A diversity of transport regimes for levitated dipole plasmas

A reduced magnetohydrodynamic (MHD) model in a Z-pinch geometry in proposed, retaining constant radial gradients of pressure, the magnetic field, and constant curvature, as well as finite plasma beta. This is a simplified model for the large-scale, low-frequency dynamics of a large-aspect-ratio levitated dipole machine. Two instabilities are recovered - the interchange instability and the ballooning instability – as well as Alfvén waves and slow waves. Five distinct regimes are found, based on varying the two input parameters - the pressure gradient and beta. The dependence of the heat transport on these parameters is determined for each regime. First, when the interchange modes are unstable but the ballooning modes are not, a state is recovered that is dominated by zonal flows and characterised by low transport. As the ballooning instability threshold is crossed (by increasing pressure gradient or beta) while the interchange modes are also unstable, saturation occurs via the standard MHD critically balanced cascade studied in many astrophysical contexts. For beta ~ 1 and smaller pressure gradients, interchange modes are stabilised, while ballooning modes can still be unstable. This instability generates a saturated state that consists of counter-propagating, non-interacting wave packets whose lifetime is dissipation-dependent. Finally, when neither of the unstable modes is present but above a critical value of beta and given a finite-amplitude initial condition, a subcritical turbulent state is discovered. The transport in this regime is stiff, which poses a challenge for operating a levitated dipole device. By inverting the dependence of the heat transport on beta and the pressure gradient in each regime, scenarios are proposed for achieving the largest value of beta given a certain input power.