Resistive Z-pinch equilibria and stability

Theoretical work is presented on the effects of resistivity in a Z-pinch. Two new classes of time-dependent resistive Z-pinch equilibria are described in detail. The stationary equilibria in the first class are sustained by a rising current, those in the second expand while carrying a failing current. A wide spectrum of equilibria is found, from models of gas-embedded pinches to thermally isolated pinches confined by skin currents at the plasma edge. The stability of the stationary equilibria in the ideal MHD regime is studied. Resistive Z-pinch stability is studied numerically by using an initial-value code. This work demonstrates that a Z-pinch can be stable to m = 0 and m = 1 perturbations in the low current regime. It is shown that this result can at least partly explain the enhanced stability observed in some Z-pinch experiments. The compressional Z-pinch experiment at Imperial College is modelled using a one-dimensional Lagrangian code. It is thereby shown to be anomalously stable. (author)