ELECTRON-DRIFT EQUILIBRIUM IN A STEADY, UNIFORM ELECTRIC-FIELD

Accurate measurement of transport and rate coefficients is complicated by the presence of nonequilibrium regions near electrodes. The purpose of this work is to estimate the spatial extent of the nonequilibrium regions. Two different theoretical methods for accomplishing this purpose are discussed: (a) the five-moment (FM) method and (b) the density-gradient expansion (DGE) method. The FM method leads to three coupled differential equations for conservation of electron density, momentum, and energy. These equations are solved numerically in one dimension for the steady state to give the motion of electrons subjected to a steady, uniform electric field, similar to conditions found in drift tube measurements of electron average velocity and characteristic energy. FM solutions predict regions near each electrode where electrons are not in equilibrium with the electric field. The equilibration length is predicted to be the same for both drift velocity and average energy; it varies linearly with electric field and inversely as the square of the gas pressure. The DGE method also leads to three coupled differential equations for conservation of electron density, momentum, and energy. DGE solutions are examined to fourth order in the expansion. Convergence is not found for any order studied. It is concluded that the density-gradient expansion method is inadequate to deal with problems of the sort discussed in this paper because proper convergence cannot be established.