Impact of the electron to ion mass ratio on unstable systems in particle-in-cell simulations

The evolution of the Buneman and two-stream instabilities driven by a cold dilute mildly relativistic electron beam is studied as a function of the ion-to-electron mass ratio. The growth rates of both instabilities are comparable for the selected parameters if the realistic ion-to-electron mass ratio is used and the Buneman instability outgrows the two-stream instability for an artificially reduced mass ratio. Particle-in-cell simulations show that both instabilities grow independently during their linear growth phase. The much lower saturation amplitude of the Buneman instability implies that it saturates first even if the linear growth rates of both instabilities are equal. The electron phase space holes it drives coalesce. Their spatial size increases in time and they start interacting with the two-stream mode, which results in the growth of electrostatic waves over a broad range of wave numbers. A reduced ion-to-electron mass ratio results in increased ion heating and in an increased energy loss of the relativistic electron beam compared to that in a simulation with the correct mass ratio.