On the validity of the local diffusive paradigm in turbulent plasma transport

Abstract

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.

Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold

“…9, which shows the heat conduction coefficient as a function of the time and the radial coordinate. Avalanches have been observed in turbulent simulations under various circumstances [18][19][20][21][22], and the behaviour here is similar to the one previously reported in connection with staircases [21]. Avalanches start in the region |ω ExB | < γ and propagate outward / inward across the staircase.…”

“…Furthermore, a radial structure can be observed to exist, with the shearing rate roughly equal to ±γ over a large part of the radial domain, with one relatively steep transition ω ExB = −γ → +γ, and a less steep transition ω ExB = +γ → −γ (note that the radial boundary conditions are periodic). This structure has been observed previously in global GISELA simulations, and is referred to as staircase [21]. Note that the fluctuations in the ExB shearing are larger than the averaged ExB shearing rate, as indicated by the dashed line.…”

Neoclassical physics in full distribution function gyrokinetics

“…Therefore, the ability to describe self-organisation at meso-scales and larger is the more relevant problem. 1 It is an acknowledgment of the fact that a tokamak is indeed an open system in which self-organisation plays a dominant role. This translates numerically in self-consistently evolving the mean profiles [the full distribution function of the system] due to the combined action of the turbulence, of the neoclassical dynamics and of an external distribution of sources and sinks.…”

“…These facts have been emphasised both theoretically: through the description of avalanching and spreading, [3][4][5][6][7][8][9] through the characterisation of nonlocal, nondiffusive behaviour 1,[10][11][12] and experimentally through some yet-to-be-understood experimental jigsaws: deep inconsistencies with a (fixed gradient) local and diffusive modeling have indeed been reported in perturbative (either hot or cold pulse) experiments, [13][14][15][16][17] off-axis heating experiments, 19,20 or whilst reporting Bohm-like scalings of the energy confinement time. 18 An accurate description of such dynamics requires the simultaneous and self-consistent treatment of the full gyrokinetic distribution function (full-f modeling), in full-torus (global) tokamak geometry and for a prescribed distribution of sources and sinks (flux-driven description).…”

Interaction between neoclassical effects and ion temperature gradient turbulence in gradient- and flux-driven gyrokinetic simulations

“…Sign changes of the shear can lead to corrugations in the temperature profile in flux-driven simulations and the resulting pattern has been given the name E × B staircase. 38,39 Curiously, in our simulations the only structure which fulfils the criteria for a stair step is occurring close to the sink region at x ∼ 0.75…”