International audiencePartially magnetized plasmas in the Hall effect thrusters remain poorly understood primarily due to the electron transport in the cross-field direction. It is recently discussed that the drift-diffusion approximation is invalid for the electron dynamics in the presence of a large drift velocity. It is therefore possible that the anomalous electron transport is strongly related with the presence of an azimuthal drift. In this paper, we discuss the importance of the azimuthal drift on cross-field electron transport based on some recent results from a one-dimensional particle-in-cell simulation, two-dimensional particle-in-cell simulation, and laser Thomson scattering measurements