Electron collision frequencies and energy transfer rates

Abstract

The rate of energy exchange, through elastic collisions, between two gases with Maxwellian velocity distributions at different temperatures, is derived from elemetary considerations. This result is then used to calculate energy transfer rates and collision frequencies for energy transfer in plasmas at thermal disequilibrium. It is found that the electron-ion energy transfer rate and the collision frequency for energy transfer are overestimated by 5–37 per cent, depending on the electron density and the electron and ion temperatures, when the classical Coulomb logarithm ln Λ appears in these expressions. A more accurate cross section for Coulomb collisions (than that obtained when the shielded potential is truncated at the Debye length) leads to a correction term for ln Λ. Electron-electron and ion-ion collision frequencies and relaxation tunes differ from the usual expressions for these quantities by as much as a factor of two. Mean experimental and theoretical cross sections for momentum transfer for N 2, O 2, O, He and H are used to obtain simple formulas for collision frequencies and energy transfer rates useful in electron gas temperature calculations.