Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence

Velocity–space structures of ion distribution function associated with the ion temperature gradient (ITG) turbulence and the collisionless damping of the zonal flow are investigated by means of a newly developed toroidal gyrokinetic-Vlasov simulation code with high velocity–space resolution. The present simulation on the zonal flow and the geodesic acoustic mode (GAM) successfully reproduces the neoclassical polarization of trapped ions as well as ballistic mode structures produced by collisionless particle motions. During the collisionless damping of GAM, the finer-scale structures of the ion distribution function in the velocity–space continue to develop while preserving an invariant defined by a sum of an entropy variable and the potential energy. The simulation results of the toroidal ITG turbulent transport clearly show generation of the fine velocity–space structures of the distribution function and their collisional dissipation. Detailed calculation of the entropy balance confirms the statistically steady state of turbulence, where the anomalous transport balances with the dissipation are given by the weak collisionality. The above results obtained by simulations with high velocity–space resolution are also understood in terms of generation, transfer and dissipation processes of the entropy variable in the phase–space.