ABSTRACT
Flux core spheromak sustainment by electrostatic helicity injection is studied in resistive MHD. The geometry has magnetized electrodes at the ends held at a potential difference V. For V>V(c) the central current column is kink unstable. The nonlinear state with V just above V(c) has a large volume of flux surfaces, with rotational transform provided by the helical kinking of the column. As V increases the kink becomes stronger, the tori are destroyed, and the field lines exhibit chaotic scattering. The distribution of field line lengths L, related to confinement and parallel current density, is studied. At larger V or larger Lundquist number S, a limit cycle appears.
ABSTRACT
The theory for a Penning-Malmberg trap predicts m = 1 diocotron stability. However, experiments with hollow profiles show robust exponential growth. We propose a new mechanism of destabilization of this mode, involving parallel compression due to end curvature. The results are in good agreement with the experiments. The resulting modified drift-Poisson equations are analogous to the geophysical shallow water equations, and conservation of line integrated density corresponds to that of potential vorticity. This analogy predicts Rossby waves in non-neutral plasmas and an m = 1 instability in fluids.
