Self-consistent kinetic model of the cathode fall of a glow discharge

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Abstract
The electrons in the cathode-fall (CF) region of a helium dc glow discharge have been modeled at the kinetic level with a self-consistent electric field using a ‘‘convective-scheme’’ (CS) (propagator or Green’s-function) solution method. The CS is both straightforward to implement and numerically efficient. CS electron calculations using one spatial and two velocity variables are shown to match Monte Carlo simulations of swarms in uniform E/N and in the CF. The CS predictions are also shown to match experimental swarm results. A self-consistent CF solution is obtained through a slow relaxation of the electric field to that indicated by Poisson’s equation. The electric field configuration as predicted by the CS agrees well with optogalvanic measurements. The discussion emphasizes both the physical nature of, and the difficulties associated with, a self-consistent-field calculation.