Quasi-linear resonance broadened model for fast ion relaxation in the presence of Alfvénic instabilities*

We present a realistic Quasi-linear (QL) model to find the energetic particle distribution function relaxed in the presence of Alfvénic instabilities. This approach is a numerically efficient method to capture the evolution of a beam ion distribution function. The spatial structure of the instabilities is computed by the eigenvalue solver for predictive simulations.

The effect of Alfvénic eigenmodes (AE) is evaluated adapting the QL theory [H. Berk Phys. Plasmas v.3 (1996) 1827] generalized for this problem. The application of the model to realistic plasma conditions is improved by going beyond the perturbative-pendulum-like approximation for the wave particle dynamics near the resonance. The resonance region is 2-3 times smaller than predicted by an earlier bump-on-tail QL model. In addition the resonance broadening includes the Coulomb collisional or anomalous pitch angle scattering.

A new Resonance Broadened Quasi-linear code (RBQ) is built taking into account the beam ion diffusion in the direction of the canonical toroidal momentum. The wave particle interaction is reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. The diffusion equation is solved simultaneously for all particles together with the evolution equation for the mode amplitudes.

We apply the RBQ code to a DIII-D plasma with elevated q-profile where the beam ion profiles show stiff transport properties [C. Collins Phys. Rev. Lett., v.116 (2016) 095001]. The sources and sinks are included via the Krook operator. The properties of AE driven fast ion distribution relaxation are studied for validations of the applied QL model to DIII-D discharges. Initial results show that the model is robust, numerically efficient, and can predict the fast ion relaxation in present and future burning plasmas.