MHD is a specific set of a assumptions you can make to reduce the plasma fluid equations to something more tractable. This includes things like assuming infinit

MHD is a specific set of a assumptions you can make to reduce the plasma fluid equations to something more tractable. This includes things like assuming infinite conductivity and combining all of your species into a single "fluid". Those are reasonable assumptions for astrophysical plasmas but not at all for Hall thrusters, so we do not use MHD. In my work, we use the Euler equations for ions (assuming they lack viscosity), with electromagnetic and ionization source terms. Electrons are treated as massless and generally steady with respect to the ions. Both of their equations of motion can be derived starting with the Boltzmann equation and applying simplifying assumptions.