Transition to subcritical turbulence in a tokamak plasma

Wyk, Ferdinand Van; Highcock, Edmund; Schekochihin, A. A.; Roach, C. M.; Field, A.R.; Dorland, W.

doi:10.1017/s0022377816001148

Cited by 37 publications

(103 citation statements)

References 46 publications

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“…Propagating phenomena have been frequently observed in tokamak turbulence simulations, especially when a background shear flow is imposed. Although these features are also present when no overall background flow shear is imposed [18], we see very clear propagating features for large shears, and, as in other works [40], these become more isolated as the shearing rate approaches the critical value. The propagating edge state (fig 4a) has some features in common with the late-time nonlinear state (figs.…”

Section: Transition To a Turbulent Statesupporting

confidence: 79%

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

2018

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In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilize linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-traveling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location.

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Section: Transition To a Turbulent Statesupporting

confidence: 79%

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

2018

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“…In the future, we plan to investigate the effect of background shear flows on the DW-ZF solitons, motivated by the radially propagating coherent structures recently identified in gyrokinetic simulations of subcritical plasmas [13][14][15]. In particular, the structures in Ref.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…6 (row 1), we present numerical simulations of the MI of the 2-beam spectrum (21) with random perturbations. These simulations employ the spectral representation of the WM equation (13) derived in the appendix of Ref. [19].…”

Section: Zonal Structures From Incoherent Drift Wavesmentioning

confidence: 99%

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Formation of solitary zonal structures via the modulational instability of drift waves

Zhou

Zhu

Dodin

2019

Plasma Phys. Control. Fusion

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The dynamics of the radial envelope of a weak coherent drift wave is approximately governed by a nonlinear Schrödinger equation, which emerges as a limit of the modified Hasegawa-Mima equation. The nonlinear Schrödinger equation has well-known soliton solutions, and its modulational instability can naturally generate solitary structures. In this paper, we demonstrate that this simple model can adequately describe the formation of solitary zonal structures in the modified Hasegawa-Mima equation, but only when the amplitude of the coherent drift wave is relatively small. At larger amplitudes, the modulational instability produces stationary zonal structures instead. Furthermore, we find that incoherent drift waves with beam-like spectra can also be modulationally unstable to the formation of solitary or stationary zonal structures, depending on the beam intensity. Notably, we show that these drift waves can be modeled as quantumlike particles ("driftons") within a recently developed phase-space (Wigner-Moyal) formulation, which intuitively depicts the solitary zonal structures as quasi-monochromatic drifton condensates. Quantumlike effects, such as diffraction, are essential to these condensates; hence, the latter cannot be described by wave-kinetic models that are based on the ray approximation.

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“…These corrugations arise due to inhomogeneous turbulent mixing and drive ITG turbulence locally, which can result in further roughening of the temperature profile and thus nonlinear turbulence drive. A sufficiently strong ambient perpendicular shear flow can also cause the turbulence to be subcritical 29,30 -this effect has been observed in gyrokinetic simulations 31,32 . Finally, we note that phase-space structures such as holes and granulations, which can interact with drift waves 33 , are known to drive nonlinear instabilities 34 .…”

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confidence: 90%

Subcritical turbulence spreading and avalanche birth

Heinonen

Diamond

2019

Physics of Plasmas

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In confined plasmas, a localized fluctuation in a marginal or weakly damped region will propagate and generate an avalanche if it exceeds a threshold. In this letter, a new model for turbulence spreading based on subcritical instability in the turbulence intensity is introduced. We derive a quantitative threshold for spreading from a seed in a stable region, based on a competition between diffusion and nonlinear growth of the turbulence intensity. The model resolves issues with the established Fisher equation model for turbulence spreading, which is supercritical and cannot support the stationary coexistence of multiple turbulence levels. Implications for turbulence spreading are discussed, including the dynamics of ballistic penetration of turbulence into the stable zone. Tests of the theory are suggested.The paradigm of directed percolation 1 is ubiquitous in non-equilibrium statistical dynamics. Directed percolation is realized by the contamination and ultimate excitation of, say, a localized nonlinear oscillator by interaction with its neighbors 2 . For the contaminated region to expand, the interaction must be strong enough to excite neighbors against their damping. This process of expansion of excited regions by directed percolation is relevant to many problems in the spatiotemporal dynamics of turbulence 3 . These include, but are not limited to, the expansion (and ultimate overlap) of turbulent slugs at the onset of turbulence in high Reynolds number pipe flow turbulence 4,5 , the spreading of a turbulent patch 6 , and the Loitsyansky problem 7 for large-scale evolution of 3D turbulence. The theme of spreading-by-contamination 8 appears in the magnetic confinement physics phenomena of turbulence spreading 9-12 and avalanching 13-15 . These closely-related phenomena are of pragmatic interest in that they delocalize the flux-gradient relation which governs turbulent transport. This letter applies the physics of spreading-by-contamination to propose a mechanism for how turbulence penetrates stable regions.Indeed, experiments and simulations of magnetic fusion (MF) plasma strongly suggest that the transport can be nonlocal : fluxes cannot be determined by local parameters and their gradients, but are generally given by some integrated spatiotemporal relation that depends on global profile structure (not only local gradients) 16,17 . Such phenomena cannot be explained by diffusive or Fickian processes and instead depend on fast propagation dynamics of turbulence in the plasma. Turbulence spreading and avalanching, both of which involve radial self-propagation of turbulence on mesoscales, are two players which influence nonlocal transport. Turbulence spreading, arguably the more general phenomenon, is the result of nonlinear coupling between ballooning modes, which results in spatial scattering and nonlinear diffusion of the turbulence energy. Standard spreading problems are the spatiotemporal evolution of a single, initially localized spot of turbulence, and the penetration of turbua) Electronic mail: robin@ph...

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Transition to subcritical turbulence in a tokamak plasma

Cited by 37 publications

References 46 publications

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

Formation of solitary zonal structures via the modulational instability of drift waves

Subcritical turbulence spreading and avalanche birth

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