A multi-term solution of the nonconservative Boltzmann equation for the analysis of temporal and spatial non-local effects in charged-particle swarms in electric and magnetic fields

Abstract

A multi-term solution of the Boltzmann equation has been developed and used to investigate the temporal and spatial relaxation of charged-particle swarms and associated phenomena induced by non-local effects under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are operative. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in both the hydrodynamic and non-hydrodynamic regimes is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a variety of Maxwellian based weighting functions. Temporal and spatial relaxation profiles of various charged-particle swarm transport properties are presented for certain model and real gases over a range of field strengths and angles between the fields. It was found that the magnetic field strength and angle between the fields have an ability to control the relaxation process: in general, these parameters can be used to enhance or suppress the oscillatory features in the relaxation profiles of various transport properties. The explicit and implicit effects of nonconservative collisions on the drift and diffusion elements in varying configurations of radio-frequency electric and magnetic fields are considered using physical arguments.