Robustness of predator-prey models for confinement regime transitions in fusion plasmas
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https://hdl.handle.net/10037/6047Date
2013Type
Journal articleTidsskriftartikkel
Peer reviewed
Abstract
Energy transport and confinement in tokamak fusion plasmas is usually determined by the
coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear
structures, such as zonal flows, 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 between
confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra.
Here, we extend a successful three-variable (temperature gradient; microturbulence level; one
class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas
16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure.
This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree
of invariance of the phenomenology generated by the model of Malkov and Diamond, given
this additional physics. We study and compare the long-time behaviour of the three-equation and
four-equation systems, their evolution towards the final state, and their attractive fixed points and
limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an
attractive fixed point of the three-equation system can become a limit cycle of the four-equation
system. Addressing these questions which we together refer to as “robustness” for convenience is
particularly important for models which, as here, generate sharp transitions in the values of
system variables which may replicate some key features of confinement transitions. Our results
help to establish the robustness of the zero-dimensional model approach to capturing observed
confinement phenomenology in tokamak fusion plasmas.
Publisher
American Institute of Physics (AIP)Citation
Physics of Plasmas 20(2013) nr. 4Metadata
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