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Simulations of radiation driven islands at the density limit

Author: D. P. Brennan
Requested Type: Consider for Invited
Submitted: 2015-01-19 18:08:33

Co-authors: L. Delgado-Aparicio, D.A. Gates, Q. Teng, R. White

Contact Info:
Princeton Plasma Physics Laboratory
100 Stellarator Road
Princeton, NJ   08550
USA

Abstract Text:
The Greenwald density limit is a surprisingly robust experimental result, the physical origins of which have been a long-standing puzzle. Recently, the thermo-resistive onset criterion for magnetic islands was shown [D.A. Gates and L. Delgado-Aparicio, PRL 108, 165004 (2012)] to be consistent with the empirical scaling of the tokamak density limit. In the current work, an imbalance between radiative cooling and Ohmic heating inside magnetic islands is shown to have a critical impact on the nonlinear growth of the islands. Numerical and analytic analyses indicate that proper inclusion of 3D thermo-resistive effects while accounting for island asymmetry leads to an exponential growth mechanism with an abrupt threshold. The helical flux is used to map the interior of the islands during the simulations, allowing for studies of varying transport inside the islands separately from regions outside the islands. While the perpendicular transport outside the islands is representative of that dominated by turbulence, inside the islands the drive to turbulent transport is assumed sub-critical (flattened), and the imbalance between radiative cooling and Ohmic heating is implemented as a small temperature gradient. This temperature perturbation is implemented in the three-dimensional Spitzer resistivity, and thus affects island current. The key result is that with even small net cooling inside the island, the island width grows exponentially at a rapid rate, while heated islands saturate at small size, for temperature variations inside the islands on the order of those observed in experiments. The configuration for the study is a cylindrical tokamak with a m/n=2/1 island and includes three dimensional resistivity and anisotropic heat conduction in the simulations. This simplified geometry allows for quantitative comparison between the simulations and reduced analytic analysis while capturing the essential physics. Asymmetry in magnetic island structure is found to be key to this physics. The mechanism is generally applicable to asymmetric islands, which could occur on multiple rational surfaces. Several aspects of these physics results support the notion that this is an explanation of the Greenwald density limit, and offer intuitive understanding of the impact of temperature gradients inside magnetic islands in general.

Comments:
Roscoe White and I would like to give our presentations in tandem. Based on recent presentations here at PPPL, our team feels this work is important, timely, and best presented in two parts.