Nonlinear regimes of the electron cyclotron drift instability in Vlasov simulations

We report on novel investigation of nonlinear features of the electron cyclotron drift instability (ECDI) with a continuum Vlasov simulations. This instability has been recently actively studied as a source of anomalous transport in Hall thrusters. It is shown that the instability occurs as a series of cyclotron resonances with the electron beam mode due to the $E\times B $ drift. Temporal and spatial spectra of nonlinear state are presented. In the nonlinear regime, fluctuations energy condensation occurs towards the low wavelength lowest mode resonance and below (inverse energy cascade) demonstrating several nonlinear mode transitions. Similar condensation picture is observed in the spectrum of the anomalous current. It is shown that the saturated state remains far from the criteria of the nonlinear transition to the ion sound regime.