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Alfvén wave heating and stability

Alfvén waves in fusion plasmas play an important role in a number of situations. First, in Alfvén Wave Heating (AWH) schemes. Second, both theory and experiment have demonstrated the existence of Global Alfvén Eigenmodes (GAEs). GAEs have been observed in different tokamaks (PRETEXT, TCA, TEXTOR, etc.) and, more recently, in a stellarator (Wendelstein 7-AS) where they were shown to become unstable under intense Neutral Beam injection. Third, the existence and possible destabilization by fast ions of Toroidicity induced Alfvén Eigenmodes (TAEs) has been evidenced both theoretically and experimentally. This destabilization could hamper the operation of a magnetically confined fusion reactor by setting a limit on the number of fusion alpha particles in the plasma. It is therefore crucial to understand the mechanisms leading to the occurrence of the instability and also those that can stabilize the TAEs by increasing the strength of the damping. The aim is to be able to devise possible ways to avoid the instability of Alfvén eigenmodes in a region of parameter space that is compatible with the functioning of a fusion reactor. A global perturbative approach is presented to tackle the problem of the linear stability of TAEs. Our model computes the overall wave particle power transfers to the different species and thus could also be applied to the study of alpha power extraction in the presence of Alfvén waves. We indicate also how to go beyond the perturbative approach.