The rigid-beam model for simulating plasmas generated by intense electron beams

TL;DR

This paper presents a simplified rigid-beam model to simulate plasma generation by intense electron beams, enabling comparison of plasma dynamics and air chemistry reductions with good approximation of electric fields.

Contribution

The paper introduces a new rigid-beam model that simplifies plasma simulation, allowing effective comparison of different plasma dynamics reductions under various conditions.

Findings

Models agree at high pressures with large energy relation rates.

Significant differences occur at low pressures where inelastic energy loss times are comparable to beam rise time.

The model effectively captures the electric field magnitude during plasma formation.

Abstract

We introduce a simplified model of the electron-beam/plasma system to model the electrical breakdown caused by the inductive electric field created by a rapidly rising electron beam current. The rigid-beam model is a reduction to the problem geometry to cylindrical coordinated and simplifications to Maxwell's equations that are driven by a prescribed electron beam current density. The model is very convenient for comparing various reductions of the plasma dynamics and air chemistry equation while maintaining a good approximation to the overall magnitude of the beam-created electric field. The usefulness of this model is demonstrated by comparing results for two different fluid reductions of the plasma dynamics: one where the collision rates are computed from the local reduced electric field (E/p) and another where the collision rates are determined from the mean energy per particle. We find that the two methods give similar results at higher pressures where the energy relation rate is large but differs significantly at lower pressures where the characteristic inelastic energy loss time scale is comparable to or greater than the rise time of the electron beam current.