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Robustness of predator-prey models for confinement regime transitions in fusionplasmas
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2013-04-10
2014-09-30

Abstract

Energy transport and confinement in tokamak fusion plasmas is usuallydetermined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherentnonlinear structures, such as zonalflows, together with free energy sources such as temperature gradients.Zero-dimensional models, designed to embody plausible physical narratives for these interactions,can help to identify the origin of enhanced energy confinement and of transitions betweenconfinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, weextend a successful three-variable (temperature gradient; microturbulence level; one class ofcoherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas ,012504 (2009)], by adding a fourth variable representing a second class of coherent structure. Thisrequires a fourth coupled nonlinear ordinary differential equation. We investigate the degree ofinvariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. Westudy and compare the long-time behaviour of the three-equation and four-equation systems, theirevolution towards the final state, and their attractive fixed points and limit cycles. We explorethe sensitivity of paths to attractors. It is found that, for example, an attractive fixed point ofthe three-equation system can become a limit cycle of the four-equation system. Addressing thesequestions which we together refer to as “robustness” for convenience is particularly important formodels which,as here, generate sharp transitions in the values of system variables which may replicate some keyfeatures of confinement transitions. Our results help to establish the robustness of thezero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas.

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Scitation: Robustness of predator-prey models for confinement regime transitions in fusionplasmas
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/4/10.1063/1.4800009
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