shao2015). Noteworthy is also a study that reports on detection of a RE beam and X rays at a N₂ pressure of tens of atmospheres with a special luminophore (Ivanov, Reference Ivanov2013). Presented below are data of detailed research in the effect of pressure and gas kind on amplitude-time and spatial characteristics of discharges and on SAEB amplitudes in a subnanosecond breakdown of different gases. Note that the time resolution of a collector with which we measured SAEBs downstream of anode foils was ≈80 ps (Balzovsky et al., Reference Balzovsky, Rybka and Tarasenko2015). It is shown that the generation of REs and X rays at negative voltage polarity is a common phenomenon in gas-filled diodes under pressure above 0.1 MPa. Figure 11 presents pressure dependences of the beam current for six gases in an interelectrode gap of 14 mm at a voltage rise time of ≈1 ns.

Fig. 11. SAEB current amplitude versus pressure for different gases.

The SAEB was registered downstream of an AlBe foil 45 µm thick and grid with 14% transparency. The voltage pulses produced by the RADAN-220 pulser were applied to the gas-filed diode at increased inductance, and this increased the voltage rise time to ≈1 ns, decreased the SAEB current amplitude, and narrowed the range of pressures at which a SAEB was detectable by the collector. However, even with the voltage rise time equal to ≈1 ns, we managed to register a SAEB in different gases, including heavy Kr, at a pressure of 0.15 MPa. As the voltage rise time was decreased to 0.5 ns and the anode foil was made thinner, a SAEB was registered in N₂ at 0.5 MPa, in xenon and SF₆ at 0.2 MPa, and in He at 1.5 MPa; see also (Baksht et al., Reference Baksht, Lomaev, Rybka, Sorokin and Tarasenko2008b , Zhang et al., Reference Zhang, Tarasenko, Shao, Beloplotov, Lomaev, Sorokin and Yan2014). Note that in heavy gases, the ionization and excitation cross-sections are larger than those in light gases (He, H₂), which decreases the number of REs downstream of an anode.

Figure 12 shows the SAEB current amplitude against the pressure of air, N₂, and SF₆ for different gap widths and anode foil thicknesses.

Fig. 12. SAEB current amplitude versus pressure for different gases. The SAEB was detected by a 20-mm-collector located behind a grid anode with 64% transparency and foil: (a) – air and SF₆, Al foil 10 µm thick, d = 8 mm; (b) – N₂, plated ketoprofen film 2 µm thick downstream of grid anode, d = 12 mm. Values for SF₆ are multiplied by 100.

The data of collector measurements demonstrate the presence of REs downstream of the anode foil in N₂, air, and SF₆ at pressures of several atmospheres. The number of electrons in the beam increases when using thin foils with low-electron absorption and gaps of optimum width for each gas. All data presented above were obtained on the RADAN-220 pulser. The presence of REs at pressures above 0.1 MPa was also detected by a collector in experiments on the SINUS pulser at a voltage amplitude of 180 kV and rise time of 0.5 ns (Alekseev et al., Reference Alekseev, Orlovskii and Tarasenko2003; Tarasenko et al., Reference Tarasenko, Yakovlenko, Orlovskii, Tkachev and Shunailov2003b ). In helium, the presence of a SAEB was detected at 0.6 MPa; measurements at higher pressures were not taken due to limited strength of the working chamber. In N₂ it was detected at 0.4 MPa. At higher pressures, the presence of REs in the discharge gap could be judged from luminescence of luminophore downstream of the anode foil.

In most experimental conditions, the SAEB current amplitude decreases with increasing pressure. However, with certain gas-filled diode and cathode designs and certain voltage pulse parameters, a different situation may arise. For example, an increase in SAEB current amplitude with increasing the He pressure from 0.1 to 0.3–0.4 MPa was observed (Baksht et al., Reference Baksht, Lomaev, Rybka, Sorokin and Tarasenko2008b ). In this pressure range, a larger number of cathode sports were formed, as was evidenced by images of the discharge and cathode plasma glow. Likely, it was the increase in cathode spots and associated increase in emission current from the cathode, which was responsible for the buildup of SAEB currents with increasing the He pressure to 0.3–0.4 MPa.

On the RADAN-220 pulser at negative voltage polarity, an RF-3 film placed in a black paper envelope downstream of the AlMg foil was also used for the SAEB detection. A single pulse was sufficient to obtain a SAEB imprint on the RF-3 film. The highest degree of film blackening was observed in the region near the discharge gap axis. The X-ray exposure dose at an air pressure of 0.1 MPa and interelectrode gap of 13 mm was 0.6 mR. This value was the average per pulse in a series of 50 pulses. For measuring the X-ray exposure dose, the collector was removed and the AlMg foil was replaced by a Cu foil 20 µm thick. The dosimeter in these measurements was located 5 mm away from the foil. The X rays were also judged from imprints left on the film for which an additional electron absorption filter was used. Because the film sensitivity to X rays was much lower than that to electrons, more than 100 pulses were required to obtain an X-ray imprint.

At positive voltage polarity, the REs moved toward the tubular anode and hence no SAEB was detected by the collector. Also no X rays were detected by the dosimeter even after 1000 pulses when the interelectrode gap was 13 mm. Detection of X rays at positive voltage polarity was possible, as before (Shao et al., Reference Shao, Zhang, Niu, Yan, Tarasenko, Baksht, Kostyrya and Shut'ko2011), only from imprints on the RF-3 film for the interelectrode gap decreased to fractions of a millimeter. However, about 10³ pulses were required to obtain an X-ray imprint.

In the experiments described above, the discharge was diffuse but became constricted with increasing the pressure and/or with decreasing the interelectrode gap. A detailed description of spatial discharge forms and their sequence is presented in (Tarasenko, Reference Tarasenko2014). From the data reported here and in other studies (Alekseev et al., Reference Alekseev, Orlovskii, Tarasenko, Tkachev and Yakovlenko2005; Baksht et al., Reference Baksht, Lomaev, Rybka, Sorokin and Tarasenko2008b ; Tarasenko et al., Reference Tarasenko, Baksht, Burachenko, Kostyrya, Lomaev and Rybka2008a ; Shao et al., Reference Shao, Zhang, Niu, Yan, Tarasenko, Baksht, Kostyrya and Shut'ko2011, Reference Shao, Tarasenko, Yang, Beloplotov, Zhang, Lomaev, Yan and Sorokin2014; Levko et al., Reference Levko, Krasik and Tarasenko2012; Tarasenko, Reference Tarasenko2014; Lomaev et al., Reference Lomaev, Beloplotov, Tarasenko and Sorokin2015), it follows that it is the REs, which provide preionization of the discharge gap and formation of a REP DD (Tarasenko, Reference Tarasenko2014).