Metamorphosis of plasma turbulence–shear-flow dynamics through a transcritical bifurcation

Abstract

The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low-to high-confinement transitions such as shear flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive. Typeset by REVT E X 1Ball, Dewar, Sugama: Metamorphosis of plasma turbulence-shear flow dynamics . . . I.Fusion plasmas, and possibly other quasi two-dimensional fluid systems, may undergo a more-or-less dramatic transition from a low to a high confinement state (the L-H transition) as the power input is increased, with the desirable outcome that particle and energy confinement is greatly improved due to localized transport reduction [1]. In this work we report on a bifurcation and stability probe of an economical model for L-H transition dynamics that uncovers a mechanism by which a radical change, or metamorphosis, may occur in the qualitative nature of the dynamics. We apply the results of this analysis to clarify the relationship between the structure of the model and the physics of the process that it describes, and draw comparisons with characteristics of L-H transitions observed in various experiments.Since 1988 there has been much progress in developing low-dimensional (low-order or reduced) descriptions of L-H transition dynamics and associated oscillatory phenomena (see, for example, Refs 2,3,4,5,6,7,8,9,10,11,12,13,14,15), the driving force being the potential power of a unified, low-dimensional model as a predictive tool for the design and control of confinement states. For example, a model that speaks of the shape and extent of hysteresis in the L-H transition would help engineers who are interested in controlling access to H-mode. Given the many variables and parameters that could be varied around a hysteretic régime, it would be cheaper-i.e., save hundreds of cpu hours and/ or many expensive diagnostics-to know in advance which ones actually do affect the hysteresis, and which do not.To help construe the context in which low-dimensional descriptions of plasma dynamics are sought, it is appropriate at this stage to make some general remarks. It makes sense to try to find the simplest description of an evolving system that is consistent with the time and space scales on which one is interested in making experimental observations of that system. One...

Bifurcation in electrostatic resistive drift wave turbulence

“…The simplest approach that captures the essential physics underlying the problem is lowdimensional dynamical modeling and analysis [13,14,15,16], which can provide a very economical tool to predict the transition. However, the tradeoff with such highly coarsegrained modeling is that it necessarily whites out information, and may therefore miss important physics and predict unphysical singular behavior [15].…”

Suppression of turbulence at low power input in a model for plasma confinement transitions

“…͑1͒-͑3͒ was found in Ref. 3 to predict shear flow suppresion of turbulence, hysteretic, nonhysteretic, and oscillatory transitions, and saturation then decline of the shear flow with increasing power input. All of these behaviors have been observed repeatably in diverse fusion plasma experiments.…”

“…The extended modeling and analysis in this work are based on the following reduced dynamical model for confinement transitions from Ref. 3:…”

Sparse identification of a predator-prey system from simulation data of a convection model

“…The creation of an edge transport barrier formed by a sheared zonal flow is closely related to the L-H transition 3 . Ordinary differential equation (ODE) models for the L-H transition are based on the predator-prey relationship between zonal flow and turbulent flow, and incorporate a potential energy related to the pressure profile as an additional state variable [4][5][6][7][8][9][10][11][12] . Miki et al 13 and Wu et al 14 have both suggested 1D partial differential equation (PDE) models for the L-H transition based on this predator-prey relationship.…”