MHD Equilibrium Equation in Symmetric Systems

In MHD symmetric systems the equilibrium physical quantities are dependent on two variables only. In this cases it is possible to find a magnetic surface function that has the same symmetry. Under the assumption that the metric determinant is also independent of a third, ignorable coordinate, a general MHD equilibrium equation in curvilinear coordinates is deduced. This equation is specially useful when non-orthogonal generalized coordinates are used.