DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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. https://doi.org/10.1017/S0022377817000708
St-Onge, Denis A. Tue . "On non-local 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 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 = {Tue Oct 10 00:00:00 EDT 2017},
month = {Tue Oct 10 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 22 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Microinstability theory in tokamaks
journal, August 1978


Bifurcation theory of the transition to collisionless ion-temperature-gradient-driven plasma turbulence
journal, December 2005

  • Kolesnikov, R. A.; Krommes, J. A.
  • Physics of Plasmas, Vol. 12, Issue 12
  • DOI: 10.1063/1.2116887

Drift wave turbulence in a low-order k space
journal, January 1983


Dimits Shift in Realistic Gyrokinetic Plasma-Turbulence Simulations
journal, September 2008


Zonostrophic instability driven by discrete particle noise
journal, April 2017

  • St-Onge, D. A.; Krommes, J. A.
  • Physics of Plasmas, Vol. 24, Issue 4
  • DOI: 10.1063/1.4978786

Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011


Subdominant Modes in Zonal-Flow-Regulated Turbulence
journal, March 2014


Zonal-flow dynamics from a phase-space perspective
journal, December 2016

  • Ruiz, D. E.; Parker, J. B.; Shi, E. L.
  • Physics of Plasmas, Vol. 23, Issue 12
  • DOI: 10.1063/1.4971813

Zonal flow as pattern formation
journal, October 2013

  • Parker, Jeffrey B.; Krommes, John A.
  • Physics of Plasmas, Vol. 20, Issue 10
  • DOI: 10.1063/1.4828717

A two‐nonlinearity model of dissipative drift wave turbulence
journal, April 1993

  • Liang, Y. ‐M.; Diamond, P. H.; Wang, X. ‐H.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 4
  • DOI: 10.1063/1.860903

Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations
journal, November 2016


Effects of Collisional Zonal Flow Damping on Turbulent Transport
journal, November 1999


Electron temperature gradient driven turbulence
journal, May 2000

  • Jenko, F.; Dorland, W.; Kotschenreuther, M.
  • Physics of Plasmas, Vol. 7, Issue 5
  • DOI: 10.1063/1.874014

Considerations of ion‐temperature‐gradient‐driven turbulence
journal, October 1991

  • Cowley, S. C.; Kulsrud, R. M.; Sudan, R.
  • Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10
  • DOI: 10.1063/1.859913

Poloidal Flow Driven by Ion-Temperature-Gradient Turbulence in Tokamaks
journal, January 1998


Generation of zonal flows through symmetry breaking of statistical homogeneity
journal, March 2014


Shear flow generation by drift waves revisited
journal, February 2001

  • Guzdar, P. N.; Kleva, R. G.; Chen, Liu
  • Physics of Plasmas, Vol. 8, Issue 2
  • DOI: 10.1063/1.1340618

Unanswered questions in ion-temperature-gradient-driven turbulence
journal, April 1997


Stochasticity and the random phase approximation for three electron drift waves
journal, January 1982


Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence
journal, December 2000


Modulational instability of Rossby and drift waves and generation of zonal jets
journal, May 2010

  • Connaughton, Colm P.; Nadiga, Balasubramanya T.; Nazarenko, Sergey V.
  • Journal of Fluid Mechanics, Vol. 654
  • DOI: 10.1017/S0022112010000510

Modification of Turbulent Transport with Continuous Variation of Flow Shear in the Large Plasma Device
journal, September 2012


Bifurcation in electrostatic resistive drift wave turbulence
journal, October 2007

  • Numata, Ryusuke; Ball, Rowena; Dewar, Robert L.
  • Physics of Plasmas, Vol. 14, Issue 10
  • DOI: 10.1063/1.2796106

Gyrofluid turbulence models with kinetic effects
journal, March 1993

  • Dorland, W.; Hammett, G. W.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 3
  • DOI: 10.1063/1.860934

Influence of sheared poloidal rotation on edge turbulence
journal, January 1990

  • Biglari, H.; Diamond, P. H.; Terry, P. W.
  • Physics of Fluids B: Plasma Physics, Vol. 2, Issue 1
  • DOI: 10.1063/1.859529

Comparisons and physics basis of tokamak transport models and turbulence simulations
journal, March 2000

  • Dimits, A. M.; Bateman, G.; Beer, M. A.
  • Physics of Plasmas, Vol. 7, Issue 3
  • DOI: 10.1063/1.873896

Zonostrophic Instability
journal, May 2012

  • Srinivasan, Kaushik; Young, W. R.
  • Journal of the Atmospheric Sciences, Vol. 69, Issue 5
  • DOI: 10.1175/JAS-D-11-0200.1

Suppression of turbulence and transport by sheared flow
journal, January 2000


Investigations of the role of nonlinear couplings in structure formation and transport regulation: experiment, simulation, and theory
journal, August 2003


Developments in the gyrofluid approach to Tokamak turbulence simulations
journal, August 1993


Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach
journal, June 2005


Role of stable modes in zonal flow regulated turbulence
journal, June 2012

  • Makwana, K. D.; Terry, P. W.; Kim, J. -H.
  • Physics of Plasmas, Vol. 19, Issue 6
  • DOI: 10.1063/1.4729906

Physics of zonal flows
journal, May 2006

  • Itoh, K.; Itoh, S. -I.; Diamond, P. H.
  • Physics of Plasmas, Vol. 13, Issue 5
  • DOI: 10.1063/1.2178779

Small-Scale Turbulence in a Closed-Field-Line Geometry
journal, December 2006


Bifurcation in electrostatic resistive drift wave turbulence
text, January 2007


Modulational instability of Rossby and drift waves and generation of zonal jets
text, January 2009


Zonal Flow as Pattern Formation
text, January 2013


Works referencing / citing this record:

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability
journal, July 2018

  • Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
  • Physics of Plasmas, Vol. 25, Issue 7
  • DOI: 10.1063/1.5039652

Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics
journal, May 2018


Nonlinear saturation and oscillations of collisionless zonal flows
text, January 2019


On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows
journal, August 2018

  • Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
  • Physics of Plasmas, Vol. 25, Issue 8
  • DOI: 10.1063/1.5038859

A flux-balanced fluid model for collisional plasma edge turbulence: Numerical simulations with different aspect ratios
journal, August 2019

  • Qi, Di; Majda, Andrew J.; Cerfon, Antoine J.
  • Physics of Plasmas, Vol. 26, Issue 8
  • DOI: 10.1063/1.5083845

Nonlinear saturation and oscillations of collisionless zonal flows
journal, June 2019


Nonlinear saturation and oscillations of collisionless zonal flows
text, January 2019


On the Rayleigh--Kuo criterion for the tertiary instability of zonal flows
text, January 2018