Structure of wave-particle resonances and Alfvén mode saturation

The dynamics of beta-induced Alfvén eigenmodes driven by anisotropic co-passing or counter-passing fast ions, in a low-shear magnetic equilibrium, is investigated by self-consistent hybrid MHD-particle simulations with the XHMGC code. Though the modes exhibit similar structure and frequency in both cases and the linear growth rate is 10% larger for counter-passing ions than for co-passing ions, the nonlinear saturation amplitude is much larger in co-passing case. Moreover, different scalings for the saturation amplitude with increasing growth rates are observed in the two cases. It is shown that these differences are caused by the different radial dependence of resonance frequencies of co-passing and counter-passing fast ions: flat in the former case, steep in the latter case, so that the resonance width is, respectively, larger (in the former case) or smaller (in the latter case) than the mode width