Lower-Hybrid Drift Instabilities in a magnetic nozzle

TL;DR

This paper presents a comprehensive linear analysis of drift instabilities in magnetic nozzles, incorporating plasma inhomogeneities, magnetic curvature, and 3D wave effects, with implications for plasma thruster performance.

Contribution

It extends previous models by including parallel inhomogeneities and finite Larmor radius effects, providing a more complete understanding of drift-driven instabilities in plasma thrusters.

Findings

Predicted azimuthal instabilities in the 1 kHz–1 MHz range.

Instabilities can be driven by parallel inhomogeneities even without axial propagation.

Cross-field transport tends to smooth out destabilizing drifts.

Abstract

Magnetic nozzles are a key component of electrodeless plasma thrusters, acting as their main acceleration stage. Non-stationary phenomena common to the entire range of $E \times B$ devices, such as oscillations and instabilities, are likely to exist in the magnetic nozzle, according to the mounting experimental evidence. These mechanisms could lead to anomalous cross-field transport, either enhancing the plasma plume divergence or favoring electron detachment. In this work we present a local linear analysis of fluid instabilities relevant for said devices, expanding on previous works with the addition of plasma inhomogeneities in the direction parallel to the magnetic field, with a rigorous inclusion of the effects of magnetic curvature, finite Larmor radius and $3$D wave propagation, allowing for a general formulation of drift-driven instabilities in partially magnetized plasmas. Instability conditions are first studied analytically, and then applied to simulation data of a helicon plasma thruster. Finally, the effect of instabilities on wave-driven cross-field electron transport is assessed by means of quasi-linear analysis. This study predicts the onset of essentially-azimuthal instabilities in the $1$ kHz--$1$ MHz range, in qualitative agreement with some of the available experimental data, and highlights the importance of including parallel inhomogeneities in the formulation of the dispersion relation of an $E \times B$ plasma, as these gradients may drive instabilities even in the absence of axial propagation. Lastly, quasi-linear analysis suggests that the induced cross-field transport acts to smooth out the zeroth-order drifts which cause the plasma to destabilize in the first place.