A Maxwell formulation for the equations of a plasma

Abstract

In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic (MHD) limit restores the typical variety of MHD waves.