Solution of the Space Charge Problem for a Pulsed Townsend Discharge

Abstract

The pulsed Townsend discharge technique for the determination of electron attachment coefficients of electronegative gases is examined for situations where the ion density is sufficiently high that space charge effects must be considered. The equations of motion for the ions are solved to yield a first‐order differential equation for a parametric function, in terms of which the current and boundary position may be expressed. For the particular case of interest, an initial distribution which decays exponentially from the cathode, an exact solution for the current is obtained by numerical evaluation of this function. Comparison with experiment shows excellent qualitative and fair quantitative agreement.