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Weakly nonlinear analysis of Alfven eigenmodes

Hirota, Makoto; Aiba, Nobuyuki

Excitation and suppression mechanisms of Alfv$'e$n eigenmodes (AEs) have received much attention. Recent experiments show that the energetic-particle-driven AEs further induce nonlinear phenomena such as mode-mode coupling and biharmonic resonance via the MHD nonlinearity. It is theoretically worth studying how much energy can transfer from the fundamental AEs to other modes. In this work, we have formulated a simple governing equation of weakly nonlinear perturbation based on the variational principle of the MHD Lagrangian. By substituting linear eigenfunctions into the third-order potential energy, one can discuss any coupling among three eigenmodes. This technique can apply to AEs in any geometry (including tokamaks with any aspect ratio). We perform analytical and numerical evaluation of the coupling among AEs, and discuss its dependence on the beta value, the aspect ratio and the mode numbers.



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