Theory of Pulsed Breakdown of Dense Gases and Optimization of the Voltage Waveform

An analytical model of a Townsend breakdown of dense gases under pulsed voltage was developed based on the dynamics of the cathode sheath. Scaling parameters for impulse breakdown were derived and these scalings agreed with experiment and elaborate numerical simulations. The model is applied to optimization of the voltage waveform for obtaining maximum plasma density. We show that the optimal conditions from the standpoint of maximal plasma production at the lowest applied voltage correspond to gas breakdown during the end of the risetime of the applied voltage pulse.