A Two-dimensional Hybrid-Direct Kinetic Model of a Hall Thruster

Abstract

The goal of this dissertation is to improve the state-of-the art modeling approaches available for simulating the discharge plasma in a Hall effect thruster (HET). A HET is a space propulsion device that utilizes electrical energy to ionize and accelerate propellant, generating thrust. The device features a cross-field configuration, whereby the transverse magnetic field traps electrons, and the axial electric field electrostatically accelerates ions out of the thruster channel. This configuration enables desirable thruster performance characteristics typically characterized by a relatively high specific impulse (1000-3000 s) and a high thrust density (a few Newtons per square meter).

High fidelity computational models are useful to investigate the physical processes that govern the HET's performance, efficiency, and lifetime limitations. The non-equilibrium nature of the plasma transport should be resolved so that the flow can be accurately characterized. A grid-based direct kinetic (DK) simulation is capable of modeling the non-equilibrium state of plasma without the numerical noise that is inherent to particle-based methods since the velocity distribution functions (VDFs) are obtained in a deterministic manner. As the primary objective of this work, a two-dimensional, hybrid-DK simulation of the discharge plasma in a HET is developed. As a secondary objective, a plasma sheath, one of the important physical structures that form in the discharge plasma of a HET near the channel walls, is examined via a two-dimensional full DK simulation that highlights slight spatial differences in the sheath as a result of electrically disparate, adjacent wall materials. The memory storage requirements and computational load for the parallelized DK simulation grow with additional species, physical space dimensions, and velocity space dimensions. Some of these numerical limitations are encountered within this work.

The hybrid-DK HET model utilizes a quasi-one-dimensional fluid electron algorithm in conjunction with a two-dimensional DK method to simulate the motion of neutral atoms and ions in a HET channel and near-field plume. Upon its development, the hybrid-DK simulation is benchmarked against results obtained from a two-dimensional hybrid-particle-in-cell (PIC) simulation with an identical fluid electron algorithm. To achieve agreement between the simulation results, a boundary condition for the DK model that satisfies particle conservation at the wall boundaries is developed, and electron model boundary conditions that provide solution stability are sought and utilized. For both high-frequency and low-frequency oscillations, the two simulations show good agreement for both time-averaged and dynamic plasma properties. Statistical noise tends to randomize plasma oscillations in the PIC simulation results, whereas the DK results exhibit coherent oscillatory behavior. Furthermore, results indicate that the DK simulation is capable of responding to small changes in electron dynamics, which is promising for future work.

The DK plasma sheath simulation models a two-dimensional plasma sheath that highlights slight spatial differences inside the sheath as a result of electrically disparate, adjacent materials. To accomplish this goal, a quasi-one-dimensional sheath model is first built in a two-dimensional framework, boundary conditions are developed, and results are verified against theoretical expectations. Then, the full two-dimensional plasma sheath is modeled. The proof-of-concept model shows that two-dimensional effects are present in the vicinity of the discontinuous plasma potential at the wall, and electron and ion VDFs both clearly exhibit changes due to these effects.