Analysis of the MHD stability and energetic particles effects on EIC events in LHD plasma using a Landau-closure model

The aim of this study is to perform a theoretical analysis of the magnetohydrodynamic (MHD) stability and energetic particle effects on a LHD equilibria, calculated during a discharge where energetic-ion-driven resistive interchange mode (EIC) events were triggered. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, multiple energetic particles (EP) species, helical couplings and helically trapped EP. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations suggest that the helically trapped EP driven by the perpendicular neutral beam injector (NBI) further destabilizes the 1/1 MHD-like mode located at the plasma periphery (r/a  =  0.88). If the of the EP driven by the perpendicular NBI is larger than 0.0025 a 1/1 EIC with a frequency around 3 kHz is destabilized. If the effect of the passing EP driven by the tangential NBI is included on the model, any enhancement of the injection intensity of the tangential NBI below leads to a decrease of the instability growth rate. The simulations indicate that the perpendicular NBI EP is the main driver of the EIC events, as it was observed in the experiment. If the effect of the helical couplings are added in the model, an 11/13 EIC is destabilized with a frequency around 9 kHz, inward shifted (r/a  =  0.81) compared to the 1/1 EIC. Thus, one possible explanation for the EIC frequency chirping down from 9 to 3 kHz is a transition between the 11/13 to the 1/1 EIC due to a weakening of the destabilizing effect of the high n modes, caused by a decrease of the EP drive due to a loss of helically trapped EP or a change in the EP distribution function after the EIC burst. The experimental data during the EIC bursting phase shows a complex mode structure and an inward shift of the instability, although no direct evidence of the proposed transition has been observed yet.