Driven, resistive, force-free plasmas and reversed-field-pinch physics revisited

Solutions of the coupled steady-state equations, Ohm's law, and curl B = λ(r)B, are obtained in slab and cylindrical geometries with two ignorable coordinates. Aside from the stark feature of small toroidal-field reversal near the plasma edge, the numerically obtained field profiles in cylindrical geometry mimic the observed experimental reversed-field-pinch profiles; e.g., B_z is a monotonically decreasing function of radius and, if the parallel resistivity is spatially independent, then also λ (i.e.,j/B) is a monotonically decreasing function of radius. It is also shown that toroidal-field reversal is impossible in a toroidally symmetric, force-free, steady-state, Ohmic plasma having nested flux surfaces. It is suggested that the more sophisticated dynamics required to sustain the observed field reversal may be able to be relegated to the outer annular region containing the reversal surface. Understanding of this dynamics then may be facilitated by the fact that only one field component, the poloidal one, is dominant throughout this region.