Vlasov Simulation of Current-Driven Instabilities Relevant to High-Current Hollow Cathode Plumes
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Understanding the sputtering of cathode surfaces is of high interest to the EP community, since hollow cathodes can be one of the main lifetime limiting components of Hall thrusters and ion engines. Current-driven instabilities in the plumes of hollow cathodes are a leading candidate for the mechanism behind the generation of high energy ions that erode hollow cathode surfaces and result in an anomalous momentum loss of the electron current. A 1D Vlasov simulation is used to study the ion kinetics and time evolution of bulk plasma properties in the nonlinear saturation regime of the current-carrying instability. The simulations are carried out over a range of initial electron Mach numbers, 0.5 ≤ M0 ≤ 2.5, where the electron Mach number is defined as the ratio of the relative drift velocity between electrons and ions to the electron thermal velocity. Time evolution of the bulk plasma properties show significant plasma heating and current dissipation, resulting in a decrease in the steady-state electron Mach number as the initial condition M0 increases. This steady state value is what is measured in experiments and illustrates the nonlinear time dependence of the instability and, due to its rapid growth, the difficulty in understanding its true nature from experimental data. High energy ions are generated due to large amplitude ion acoustic waves of large phase velocities. A significant population of backstreaming high energy ions is observed when the initial electron Mach number is greater than or equal to 1.3, indicating a transition to the Buneman instability, where nonlinear kinetic effects are dominant. The population and velocity ranges of the high energy ions are extracted and used to calculate sputtering rates, which are compared to calculations using the non-Maxwellian distributions for ions obtained from the simulation and Maxwellian ion distributions of temperatures ranging from 0.5 eV to 4.0 eV. The very large ion temperatures required by the Maxwellian distributions to obtain the same level of sputtering as the kinetic model illustrate the necessity of self-consistent kinetic models in fluid simulations to capture the cathode erosion.
Treece, Cameron James (2019). Vlasov Simulation of Current-Driven Instabilities Relevant to High-Current Hollow Cathode Plumes. Master's thesis, Texas A&M University. Available electronically from