Onset of self-breakdown in a low-pressure spark gap

Conditions for self-breakdown are studied with a time-dependent one-dimensional model which includes effects of ionization by electrons, ions, and energetic neutrals, charge exchange, secondary-electron emission from the cathode due to impact of ions and neutrals, and backscattering of electrons from the anode. Theoretical predictions for the low-pressure branch of the Paschen curve are reported. $\mathrm{Pd}$ scaling is explicitly verified. In addition, the rates for current buildup above the critical pressure are calculated. The relative importance of various physical effects on the onset of self-breakdown are studied.