Analyses of electron swarms in gases under steady-state Townsend conditions

A new simulation technique for obtaining the equilibrium electron energy distributions of electron swarms in gases under steady-state Townsend conditions is proposed based on a propagator method. The electron energy distribution function could be obtained from calculations in only one slab in real space, assuming exponential spatial growth of an electron swarm and similarity of the electron energy distribution at any position. The electron energy distributions were analysed in argon at E/N=1414 Td for a case of a positive large value of the effective ionization coefficient alpha and in an argon ((90%)/fluorine (10%) mixture at E/N=56.6, 84.8, 113.1 and 141.1 Td for a case of values of alpha crossing zero. The results agreed excellently with those of a Monte Carlo simulation and a Boltzmann equation analysis. This propagator method was found to deduce stably proper solutions for both positive and negative values of alpha . A relation between the present method for a steady-state Townsend condition and a similar method for a pulsed Townsend condition is discussed.