Abstract
Abstract. Alfv´en Eigenmodes (AE) can be destabilized by energetic particles in neutral beam injection (NBI) heated plasmas 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, as well as the geodesic acoustic wave dynamics. We add the Landau damping and resonant destabilization effects through a closure relation. We apply the model to study the Alfv´en modes stability in TJ-II, performing a parametric analysis in a range of realistic values of energetic particle β (βf), ratios of thermal/Alfv´en velocities (Vth/VA0), energetic particle density profiles and toroidal modes (n) including toroidal and helical couplings. The study predicts a large helical coupling between different toroidal modes and the destabilization of helical Alfv´en Eigenmodes (HAE) with frequencies similar to the AE activity measured in TJ-II, between 50−400 kHz. The analysis has also revealed the destabilization of GAE (Global Alfv´en Eigenmodes), TAE (Toroidal Alfv´en Eigenmodes) and EPM (Energetic Particle Modes). For the modes considered here, optimized TJ-II operations require a ι profile in the range of [0.845,0.979] to stabilize AEs in the inner and middle plasma. AEs in the plasma periphery cannot be fully stabilized, although for a configuration with ι = [0.945,1.079], only n = 7,11,15 AE are unstable with a growth rate 4 times smaller compared to the standard ι = [1.54,1.68] case and a frequency of 100 kHz. We reproduce the frequency sweeping evolution of the AE frequency observed in TJ-II as the ι profile is varied. The AE frequency sweeping is caused by consecutive changes of the instability dominant modes between different helical families.
