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

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.

Authors:
ORCiD logo [1]
  1. 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:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 83; Journal Issue: 05; Journal ID: ISSN 0022-3778
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

St-Onge, Denis A. On non-local energy transfer via zonal flow in the Dimits shift. United States: N. p., 2017. Web. doi:10.1017/S0022377817000708.
St-Onge, Denis A. On non-local energy transfer via zonal flow in the Dimits shift. United States. doi:10.1017/S0022377817000708.
St-Onge, Denis A. Tue . "On non-local energy transfer via zonal flow in the Dimits shift". United States. doi:10.1017/S0022377817000708. https://www.osti.gov/servlets/purl/1412673.
@article{osti_1412673,
title = {On non-local energy transfer via zonal flow in the Dimits shift},
author = {St-Onge, Denis A.},
abstractNote = {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.},
doi = {10.1017/S0022377817000708},
journal = {Journal of Plasma Physics},
number = 05,
volume = 83,
place = {United States},
year = {2017},
month = {10}
}

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