Friction coefficient, mean velocity, and conductivity tensor of large, heavy ions in a gas in any regime in external fields

Abstract

The general expression for the time-dependent mean velocity of large, heavy (l.h.) ions in a gas in any regime in time-varying (or static) electric fields and/or in static magnetic fields is obtained as solution of the appropriate equation of motion for the average l.h. ion. It is shown that such an equation follows directly from the Newton's law for a single ion once appropriate averages are carried out. The procedure puts in evidence that an effective friction coefficient can be defined whose expression tends, in the hydrodynamic regime, to the usual expression following from the Stokes' law, and, in the molecular regime, to the expression relevant to the heavy particles of a Rayleigh gas. In the case of l.h. ions in static or alternate electric fields and static magnetic fields, the conductivity tensor is also obtained. Moreover, the limits of validity of the theory are briefly discussed. Finally it is shown that, when the l.h. ions are supposed to move in a hard-sphere gas, all the obtained results can explicitly be expressed in terms of the Knudsen number.