High-pressure pulsed avalanche discharges: formulas for required preionization density and rate for homogeneity

The requirements on preionization for the formation of spatially homogeneous pulsed avalanche discharges are examined. We derive two formulas which apply in the case of a slowly rising electric field, one which gives the required preionization density at breakdown, and one which gives the required preionization rate. These quantities are expressed as functions of the electrochemical properties of the gas, the neutral density, and the electric field rise time. We also treat the statistical effect that the electrons tend to form groups, in contrast to being randomly distributed in space, during the prebreakdown phase. This process is found to increase the required preionization rate significantly, typically by a factor of five for a discharge at atmospheric pressure.