A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-line magnetic coordinates and a field aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Anoter feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 10 9 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests.

Surface and globally averaged heat fluxes can be highly time variable in gyrokinetic simulations. During a burst of turbulence, instantaneous surface averaged fluxes may momentarily reach levels several times higher than their typical (median) levels: the result is that time-averaged flux levels are often considerably larger than typical (median) values. The bursts can in this sense be said to drive a substantial fraction of the transport. Burstdriven fluxes and flows often have long radial correlation lengths, and frequently take the form of radially propagating fronts, or avalanches. Given the large radial scale lengths of the bursts, they could play a significant role in non-local transport, and possibly in departures from gyro-Bohm scaling. We explore the characteristics of the bursts and examine how levels of fluctuation in the system depend on parameters like plasma size and gradient scale lengths. One interesting result is that there is a strong relationship between the avalanche properties and time-averaged global flow structures in the simulation. We find that the propagation direction of the avalanches depends on the sign of the shearing rate. We test an explanation for avalanche propagation based on the linear dispersion of waves which have been tilted by sheared flow.

Drift wave turbulence is known to self-organize to form axisymmetric macroscopic flows. The basic mechanism for macroscopic flow generation is called inverse energy cascade. Essentially, it is an energy transfer from the short wavelengths to the long wavelengths in the turbulent spectrum due to nonlinear interactions. A class of macroscopic flows, the poloidally symmetric zonal flows, is widely recognized as a key constituent in nearly all cases and regimes of microturbulence, also because of the realization that zonal flows are a critical agent of self-regulation for turbulent transport. In tokamaks and other toroidal magnetic confinement systems, axisymmetric flows exist in two branches, a zero frequency branch and a finite frequency branch, named Geodesic Acoustic Modes ͑GAMs͒. The finite frequency is due to the geodesic curvature of the magnetic field. There is a growing body of evidence that suggests strong GAM activity in most devices. Theoretical investigation of the GAMs is still an open field of research. Part of the difficulty of modelling the GAMs stems from the requirement of running global codes. Another issue is that one cannot determine a simple one to one relation between turbulence stabilization and GAM activity. This paper focuses on the study of ion temperature gradient turbulence in realistic tokamak magnetohydrodynamic equilibria. Analytical and numerical analyses are applied to the study of geometrical effects on zonal flows oscillations. Results are shown on the effects of the plasma elongation on the GAM amplitude and frequency and on the zonal flow residual amplitude.

Flux-driven global gyrokinetic codes are now mature enough to make predictions in terms of turbulence and transport in tokamak plasmas. Some of the recent breakthroughs of three such codes, namely GYSELA, ORB5 and XGC1, are reported and compared wherever appropriate. In all three codes, turbulent transport appears to be mediated by avalanche-like events, for a broad range of ρ * = ρ i /a values, ratio of the gyro-radius over the minor radius. Still, the radial correlation length scales with ρ i , leading to the gyroBohm scaling of the effective transport coefficient below ρ * ≈ 1/300. The possible explanation could be due to the fact that avalanches remain meso-scale due to the interaction with zonal flows, whose characteristic radial wave-length appears to be almost independent of the system size. As a result of the radial corrugation of the turbulence driven zonal and mean flows, the shear of the radial electric field can be significantly underestimated if poloidal rotation is assumed to be governed by the neoclassical theory, , especially at low collisionality. Indeed, the turbulence contribution to the poloidal rotation increases when collisionality decreases. Finally, the numerical verification of toroidal momentum balance shows that both neoclassical and turbulent contributions to the Reynolds' stress tensor play the dominant role. The phase space analysis further reveals that barely passing supra-thermal particles mostly contribute to the toroidal flow generation, consistently with quasi-linear predictions.

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