Interchange turbulence in two dimensions is investigated in the scrape-off layer (SOL) of fusion devices, when driven by a constant core particle influx. Contrary to the standard gradient-driven approach, density is allowed to fluctuate around its average profile. Transverse transport exhibits some of the features of self-organized critical systems, namely inward and outward avalanches, together with a frequency spectrum decrease in 1/f and f−2 at intermediate and high frequencies, respectively. An avalanche occurs when the local radial density gradient exceeds the critical one. A self-sustained particle flux then follows the large radial structures of the electric potential. As observed experimentally, the radial profile of density relative fluctuations decreases from the wall into the core plasma, while that of electric potential relative fluctuations peaks inside the SOL. Equilibrium density exhibits the experimental exponential decrease. An analytical expression of the SOL width ΔSOL is obtained, which maximizes the linear growth rate, when the poloidal modulation of electric potential equilibrium is taken into account. The parametric dependencies of ΔSOL are compared to experimental data.

A systematic, constructive and self-consistent procedure to quantify nonlocal, nondiffusive action at a distance in plasma turbulence is exposed and applied to turbulent heat fluxes computed from the state-of-the-art full- f, flux-driven gyrokinetic GYSELA and XGC1 codes. A striking commonality is found: heat transport below a dynamically selected mesoscale has the structure of a Lévy distribution, is strongly nonlocal, nondiffusive, scale-free, and avalanche mediated; at larger scales, we report the observation of a self-organized flow structure which we call the " E × B staircase" after its planetary analog.

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We show in this paper that geodesic acoustic modes (GAMs) can be efficiently excited by a population of fast ions even when Landau damping on thermal ions is accounted for. We report in particular fully kinetic calculations of the GAM dispersion relation and its complete solution. Written under a variational form, the quasi-neutrality condition, together with the kinetic Vlasov equation, leads to the density of exchanged energy between particles and the mode. In particular, a linear threshold for the GAMs excitation is derived. Two examples of fast ion distribution have been discussed analytically. It turns out that particles with high perpendicular energy compared to the parallel resonance energy are most responsible for the excitation of the mode. Subsequent numerical simulations of circular plasmas using GYSELA code have been carried out. In particular, the linear kinetic threshold has been reproduced during the excitation phase, and a nonlinear saturation has been observed. Analysis in the phase space of the evolution of the equilibrium distribution function is presented and the saturation level quantified.

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 ...

An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and ECH-driven counter torque are discussed in some detail. Symmetry breaking by LSN vs. USN asymmetry is related to the origin of intrinsic torque at the separatrix.

We show that a class of near-marginal and low-collisional magnetised plasmas naturally evolve into a globally organised state dubbed the ' × E B staircase'. A key signature of this self-organised state is the containment of avalanche activity, detrimental for confinement, by a series of microbarriers for transport, the staircase steps, beneficial for confinement. Conditions for existence of the × E B staircase, impact on transport and confinement and robustness in parameter space are discussed.

This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.