Nonlinear behavior of the electron cyclotron drift instability in long term PIC simulations

Electron cyclotron drift instability (ECDI) has been discussed in the context of turbulence in collisionless shocks in the magnetosphere and is considered a leading cause of anomalous transport in regions with large electric fields in Hall thrusters. In space conditions and laboratory experiments, ECDI is driven by the ion beam injected perpendicular to the magnetic field. For Hall thruster applications, ECDI is considered a result of the external electric field driving the electron beam due to the ExB drift. ECDI and its associated anomalous transport have been studied using particle-in-cell (PIC) and Vlasov simulations in various settings of one- and two-dimensional geometries. One puzzling feature of ECDI is the strong growth of electron temperature and fluctuation energy, especially apparent in one-dimensional simulations. This growth is interpreted as a result of continuous energy input from the external electric field. Another much-discussed issue is the nonlinear development of the instability and the transition to the ion sound instability similar to the ion sound mode in unmagnetized plasmas. Here, we present the results of one-dimensional simulations of ECDI using the PIC WarpX code. Our long-term simulations for xenon ions, using parameters typical for Hall thruster conditions, show that after some intermediate nonlinear stages, the system enters a stationary state with significantly increased electron temperature and a finite level of electrostatic energy in fluctuations. In this stage, the anomalous electron current existing in intermediate stages is quenched to zero value. The nonlinear stages of ECDI driven by ion beam and ExB electron drift are compared.