Analysis of Alfven Eigenmodes destabilization by energetic particles in Large Helical Device using a Landau-closure model

Energetic particle populations in nuclear fusion experiments can destabilize Alfv\' en Eigenmodes through inverse Landau damping and couplings with gap modes in the shear Alfv\' en continua. 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. We add the Landau damping and resonant destabilization effects by a closure relation. We apply the model to study the Alfv\' en modes stability in Large Helical Device (LHD) inward-shifted configurations, performing a parametric analysis in a range of realistic values of energetic particle $\beta$ ($\beta_{f}$), ratios of the energetic particle thermal/Alfv\' en velocities ($V_{th}/V_{A0}$), magnetic Lundquist numbers ($S$) and toroidal modes ($n$). The $n = 1$ and $n = 2$ TAE are destabilized although $n = 3$ and $n = 4$ TAE are weakly perturbed. The most unstable configurations are associated with density gradients of energetic particles in the plasma core: TAE are destabilized even for small energetic particle populations if their thermal velocity is lower than $0.4$ times the Alfv\' en velocity. The frequency range of MHD bursts measured in LHD are $50-70$ kHz for $n=1$ and $60-80$ kHz for $n=2$ TAE, consistent with the model predictions.