Two-term Boltzmann approximation versus Monte-Carlo simulation: effect of magnetic field

Abstract

In this paper, we investigate the spatial-local electron energy distribution function (eEDF) interacting with a background
gas at the sub-atmospheric pressure in a wide range of applied crossed electric and magnetic fields using the Boltzmann
kinetic equation. We compare solutions obtained using two numerical approaches (deterministic two-term approximation and
stochastic Monte Carlo method) to identify their applicability in the context of determining drift velocity and reaction constants
for electrons. For argon and helium, the upper limit of the reduced electric field applicability of the two-term approximation
is discussed. It has been shown that the presence of a magnetic field can reduce this limit. Two explanations are given, one
is based on the math of two-term formalism, and the other is based on velocity-space analysis. Two-term approximation fails
due to it’s inability to resolve underlying cyclotron oscillation (it should result in an energy variation along the electron’s
trajectory). The absence of this feature causes an incorrect estimation of momentum-transfer rate. This results an inaccuracy
in the estimation of the angle between electric field and drift velocity.