Bistable solutions for the electron energy distribution function in electron swarms in xenon via Boltzmann equation analysis and particle simulations

TL;DR

This paper investigates the bistability of the electron energy distribution function in xenon at low electric fields, using both Boltzmann equation analysis with approximations and particle simulations that include many-body Coulomb interactions.

Contribution

It provides a comparative analysis of Boltzmann equation solutions and particle simulations to understand bistability in electron swarms in xenon, validating the approximations used in the Boltzmann approach.

Findings

Good agreement between Boltzmann and particle simulation results.

Bistability effect confirmed in xenon at low electric fields.

Differences attributed to approximations and statistical noise.

Abstract

At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This "bistability effect" - in which electron-electron (Coulomb) collisions play an essential role - is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms ("two-term approximation"), (ii) neglecting the Coulomb part of the collision integral for the anisotropic part of the distribution function, (iii) treating Coulomb collisions as binary events, and (iv) truncating the range of the electron-electron interaction beyond a characteristic distance. The particle-based simulation method avoids these approximations: the many-body interactions within the electron gas with a true (un- truncated) Coulomb potential are described by a Molecular Dynamics algorithm, while the collisions between electrons and the background gas atoms are treated with Monte Carlo simulation. We find a good general agreement between the results of the two techniques, which confirms, to a certain extent, the approximations used in the solution of the Boltzmann equation. The differences observed between the results are believed to originate from these approximations and from the presence of statistical noise in the particle simulations.