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 ...

Anomalous transport in tokamaks is generally attributed to turbulent fluctuations. Since a large variety of modes are potentially unstable, a wide range of short-scale fluctuations should be measured, with wavenumbers from kρ i ∼ 0.1 to kρ i >> 1. On the Tore Supra tokamak, a light scattering experiment has made possible fluctuation measurements in the medium and high-k domains where a transition in the k-spectrum is observed: The fluctuation level decreases much faster than usual observations, typically with a power law S(k) ≡ k −6 . A scan of the ion Larmor radius shows that the transition wavenumber scales with ρ i around kρ i ∼ 1.5. This transition indicates that a characteristic length scale should be involved to describe the fluctuation non linear dynamics in this range. The resulting very low level of fluctuations at high k does not support a strong effect of turbulence driven by electron temperature gradient. For this gyroradius scan, the characteristics of turbulence also exhibit a good matching with predictions from gyro-Bohm scaling: the typical scale length of turbulence scales with the ion Larmor radius, the typical time scales with a/c s ; the turbulence level also scales with ρ i , according to the mixing length rule.