Radial density and heat fluxes description in the velocity space: Nonlinear simulations and quasi-linear calculations

In the context of temperature gradient-driven, collisionless trapped-ion modes in magnetic confinement fusion, we perform and analyse numerical simulations to explore the turbulent transport of density and heat, with a focus on the velocity dimension (without compromising the details in the real space). We adopt the bounce-averaged gyrokinetic code TERESA, which focuses on trapped particles dynamics and allows one to study low frequency phenomena at a reduced computational cost. We focus on a time in the simulation where the trapped-ion modes have just saturated in amplitude. We present the structure in velocity space of the fluxes. Both density and heat fluxes present a narrow (temperature-normalized energy width ΔE/T ≈ 0.15) resonance peak with an amplitude high enough for resonant particles to contribute for 90% of the heat flux. We then compare these results obtained from a nonlinear simulation to the prediction from the quasi-linear theory and we find a qualitative agreement throughout the whole energy dimension: from thermal particles to high-energy particles. Quasi-linear theory over-predicts the fluxes by about 15%; however, this reasonable agreement is the result of a compensation between two larger errors of about 50%, both at the resonant energy and at the thermal energy.