Previous research at Texas Tech University has been conducted on the physics governing highly over-voltaged gas breakdown resulting from ultrafast applied voltage pulses with risetimes less than 200 ps and durations less than 400 ps. Experimental results have shown that the breakdown characteristics of such events significantly differ from those observed in standard gas breakdown and a complete understanding of the physics behind ultrafast discharges is far from being clear. As a companion to experimental work, a numerical model is an attractive means of discerning more about the underlying physics behind such events. In this paper, a relativistic, Particle in Cell model utilizing Monte-Carlo calculations is discussed as a way to directly simulate the experimental conditions, with similar geometry, background gas, and pulse characteristics. Diagnostic output from the simulation includes space-charge development over time, field and particle energy distributions, and particle number growth rates and spatial distributions. An overview of the structure and formulation behind the simulation code is given followed by a comparison of output data to experimental results. Specific points of interest for comparison include formative and statistical delay times, examination of inhomogeneous ionization regions in the discharge, and the behavior of high-energy particles in the runaway state.
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