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Plasma discharges in electromagnetic thrusters often operate with weakly-collisional, magnetized electrons. Macroscopic models of electrons provide affordable simulation times but require to be solved in magnetically aligned meshes so that large numerical diffusion does not ruin the solution. This work discusses suitable numerical schemes to solve the axisymmetric equations for the electric current continuity and the tensorial Ohm's law in such meshes, when bounded by the thruster cylindrical or annular chamber. A finite volume method is appropriate for the current continuity equation, even when meshes present singular magnetic points. Finite differences and weighted least squares methods are compared for the Ohm's law. The last method is more prone to producing numerical diffusion and should be used only in the boundary cells and requires a special formulation in the boundary faces. In addition, the use of the thermalized potential is suggested for an accurate computation of parallel electron current densities for very high conductivity. The numerical algorithms are tested in a hybrid (particle/fluid) simulation code of a helicon plasma thruster, for different magnetic fields, mesh refinement, and plume lengths. The different contributions to the electric current density are assessed and the formation and relevance of longitudinal electric current loops are discussed.
electric propulsion; numerical simulations; magnetized electron fluids