Charged particle transport in harmonically varying electric fields: Foundations and phenomenology

The transport theory of ions and electrons in an oscillating electric field, typically at radio frequencies, is of interest both as a problem in basic physics and for its potential for application to modern technology, e.g., plasma processing. Our research has been motivated by both these considerations, but the present paper concerns theory and focuses on Boltzmann's kinetic equation in particular. We note that as far as kinetic theory is concerned, any substantial advances on the pioneering work of Margenau and Hartmann nearly fifty years ago have been remarkably limited in comparison with the extensive, systematic development of d.c. transport theory over the past two decades. Our goal has been to develop a comprehensive theory of a.c. charged particle transport, at a level of sophistication comparable with the d.c. theory, and the first steps are reported in the present paper, which deals with theoretical foundations and phenomenology. After examining the broader implications of space-time symmetries, namely, parity and phase-reversal invariance, we proceed through low-order moments of Boltzmann's equation, with collision terms approximated in the same way as for d.c. momentum-transfer theory, and look for relationships, however approximate, connecting experimentally measurable quantities, and otherwise attempt to shed light on transport phenomena peculiar to harmonically varying electric fields. In this way we obtain: (a) A full set of momentum-energy balance equations for both ions and electrons, to be solved simultaneously with Poisson's equation where appropriate; (b) A generalisation of Wannier's energy relation for ion swarms in an a.c. field; (c) Generalised Einstein relations for cycle-averaged electron swarm diffusion coefficients; (d) Information about a.c. negative differential conductivity and the anomalous character of anisotropic diffusion in a.c. fields; (e) A procedure for adaptation of d.c. experimental swarm data to a.c. swarms and r.f. discharges. The discussion is at the semiquantitative level, with emphasis on physical understanding.