Robustness of reduced quasilinear transport models as compared with fully nonlinear frameworks

Auxiliary heating, essential to bringing plasmas up to fusion temperatures, produces an inverted distribution function of a minority fast ion species that can strongly resonate with Alfvén waves and potentially cause global transport. In the study of fast ion redistribution, it is instructive to determine how far reduced approaches can be employed, in comparison with more comprehensive but numerically costly ones. To investigate this question in a simplified geometry, we focus on the 1D bump-on-tail problem. Previous studies (K. Ghantous et al, Phys. Plasmas 21, 032119 (2014)) used a quasilinear model that employed a diffusion equation with a heuristically prescribed rectangular resonance function as its broadened diffusion coefficient. In the present study, we use the theory recently developed by Duarte et al, [Phys. Plasmas 26, 120701 (2019)], which self-consistently derived an analytic expression for such a resonance function for marginally unstable modes. We simulate the quasilinear evolution of the distribution function and the mode amplitude in systems with different degrees of instability strength and collisionality. The results are compared against fully nonlinear simulations of the Vlasov equation for the same system.