Diffusion theory of electrons in a uniform electric field: Steady-stream analysis

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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 well-known linear diffusion equation for the spatial variation of electron density. This assumption is not made in the present paper. Results for the spatial variation of average energy are close to those obtained from exact solution to the linearized Boltzmann equation. In addition, it is shown that diffusion theory with energy balance gives a relation between characteristic energy and drift-tube geometry which is in close agreement with the empirical relation that has been used for years to analyze steady drift-tube measurements, without invoking the assumption of anisotropic diffusion.