The modified Magnetohydrodynamic equations

TL;DR

This paper derives a modified set of Magnetohydrodynamic (MHD) equations based on self-consistent electromagnetic equations for plasma, replacing the Lorentz force with a more accurate force expression using vector potential.

Contribution

It introduces a new formulation of MHD equations by incorporating self-consistent electromagnetic equations and replacing the Lorentz force with a force equation involving vector potential.

Findings

Derived a set of eight equations in eight unknowns for plasma dynamics.

Replaced the Lorentz force with a force equation involving vector potential.

Provided a formal derivation consistent with classical vector analysis.

Abstract

After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the MHD equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity.The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight (8) equations in eight (8) unknowns, as previously known concerning the tradditional MHD equations.