Nonlocal Electron Kinetics in DC Discharges

Abstract
The self-consistent modeling of a DC discharge must consider the spatial dependences introduced by the inhomogeneous structure of the radial field and the density gradient. To start tackling the problem, we develop a self-contained formulation 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 boundary conditions for the electron velocity distribution function, especially at the tube wall. The present formulation is self-contained in the sense that the relationship between the applied maintaining field and the gas pressure, termed the discharge characteristic, is obtained as an eigenvalue solution to the problem. A progress report on the self-consistent solution to this nonlocal kinetic problem is also presented.