Massively parallel modeling of the sawtooth instability in tokamaks

The sawtooth instability is one of the most fundamental dynamics of an inductive tokamak discharge such as will occur in ITER. The sawtooth occurs when the current peaks in a tokamak, creating a region in the core where the safety factor is less than unity, q<1. While this instability is confined to the center of the plasma in low-pressure, low-current, large-aspect-ratio discharges, under certain conditions it can create magnetic islands at the outer resonant surfaces or set off a sequence of events that leads to a major disruption. Sawtooth behavior is complex and remains incompletely explained. The SciDAC Center for Extended MHD Modeling (CEMM) has undertaken an ambitious campaign to model this periodic motion as accurately as possible using the most complete fluid-like description of the plasma - the Extended MHD model. The multiple time and space scales associated with the reconnection layer and growth time make this an extremely challenging computational problem. The most recent simulation by the M3D code used over 500,000 elements for 400,000 partially implicit time steps for a total of 2×10¹¹ space-time points, and there still remain some resolution issues. However, these calculations are providing insight into the nonlinear mechanisms of surface breakup and healing. We have been able to match many features of a small tokamak and can now project to the computational requirements for simulations of larger, hotter devices such as ITER.