Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities

The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfvén eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfvén eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2-3 times smaller than that predicted by an earlier bump-on-tail quasilinear model that employed uniform mode structures. We apply the RBQ code to a DIII-D plasma with an elevated q-profile where the beam ion profiles exhibit stiff transport properties [Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. The properties of AE driven fast ion distribution relaxation are studied for validations of the applied RBQ model in DIII-D discharges. Initial results show that the model is robust, is numerically efficient, and can predict fast ion relaxation in present and future burning plasma experiments.