Geant4 simulations of x-ray photon pileup produced by runaway electrons in streamer discharges

Abstract

Runaway electron acceleration is the keystone process responsible for the production of energetic radiation by lightning and thunderstorms. In the laboratory, it remains undetermined if runaway electrons are merely a consequence of high electric fields produced at the ionization fronts of electrical discharges, or if they impact the discharge formation and propagation. In this work, we simulate photon pileup in a detector next to a spark gap. We compare laboratory measurements to ensembles of monoenergetic electron beam simulations performed with Geant4 (using the Monte Carlo method). First, we describe the x-ray emission properties of monoenergetic beams with initial energies in the 20 to 75 keV range. Second, we introduce a series of techniques to combine monoenergetic beams to produce general-shape electron energy spectra. Third, we proceed to attempt to fit the experimental data collected in the laboratory, and to discuss the ambiguities created by photon pileup and how it constrains the amount of information that can be inferred from the measurements. We show that pileup ambiguities arise from the fact that every single monoenergetic electron beam produces photon deposited energy spectra of similar qualitative shape and that increasing the electron count in any beam has the same qualitative effect of shifting the peak of the deposited energy spectrum toward higher energies. The best agreement between simulations and measurements yields a mean average error of 8.6% and a R-squared value of 0.74.

Production of runaway electrons and x-rays during streamer inception phase

“…Fields higher than 25 kV cm −1 should not exist for long, as they will generate prolific ionization leading to field collapse [11]. At these range of energies Bremsstrahlung x-rays are only produced when energetic electrons hit the ground electrode, as verified by Monte Carlo simulations [24]. Using this range of K th 's we can estimate the distance traveled across the gap (d s ) by the discharge at the moment of runaway electron production by the formula:…”

“…This must be a result of photon pile-up, i.e. several photons are produced and arrive simultaneously at the detector [24,30]. In order for the resulting energy pulse to resemble that of a single photon, the transit time spread as photons travel from source to detector must be a small fraction of the 16 ns decay time of the crystal.…”

“…Because bremsstrahlung radiation due to runaway electrons impacting the ground electrode is known to be the key process responsible for the production of laboratory x-rays on short air gaps [24,30], we present an analysis of the transit times of runaway electrons to determine the precise moment of runaway electron production and whether they are the likely agent for the x-ray observations we have made.…”

“…For runaway electrons, the electric field supplies more energy than is lost to collisions [15,21]. In the energy range between 300 eV and 300 keV, the runaway electron threshold energy (in eV) can be approximated by equation ( 2) [24]: 4 (2…”

“…However, the details of how this mechanism takes place in the complex streamer zone of negative lightning channels is yet to be understood. This idea has been generalized with a suggestion that runaway electrons may be a universal process in all electrical discharges [30], but it remains unclear if runaway electrons are a mere consequence of high electric fields produced at the electrical discharge ionization front, or if they impact the discharge formation and propagation [24].…”