A method to solve the nonlinear kinetic equation of the “nonlocal approach” including Coulomb interaction of electrons

Abstract

The detailed study of the radially dependent kinetics of the electrons in the space charge confined, cylindrically symmetric positive column plasma of low current dc discharges requires the solution of a complicated elliptic boundary value problem for the isotropic part of the electron velocity distribution function. To avoid this laborious and time consuming task, in the limit of weak energy dissipation in electron—atom collisions the elliptic kinetic equation has been replaced by the so-called “nonlocal approach”. In this approximation a much simpler, spatially integrated kinetic equation is finally deduced which has to be solved numerically. When increasing the discharge current the nonlinear Coulomb interaction between the electrons becomes more and more important and has, in addition to the electron—atom collisions, to be included in the kinetic treatment. The paper reports on basic aspects of the numerical solution method, developed for the nonlinear kinetic equation of the nonlocal approach when additionally including the electron—electron interaction, and on several applications of the method. In particular, the impact of increasing electron density and thus of the COULOMB interaction between the electrons on their kinetics in the column plasma is investigated and discussed in the frame of the nonlocal approach.