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We study the cross-field electron transport in Hall thruster induced by ExB cyclotron drift instability. The investigation tool, consisting of one-dimensional Particle-in-Cell model in the azimuthal drift direction, has been subjected to a convergence study to verify the effects of numerical parameters. The instability evolves keeping the discrete nature of its cyclotron harmonics only for low wavenumbers. A resonance broadening mechanism induced by the electron heating and velocity distribution deformation makes the high-wave numbers disappear in the long non-linear stage. A large wavelength modulation, comparable to the entire azimuthal domain considered is always superimposed. The saturation mechanism is conducted by ions that, due to friction with electrons and trapping in the potential well, heat up and rotate along the electron drift direction. With the best numerical parameters found, the scaling of anomalous mobility with the most important physical quantities (gas and plasma density, magnetic field, accelerating axial electric field, and ion mass) has been obtained. Results show that the electron cross-field mobility has a strong dependence from the plasma density and ion mass: for large plasma density, the system undergoes an abrupt change entering in a mode dominated by fluctuation-induced transport, while lighter ions present larger mobility. The scaling of the dominant wavelength detected is compatible with the first harmonic and no transition toward ion acoustic like instability has been observed.
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