Nonhydrodynamic aspects of electron transport near a boundary: The Milne problem

The nonhydrodynamic behavior of electrons near a boundary is studied with the Milne problem of transport theory. A system of electrons dilutely dispersed in a hear bath of atomic moderators is considered in the positive one-dimensional spatial half-space with an absorbing boundary at the origin which mimics an electrode. A flux of electrons is assumed to originate at an infinite distance Rom the boundary. The Fokker-Planck equation for the electron distribution function in space and velocity is considered. The density and temperature profiles are determined, and the departure from hydrodynamic behavior near the boundary is studied. Argon and helium are chosen as the moderators, and results with different cross sections are obtained. The Fokker-Planck equation is solved with an expansion in Legendre and Speed polynomials, and compared wherever possible with results obtained with a Monte Carlo simulation. The behavior near the boundary is shown to be strongly influenced by the Ramsauer-Townsend minimum in the electron-Ar momentum transfer cross section.