Results from a fully nonlinear three-dimensional toroidal electrostatic gyrokinetic simulation of the ion temperature gradient instability are presented. The model has adiabatic electrons and the complete gyrophase-averaged ion dynamics, including trapped particles. Results include the confirmation of the radially elongated ballooning mode structure predicted by linear theory, and the nonlinear saturation of these toroidal modes. The ensuing turbulent spectrum retains remnants of the linear mode structure, and has very similar features as recent experimental fluctuation measurements.PACS numbers: 52.35. Ra, 52.25.Gj, 52.35.Qz Recent advances in both nonlinear df methods for gyrokinetic simulation [1,2] and massively parallel supercomputing now make it possible to simulate a sizable fraction of a tokamak plasma using realistic physical parameters. Here, we report results from the first whole cross section three-dimensional (3D) electrostatic toroidal gyrokinetic simulation. We investigate the nonlinear evolution of the ion temperature gradient (ITG) driven instability and the associated turbulence and transport in realistic geometry and dimensionality. The ITG mode has long been considered a plausible candidate to explain the observed anomalous ion heat transport in tokamak plasmas, which is substantially above the predicted neoclassical values [3,4]. The simulation results presented below show very similar features in terms of the fluctuation spectrum as the recent beam emission spectroscopy (BES) diagnostic on TFTR [5].In these simulations, the ions are fully gyrokinetic, including trapped particles. The electrons are treated as adiabatic which permits a moderate size time step (simulations with kinetic electrons are feasible, but the time step would need to be smaller by the factor ivAv/). The simulation is running efficiently on massively parallel supercomputers (currently the CM-200 and CM-5) which allow simulations of relatively large systems (e.g., a ^ lOOp/ minor radius. Ax ^=^ pi). Typical runs up to this point have used 10^ to 10^ particles with 1 to 2 particles per grid cell, and a timing of 2-3 jUS per particle per time step on a fully configured CM-200. Fine grid resolution is needed in the toroidal direction because the mode structure is helical (elongated along the magnetic field lines, i.e., k\\<^k±), resulting in a smaller number of particles per grid cell relative to conventional slab simulations.Starting with the electrostatic gyrokinetic equations with a nonuniform equilibrium B field [6], we write /(z,r) ==/o(z) + ^/(z,/), where z = (R,rii,/x), and expand z into its equilibrium and perturbed parts: z=z^-f-z^ /o(z) is a Maxwellian and satisfies z^S^o(z)=0. The equation for the perturbed ion distribution function 5f is then [1] S,5/+z9z^/=--z^9j^o,where the magnetic moment fi is time independent and the other equilibrium and perturbed phase space variables are evolved using (R",r,r)=(-riib*-h^bxV5,b*-A/V5), tLu^ ii /,i^ = (R\n|)

The dynamics of turbulence-driven E B zonal ows has been systematically studied in fully 3-dimensional gyrokinetic simulations of microturbulence in magnetically-conned toroidal plasmas using recently available massively parallel computers. Linear ow damping simulations exhibit an asymptotic residual ow in agreement with recent analytic calculations. Nonlinear global simulations of instabilities driven by temperature gradients in the ion component of the plasma provide key rst principles results supporting the physics picture that turbulence-driven uctuating E B zonal ows can signicantly reduce turbulent transport.Turbulence shear suppression by E B ows is the most likely mechanism responsible for the transition to various forms of enhanced connement regimes observed in magnetically-conned plasmas [1]. Understanding the physical mechanisms of turbulence suppression processes [2,3] here is what controls the generation of the ows and how strongly the ows aects the turbulent transport which is believed to arise from electrostatic pressuregradient driven instabilities. These highly complex nonlinear phenomena can be most eectively investigated by n umerical experiments. One of the most promising approaches is gyrokinetic particle-in-cell simulation [6] which suppress the rapid gyromotion of a charged particle about the magnetic eld line. By making use of recent advances of new low-noise numerical algorithms and by taking advantage of the exciting opportunities oered by high-end massively parallel computing power, it has been able to reproduce key features of turbulent transport observed at the core of tokamak plasmas.The present n umerical experiments clearly demonstrate that turbulence-driven uctuating E B zonal ows play a crucial role in regulating nonlinear saturation and transport levels. This is in agreement with previous toroidal gyrokinetic and gyrouid (a uid model with kinetic eect) simulations of instabilities driven by iontemperature-gradient (ITG) in a local geometry which follows a magnetic eld line [7{9]. However, previous global gyrokinetic simulations, which treat the whole plasma volume, either did not include [10] or did not observe [11,12] signicant eects of these self-generated ows. Since local simulations are restricted to a uxtube domain with radially periodic boundary conditions and since they rely on the assumption of scale separation between the turbulence and equilibrium proles, the key issues of transport scaling and eects of steep pressure proles in transport barriers can only be eectively studied in global simulations. In this report, nonlinear simulation results from a newly developed global gyrokinetic code [13] yield the important conclusion that turbulencedriven uctuating E B ows can signicantly reduce the anomalous transport. In order to understand this key process, the dynamics of E B ows have been systematically analyzed. Linear ow damping simulations exhibit a time asymptotic residual ow in agreement with a recent analytic calculation [14]. The present nonlinear global simulation...

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