skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

Abstract

The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.

Authors:
 [1];  [1];  [2];  [3]
  1. General Atomics, San Diego, CA (United States)
  2. Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States)
  3. Univ. of California, San Diego, CA (United States)
Publication Date:
Research Org.:
General Atomics, San Diego, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1354781
Grant/Contract Number:  
FC02-04ER54698
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 6; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Staebler, Gary M., Candy, John, Howard, Nathan T., and Holland, Christopher. The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence. United States: N. p., 2016. Web. doi:10.1063/1.4954905.
Staebler, Gary M., Candy, John, Howard, Nathan T., & Holland, Christopher. The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence. United States. doi:10.1063/1.4954905.
Staebler, Gary M., Candy, John, Howard, Nathan T., and Holland, Christopher. Wed . "The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence". United States. doi:10.1063/1.4954905. https://www.osti.gov/servlets/purl/1354781.
@article{osti_1354781,
title = {The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence},
author = {Staebler, Gary M. and Candy, John and Howard, Nathan T. and Holland, Christopher},
abstractNote = {The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.},
doi = {10.1063/1.4954905},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = {2016},
month = {6}
}

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

Citation Metrics:
Cited by: 14 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Numerical experiments on the drift wave–zonal flow paradigm for nonlinear saturation
journal, December 2008

  • Waltz, R. E.; Holland, C.
  • Physics of Plasmas, Vol. 15, Issue 12
  • DOI: 10.1063/1.3033206

Plasma microturbulence simulation of instabilities at highly disparate scales
journal, July 2007


Advances in validating gyrokinetic turbulence models against L- and H-mode plasmas
journal, May 2011

  • Holland, C.; Schmitz, L.; Rhodes, T. L.
  • Physics of Plasmas, Vol. 18, Issue 5
  • DOI: 10.1063/1.3574518

Toroidal gyro‐Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes
journal, July 1994

  • Waltz, R. E.; Kerbel, G. D.; Milovich, J.
  • Physics of Plasmas, Vol. 1, Issue 7
  • DOI: 10.1063/1.870934

Multi-scale gyrokinetic simulation of tokamak plasmas: enhanced heat loss due to cross-scale coupling of plasma turbulence
journal, December 2015


An Eulerian gyrokinetic-Maxwell solver
journal, April 2003


Electron Temperature Gradient Turbulence
journal, December 2000


Nonlinear Stabilization of Tokamak Microturbulence by Fast Ions
journal, October 2013


Prediction of Significant Tokamak Turbulence at Electron Gyroradius Scales
journal, November 2002


Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011


Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks
journal, July 1996


Advances in the simulation of toroidal gyro‐Landau fluid model turbulence
journal, June 1995

  • Waltz, R. E.; Kerbel, G. D.; Milovich, J.
  • Physics of Plasmas, Vol. 2, Issue 6
  • DOI: 10.1063/1.871264

Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence
journal, March 2015


Zonal flows in plasma—a review
journal, April 2005


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

The first transport code simulations using the trapped gyro-Landau-fluid model
journal, May 2008

  • Kinsey, J. E.; Staebler, G. M.; Waltz, R. E.
  • Physics of Plasmas, Vol. 15, Issue 5
  • DOI: 10.1063/1.2889008

New Paradigm for Suppression of Gyrokinetic Turbulence by Velocity Shear
journal, January 2013


Nonlinear Saturation of Trapped Electron Modes via Perpendicular Particle Diffusion
journal, January 2008


Compatibility of internal transport barrier with steady-state operation in the high bootstrap fraction regime on DIII-D
journal, November 2015


A theory-based transport model with comprehensive physics
journal, May 2007

  • Staebler, G. M.; Kinsey, J. E.; Waltz, R. E.
  • Physics of Plasmas, Vol. 14, Issue 5
  • DOI: 10.1063/1.2436852

Coupled ion temperature gradient and trapped electron mode to electron temperature gradient mode gyrokinetic simulations
journal, May 2007

  • Waltz, R. E.; Candy, J.; Fahey, M.
  • Physics of Plasmas, Vol. 14, Issue 5
  • DOI: 10.1063/1.2436851

Resolving electron scale turbulence in spherical tokamaks with flow shear
journal, February 2011

  • Guttenfelder, W.; Candy, J.
  • Physics of Plasmas, Vol. 18, Issue 2
  • DOI: 10.1063/1.3551701

Cross-Scale Interactions between Electron and Ion Scale Turbulence in a Tokamak Plasma
journal, June 2015