2D fluid model of a magnetized plasma in a closed chamber

Understanding the behaviour of the magnetized plasma in the thruster ionization chamber is crucial to optimize the design and operation of this kind of thrusters. In particular, in Onera ECR thruster, the walls of the chamber can be dielectric, grounded or floating conductors. Depending on the boundary conditions, swirl currents may appear in the plasma; their effects on the plasma behaviour and overall thruster performances are unknown. Our goal in this work is to develop a model for the magnetized plasma produced in the chamber, using a 1and a 2-fluid MHD framework. The models are based on the following assumptions: the problem is assumed to have an axial symmetry, and the electrons are supposed to be isothermal in the chamber. The magnetic field is assumed to be static, with a plasma β small enough to neglect induced magnetic fields. In the 1-fluid approach, the plasma is supposed to be quasi-neutral, and to obey local ambipolarity (ion and electron axial and radial velocities are equal). The sheath is not resolved, and the plasma is supposed to reach the boundaries of the vessel with the Bohm velocity. In the 2-fluid approach, electrons and ions are treated separately; they are coupled through the Poisson equation. In this case, the sheath is resolved, and electrostatic boundary conditions are prescribed at the wall, depending on the wall property. The model equations are solved using a finite element technique. Some preliminary computations are shown; they focus on a discharge in a closed chamber with an axial magnetic field. In the 1-fluid model, the evolution of the ionization rate required to sustain the plasma as a function of the plasma magnetization shows three regimes: a fully magnetized case, a non-magnetized case, and a transitional region. In the 2fluid model the same trend is observed. The development of swirl current in the plasma is also observed.