Collision-Dominated Positive Column of a Weakly Ionized Gas

Abstract

To obtain criteria for the validity of the constant coefficient electron diffusion equation, the problem of the positive column is treated using the Boltzmann equation for the electrons. The problem is solved completely for the case of a constant electron-neutral recoil collision time for momentum transfer, in the limit where inelastic collisions play a weak role in determining the shape of the body of the electron distribution function. Here the bulk of electrons is confined by a space charge potential well, and except for a thin boundary layer near the wall, the electron density assumes a Boltzmann distribution, and the electron temperature and diffusion coefficient are constant. For a general collision frequency it is established that, unless the electron energy relaxation length is small compared with the macroscopic length scale, these results are correct only if the following conditions exist: the recoil collision time is reasonably constant over the domain which makes the major contribution to the velocity space moments of the electron distribution function, and the electron fluxes in configuration and velocity spaces are appropriately small.