Nonlinear MHD Simulations of Sawtooth Instabilities using M3D-C1

Linear and nonlinear, reduced as well as full resistive and two-fluid magnetohydrodynamic simulations of sawtooth instabilities are carried out using the high-order finite element code M3D-C1 [1]. The objective of this project is to take advantage of the high accuracy of M3D-C1 and its ability to use locally refined meshes in order to perform sawtooth simulations at high Lundquist numbers, focusing on the reconnection process. The code’s high versatility allows the comparison of reduced, full and two-fluid MHD models as well as cylindrical and toroidal geometries. First linear studies include benchmarks of simulations of the resistive internal kink instability in cylindrical geometry with analytic dispersion relations for the different MHD models. The nonlinear studies are focused on two aspects. (1), nonlinear reduced MHD simulations in cylindrical geometry are compared to reduced MHD simulations performed by a helical MHD code developed by Q. Yu [2]. At high Lundquist numbers Yu’s simulations show the emergence of plasmoids (small additional islands) at the q = 1 surface which lead to higher reconnection rates [3]. (2), the two-fluid MHD model of M3D-C1 will be used for more realistic nonlinear simulations in toroidal X-point geometry in order to study the phenomenon of incomplete sawtooth reconnection, which is often observed in experiments [4]. To enable detailed comparisons with experimental observations, simulations based on realistic ASDEX Upgrade tokamak [5] geometry and parameters are as well planned.