A multi-term solution of the space-time Boltzmann equation for electrons in gaseous and liquid Argon

TL;DR

This paper develops a comprehensive multi-term space-time solution to Boltzmann's equation for electron transport in gases and liquids, extending previous hydrodynamic models to non-hydrodynamic regimes with novel operator-splitting methods.

Contribution

It introduces a new operator-splitting approach for solving the full multi-term Boltzmann equation in space and time, applicable to both gaseous and liquid argon, and compares results with hydrodynamic models.

Findings

Observation of Franck-Hertz oscillations in liquids

Differences in velocity distribution evolution between gas and liquid

Benchmarking of transport coefficients against hydrodynamic limits

Abstract

In a recent paper [1] the scattering and transport of excess electrons in liquid argon in the hydrodynamic regime was investigated, generalizing the seminal works of Lekner and Cohen [2,3] with modern scattering theory techniques and kinetic theory. In this paper, the discussion is extended to the non-hydrodynamic regime through the development of a full multi-term space-time solution of Boltzmann's equation for electron transport in gases and liquids using a novel operator-splitting method. A Green's function formalism is considered that enables flexible adaptation to various experimental systems. The spatio-temporal evolution of electrons in liquids in the hydrodynamic regime is studied for a benchmark model Percus-Yevick liquid as well as for liquid argon. The temporal evolution of Franck-Hertz oscillations are observed for liquids, with striking differences in the spatio-temporal development of the velocity distribution function components between the uncorrelated gas and true liquid approximations in argon. Transport properties calculated from the non-hydrodynamic theory in the long time limit, and under steady-state Townsend conditions, are benchmarked against hydrodynamic transport coefficients.