Curvature effects on the dynamics of tearing modes in tokamaks

Abstract

The curvature effects on the dynamics of magnetic island evolution in tokamaks are investigated both theoretically and numerically. By taking into account perpendicular and parallel heat diffusion, a new dispersion relation is derived for tearing modes that match the linear and nonlinear results. This evolution equation allows a quantitative description over the whole range of island sizes. It predicts a nonlinear instability, i.e., growing magnetic islands in linearly stable magnetic configurations. All these predictions are in excellent agreement with full tridimensional linear and nonlinear magnetohydrodynamic (MHD) computations with the latest version of XTOR [K. Lerbinger and J. F. Luciani, J. Comput. Phys. 97, 444 (1991)]. These results have important consequences on the onset of neoclassical tearing modes because they predict a resistive MHD threshold.

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

“…67 Although this effect is likely very small in the Rutherford regime, 46 it is possible that a modified viscosity coefficient could be introduced. The goal of the closures to date has been to reproduce the analytic results that have been successfully used [72][73][74][75][76][77][78] to analyze experimental results, and to allow the extension of analytic studies to include effects such as geometry and mode coupling.…”

“…Using a local approximation to the Landau fluid closures would be useful and consistent with the philosophy of the heuristic closure; however all neoclassical tearing mode calculations to date have used a Braginskii heat flux closure. 44,71,74,77 The implementation of Landau-fluid models for the parallel heat flux closure would be an improvement to existing models and remains an active area of research.…”

On the requirements to control neoclassical tearing modes in burning plasmas

“…It is argued that using both forms proposed in equations (11) and (12) should span the effective dependence of the growth rate at small island width. The latter can indeed be rather complicated once the effects on the curvature term [32] or of finite orbit width [33], for example, are taken into account. Note that we use the simplest form which still takes the main physical effects.…”

Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry

“…Recent work by Lütjens, Luciani, and Garbet suggests that the resistive term scales differently than the neoclassical term when the island width is smaller than the critical width [13]. Namely, the interchange term asymptotes to a non-zero value as the island width goes to zero.…”

“…2 through by ψ t and including transport effects as per Refs. [11] and [13], it may be rewritten in completely dimensionless form as follows:…”