Weak hysteresis in a simplified model of the L-H transition

Malkov, Mikhail; Diamond, P. H.

doi:10.1063/1.3062834

Cited by 32 publications

(62 citation statements)

References 42 publications

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“…[3], by including the evolution of zonal flows self-consistently, the critical input power for the transition is lowered. Further studies [4] show that zonal flows are a necessary step for the transition. Zonal flows trigger the transition by regulating the turbulence until the mean shear flow is high enough to suppress turbulence effectively, which in turn subsequently impedes the zonal flow generation.…”

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confidence: 99%

Spatiotemporal Structure of the Interaction between Turbulence and Flows at the L-H Transition in a Toroidal Plasma

Estrada¹,

Hidalgo²,

et al. 2011

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The spatio-temporal behavior of the interaction between turbulence and flows has been studied close to the L−H transition threshold conditions in the edge region (ρ ≥ 0.7) of TJ−II plasmas. The temporal dynamics of the interaction displays an oscillatory behaviour with a characteristic predator−prey relationship. The spatial evolution of this turbulence−flow oscillation−pattern has been measured, for the first time, showing both, radial outward and inward propagation velocities of the turbulence−flow front. The results indicate that the edge shear flow linked to the L−H transition can behave either as a slowing−down, damping mechanism of outward propagating turbulent−flow oscillating structures, or as a source of inward propagating turbulence-flow events.The High confinement mode (H−mode) regime has been extensively studied since its discovery in the AS-DEX tokamak [1]. Although significant progress has been made in describing the transition, the physical mechanism triggering the H-mode has still not been clearly identified. Bifurcation theory models based on the coupling between turbulence and radially sheared E×B flows (sheared flows) describes the Low to High confinement mode transition (L−H transition) passing through an intermediate, oscillatory transient stage [2,3]. These models consist of coupled evolution equations for turbulence, sheared flow and pressure gradient. Using the input power as a control parameter for the pressure gradient, these dynamical systems evolve from L− to H−mode. By increasing the pressure gradient, the instability grows until it is damped by the self-generated sheared flows. The transition occurs when the turbulence driven sheared flow is high enough to overcome the flow damping. As it is discussed in Ref. [3], by including the evolution of zonal flows self-consistently, the critical input power for the transition is lowered. Further studies [4] show that zonal flows are a necessary step for the transition. Zonal flows trigger the transition by regulating the turbulence until the mean shear flow is high enough to suppress turbulence effectively, which in turn subsequently impedes the zonal flow generation. Due to the self-regulation between turbulence and flows, the transition is marked by an oscillatory behavior with a characteristic predator−prey relationship and EAST [12].In these experiments, as in the predator−prey theory model [3], only the temporal dynamics of the turbulence−flow interaction is studied. Even though the spatial structure of the oscillating flow in the plasma edge region is shown in TJ−II [10] and AUG [11] and in a wider radial region in H−1 [13,14], no information is given on its spatial evolution or spatial propagation. However, as it has been pointed out in Ref. [15], where the 0−dimensional predator−prey theory model is upgraded toward a 1−dimensional one, the spatial evolution should also be taken into account as a necessary step to go towards the L−H transition model.The present work addresses for the first time this fundamental issue from the experime...

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confidence: 99%

Spatiotemporal Structure of the Interaction between Turbulence and Flows at the L-H Transition in a Toroidal Plasma

Estrada¹,

Hidalgo²,

et al. 2011

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“…Approaches to modelling this span the zero-dimensional Lotka-Volterra predatorprey paradigm (Malkov and Diamond 2009), nonlinear few-wave coupling (Manfredi et al 2001), and large scale numerical simulations, which however are challenged by the need to incorporate a wide range of physically relevant lengthscales. It is therefore interesting to include finite Larmor radius test particle dynamics in a plasma model which can incorporate the coexistence and interaction of small scale turbulence and coherent nonlinear structures.…”

Section: Non-diffusive Transport Arising From the Combination Of Smalmentioning

confidence: 99%

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

Perrone

Dendy

Furno

et al. 2013

Microphysics of Cosmic Plasmas

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Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave-particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.

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“…IV) influence the parameters of the function G(Z). The entire system can also be extended to incorporate extra dynamical degrees of freedom, such as, for instance, the evolution of the turbulence level in combination with the zonal flows [19][20][21] and/or geodesic acoustic modes. 22 …”

Section: -9mentioning

confidence: 99%

Bifurcation theory for the L-H transition in magnetically confined fusion plasmas

et al. 2012

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The mathematical field of bifurcation theory is extended to be applicable to 1-dimensionally resolved systems of nonlinear partial differential equations, aimed at the determination of a certain specific bifurcation. This extension is needed to be able to properly analyze the bifurcations of the radial transport in magnetically confined fusion plasmas. This is of special interest when describing the transition from the low-energy-confinement state to the high-energy-confinement state of the radial transport in fusion plasmas (i.e., the L-H transition), because the nonlinear dynamical behavior during the transition corresponds to the dynamical behavior of a system containing such a specific bifurcation. This bifurcation determines how the three types (sharp, smooth, and oscillating) of observed L-H transitions are organized as function of all the parameters contained in the model.

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Weak hysteresis in a simplified model of the L-H transition

Cited by 32 publications

References 42 publications

Spatiotemporal Structure of the Interaction between Turbulence and Flows at the L-H Transition in a Toroidal Plasma

Spatiotemporal Structure of the Interaction between Turbulence and Flows at the L-H Transition in a Toroidal Plasma

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

Bifurcation theory for the L-H transition in magnetically confined fusion plasmas

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