Axial-azimuthal (2D3V) full-kinetic PiC+MCC-model was built to simulate dynamics of Hall effect thruster discharge plasma taking into account azimuthal waves and diamagnetic effect. The transition from ignition to the steady-state regime was simulated. Calculation of discharge ignition shows a significant distortion in the shape of the magnetic field caused by high azimuthal-drift current. This effect and intensive ionization lead to the fact that full potential drop localizes in a thin non-magnetized cathode layer. In the steady-state regime, the distortion of the magnetic field is small. Plasma divides into three regions: dense anode plasma where ionization occurs; magnetic layer where ions accelerate and quasineutral cathodeside plasma (plume). The steady-state regime is subject to auto-oscillations at a gas-transit frequency (20 kHz 'breathing modes'). Also, two types of azimuthal instabilities have been observed: gradient drift instability and electron cyclotron instability. All these instabilities lead to collisionless 'anomalous' electron transport across the magnetic field. Kinetic effects also were considered. It was found that the electron distribution function evolves from initial isotropic (Maxwellian) to essentially anisotropic due to electric field heating. Isotropy is partially restored inside anode plasma due to collisions.

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