A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

TL;DR

This paper develops a 14-moment maximum-entropy model to accurately describe non-equilibrium electrons in crossed electric and magnetic fields, validated against analytical and particle-based solutions in low-temperature plasma conditions.

Contribution

It introduces a novel 14-moment maximum-entropy system with derived source terms and a simplified collision model tailored for low-collisionality plasma environments.

Findings

Accurately captures non-equilibrium electron behavior in Hall thruster conditions.

Demonstrates good agreement with analytical and particle-based solutions.

Provides a flexible framework for modeling low-temperature plasma electrons.

Abstract

A 14-moment maximum-entropy system of equations is applied to the description of non-equilibrium electrons in crossed electric and magnetic fields and in the presence of low collisionality, characteristic of low-temperature plasma devices. The flexibility of this formulation is analyzed through comparison with analytical results for steady-state non-equilibrium velocity distribution functions and against particle-based solutions of the time-dependent kinetic equation. Electric and magnetic source terms are derived for the 14-moment equations, starting from kinetic theory. A simplified BGK-like collision term is formulated to describe the collision of electrons with background neutrals, accounting for the large mass disparity and for energy exchange. An approximated expression is proposed for the collision frequency, to include the effect of the electrons drift velocity, showing good accuracy in the considered conditions. The capabilities of the proposed 14-moment closure to capture accurately non-equilibrium behaviour of electrons for space homogeneous problems under conditions representative of those found in Hall thrusters is demonstrated.