The partial continuous slowing down approximation (PCSDA) in the solution of the Spencer — Fano equation

Abstract

The Spencer—Fano equation (SFE) is often used to study the energy distribution of energetic electrons and their moderation in gases. Although accurate results can be obtained from a numerical solution of the SFE, the calculations are time-consuming and instead the continuous slowing down approximation (CSDA), applied to all the collision terms in the SFE, is often used as an alternate more efficient methodology. The work in the present paper considers a modification of the usual CSDA which involves the application of the CSDA to specific collision terms in the SFE rather than to all the terms. This new approximation scheme referred to as the partial continuous slowing down approximation (PCSDA) is applied to the degradation of electrons in N 2. The new method is found to give better results than the conventional CSDA and provides a more efficient determination of the degradation spectrum than does the solution of the SFE.