OHM'S Law in the Slow Lane: Galilean Invariant Electromagnetic Closures for Electronion Plasmas

Modeling the dynamics of plasmas typically involves understanding the dynamics of ions and electrons coupled through collisions and electromagnetic fields. In terrestrial plasmas, the dynamics of the ions and electrons are usually assumed to be slow with respect to the speed of light and as such, the treatment of these species is derived from the non- relativistic form of the Maxwell-Boltzmann equation, either through direct treatment or through a moment hierarchy. The electromagnetic closure is provided through one of a multitude of options, including electrostatics, MagnetoHydroDynamics (MHD), Darwin or full-wave Maxwell. However, of these, only electrostatics and MHD can be shown to be consistent with non-relativistic plasma models.