Regular Article

Third-order transport coefficient tensor of electron swarms in noble gases^★

¹ Institute of Physics, University of Belgrade, P.O. Box 68, 11080 Belgrade, Serbia
² Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11001 Belgrade, Serbia
³ College of Science and Engineering, James Cook University, 4810 Townsville, Australia

^a e-mail: sasa.dujko@ipb.ac.rs

Received: 14 November 2019
Received in final form: 11 February 2020
Published online: 1 April 2020

Abstract

In this work we extend a multi term solution of the Boltzmann equation for electrons in neutral gases to consider the third-order transport coefficient tensor. Calculations of the third-order transport coefficients have been carried out for electrons in noble gases, including helium (He), neon (Ne), argon (Ar), krypton (Kr) and xenon (Xe) as a function of the reduced electric field, E/n₀ (where E is the electric field while n₀ is the gas number density). Three fundamental issues are considered: (i) the correlation between the longitudinal component of the third-order transport tensor and the longitudinal component of the diffusion tensor, (ii) the influence of the third-order transport coefficients on the spatial profile of electron swarm, and (iii) the errors associated with the two term approximation for calculating the third-order transport coefficients for electron swarms in noble gases. It is found that a very strong correlation exists between the longitudinal components of the third-order transport coefficient tensor and diffusion tensor for the higher values of E/n₀. The effects of the third-order transport coefficients on the spatial profile of electron swarms are the most pronounced for noble gases with the Ramsauer-Townsend minimum in the cross sections for elastic scattering. The largest errors of two term approximation are observed in the off-diagonal elements of the third-order transport coefficient tensor in Ar, Kr and Xe for the higher values of E/n₀.