A Useful Simple Recursion Formula to Account for Inelastic Collision Effects on the Electron Distribution in a Plasma

Abstract

The competitive effects of inelastic electron-atom collisions and electron-electron interactions on a sufficiently isotropic electron distribution is considered for a low temperature monatomic plasma. It is presupposed that unbalanced collisional transitions between ground state and resonance level of the plasma atoms are the dominant disturbance effect on the electron distribution. The unbalance is assumed to be due to resonance radiation escape and excitation diffusion. An analytical solution, which permits the calculation of the electron distribution even well above the ionization energy of the atomic ground state, is presented. In particular, it is demonstrated that due to the rapid decrease of the Coulomb cross section with increasing electron energy, the solution for the high energy tail of the electron distribution can be related to its form at lower energies by a simple recursion formula. The latter enables an easy computation of the ionization coefficients even for the lowest atomic energy levels. The analytical solution and its high energy approximation are numerically evaluated for the example of a low temperature -low pressure cesium plasma.