The aim of the present study is to analyze the saturation regime of the Toroidal Alfven Eigenmodes (TAE) in the LHD plasma, particularly the MHD burst. The linear and non linear evolution of the TAEs are simulated by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The linear simulations indicate the overlapping of $1/2-1/1$, $2/3-2/4$ and $3/5-3/6$ TAEs in the inner-middle plasma region and frequency range of $45-75$ kHz, triggered by EPs with an energy of $T_{f} = 45$ keV and EP $\beta = 0.022 $. The non linear simulations show that $2/3-2/4$ and $3/4-3/5$ TAEs are further destabilized due to the energy transfer from $1/1-1/2$ TAE, leading to a broad TAEs radial overlapping and the MHD burst triggering. The energy of $1/1-1/2$ TAE is also non linearly transferred to the thermal plasma destabilizing the $0/0$ and $0/1$ modes, inducing the generation of shear flows and zonal currents as well as large deformations in the thermal pressure and EP density radial profiles. The non linear simulation reproduces the same succession of instabilities and the same frequency range with respect to the experiment. The instability propagates outward during the bursting phase, showing a large decrease of the EP density profile between the middle-outer plasma, pointing out the loss of part of the EP population that explains the decrease of the plasma heating efficiency observed during the MHD burst.
The aim of this study is to analyze the linear stability of Alfvén Eigenmodes (AE) in QPS device heated by a tangential NBI. The analysis is performed using the gyro-fluid code FAR3d, that solves the reduced MHD equations for the thermal plasma coupled with moments of the kinetic equation for the energetic particles (EP). The AE stability is calculated in several operational regimes of the tangential NBI: EP β between 0.001 − 0.1, EP energy between 12−180 keV and different radial locations of the beam. The analysis is performed for vacuum and finite β equilibria as well as QPS configurations with 2 and 3 periods. The EP β threshold in the vacuum case is 0.001 and the AE frequency is lower as the energy of the EP population decreases. Toroidal Alfvén Eigenmodes (TAEs) with f = 80 − 120 kHz and Elliptical AE (EAEs) between f = 120 − 350 kHz are triggered between the middle-outer plasma region (r/a > 0.5). The AE stability improves in the simulations with finite β equilibria and 3 period configurations with respect to the vacuum case with 2 periods because the continuum gaps are slender, leading to a higher threshold of the EP β, above 0.03 for the AEs triggered by the helical mode families. Helical effects are not strong enough to destabilize Helical Alfvén Eigenmodes (HAEs), the AEs with the largest growth rates are triggered by the n = 1 and n = 2 toroidal families.
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