Ion kinetics and nonlinear saturation of current-driven instabilities relevant to hollow cathode plasmas

Ion kinetics and time evolution of bulk plasma properties in the nonlinear saturation regime of a collisionless current-driven instability are studied using a 1D Vlasov-Poisson simulation. In the simulations, the ratio of initial electron bulk velocity to initial electron thermal velocity, called the electron Mach number, ranges from 0.5 to 2.5, and electron-to-ion temperature ratio is 10. A significant population of backstreaming high-energy ions is observed when the initial electron Mach number is larger than or equal to 1.3, which agrees with previous literature indicating transition to the Buneman instability. The simulations suggest that the electrons trapped in large-amplitude waves result in a bi-directional ion acoustic wave, which generates a backward-propagating high-energy ion distribution. A concise formula that describes the high-energy ion distribution and potential fluctuation amplitude are obtained as a function of initial electron Mach numbers. Sputtering rate calculations using the non-Maxwellian distributions for ions obtained from the simulation and Maxwellian ion distributions of temperatures ranging from 0.5 to 4.0 eV are compared, illustrating the potential contribution of kinetic effects on cathode erosion.