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On One-Fluid MHD Models with Electron Inertia

We investigate the limitations of various MHD models that include electron inertia by considering expansion in terms of non-dimensional parameters, and by classifying those that have energy conservation. It is revealed that a correction term in the momentum equation, which is usually neglected, is needed to conserve the total energy. In order to investigate the effect of this correction term, a modified Grad-Shafranov equation is obtained in the “straight torus,” i.e., where toroidal curvature is neglected, for the cases when the plasma has constant density or is barotropic. In the case with toroidal curvature, some conditions on the magnetic field in a torus are needed even if the plasma has constant density.