Molecular gas electron distribution function with space and time variation

Summary form only given, as follows. An approximate, electron energy distribution function, f(/spl epsi/,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, E(x,t). This analysis yields an approximate solution for the isotropic leading term of the spherical harmonic expansion of the Boltzmann equation. This result is considered valid when the electric field has a characteristic frequency |/spl omega/|/spl lambda//sub m/, where these parameters are defined as: w(x,t)=(3/2)(/sup /spl part////spl part/t) 1n[IE(x,t)l+/sup kT//e/spl lambda/m], and where v/sub m/ and /spl lambda//sub m/ are respectively the electron-molecule elastic collision frequency and mean free path at thermal energy. There are no other limiting assumptions made about gas mixture composition, cross-section shapes, or electric field space and time behavior. An interesting feature of this analytical distribution function is its explicit dependence on both the magnitude of the field, E(x,t), and its gradients, /spl omega/(x,t) and /spl lambda//sub e/(x,t). Example distribution functions are shown for an idealized N/sub 2/-like gas. These examples include electric fields with ramp or sinusoidal temporal variations, or an exponential spatial decay.