The turbulent convective flux of the toroidal angular momentum density is derived using the nonlinear toroidal gyrokinetic equation which conserves phase space density and energy ͓T. S. Hahm, Phys. Fluids, 31, 2670 ͑1988͔͒. A novel pinch mechanism is identified which originates from the symmetry breaking due to the magnetic field curvature. A net parallel momentum transfer from the waves to the ion guiding centers is possible when the fluctuation intensity varies on the flux surface, resulting in imperfect cancellation of the curvature drift contribution to the parallel acceleration. This mechanism is inherently a toroidal effect, and complements the k ʈ symmetry breaking mechanism due to the mean E ϫ B shear ͓O. Gurcan et al., Phys. Plasmas 14, 042306 ͑2007͔͒ which exists in a simpler geometry. In the absence of ion thermal effects, this pinch velocity of the angular momentum density can also be understood as a manifestation of a tendency to homogenize the profile of "magnetically weighted angular momentum density," nm i R 2 ʈ / B 2. This part of the pinch flux is mode-independent ͑whether it is trapped electron mode or ion temperature gradient mode driven͒, and radially inward for fluctuations peaked at the low-B-field side, with a pinch velocity typically, V Ang TEP ϳ −2 / R 0. Ion thermal effects introduce an additional radial pinch flux from the coupling with the curvature and grad-B drifts. This curvature driven thermal pinch can be inward or outward, depending on the mode-propagation direction. Explicit formulas in general toroidal geometry are presented.

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation. A puzzling result in recent years in plasma turbulence has arguably been the discovery of the quasiregular pattern of E × B flows and interacting avalanches that we have come to call the "E × B staircase," or the "plasma staircase" in short [1]. This structure may be defined as a spontaneously formed, self-organizing pattern of quasiregular, long-lived, localized shear flow and stress layers coinciding with similarly long-lived pressure corrugations and interspersed between regions of turbulent avalanching. The plasma staircase exemplifies how a systematic organization of turbulent fluctuations may lead to the onset of strongly correlated flows on magnetic flux surfaces.Flow patterning is a prominent topic in many fluidrelated systems and hot magnetized plasmas are no exception to that. In fact the "staircase" name is borrowed from the vast literature in planetary flows motivated by the desire to explain the banded structure of observed atmospheres in our Solar System-including Earth [2] or Jupiter [3]-and of terrestrial oceans [4]. Just as in the geophysical or astrophysical systems where the planetary staircase strongly influences the general circulation, the plasma staircase plays an important role in organizing the heat transport [1]: avalanches and the staircase interplay, statistically interrupting at mesoscales the long-range radial avalanching that could otherwise expand over the whole system. The nonlocal heat transport thus remains contained at the mesoscale staircase step spacing, resulting in a beneficial scaling of confinement with machine size. This flow patterning is primarily a spontaneous mean zonal shear patterning. "Zonal" denotes the axisymmetric n ¼ m ¼ 0 component of the E × B flows [5], n and m respectively being the toroidal and poloidal mode numbers while "mean" refers to the ensemble-averaged part of the zonal flows. Remarkably, the plasma spontaneously generates robust shear patterns that endure despite the strong background turbulence and retain their coherence over long (several milliseconds) to very long (hundreds of milliseconds) periods of time. The results presented throughout this Letter are based on state-of-the-art flux-driven gyrokinetic [6] computations using the GYSELA code [7] with realistic tokamak plasma parameters. Systematic features of the plasma staircase can be inferred from extensive computational scans, see ...

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz [C. Bourdelle et al. 2016 Plasma Phys. Control. Fusion 58 014036], which employs an approximated solution of the mode structures to significantly speed up computation time compared to full linear gyrokinetic solvers. Optimization of the dispersion relation solution algorithm within integrated modelling applications leads to flux calculations ×10 6−7 faster than local nonlinear simulations. This allows tractable simulation of flux-driven dynamic profile evolution including all transport channels: ion and electron heat, main particles, impurities, and momentum. Furthermore, QuaLiKiz now includes the impact of rotation and temperature anisotropy induced poloidal asymmetry on heavy impurity transport, important for W-transport applications. Application within the JETTO arXiv:1708.01224v2 [physics.plasm-ph] 7 Aug 2017Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic tran integrated modelling code results in 1 s of JET plasma simulation within 10 hours using 10 CPUs. Simultaneous predictions of core density, temperature, and toroidal rotation profiles for both JET hybrid and baseline experiments are presented, covering both ion and electron turbulence scales. The simulations are successfully compared to measured profiles, with agreement mostly in the 5-25% range according to standard figures of merit. QuaLiKiz is now open source and available at www.qualikiz.com.Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic tran

The mode-independent part of the magnetic curvature driven turbulent convective (TurCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14, 072302 (2007)], which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of “magnetically weighted angular momentum density,” nmiU∥R∕B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustrated that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms that exist in a simpler geometry.

Abstract. The inviscid invariance of potential vorticity is used to derive momentum balance relations for zonal flows in drift wave turbulence. The relations are constructed by exploiting potential enstrophy balance and the Taylor identity, and link flow momentum to turbulence pseudomomentum, along with the driving flux, the dissipation and turbulence spreading. Applications to atmospheric jets and to zonal flows in plasmas are discussed.

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

International audienceThe influence of changing collisionality on density fluctuation characteristics is studied during dedicated ν∗ scaling experiments, using Doppler backscattering system. First, the repartition of fluctuation energy over different spatial scales, as represented by the wavenumber spectrum, is investigated and a modification of the shape of the perpendicular wavenumber spectrum in the low wavenumber part of the spectrum is observed when changing collisionality. In addition, a new procedure to evaluate the dispersion relation of micro-turbulence is presented. From the behavior of the perpendicular mean velocity of density fluctuations with the perpendicular wavenumber, different dispersion relations are obtained between low and high collisionality cases

In this paper, we report on an integrated program of experimental, computational, and theoretical studies of sheared zonal flows and radially extended convective cells, with the aim of assessing the results of theory-experiment and theory-simulation comparisons. In particular, simulations are used as test beds for verifying analytical predictions (specifically locality and directionality of energy transfer) of nonlinear dynamics and to investigate the suitability of bispectral analysis for studying nonlinear couplings. Initial comparisons to experimental results are presented, and future experimental studies are motivated. We also present analytic and numerical work investigating the role of structures in transport.