Stability of toroidal Alfven eigenmodes using an initial value hybrid code

Toroidal Alfven Eigenmodes (TAE) have been shown to exist, in a plasma, in the gap of the continuum spectrum. These discrete, global modes, induced by toroidicity, could be strongly destabilized by energetic particles as alpha particles produced in fusion reactions. The TAE stability is determined by the competition of the driving term associated to the resonant interaction between the mode and the parallel motion of the energetic ions, and the coupling with the Alfven continuum which introduces a damping. An initial value code has been used to solve the reduced resistive magnetohydrodynamic (MHD) equations for the bulk plasma and the gyrokinetic equations for the high energy particles. The MHD equations have been expanded in the inverse aspect ratio var-epsilon=a/R to the lowest order at which the toroidal corrections enter the equations (that is the third order in var-epsilon) and for low-β[O(var-epsilon 2)]. In the gyrokinetic part of the code the high energy particles are pushed using the electric potential and the parallel component of the vector potential as obtained by the MHD part of the code. The linear dynamic of the Toroidal Alfven Eigenmode in the absence of energetic particles has been studied, considering the resistive damping rate and the interaction with the Alfven continuum. Results of non-linear simulations are presented particularly referring to the MHD non-linearity. The MHD non-linearity is the result of the interaction of two Fourier components of the mode with poloidal and toroidal mode numbers respectively (m,n) and (m+1,n) which oscillate in time at a frequency ω0 ∼ O(ωA) (ωA is the Alfven frequency). The coupling of the two modes leads to a perturbation of the poloidal flux function δψ with mode numbers (m=1,n=0) slowly varying in time