Three-dimensional modeling of the sawtooth instability in a small tokamak

The sawtooth instability is one of the most fundamental dynamics of an inductive tokamak discharge such as will occur in ITER [R. Aymar, Plasma Phys. Controlled Fusion 44, 519 (2002)]. Sawtooth behavior is complex and remains incompletely explained. The Center for Extended MHD Modeling (CEMM) SciDAC project has undertaken an ambitious campaign to model this periodic motion in a small tokamak as accurately as possible using the extended MHD model. Both M3D [W. Park, Phys. Plasmas 6, 1796 (1999)] and NIMROD [C. R. Sovinec, Phys. Plasmas 10, 1727 (2003)] have been applied to this problem. Preliminary nonlinear MHD results show pronounced stochasticity in the magnetic field following the sawtooth crash but are not yet fully converged. Compared to the MHD model, extended MHD predicts plasma rotation, faster reconnection, and reduced field line stochasticity in the crash aftermath. The multiple time and space scales associated with the reconnection layer and growth time make this an extremely challenging computational problem. However, these calculations are providing useful guidelines to the numerical and physical requirements for more rigorous future studies.