  The electron-cyclotron drift instability (ECDI) has been proposed as one of
the main actors behind the anomalous transport of electrons in Hall thruster
devices. In this work, we revisit the theory and perform two-dimensional PIC
simulations under several conditions to analyze the non-linear behavior and the
induced transport under several boundary conditions. Simulation results with
fully-periodic boundaries and conditions faithful to the linear theory show the
growth of ECDI modes, ion-wave trapping vortexes and agree with the existing
literature in early times. In the long term, however, we observe very mild
oscillations and null anomalous current. The evolution towards this new
equilibrium is coherent to what can be expected from energy conservation. The
quenching of the oscillations seem to be highly related with the distortion of
ion-trapping vortexes in phase space after a long-term interaction of ion
particles with the electrostatic wave. This result suggests that sustained
oscillations and turbulent current could benefit from the renewal of ions by,
e.g., removing and injecting particles through axial boundaries instead of
applying periodicity. This second type of simulations shows that injection
conditions highly impact the late simulation behavior of ECDI oscillations,
where we identify several regimes depending on the value of the ion residence
time compared to the characteristic saturation time in the fully periodic case.
The intermediate regime, where these two times are close, is the only one
providing sustained oscillations and electron transport and seems to be the
relevant one in Hall devices.
