Calculation of spatially inhomogeneous electron distribution functions

The self-consistent modeling of microwave discharges must consider the spat ial dependences introduced by the inhomogeneous structure of the field dist ribution. To start tackling the problem, we develop a self-contained formul ation to solve the steady-state spatially inhomogeneous electron Boltzmann equation in a plasma, positive column. The problem is solved in cylindrical geometry using the classical two-term. approximation, with appropriate bou ndary conditions for the electron velocity distribution function, especiall y at the tube wall. The present formulation is self-contained in the sense that the relationship between the applied maintaining field and the gas pre ssure, termed the discharge characteristic, is obtained as an eigenvalue so lution to the problem.