RF current condensation in magnetic islands and associated hysteresis phenomena

Abstract

The nonlinear RF current condensation effect suggests that magnetic islands might be well controlled with broader deposition profiles than previously thought possible. To assess this possibility, a simplified energy deposition model in a symmetrised 1D slab geometry is constructed. By limiting the RF wave power that can be absorbed through damping, this model describes also the predicted hysteresis phenomena. Compared to the linear model, the nonlinear effects lead to larger temperature variations, narrower deposition widths, and more robust island stabilisation. Although, in certain regimes, the island centre can be disadvantageously shaded because of the nonlinear effects, in general, the RF condensation effect can take place, with current preferentially generated, advantageously, close to the island centre.

RF current condensation in the presence of turbulent enhanced transport

“…The enhancement occurs when the temperature gradient exceeds a certain threshold, and it is shown to act as an additional island edge localised energy loss mechanism. This way, a very strong stiffness may constrain temperature, giving rise to phenomena similar formally to that in [40], even without the need to limit the wave energy.…”

“…Thus, we introduce here a more physical finite energy wave damping model, to study its interaction with stiffness and condensation. The wave damping model used is inherited from previous work 40 , to which the reader is referred for further details. Fundamentally, the model describes the RF wave energy density, V , as it travels left to right (increasing x) through the island and becomes damped.…”

“…Nevertheless, the quoted values are taken as representative and used in our species-independent picture, which would have to be refined in future work. For guidance on the experimentally relevant values of V 0 and α 0 in the wave-damping model, we refer the reader to [40], where an extensive discussion may be found. Here, we limit ourselves to quoting typical values that may be expected to be α 0 ∼ 0.1 − 3 while V 0 ∼ 1 − 10.…”

“…However, if the electron temperature is raised throughout the island, then significant extra wave damping may be incurred near the island periphery. The damping near the island periphery leads to increased temperature and damping there, leading to a feedback effect that can effectively shadow the island centre, preventing the wave energy from penetrating deep inside the island 40 . This shadowing effect can be overcome by taking into account the nonlinearity of the power deposition in aiming the a) Email: eduardor@princeton.edu b) Email: areiman@pppl.gov c) Email: fisch@princeton.edu ray trajectories, but it can place a premium on accurate aiming of the ray trajectories.…”

“…The paper is organised as follows: In Sec. II, we briefly introduce a first form of the model and show that stiffness leads to multiple steady state solutions and a new hysteresis effect, alternative to the hysteresis effect due to the finite available power that was previously explored 40 . In Sec.…”