University of Michigan, Ann Arbor, Michigan, USA
We derive a system of equations for semi-relativistic magnetohydrodynamics, in which the bulk speed and the sound speed of the plasma are non-relativistic, but the Alfvén speed can be relativistic. The characteristic wave speeds of the modified equation set are determined and compared to the wave speeds in "classical" MHD. The stability conditions of the semi-relativistic MHD equations are also investigated in detail.
This form of the MHD equations has a use beyond modeling flows with high Alfvén speeds. Even in cases with moderate Alfvén speeds, the semi-relativistic form or certain approximations of it can be used to achieve accelerated numerical convergence to steady-state solutions by artificially reducing the speed of light, provided that the steady-state solutions of these equations are fully independent of the speed of light. Numerical tests are presented that demonstrate the behavior of solutions at high Alfvén speeds, and the convergence acceleration that can be achieved when a steady-state solution is desired.