Diffusion of Electrons in a Constant Field: Steady Stream Analysis

Abstract

Diffusion theory of electrons in a drift tube is extended to satisfy approximate energy balance as the electrons migrate radially and axially in a steady, uniform electric field. Previously, it was assumed that the characteristic energy is independent of position in the drift region, leading to the concept of different diffusion coefficients in the radial and axial directions. However, this assumption is inconsistent with electron energy balance. In the present paper, it is shown that different transverse and longitudinal diffusion coefficients are not needed when energy is conserved, as the electrons migrate radially and axially from a point source. It is also shown that diffusion theory with energy balance gives results similar to those obtained from exact solution to the Boltzmann equation by Parker (1963). In addition, it is shown that the heretofore empirical relation between characteristic energy and drift tube geometry results naturally from theoretical analysis.