Theory of Electron Diffusion Parallel to Electric Fields. I. Theory

Recent experimental results in many gases demonstrate that the apparent rate of electron diffusion parallel to an electric field can differ significantly from that in the perpendicular direction. We have explained this anomalous behavior by taking account of the effect of electron density gradients on the solution of the Boltzmann equation representing a pulse of electrons under the influence of a uniform electric field. When the electron collision frequency increases with energy, the theory predicts that the leading edge of the pulse has a reduced mobility because of a higher-average electron speed and collision rate. Similarly the mobility of the trailing edge is enhanced, and consequently the half width of the pulse in the field direction is characterized by a new diffusion coefficient. The ratio of the longitudinal diffusion coefficient to the transverse diffusion coefficient is given as integrals involving the momentum transfer cross section and the unperturbed energy distribution. This ratio at high electric fields is found to be approximately one-half and one-fifth, for momentum transfer cross sections that are independent of and linearly proportional to the electron energy.