Electron Kinetics in Space-Dependent Plasmas

Basic Equations and Their Representation by the Total Energy 

When specifying the kinetic treatment based on the two-term approximation to purely space-dependent plasmas with isotropic scattering in the important 

As detailed below, the parabolic equation, Eq. (54), describes the evolution of the isotropic distribution and has to be solved as an initial-boundary-value problem on a nonrectangular solution region whose boundaries are partly determined by the spatial course of the electric field and thus by the specific kinetic problem considered. The parabolic problem has to be completed by appropriate initial and boundary conditions, which are briefly described below. 

The Consistent Balance Equations in Space-Dependent Plasmas 

In purely space-dependent plasmas, the consistent particle, power, and momentum balance equations of the electrons, Eqs. (31) to (33), have the simplified representation (Sigeneger and Winkler, 1997a Sigeneger and Winkler, 1996) 

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