The properties of the ExB drift mode in Hall thrusters were investigated through particle-based simulations. Two different two-dimensional models coupling the ExB drift azimuthal direction with the axial accelerating field and radial magnetic field directions, respectively, were implemented assuming Cartesian slab geometry. While the azimuthal-axial model is selfsustaining through the closure of the anode-cathode circuit, the radial-azimuthal one is equipped with an injection system that preserves the number of ions and with a secondary electron emission module for electron-wall interaction. Results identify the linear growth and nonlinear saturation mechanisms consisting of electron heating along azimuthal and radial directions and of ion wave trapping. The latter leads to the ion rotation along the azimuthal direction giving the ion distribution a long tail. The discrete band structure of ExB electron drift instability evolves by an inverse cascade process toward small wavenumbers characterized by broader resonances giving to the spectrum an ion-acoustic-like nature. The larger lobes are due to electron heating and to the presence of a radial component by a modified two-stream instability. Important correlations at macroscopic level between the azimuthal modulation of the azimuthal electric field and the axial modulation of the accelerating field are proof of the complexity of the electron transport in Hall thrusters.

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