Theoretical analysis of the energetic particle mode decay: Frequency down-sweeping and the role of the shear flows

The present study is dedicated to the analysis of energetic particle modes (EPMs) in fusion devices. The aim of the analysis is reproducing the EPM frequency down-sweeping and the transition from energetic particle (EP)-driven to current- or pressure-gradient-driven instabilities observed in the experiments. In addition, the shear flow generation and its effect on the EPM saturation and decay phases are analyzed. Two test cases are considered: Fish-bones destabilized in a JET configuration and energetic-ion-driven resistive interchange modes (EICs) triggered in a Large Helical Device (LHD) discharge. A set of nonlinear simulations using the gyro-fluid code FAR3d are performed, removing the EP drive along the saturation phase of Fish-bones and EIC, analyzing the EPMs' decay with and without the presence of shear flows. The simulations reproduce the EPM's frequency down-sweeping along with the transition from a Fish-bone to the current-driven 1/1 internal kink in the JET case, as well as the transition from EIC to the pressure gradient-driven 1/1 resistive interchange mode in the LHD case. The simulations show the generation of shear flows and radial electric fields in the plasma location where the Fish-bone/EIC decay, linked to the energy transfer from the modes toward the thermal plasma. Linear simulations performed using the evolved profiles from nonlinear simulations highlight the key role of the shear flows in the decay of Fish-bones, pointing out the mode frequency down-sweeping can only be reproduced in simulations including the effect of the shear flows. In addition, the analysis may indicate shear flows have a regulatory effect on the Fish-bone saturation, leading to a smoother mode decay by balancing the energy extraction caused by the continuum damping. On the other hand, the role of shear flows in the EIC decay is smaller compared to the Fish-bones, explained by narrower and almost steady shear flow bands observed in the simulations.