Fully kinetic model of plasma expansion in a magnetic nozzle

TL;DR

This paper introduces a fully kinetic, self-consistent Particle-in-Cell model for plasma expansion in magnetic nozzles, validated against experiments, revealing how magnetisation affects electron cooling regimes and plasma behavior.

Contribution

The paper presents a novel kinetic simulation method with domain-independent boundary conditions for plasma plumes in magnetic nozzles, validated against experimental data.

Findings

Validation of the model against experimental measurements.

Identification of a potential well due to charge separation.

Dependence of electron polytropic index on magnetisation.

Abstract

A self-consistent model is presented for performing steady-state fully kinetic Particle-in-Cell simulations of magnetised plasma plumes. An energy-based electron reflection prevents the numerical pump instability associated with a typical open-outflow boundary, and is shown to be sufficiently general that both the plume kinetics and plasma potential demonstrate domain independence (within 4%). This is upheld by non-stationary Robin-type boundary conditions on the Poisson's equation, coupled to a capacitive circuit that allows physical evolution of the downstream potential drop in the transient. The method has been validated against experiments, providing results that fall within the uncertainty of measurements. Simulations are then carried out to study collisional xenon discharges into axisymmetric diverging magnetic nozzles. Particular discussion is given to the identification of a potential well arising from charge separation at the edge of the plume, the role of ion-neutral charge exchange, and a three-region piecewise polytropic cooling regime for electrons. The polytropic index is shown to depend on the degree of magnetisation. Specifically, in the region near the thruster outlet, the plume is weakly-magnetised due to the cross-field diffusion of electron-heavy particle collisions. Downstream, a strongly-magnetised region of near-isothermal expansion occurs. Finally, in the detached region, the polytropic index tends to that of a more adiabatic unmagnetised case. With an increasing magnetic nozzle field strength, an inferior limit is found to the average polytropic index of $\bar{\gamma}_e\sim1.16$.