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 works 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 is discussed.1

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This manuscript explores numerical errors in highly anisotropic diffusion problems. First, the paper addresses the use of regular structured meshes in numerical solutions versus meshes aligned with the preferential directions of the problem. Numerical diffusion in structured meshes is quantified by solving the classical anisotropic diffusion problem; the analysis is exemplified with the application to a numerical model of conducting fluids under magnetic confinement, where rates of transport in directions parallel and perpendicular to a magnetic field are quite different. Numerical diffusion errors in this problem promote the use of magnetic field aligned meshes (MFAM). The generation of this type of meshes presents some challenges; several meshing strategies are implemented and analyzed in order to provide insight into achieving acceptable mesh regularity. Second, Gradient Reconstruction methods for magnetically aligned meshes are addressed and numerical errors are compared for the structured and magnetically aligned meshes. It is concluded that using the latter provides a more correct and straightforward approach to solving problems where anisotropicity is present, especially, if the anisotropicity level is high or difficult to quantify. The conclusions of the study may be extrapolated to the study of anisotropic flows different from conducting fluids.

Due to the advances in miniaturization Cubesats are becoming more versatile, with projected mission capabilities that are traditionally reserved for larger satellites. However they are still limited by a lack of efficient propulsive means. A novel electric thruster based on Electron Cyclotron Resonance heating and Magnetic Nozzle acceleration may provide a suitable yet simple solution. This device, while currently providing 1000 s Isp and 1 mN of thrust at 30W of power, may enable Lunar CubeSat missions from GEO using on-board propulsion. An example mission to provide GPS on the Lunar surface using 3U CubeSats in a 60°:28/4/6 Walker constellation with a semi-major axis of 4000 km is proposed; a preliminary assessment of this mission, together with the satellite architecture and cost, is performed. Concurrent trajectory design for very-low-energy transfers is used to demonstrate the feasibility of the mission and its impact on the space-craft design.