Non-linear MHD simulations of sawteeth and their control by current and power depositions

Sawteeth in tokamak plasmas correspond to periodic relaxations of the temperature and density in the central region of the plasma, caused by the internal kink mode. They play an important role in core confinement and impurity transport in the central region of a tokamak discharge, and they can trigger secondary instabilities. Being able to control their dynamics is therefore important. In this article, we explore by means of MHD simulations the control of sawteeth, relying on current or power deposition in the vicinity of the q  =  1 surface. To do so, simulations with the full-MHD code xtor-2f (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), which features power and current source terms mimicking the effects of ECCD and ECRH, are performed. Simulations show that a deposition of current inside the inversion radius leads to an increase of the sawtooth frequency whereas a deposition near or outside the inversion radius leads to a decrease of the sawtooth frequency, in agreement with theoretical and experimental predictions. For power depositions, the situation appears however to be more complex. The modification of the sawtooth shape in presence of additional heating or current drive is also investigated. The existence of a critical shear setting the condition of the sawtooth crash is found to apply, although the inter-crash dynamics is often too complex and MHD-dependent to be summarized as a periodic instantaneous redistribution of current and energy, as assumed in the analytical models. Finally, we briefly explore possible scenarios for the triggering of magnetic islands, and show how controlling the sawteeth can help to prevent the triggering of tearing instabilities.