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On non-local energy transfer via zonal flow in the Dimits shift

Part of: Focus on Fusion

Published online by Cambridge University Press:  10 October 2017

Denis A. St-Onge Open the ORCID record for Denis A. St-Onge [Opens in a new window]
Denis A. St-Onge*
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
*
†Email address for correspondence: dstonge@princeton.edu
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Abstract

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

Keywords

fusion plasmaplasma instabilitiesplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 5 , October 2017 , 905830504
Copyright
© Cambridge University Press 2017 

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