Resistive magnetohydrodynamic equilibria in a torus

It was recently demonstrated that static, resistive, magnetohydrodynamic equilibria, in the presence of spatially-uniform electrical conductivity, do not exist in a torus under a standard set of assumed symmetries and boundary conditions. The difficulty, which goes away in the “periodic straight cylinder approximation,” is associated with the necessarily non-vanishing character of the curl of the Lorentz force, j×B. Here, we ask if there exists a spatial profile of electrical conductivity that permits the existence of zero-flow, axisymmetric resistive equilibria in a torus, and answer the question in the affirmative. However, the physical properties of the conductivity profile are unusual (the conductivity cannot be constant on a magnetic surface, for example) and whether such equilibria are to be considered physically possible remains an open question. PACS numbers: 52.30.Bt, 52.30.Jb, 52.55.-s, 52.65.Kj Typeset using REVTEX 1