Numerical methods and macroscopic models of magnetically confined low temperature plasmas

In this paper a hierarchy of macroscopic plasma models is derived for the numerical study of magnetically confined low temperature plasmas with a specific interest in plasma thrusters. This derivation outlines the multi-scale nature of the problem and the difficulty for numerical methods to address efficiently this challenge. A specific focus is made on quasi-neutral models built on the anisotropic equations of the particles transport. A numerical method is proposed for this class of problems offering an accuracy unrelated to the anisotropy strength without resorting to the approximation of equipotential magnetic field lines.