On nonlocal energy transfer via zonal flow in the Dimits shift
Abstract
The twodimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/driftwave 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 fourmode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the fluxaveraged potential, results in an $$\boldsymbol{E}\times \boldsymbol{B}$$ nonlinearity that can efficiently transfer energy nonlocally 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 nonlocal mechanism of energy transfer is argued to be generically important even for more physically complete systems.
 Authors:

 Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1412673
 Grant/Contract Number:
 AC0209CH11466
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Plasma Physics
 Additional Journal Information:
 Journal Volume: 83; Journal Issue: 05; Journal ID: ISSN 00223778
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma instabilities; plasma nonlinear phenomena
Citation Formats
StOnge, Denis A. On nonlocal energy transfer via zonal flow in the Dimits shift. United States: N. p., 2017.
Web. https://doi.org/10.1017/S0022377817000708.
StOnge, Denis A. On nonlocal energy transfer via zonal flow in the Dimits shift. United States. https://doi.org/10.1017/S0022377817000708
StOnge, Denis A. Tue .
"On nonlocal energy transfer via zonal flow in the Dimits shift". United States. https://doi.org/10.1017/S0022377817000708. https://www.osti.gov/servlets/purl/1412673.
@article{osti_1412673,
title = {On nonlocal energy transfer via zonal flow in the Dimits shift},
author = {StOnge, Denis A.},
abstractNote = {The twodimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/driftwave 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 fourmode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the fluxaveraged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy nonlocally 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 nonlocal mechanism of energy transfer is argued to be generically important even for more physically complete systems.},
doi = {10.1017/S0022377817000708},
journal = {Journal of Plasma Physics},
number = 05,
volume = 83,
place = {United States},
year = {2017},
month = {10}
}
Web of Science
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