Description
This work develops an integrated model of sawtooth cycles and fishbone oscillations. Sawtooth cycles are periodic relaxations of the plasma core commonly observed in tokamak discharges. The cycle is characterized by a rapid MHD-driven collapse of the core kinetic and current profiles, followed by a profile recovery driven by core heating and fueling. While sawtooth crashes limit core performance and can trigger disruptive secondary instabilities, they can also expel impurities and helium ash, aiding ash control in reactors.
We have developed a model that encompasses all phases of a sawtooth cycle. The onset criterion is given by a first-principle model, and the collapse via an ad-hoc relaxation model. The background transport in between sawteeth is modeled with TGLF-SAT2 for the turbuluence-driven contribution and NCLASS for the neoclassical one. The collapse of the fast particle population and rotation profiles are also modelled, as they actively and passively affect the sawtooth cycle.
Both TGLF-SAT2 default settings and settings aiming at better capturing Kinetic Ballooning Modes (KBMs) at high $\beta$ are tested. It is found that around the $q=1$ surface TGLF with KBM settings agrees with the linear calculations of GENE for $k_y\rho_s>0.1$, while TGLF with default settings finds modes with significantly lower growth rates. However, the transport from TGLF with KBM settings is much higher than the one needed to recover the experimental profiles, while TGLF with default settings agrees well with the experiments. This finding hints at possibly missing turbulence stabilisation mechanisms, such as the ones of fast ions, which are compensated by the low growth rates found by TGLF with default settings.
Fishbone oscillations are often observed between sawtooth crashes, in discharges with a substantial population of fast ions. These instabilities are driven by a resonance of the internal kink with the precession frequency of fast ions. In this work, the fishbone onset criterion, redistribution of fast ions and driven radial electric field are modelled from first principles. The fishbone-driven radial electric field obtained from reduced models is found to have little effects on turbulence in the analyzed discharges, as it is predicted to be one order of magnitude smaller than the one driven by toroidal rotation and neoclassical poloidal rotation. On the other hand, fishbones are observed to have a significant effect on the redistribution of thermal plasma, which affects also the sawtooth cycle and is predicted in the simulations.
The results are validated on ASDEX Upgrade discharges in presence of NBI and ECRH heating schemes. The integration of sawtooth cycles and fishbones within a transport code represents a significant advance for predictive simulations, enabling applications such as performance prediction and control strategies for future machines.