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.

In this paper, we examine the energy distribution function of electrons in the case of a very weakly ionized
argon plasma at sub-atmospheric pressure and external electric field using Boltzmann kinetic equation. We are
interested in the behavior of the collisional part of the equation, thus spatially uniform model is considered. The
goal of the research is to compare two different numerical approaches: a deterministic one (using a two-term local
non-stationary approximation) and a stochastic approach (using the Monte Carlo method) over a wide range of
reduced electric fields: from several Td to kTd. We present the comparison for steady-state and time-dependent
solutions, isotropic and anisotropic parts of the electron energy distribution function, and reaction constants.
The research will also help to identify any limitations and challenges of these methods.

A new mathematical processing method for current signals from surface dielectric barrier discharge in conditions of high noise is suggested. This technique is based on the analysis of isolated microdischarge parameters: charge transfer, impulse duration, and voltage/phase, followed by statistical analysis. Research was carried out on surface dielectric barrier discharge units with a copper thin corona electrode on a 1 mm aluminum nitride barrier. Four modes with the corresponding rms-voltages of 1.8, 2.0, 2.2, and 2.4 kV were considered. Distributions of microdischarge parameters and overall phase characteristics were collected.

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