A Multigroup Approach to Electron Kinetics

Abstract

Given initial and/or boundary conditions, the behavior of an assembly of electrons in a gas can be obtained from solution of the kinetic equation for the distribution function, f(v,r,t). By expanding the distribution in terms of localized functions in v-space, an equivalent formulation can be obtained in terms of the expansion coefficients. For a set of modulated gaussian functions, the expansion coefficients are proportional to the density of “electron groups” associated with the localized functions. Equations of evolution for these coefficients are explicity derived. With this formulation, the dynamical behavior of the electrons in various regions of velocity space and the influence of the scattering process on these dynamics can be elucidated. This approach is illustrated by numerically solving the initial-value problem for the amplitude equations.