Geophysical Research Letters

Influence of the voltage-time derivative in X-ray emission from laboratory sparks



[1] X-rays produced by laboratory sparks in air at atmospheric pressure for rod-rod and rod-plane configurations were observed. A total of 510 sparks were applied for both polarities. The paper shows the effects of the voltage rise time and the peak voltage in the generation of X-rays. It is found here that shorter rise times and high peak voltages tend to produce more X-rays emissions with higher energies than longer front waveforms or lower peak voltages. In a similar way, higher voltage variations produce more energetic emissions. This finding suggests that the variation of the electric field before the breakdown can play a fundamental role in the X-ray production. The results are similar with the observations of X-rays produced in natural lightning where detections have been associated to leader steps before the return stroke.

1. Introduction

[2] The acceleration of electrons due to the electric fields inside the thunderclouds was previously predicted by Wilson [1924]. Gurevich [1961] developed a theory of runaway electrons, for which electrons in a constant electric field become continuously accelerated. Under strong electric fields these can become “runaway electrons” when its energy is higher than 100 eV [Dwyer et al., 2008]. Later, Gurevich et al. [1992] presented a theory on the mechanism of air breakdown during a thunderstorm. In it, cosmic rays play a fundamental role in the development of the lightning ionization process. This process disagrees with conventional breakdown theory and requires “seed” cosmic rays to trigger the called Runaway Breakdown (RB) discharge. While in conventional breakdown thermal electrons are responsible of stepped leader development, RB requires high energetic particles to trigger and develop the discharge. The increase of X-rays during thunderstorms has been reported by some observations [e.g., Shaw, 1967]. Moreover, X-rays have been observed during lightning stepped leader and dart leaders in natural and rocket-triggered lightning [e.g., Moore et al., 2001; Dwyer et al., 2004]. At higher altitudes, spacecraft also have received the energy from the called terrestrial gamma-ray flashes (TGFs) created during thunderstorms at the troposphere [Fishman et al., 1994].

[3] Five years ago [Dwyer et al., 2005a] a relevant experiment was conducted in a high voltage laboratory to study the formation of X-rays during 14 electrical discharges of both polarities in a rod to plane gap applying standard 1,2/50 μs voltage waveforms. In all 14 discharges detections of X-rays by a NaI(Tl) scintillator were present. Later, two more experiments were conducted [Nguyen et al., 2008; Rahman et al., 2008] with rod-rod geometries and confirmed the results observed by Dwyer at al. [2005a]. In a recent article [Dwyer et al., 2008], the authors presented an investigation consisting of 231 sparks for different geometries using the 1 MV Marx generator previously used by Rahman et al. [2008]. The laboratory experiments showed difference in the X-ray production between positive and negative polarities, electrode geometry and an increase of detections by increasing gap distances.

[4] This paper presents the detections and energies in two different experiments. The electrodes geometries considered here were rod-rod and rod-plane. A total of 510 sparks were analyzed. The Marx generator used had 1 MV similar as used by Rahman et al. [2008] and Dwyer et al. [2008]. The goal of this work is to study the influence of the derivative of the applied voltage by changing the peak voltage and rise-time. The effect of this parameter has not been presented before and it provides more clues to understand the high energy emissions associated with lightning. In these experiments, the appearance of the X-rays occurs around the peak voltage of the impulse. In some cases, multiple bursts can also be observed.

2. Experiment

[5] The tests were performed at Labelec High Voltage Laboratory in Terrassa (Spain). The Marx Generator used in this experiment is a Haefely SGSA 1000-50, which is a 10 stages generator with a maximum energy of 50 kJ, and a maximum charging voltage of 1 MV. The applied impulse voltage is measured by capacitive voltage divider. The earthed electrode contained a shunt for the current measurement. The rise and fall times can be achieved by the use of different generator's front and tail resistors. The front and tail times of the impulses used in the experiments are presented in Table 1.

Table 1. Characteristic Times of the Applied Waveforms
Front Time [μs]Fall Time [μs]

[6] Two different electrodes geometries have been used for the two experiments. The first geometry was a horizontal rod-rod configuration with two identical 20 mm round stainless steel (AISI 316L) rods. The rods were round finished and separated forming a 58 cm gap at 81 cm above the ground. For this geometry a total of 450 positive impulses were applied in series of 25. The objective of the first test was to study the influence of the peak voltage and the voltage rise time. For that, the peak voltage was increased for the three waveforms in Table 1. The second configuration was a vertical orientated rod-plane for both positive and negative polarities. The electrode distance was maintained at 58 cm over the ground. The diameter of the rod was 16 mm (sharp ended) stainless steel AISI 316L. The ground plane was a copper electrode. This second geometry was chosen to study both positive and negative ionization processes, as the discharges first develop from the rod electrode.

[7] The high energy detector was a 3″ × 3″ NaI(Tl) scintillator (cylindrical shape). The detector was previously calibrated using a 137Cs radioactive source. It was placed at 1.20 meters perpendicular from the center of the air gap (on both configurations) and shielded by an aluminium cabinet of 8 mm thickness. The EMC cabinet contained the scintillator detector, the oscilloscope and the triggering system. In order to minimize electromagnetic disturbances, a fibre optical system was used for the synchronization with voltage generator. Signals from scintillator were recorded at the oscilloscope. The signal noise was lower than 20 mV which corresponds to an energy of 5 keV. The minimum energy detected by the scintillator during the experiments was of 17,5 keV, corresponding to a peak signal of 70 mV. The higher signal had an energy of 1249 keV. A detailed view of the experiments set-up is represented in Figure 1. The tests were performed during 6 days. The variation of the climatic parameters were: Temperature 21–23.4°C, relative humidity 55–61% and pressure 977–982 mbar.

Figure 1.

Diagram of the experiments set-up.

3. Results

3.1. Effect of Peak Voltage and Rise Time

[8] The 450 voltage impulses in this experiment had the objective to study the influence of the voltage derivative with respect to time on the X-rays appearance and the detected energy. For each rise time (or front time), the breakdown voltage was determined using the U50%, which is a value of a 50% probability to breakdown [see International Electrotechnical Commission, 1989]. Then, due to the electrode arrangement and the voltage waveforms, peak voltages higher than the minimum required for U50% breakdown were applied, which are referred as overvoltages. The overvoltage percentage (respect U50%) necessary for the appearance of the X-rays varied for each waveform.

[9] The first voltage waveform was a 1/45 μs (see Table 1). The peak voltage was varied between 413 and 680 kV while the U50% was 380 kV. After 9 series (of 25 sparks) with different peak values the number of detections increased as voltage. The average detected energy also increased in the same way. After, it was increased and decreased the front time and completed 3 and 6 series more with slower (2 μs) and faster (0.6 μs) front times, respectively. The peak voltage varied from 495 to 555 kV for a rise time of 2 μs, and between 412 to 722 kV for a rise time of 0.6 μs. Again, increasing the peak voltage resulted in an increase of the X-rays detections. Moreover, the average energy (calculated as the sum of all the energy of the detections for each series divided by the number of detections) detected by the NaI(Tl) scintillator also increased. The results are plotted in Figures 2 and 3. Focusing on the variation of the rise time, the faster the rise time the higher the detections' percentage and average energies than slower rise times. As seen in Figures 2 and 3, the voltage derivative required for faster rise times is higher than for slower front times.

Figure 2.

Detections percentage as a function of the voltage derivative for the three different impulse rise times.

Figure 3.

Average energy of the detections as a function of the voltage derivative for the different impulse rise times.

[10] The breakdown voltage and the minimum voltage for having at least one detection are shown in Table 2. Note that the overvoltage necessary for the appearance of an X-ray depends on the rise time. Then, the level of overvoltage in the spark discharge is fundamental when presenting and analyzing the detection efficiency of a specific test configuration. For example, for a rise time of 600 ns approximately no overvoltage is required whereas for a 2 μs an overvoltage higher than 38% is necessary to detect X-rays. In Figure 4 is shown the voltage and X-ray occurrence for a voltage impulse of 526.5 kV with a rise time of 626 ns. In it, the emission occurs during the rise of the voltage impulse, whereas breakdown is located after 3.6 μs.

Figure 4.

Voltage impulse with a recorded peak value of 526.5 kV, and rise and breakdown time of 626 ns and 3.6 μs respectively (solid line). X-ray signal (dashed line) for the NaI(Tl) detector for the same spark.

Table 2. Breakdown and Minimum X-Ray Emission Voltages
Front Time [μs]U50% Breakdown Voltage [kV]Minimum Voltage for X-Ray Detection[kV]

3.2. Effect of Voltage Polarity

[11] A rod-plane (grounded plane) test for both polarities was performed to study separately the formation of positive and negative leaders. The rod intensifies the electric field in the surrounding volume of it. Then, the development of the ionization wave is produced primarily by the sharp electrode. For this geometry were applied 3 series of 10 impulses for each polarity. The rise time was established at 600 ns. Results show that only for negative rod polarity the scintillator detected X-rays. The results for this geometry are represented in Table 3. The number of detections also increases when increasing peak voltage.

Table 3. Number of Detections for Rod-Plane Configuration
Peak Voltage [kV]Total Detections

4. Discussion

[12] The objective of the first experiment was to determine the influence of the voltage and rise time on the detection of X-rays during spark discharges at the laboratory. The second experiment, was developed to study the influence of the positive and negative polarities on the X-rays emission.

[13] From Dwyer et al. [2005a], it was shown that X-rays could be detected during high voltage tests with Marx generators. After, other experiments [Nguyen et al., 2008; Rahman et al., 2008] were developed to study different geometries and determine the position of the X-rays, the time of appearance and the influence of different geometries. In all of these works, the experimental set-up did not take into account the parameters analyzed here such as the overvoltage percentage, the rise time and the peak voltage. As demonstrated, when studying the appearance of X-rays in a spark discharge, these parameters are determinant, because the influence in the results may be significant. For example, experiment one could be performed with a 1/45 μs impulse waveform with peak voltage of 410 kV, which is 30 kV higher than the breakdown voltage. In this case, no X-rays would be expected. But at higher peak voltages, detections would start and would represent different percentages as the overvoltage increase.

[14] The results from average energy and detections' percentage show the influence of the voltage derivative parameter (dV/dt). It is very interesting the fact that, when increasing the peak voltage both the detection percentage and the average energy increase as shown in Figures 2 and 3. Note that emissions occurred around the peak maximum of the impulse. This influence demonstrates that the electric field is fundamental for the acceleration of electrons.

[15] In the runaway theory proposed by Gurevich [1961] the electrons accelerate within a constant electric field. Later Gurevich et al. [2007], showed that high electric fields in the head of a lightning stepped leader could produce runaway electrons. The increase of detection's percentage and energy with voltage supports the runaway theory as electric field plays an important role. However, the results showed that for a faster rise time a lower voltage was required to produce X-ray. This may suggest that the electric field derivative may play an important role in the runaway flux production. Moreover, the possible influence of the electric field derivative on the production of X-rays is consistent with the observations in natural lightning [Moore et al., 2001; Dwyer et al., 2005b] where the burst of detections appear just at leader steps while the electric field rapidly changes.

[16] Radio emission from thunderclouds have been widely studied and detected [e.g., Sonnadara et al., 2006]. Emissions on the MHz scale are related with fast transient pulses developed inside the thundercloud. These pulses can be a source of energetic electrons as observed on the laboratory experiments. Then, Runaway Breakdown mechanism may have more “seed” electrons for the lightning inception according to the theory [Gurevich et al., 1992].

[17] The lack of detections in the second experiment with positive polarity suggests the influence of the discharge mechanism on the production of X-rays. Bazelyan and Raizer [1998] show that negative discharges require higher electric fields than positive discharges. Furthermore, the effect of polarity asymmetry is well known in lightning [e.g., Williams, 2006]. For this reason, the differences observed for both polarities can be attributed to the difference on the ionization mechanism in positive and negative polarity. Table 3 presents the peak voltages of the series. Due to the gap distance, increasing the charging voltage of the generator for positive polarity the peak voltage was 740 kV at maximum. Then, the resulted electric fields were higher for negative polarity where X-ray emission was present.


[18] The authors would like to thank the Spanish MICINN for supporting this study under grant AYA2009-14027-C05-05. We wish to thank Labelec to allow test execution. The authors are grateful to M. Arrayás and J.L. Trueba for helpful discussions.