This overview is an assessment of the gyrokinetic framework and simulations to compute turbulent transport in fusion plasmas. It covers an introduction to the gyrokinetic theory, the principal numerical techniques which are being used to solve the gyrokinetic equations, fundamentals in gyrokinetic turbulence and the main results which have been brought by simulations with regard to transport in fusion devices and fluctuation measurements.

Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode ͑GAM͒ in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.

Abstract. Collisionless time evolutions of geodesic acoustic modes (GAMs) in tokamaks are investigated by the gyrokinetic theory and simulation. It is shown that the collisionless damping of the GAM oscillations is enhanced when the ratio of the typical drift orbit width of passing ions to the radial wavelength of the zonal flow increases.

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.

Multiscale gyrokinetic turbulence simulations with the real ion-to-electron mass ratio and β value are realized for the first time, where the β value is given by the ratio of plasma pressure to magnetic pressure and characterizes electromagnetic effects on microinstabilities. Numerical analysis at both the electron scale and the ion scale is used to reveal the mechanism of their cross-scale interactions. Even with the real-mass scale separation, ion-scale turbulence eliminates electron-scale streamers and dominates heat transport, not only of ions but also of electrons. Suppression of electron-scale turbulence by ion-scale eddies, rather than by long-wavelength zonal flows, is also demonstrated by means of direct measurement of nonlinear mode-to-mode coupling. When the ion-scale modes are stabilized by finite-β effects, the contribution of the electron-scale dynamics to the turbulent transport becomes non-negligible and turns out to enhance ion-scale turbulent transport. Damping of the ion-scale zonal flows by electron-scale turbulence is responsible for the enhancement of ion-scale transport.