Theoretical model of suppression of electron instability in hall thrusters by boundary feedback system

Among plasma instabilities in Hall thrusters, large-scale electron instability of Rayleigh type holds one of the main positions. Its arising brings about redistribution of the electrical field in the acceleration layer that can increase losses of ions on the walls of the thruster. In the paper, the possibility of suppression of this instability by a boundary feedback system (BFS) is theoretically considered. The analysis is carried out with the use of hydrodynamic approximation. The eigenvalue problem is solved in assumption that the BFS creates an azimuthal distribution of the electrical potential on the surface of the anode, which is a function of the perturbation electrical field near the anode. From the solution of the eigenvalue problem, it follows that for the suppression of the electron instability, the transformation coefficient of the BFS should lie in the region limited by both a lower value and upper value, which depend on the length of the wave and distance between the anode and a maximum of the drift velocity.