Monte Carlo simulation of electrical discharges in gases

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Abstract
New Monte Carlo methods of calculation for tracing the motion of electrons in gases are described. Two problems have been treated by these methods, and the techniques applied to electron swarms in neon. Firstly, the probability of back-scatter of electrons to the cathode has been estimated for values ofE/p0between 10 and 200 V cm-1torr-1(Eis the electric field andp0the pressure reduced to 0 °C) and for emission energies up to the lowest excitation potential. Secondly, Townsend primary ionization coefficients α/p0and drift velocities have been evaluated for values ofE/p0from 20 to 400 V cm-1torr-1. It is shown that the use of the ergodic hypothesis is not valid, yielding values of α/p0which are up to 40% too high in neon, and that entire avalanches must be simulated before meaningful results can be obtained. The present results agree well with those obtained recently at Swansea using the Boltzmann equation, indicating that the Lorentz approximation employed in the latter method leads to only small errors in estimates of the mean properties of the electron swarms.The equilibrium of the swarm with the field is considered in detail. It is shown that, for uniform fields, deviations from exponential growth of current with increasing electrode separation occur if the interelectrode voltage is not at least three times the mean energy of electrons impinging on the anode.