Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma

TL;DR

This paper develops approximate semi-analytical solutions for the steady-state expansion of collisionless, electrostatic plasma plumes, offering a computationally efficient alternative to numerical methods and extending previous models to broader conditions.

Contribution

It introduces a generalized semi-analytical model for plasma plume expansion, improving applicability and accuracy over earlier models, including non-zero azimuthal velocity cases.

Findings

The semi-analytical solutions closely match numerical results within certain parameter ranges.

The generalized model extends applicability to various plasma injection profiles.

Error analysis defines the validity range of the approximate solutions.

Abstract

We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979), Korsun and Tverdokhlebova (1997), and Ashkenazy and Fruchtman (2001). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.