Collisionless ion modeling in Hall thrusters: analytical axial velocity distribution function and heat flux closures

TL;DR

This paper develops an analytical model for the ion axial velocity distribution function in collisionless Hall thrusters, deriving moment equations and comparing results with simulations and experiments to improve understanding of ion dynamics.

Contribution

It introduces a novel analytical form of the ion VDF and simple closures for heat flux, validated against PIC simulations and experimental data.

Findings

Analytical VDF matches PIC simulation results.

Polynomial VDF closures effectively model heat flux.

Model agrees with experimental measurements.

Abstract

The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks-Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ions VDF. The analytical results and the anisotropic moment equations are compared to collisionless PIC simulations, employing either a zero heat flux (Euler-like equations) or the polynomial-VDF closure for the heat flux. The analytical ion VDF and its moments are then compared to experimental measurements.