X-rays from laboratory sparks in air: The role of the cathode in the production of runaway electrons



[1] Very little is known about how X-rays are produced from long laboratory sparks. Up to now, nobody has studied separately the influence of positive and negative electrodes. Thus, the goal of this letter is to demonstrate the influence of the positive and the negative electrode in the production of runaway electrons in laboratory sparks. Results show that, emissions are affected by the distribution of the equipotential lines around the cathode. This mechanism could also be related to negative stepped leaders during their path to the ground and perhaps could also be present in TGF's development.

1. Introduction

[2] X-rays from laboratory sparks were discovered five years ago in a experiment conducted using a 1.5 MV Marx Generator [Dwyer et al., 2005a]. For a rod-plane geometry and voltage impulses of both polarities, emissions of X-rays occurred near the peak voltage of the applied impulse, and within the small gap of the generator's spheres. For all the 15 sparks, emissions of X-rays were detected simultaneously by several NaI(Tl) scintillators. This article demonstrated for the first time that electrons can become runaway using a High Impulse Voltage Generator; in this letter it was stated that very large electric fields, as predicted in the cold runaway electron model [Gurevich, 1961], can produce high energy electrons. It was hypothesized that “such high electric fields may be produced by the rapid over-voltages that are created by the Marx generator, which can produce electric fields many times larger than is necessary to initiate a conventional discharge”. And that “whatever be the underlying mechanism for producing the x-rays, it certainly does not involve the standard physics of conventional air breakdown”.

[3] Three experiments were also conducted in 2008 to know more properties of these emissions. Firstly, Rahman et al. [2008] from the University of Uppsala, reported results from 83 negative sparks for a rod-rod geometry. X-rays appeared in two different moments, the first one near the peak of the applied voltage, whereas the second occurred around the main discharge current peak. About the mechanism of acceleration of electrons, they suggested that “there are apparently two possible sources of X-rays during our experiments: developing streamers of either positive or negative polarity and processes associated with the final jump”.

[4] The second experiment in 2008, was conducted at the Technische Universiteit Eindhoven [Nguyen et al., 2008]. A rod-rod geometry was used in this experiment. However, impulse voltages of both polarities were applied to the gap. For positive polarity all 50 sparks applied emitted X-rays. For negative polarity, in 14 of a total of 20 sparks X-rays were present. X-rays emissions occurred near the peak value of the applied voltage. In this work, they used collimators to locate the region responsible of emissions. They concluded that for both polarities, X-rays were originated near the positive electrode. They suggested that “X-rays originate not only from the spark gap, but can also be formed elsewhere if the local electric field is large enough for discharge initiation”. And noted that, “the electric field conditions are most likely met at the heads of streamers emanating from the HV electrode”.

[5] The third experiment was conducted again using the High Voltage Laboratory at Uppsala University [Dwyer et al., 2008]. A total of 231 sparks were studied for different gap lengths and electrodes' geometries. Gap lengths ranged from 10 to 140 cm. Electrode geometries included both spheres (2–12 cm in diameter), a rod and a sphere, or a rod and a plane. Again, they reported that X-rays occurred either near the peak of the applied voltage or around the main discharge current peak. But the second occurrence was only observed for negative polarity, and not for both. Using collimators, they located the emissions near the peak voltage within the gap, whereas the emissions around the main discharge current peak seemed to be originating from the space immediately above the voltage divider. In this article, it was also noted that it possibly exists a polarity asymmetry. It was also suggested that runaway electrons are generated by processes within the gap and not by processes at the electrode. They stated that “Runaway electron production could be either the leader channel that is in the process of traversing the gap or the streamers in the gap”. And “As the streamers approach the opposite electrode or streamers of opposite polarity then the electric field could be enhanced above that which normally occurs near the streamer tips”.

[6] Recently, March and Montanyà [2010] conducted an experiment to study the influence of the voltage-time derivative for a positive rod-rod geometry. In this experiment, the peak voltage and the rise time of the impulse was varied. It was demonstrated that X-ray emissions are affected by both peak voltage and impulse rise time.

[7] Finally, a theory on the origin of X-rays from long laboratory sparks was proposed by Cooray et al. [2009]. The basis of this theory is that X-rays are produced at the encounter of the positive and negative streamers and due to the high electric fields before their encounter. This theory was based on the results of Dwyer et al. [2005a] and Rahman et al. [2008]. In this theory, the acceleration of electrons and X-rays emission occurs at the final encounter between the positive and negative streamer heads.

[8] At this point in time, the goal of this letter is to show the influence of the positive and the negative electrodes in the production of runaway electrons in laboratory sparks. It is known that the properties of positive or negative streamers are a function of the electric field distribution [Bazelyan and Raizer, 1998]. Hence, the experiment is conducted with a fixed length electrode connected to the generator, and a variable length of the earthed electrode of 42, 17, 12 and 0 cm rod, maintaining the gap distance at 58 cm. This special geometry allows us to analyze the effect of each electrode in the mechanism of production of X-rays from laboratory sparks.

[9] On the other hand, natural X-rays emissions from thunderclouds have been studied in different ways. Firstly, an increase of emissions was observed during thunderstorms from the natural background radiation [i.e., Shaw, 1967]. More actual works have studied the emissions during natural lightning flashes and rocket-triggered lightning [Moore et al., 2001; Dwyer et al., 2004]. Also, observations have been related to the formation of leader steps during negative natural cloud-to-ground lightning [Dwyer et al., 2005b]. Moreover, detection of high energy radiation associated with thundercloud activity has been observed from space [Fishman et al., 1994], named Terrestrial gamma-flashes (TGF). Studies on the origin of TGF have established a relationship between TGF and lightning flashes inside thunderclouds [e.g., Cummer et al., 2005].

2. Experiment

[10] All the details about equipment and experimental conditions are the same as described in our previous work [see March and Montanyà, 2010].

[11] The experiment consisted on 315 sparks, 165 for positive polarity and 150 for negative polarity. We applied 11 series of 15 sparks for positive polarity and 10 series of 15 sparks for negative polarity. Emissions occurred near the peak value of the applied voltage (as in previous experiments). The electrode connected to the Marx Generator was the same during the experiment. It was a 12 cm rod connected to the high voltage cable (see Figure 1). The earthed rod was varied to 0, 12, 17 and 42 cm. The earthed rod was placed on a copper plane earth of 4,5 × 4,5 meters. The gap length was maintained at 58 cm. The four different geometries are presented in Figure 1. The NaI(Tl) scintillator was placed at 1 meter from the perpendicular of the mid gap point.

Figure 1.

Experimental setup of the four geometries.

3. Results

[12] Figures 2 and 3 show the variation of the emission percentage as a function of the voltage-time derivative. Results are presented as a function of the voltage-time derivative as this parameter agrees better than the peak voltage as it was demonstrated by March and Montanyà [2010]. In both Figures 2 and 3, it is firstly seen the influence of the peak voltage (as the rise time is maintained constant) on the percentage of emissions.

Figure 2.

Percentage of detection as a function of the voltage-time derivative for the four different lengths of the negative earthed electrode.

Figure 3.

Percentage of detection as a function of the voltage-time derivative for the four different lengths of the positive earthed electrode.

[13] Figure 2 shows the percentage of emissions for the series of positive impulses changing the length of the negative earthed electrode. It can be seen that, as rod length is reduced at the cathode, the percentage of detection decreases for the same voltage-time derivative. Breakdown voltages do not change significantly for the three different rod lengths according to the U50% breakdown voltage probability in Table 1. The U50% breakdown voltage does not vary significantly.

Table 1. U50% Breakdown Voltage for Positive and Negative Polarities for the Four Different Configurations and a Gap Distance of 58 cm
Earthed Electrode Length [cm]Positive U50% Breakdown Voltage [kV]Negative U50% Breakdown Voltage [kV]

[14] Results for negative polarity are presented in Figure 3. For negative polarity we see that there is not any influence on the length of the earthed anode. A perfect trend line could be plotted for the three different heights of the earthed rod. The only difference is exhibited when the earthed electrode is a plane (in this case, 2 of the 4 points do not agree with the rest). The 50% breakdown voltage probabilities (U50%) for negative polarity are also shown on Table 1. As occurred for positive polarity, U50% breakdown voltage does not vary considerably for the three different heights of the earthed rod. For rod-plane configurations U50% breakdown voltage are higher for negative polarity because streamer development requires a field of 1 MV/m whereas U50% is lower for positive polarity as streamer development requires an electric field of 0.5 MV/m [Bazelyan and Raizer, 1998]. For all the rod-rod configurations, U50% breakdown voltage is lower always for positive polarity than for negative polarity.

[15] For each series, measured energies can widely range from one spark to another. For example, the maximum and minimum energies measured for a positive 42 cm earthed rod length with peak voltages of 734 kV were 1.05 MeV and 75 keV, from 11 total detections.

4. Discussion

4.1. Runaway Electrons Around the Cathode

[16] In lightning and spark discharges, polarity asymmetry has been always present and documented [Williams, 2006]. Positive and negative ionization mechanisms known as streamers and leaders are also different. In positive streamers, electrons are absorbed by the ionization front whereas in negative streamers a negative head moves towards the anode. Williams [2006] referred the positive front advancement as the “mobile electrons are converging into higher field towards positive charge (the easy way)”, while in negative fronts “mobile electrons are diverging into a region of weaker electric field (the hard way)”.

[17] Dwyer et al. [2008], also noted that the emission of X-rays was affected by polarity asymmetry. In that case the dependence was on the polarity of impulse voltages, positive or negative, and not as observed here on polarity of the streamer or leader.

[18] This experiment has determined the influence of each electrode in the process of electrons' acceleration. The experimental setup permitted to study separately both ionization mechanisms, positive and negative streamers and leaders. In Runaway Electron theory [Gurevich, 1961], electrons are accelerated by the influence of the electric field to which they are submitted. The percentage of X-rays emission is increased with voltage. The effects of the peak voltage and the voltage growth rate have been demonstrated experimentally in our previous work [March and Montanyà, 2010]. The reason is that the force on an electron depends on the electric field by the Lorentz Law, F = q · E. In Figure 2, it is shown that the percentage of emissions does not depend on the applied voltage on the anode, and that as the length of the cathode is reduced, the percentage of emissions is decreased. The electric field depends on the voltage, the gap distance and the geometry of the electrodes. In the series of impulses, as rod length is increased, the distance between the equipotential lines around the cathode is reduced, whereas the other parameters remain constant. The results of this experiment show that emissions are influenced by the negative electric field distribution at the cathode. The length of the earthed electrode affects the distribution of the equipotential lines around it. Equipotential lines become narrower around the rod in the case of a longer earthed electrode increasing the non uniformity of the electric field in the earthed rod. Narrow equipotential lines mean that the electric field gradient is amplified at the vicinity of the rod. Thus, streamer properties depend on the distribution of the equipotential lines. For example, with longer earthed rod, the distance between equipotential lines in the vicinity of the cathode is reduced and electrons are submitted to a higher electric field gradient. In this way, during the experiment we could alter the properties of the ground streamer and leader without disturbing the streamer and leader emerging from opposite electrode connected to the impulse generator.

[19] The rise time is not varied, according to our previous demonstration, where a significant variation of the rise time could alter the results [see March and Montanyà, 2010]. On the contrary, for negative impulse voltages (see Figure 3), the percentage of emission did not depend on the length of the earthed anode. The variation of the equipotential lines due to a reduction of the positive earthed rod had not any influence on emissions.

[20] The results should be discussed taking into account spark discharge theory. We should focus only on the development of the negative ionization. Negative streamers start from the cathode when electric field reaches a sufficient value. Streamer lengths have no limits if the electric field is higher than 1 MV/m [Bazelyan and Raizer, 1998]. In air at atmospheric pressure, leaders are always present. Only for small gap distances electrical breakdown could occur in absence of leaders [Bazelyan and Raizer, 1998]. A leader is composed by three regions: channel, head and streamer region. The streamer region development is affected by the electric field, and in fact, it has the same properties as streamers.

[21] Results presented in this letter demonstrated, by the variation of the electric field in the earthed electrode, that the runaway electron mechanism depends on the electric field at the cathode. The results in Figure 2 demonstrate that the voltage-time derivative is not the fundamental parameter to accelerate the electrons. This is because the velocity of electrons is a function of the cathode's electric field distribution and its growth rate [see March and Montanyà, 2010], and not of the generator's impulse applied voltage.

[22] The mechanism of X-rays emission presented by Cooray et al. [2009] predicts that longer positive streamers, would be preferable to obtain X-rays at the encounter electric field between both streamers. In this letter it is seen that the main mechanism is probably a function of the electric field around the cathode.

[23] In the works by Dwyer et al. [2008] and by Rahman et al. [2008], the unknown secondary X-rays, which appeared near the peak current, only occurred for negative polarity. It could be possible that the mechanism explained in this letter would be present in one point of the Marx Generator, which acted as a big cathode for negative impulses.

[24] There are still many experiments that should be performed using the high voltage generators before understanding the mechanism of runaway electrons in the laboratory. Anyway, at this time all the studies should give a qualitative idea of the mechanism and be a key starting point in understanding runaway electron mechanism. Next experiments should describe perfectly the distribution of the electric field within the gaps, as streamers and leaders depend on the electric field seen by an electrode.

4.2. Runaway Breakdown, X-Rays From Stepped-Leader Advancement and Terrestrial Gamma-Ray Flashes

[25] Nowadays, research on high energy radiation during thunderstorms is based on these three concepts. Runaway breakdown (RB) theory [Gurevich et al., 1992] was developed because it existed evidences that during thunderstorms X-ray detections increased. According to this theory, cosmic ray secondary electrons trigger and guide the stepped-leader process with avalanches of high energetic electrons, playing a fundamental role in the preliminary ionization of the media.

[26] Measurements of high energetic particles and radio atmospherics have been conducted to test this theory [Gurevich and Zybin, 2005]. However, results are not conclusive, because as it is demonstrated in this study, relativistic electrons can be created in a negative stepped-leader during electric field variations during its path to ground. In RB theory, which is applied in a relatively low electric field, relativistic electrons can only be created from another relativistic particle, and not from electric field variations.

[27] X-rays during stepped-leader advancement constitute, nowadays, the most valuable detections, and agree, in this moment, with our results. Firstly, emissions coincide with electric field variations at each step advancement [see March and Montanyà, 2010]. Secondly, emissions from natural lightning have only been observed for negative stepped-leaders [Dwyer et al., 2005b]. The results presented in this letter agree with these observations as the electric field derivative due to negative charges can trigger the runaway process. Emissions from laboratory sparks could represent in small scale the mechanism of acceleration of electrons in natural cloud-to-ground lightning.

[28] TGF have been studied since its discovery, and different observations from both gamma radiation in satellites and radio emissions associated to lightning discharges relate these phenomena [e.g., Cummer et al., 2005]. Williams et al. [2006] conducted a study on the possible lightning flashes types as a source of the TGF. Upward flux of negative leaders as a consequence of high altitude positive intra-cloud lightnings could be the source of the TGF. This mechanism would be the same as observed in negative stepped-leaders to ground. Thus, the study of both high energy radiations detected at ground and space could be studied from high voltage impulses at the laboratory. At the moment, X-ray detections from laboratory sparks have shown many similarities with the emission process in negative cloud-to-ground lightning. The source of the TGF is still under debate, but high altitude transient negative fluxes (in the form of negative lightning leaders or negative blue jets) could allow high energy electrons to escape from earth atmosphere.


[29] 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.

[30] W. K. Peterson thanks two anonymous reviewers.