Magnetic field effects on spatial relaxation of swarm particles in the idealized steady-state Townsend experiment

Abstract

The effect of a magnetic field at right angles to an electric field on spatial relaxation of a swarm of charged particles emitted by a plane source into a gas—the idealized steady-state Townsend experiment—is examined. The Boltzmann equation is solved using an adaptation of the "two-temperature" moment method, involving a Burnett function representation of the velocity distribution function, a technique which is valid for charged particles of arbitrary mass and is intrinsically of a "multiterm" nature. Results are presented for electrons in model and real gases, and are benchmarked against an exact analytical solution of the Boltzmann equation for a particular collision model. The application of a magnetic field significantly alters the relaxation profiles: in general, it can both enhance or retard spatial relaxation of transport properties. For methane gas, a multiterm analysis is essential to correctly account for the relaxation near the source, even though a two-term approximation may be sufficient when the magnetic field is sufficiently strong and hydrodynamic conditions dominate.