Modeling DC electrical breakdown using a truncated emission spectrum for trapped radiation

Abstract

Spontaneously emitted radiation from excited atoms can be of principle importance in certain modes of electrical breakdown, especially positive streamers and some regimes of Townsend breakdown. The electrostatic particle-in-cell code Aleph utilizes the direct simulation Monte Carlo method to compute radiation transport. When there is strong radiation trapping, this approach is limited in that it must resolve the timescale associated with self-absorption. This renders many cases computationally intractable as sub-femtosecond time steps can be required to compute solutions for phenomena that occur over nanoseconds or microseconds. For two specific cases which exhibit strong radiation trapping, we find that spontaneous emissions having a frequency near the line center are inactive in the breakdown process and can be neglected. This enables larger time steps and a computational speedup of up to two orders of magnitude is observed. Some considerations for determining the validity of making such an approximation for Townsend breakdown problems and positive ionization wave problems are presented.