Deterministic-Kinetic Computational Analyses of Expansion Flows and Current-Carrying Plasmas

Abstract

Spacecraft electric propulsion (EP) takes advantage of the ability of electric and magnetic fields to accelerate plasmas to high velocities to generate efficient thrust. The thermionic hollow cathode is a critical component to both gridded-ion and Hall-effect thrusters, the state-of-the-art devices of the EP discipline. However, experiments demonstrate that the hollow cathode is plagued by erosion of its surfaces by the plasma, which may eventually cause premature failure of the device. This erosion has been linked to the ion-acoustic instability (IAI), a kinetic plasma instability which operates in the cathode plume. Existence of this kinetic instability has prevented numerical simulation from predicting the operating characteristics and lifetime of the hollow cathode device. Therefore, this thesis utilizes deterministic-kinetic (DK) simulation of gas and plasma flows to further the understanding of the IAI as it relates to the hollow cathode plume and to ultimately develop a predictive hollow cathode simulation platform. Towards these goals, two approaches to applying the DK simulation method to the hollow cathode plasma are undertaken: hybrid-kinetic simulation and fully-kinetic simulation.

Hybrid-kinetic simulations utilize a kinetic description of the heavy propellant particles while using a reduced-order, fluid approach for the light electrons. Two unique two-dimensional, axisymmetric kinetic schemes are developed, one for neutral particles and one for ions; the schemes are verified by comparison with solutions obtained using the direct-simulation Monte Carlo method and with an analytic solution for a rarefied neutral jet flow. Assuming quasi-neutrality in the hollow cathode plasma and using the Boltzmann relation for the plasma potential, the hybrid-kinetic solver is applied to the problem of NASA's NSTAR discharge hollow cathode. Partial validation is achieved through agreement with experimental Langmuir probe data in the near-orifice region, while shortcomings of the solver such as use of a simplified electron model are discussed.

Fully-kinetic simulations, where all species are considered kinetically, are carried out to study the IAI. The anomalous resistivity generated by the IAI is measured from one-dimensional fully-kinetic simulations and compared with a closure model commonly used in hollow cathode fluid codes, finding that the agreement with the closure model varies based on simulation domain size and electron Mach number. Further, the formation of high-energy tails in the ion velocity distribution function is observed near the transition to the Buneman instability, another instability of current-carrying plasmas. Two-dimensional kinetic simulations of current-carrying instabilities are carried out, finding that the nature of nonlinear saturation of the IAI differs significantly from that shown in one-dimensional simulations. A phenomenon known as the off-axis instability generates waves propagating normal to the current direction which eventually reach energy levels close to that of the waves along the current direction.

Further fully-kinetic simulations demonstrate the formation of weak plasma double layers, regions of plasma which sustain a potential gradient, in the nonlinear saturation stage of the IAI. These double layers are found to be ubiquitous in all plasma species considered, even the heavy xenon ions commonly used in hollow cathodes. Phase space analysis suggests the double layers form from ion-acoustic wave packets which grow into ion phase space holes. Spectral analysis demonstrates a shift towards smaller wavenumbers which marks this transition. An electron two-stream instability is spawned due to the potential well of the double layer, where spectral analyses demonstrate that a simple theoretical expression well-predicts the resulting wave phase velocity.