Destabilization of global Alfvén eigenmodes and kinetic Alfvén waves by alpha particles in a tokamak plasma

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Alfvén wave instabilities in a reacting tokamak plasma are calculated both analytically and numerically. Two distinct classes of eigenmodes are considered, global Alfvén eigenmodes and kinetic Alfvén waves, each driven unstable by the free energy associated with the alpha particle density gradient. The growth rates of the global Alfvén eigenmodes are given for the first time. These are basically magnetohydrodynamic (MHD) modes, whose resonances with electrons and alpha particles are calculated using kinetic theory. The calculation of kinetic Alfvén wave growth rates is improved from earlier treatments. These modes depend on electron inertia and finite ion gyroradius for their existence and have no counterpart in MHD theory. In both sets of calculations toroidal coupling of the alpha particle response to sidebands in the poloidal mode number is fully taken into account. Global modes with small parallel phase velocity are identified as the most dangerous, both because of their substantial growth rates and the expected ineffectiveness of quasilinear stabilization. The kinetic waves, on the other hand, are likely to be stabilized easily by quasilinear flattening of the alpha particle profile. Calculations using both Maxwellian and slowing-down alpha distributions are performed, showing that, for the same alpha density and energy density, the slowing-down distribution yields somewhat larger growth rates.