Numerical treatment of a magnetized electron fluid model in a 3D simulator of plasma thruster plumes

Simulations of energetic plumes from plasma thrusters are of great interest for estimating performances and interactions with the spacecraft. Both in fully fluid and hybrid (particle/fluid) models, the electron population is described by a set of fluid equations whose resolution by different numerical schemes can be strongly affected by convergence and accuracy issues. The case of magnetized plumes is more critical. Here, the numerical discretization of the electron fluid model of a 3D hybrid simulator of plasma plumes was upgraded from a finite-differences (FD) formulation in a collocated grid to a finite-volumes (FV) approach in a staggered grid. Both approaches make use of structured meshes of different resolutions and are compared in two scenarios of interest: 1) an unmagnetized plasma plume around a spacecraft and 2) a magnetized plume expansion in free space. In both physical scenarios, the FD scheme exhibits a global continuity error related to truncation errors that can be reduced only by refining the mesh. The origin of this error is further investigated and explained here. The FV scheme instead can save much computational time using coarser meshes since it is unaffected by these errors due to the conservativeness of its formulation. The physical advantage of the FV scheme over the FD approach is more evident for magnetized plumes with high Hall parameters since it allows us to reach higher anisotropy conditions, here assessed in order to gain insights into the plume magnetization effects, finding that the already foreseen saturation of circulating electric current occurs for Hall parameters of several hundreds.