Improvement of a simulation platform for Helicon Plasma Thrusters: analysis of the boundary conditions and modelling of the sheath

The proper treatment of the boundary conditions when dealing with fluid simulations of plasma processes constitutes a non-negligible issue that might affect the results, especially when dealing with plasma sources for propulsion applications, e.g., as in Helicon Plasma Thrusters (HPT). In this work, we handle the problem of boundary conditions modelling. Firstly, we have reviewed several established physical models to assess how to properly treat the HPTs. Then, three approaches to account for the sheath have been considered, namely, I) the direct solution of the sheath region through the finite volume discretization, II) the modelling of the sheath through analytical solutions, and III) a hybrid approach in which we coupled two distinguished solvers that handle respectively the bulk region of the plasma and the sheath. The bulk region solver is based on the classical multi-fluid approach. The sheath is solved either by a fluid or a Lagrangian approach, to account for deviations from the Maxwellian velocity distribution function for each species present in the plasma. The proposed approaches have been tested in terms of plasma profiles (e.g., density) against the experimental case of a Piglet reactor. Generally, all three approaches have given a satisfactory agreement with the experimental measurements. In particular, the first and third approaches have shown similar results, with the latter being assessed with the fluid approach only. As for the computational cost, both methods required similar computation time. Regarding the second approach, the results under-estimate the plasma density if compared to the other methods. Nonetheless, this approach required 97% less computational effort. Ultimately, the hybrid approach achieved good results and it offers interesting possibilities of further development, some of which have been discussed.