MHD Equilibrium Equation with Azimuthal Rotation in a Curvilinear Coordinate System

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We derive, according to a procedure introduced by Maschke and Perrin, an equation for MHD stationary equilibrium with azimuthal rotation in an orthogonal curvilinear coordinate system. We assume that there is an ignorable coordinate so that surface quantities like the magnetic flux and the rotation frequency do not depend on it. The temperature is also considered a surface quantity. As an application of the formalism, we consider prolate spheroidal coordinates, which are convenient for studying plasma rotation in compact tori configurations like Spheromaks.

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