Meter-scale spark X-ray spectrumstatistics

X-ray emission by sparks implies bremsstrahlung from a population of energetic electrons, but the details of this process remain a mystery. We present detailed statistical analysis of X-ray spectra detected by multiple detectors during sparks produced by 1 MV negative high-voltage pulses with 1 $\mu$s risetime. With over 900 shots, we statistically analyze the signals, assuming that the distribution of spark X-ray fluence behaves as a power law and that the energy spectrum of X-rays detectable after traversing $\sim$2 m of air and a thin aluminum shield is exponential. We then determine the parameters of those distributions by fitting cumulative distribution functions to the observations. The fit results match the observations very well if the mean of the exponential X-ray energy distribution is 86 $\pm$ 7 keV and the spark X-ray fluence power law distribution has index -1.29 $\pm$ 0.04 and spans at least 3 orders of magnitude in fluence.