An analytical, inelastic, space and time dependent electron distribution for electrically excited gases

An approximate, electron energy distribution function, f((var epsilon), x, t), is obtained for the case of a slightly ionized gas with inelastic electron-molecule collisions, and for an external electric field with both spatial and temporal variation. A previous analysis of the Boltzmann equation, for a slightly ionized gas with time-varying electric field and inelastic collisions, has been extended to include the effect of a spatial gradient in the electric field. This paper describes the spatial variation effect by continuing the discussion on the electron distribution initiated in that previous report. An interesting feature of this analytical distribution function is its explicit dependence on both the magnitude of the field and its gradients. An example is included of the combined effect of field variations in space and time upon the local average electron energy in an idealized N2-like gas.