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.

Trapped ion resonance-driven turbulence is investigated in the presence of electron dissipation in a simplified tokamak geometry. A reduced gyrokinetic bounce-averaged model for trapped ions is adopted. Electron dissipation is modeled by a simple phase-shift δ between density and electric potential perturbations. The linear eigenfunction features a peak at the resonant energy, which becomes stronger with increasing electron dissipation. Accurately resolving this narrow peak in numerical simulation of the initial-value problem yields a stringent lower bound on the number of grid points in the energy space. Further, the radial particle flux is investigated in the presence of electron dissipation, including kinetic effects. When the density gradient is higher than the temperature gradient, and the phase-shift is finite but moderate (δ≈0.02), the particle flux peaks at an order-of-magnitude above the gyro-Bohm estimate. Slight particle pinch is observed for δ<0.003.