Electron kinetic effects and beam related instabilities in Hall thrusters

Recent analytical studies and particle-in-cell simulations suggested that the electron velocity distribution function in a Hall thruster plasma is non-Maxwellian and anisotropic. The electron average kinetic energy in the direction parallel to walls is several times larger than the electron average kinetic energy in direction normal to the walls. Electrons are stratified into several groups depending on their origin (e.g., plasma discharge volume or thruster channel walls) and confinement (e.g., lost on the walls or trapped in the plasma). Practical analytical formulas are derived for wall fluxes, secondary electron fluxes, plasma parameters and conductivity. The calculations based on analytical formulas agree well with the results of numerical simulations. The self-consistent analysis demonstrates that elastic electron scattering on collisions with atoms and ions plays a key role in formation of the electron velocity distribution function and plasma-wall interaction. The fluxes of electrons from the plasma bulk are shown to be proportional to the rate of scattering to loss cone, thus collision frequency determines the wall potential and secondary electron fluxes. Secondary electron emission from the walls is shown to enhance the electron conductivity across the magnetic field, while having almost no effect on insulating properties of the near-wall sheaths. Such a self-consistent decoupling between secondary electron emission effects on electron energy losses and electron crossed-field transport is currently not captured by the existing fluid and hybrid models of the Hall thrusters. The sheath near the electron-emitting surface may become unstable if it is characterized by the negative volt-ampere characteristics, which occurs in presence of strong secondary electron emission. It is found that in stable stationary plasma state the final phase of cyclotron rotation of secondary electrons emitted from the thruster walls is not arbitrary but belongs to the discrete set of stability intervals. In the limit of high discharge voltages, a new regime with relaxation oscillations is identified. In this regime, the plasma constantly switches between a state with non-space charge limited emission and a state with a space charge limited emission.