Magnetic islands and their effects in tokamak plasmas

The vast majority of theoretical plasma physics investigations of tokamaks rely on the presence of a continuous symmetry in the magnetostatic equilibria so that the existence of a set of nested, toroidal magnetic flux surfaces is guaranteed. In this presentation the authors propose that the fundamental underlying magnetic topology of a tokamak plasma is not described by this idealized limit, but instead by a collection of magnetic island chains located at low-order rational surfaces and localized regions of intermittent magnetic stochasticity. In particular, the fluctuating bootstrap current of neoclassical-MHD provides a robust mechanism for the formation of resonant symmetry-breaking magnetic perturbation and the resulting magnetic islands. Simulations of interacting bootstrap-current-driven magnetic islands show that the distribution of magnetic island widths exhibit a quasi-equipartition where the steady-state magnetic topology is described by magnetic island chains radially separated by regions with toroidal magnetic surfaces that support plasma density and temperature gradients. This result is in sharp contrast to the naive single-helicity theory (where island interactions are ignored), that would incorrectly predict that islands forming at low-order rational surface grow to be substantial fractions of the plasma confinement region and thus cause island overlap. A self-consistent evolution of the plasma pressure profile in this magnetic topology is necessary to characterize the magnetic island dynamics and the subsequent plasma transport. A simple calculation of the quasi-static pressure profile near a single isolated magnetic island can be made; however island interactions and time-dependent processes seriously complicates this calculation. Additionally, ideal ballooning mode stability can be significantly effected near a magnetic island when the ballooning mode is localized near the island X-point