The evolution of simple velocity average of ions in gases in time-varying electric fields and static magnetic fields

Abstract

The general time-dependent expressions of the simplest velocity averages of ions in gases in arbitrary time-varying electric fields and static magnetic fields are obtained under the assumption of an ion-neutral Maxwellian interaction. To this end, the relaxation equations for mean velocity, mean square speed (or mean energy), and mean square velocity components of the ions are deduced from the Boltzmann equation and solved under quite general initial conditions. In this context the general time-dependent expression of the ion temperature is also discussed, and the need to separately consider the equal-mass case (ions in their parent gas) is pointed out. All The results obtained are then properly extended to the more general case of ions in gas mixtures. In Addition, the Rayleigh-gas limit is examined in order to compare the results following from Boltzmann and Fokker-Planck equations. Finally, ions in alternate electric fields and static magnetic fields are considered as a specific example, and comparisons are made with previous results.