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. Electron emission from discharge chamber walls or cathodes is important for plasma maintenance in many thrusters. The electrons emitted from surfaces are accelerated by the sheath electric field and are injected into the plasma as an electron beam. Penetration of this beam through the plasma is a subject of the two-stream instability, which tends to slow down the beam electrons and heat the plasma electrons. The two-stream instability occurs if the total electron velocity distribution function of the plasma-beam system is a non-monotonic function of electron energy. For correct description of the two-stream instability and, hence, penetration of emitted electrons through the plasma, the accurate kinetic description is necessary for both the plasma and the beam. It is also found in one-dimensional particle-in-cell simulations that the two-stream instability depends crucially on the velocity distribution function of electron emission.