On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks

Abstract

A fundamental requirement for the validity and accuracy of any large-scale computation is sufficiently well-resolved length and time scales relevant to the problem under study. Ironically, despite the enormous computational resources available today, poorly resolved length scales in sophisticated nonlinear calculations are not uncommon. Using the internal kink mode that is responsible for tokamak sawtooth oscillations as an example, consequences of not resolving in sufficient detail the linear and nonlinear layer widths of the resistive n = 1 mode and its nonlinear spectrum are examined. Poor radial and spectral resolution are shown to cause nonphysical, large-scale stochasticity that can be erroneously associated with a fast temperature collapse and sawtooth crash. With the assistance of a nonlinear mode coupling model, a sufficiently well-resolved toroidal spectrum is shown to require at least an order of magnitude more toroidal modes than is commonly used at dissipation levels relevant to today's tokamaks. A subgrid-scale model is introduced that helps with the spectral resolution problem by reducing the required number of degrees of freedom from that of a well-resolved direct numerical simulation.