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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. 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 ion-scale gyrokinetic simulations.

Authors:
;  [1];  [2];  [3]
  1. General Atomics, San Diego, California 92186 (United States)
  2. Oak Ridge Institute for Science Education (ORISE), Oak Ridge, Tennessee 37831 (United States)
  3. University of California San Diego, San Diego, California 92093 (United States)
Publication Date:
OSTI Identifier:
22598922
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AXIAL SYMMETRY; CRITICAL TEMPERATURE; DISTRIBUTION FUNCTIONS; ELECTRIC POTENTIAL; ELECTROMAGNETIC FIELDS; ELECTRONS; GEOMETRY; MIXING; NONLINEAR PROBLEMS; SATURATION; SIMULATION; SPECTRA; TEMPERATURE GRADIENTS; TOKAMAK DEVICES; TRANSPORT THEORY; TURBULENCE; VELOCITY

Citation Formats

Staebler, G. M., Candy, J., Howard, N. T., and Holland, C.. 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, G. M., Candy, J., Howard, N. T., & Holland, C.. The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence. United States. doi:10.1063/1.4954905.
Staebler, G. M., Candy, J., Howard, N. T., and Holland, C.. Wed . "The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence". United States. doi:10.1063/1.4954905.
@article{osti_22598922,
title = {The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence},
author = {Staebler, G. M. and Candy, J. and Howard, N. T. and Holland, C.},
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. 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 ion-scale gyrokinetic simulations.},
doi = {10.1063/1.4954905},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2016},
month = {Wed Jun 15 00:00:00 EDT 2016}
}
  • 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 thresholdmore » 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.« less
  • Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at {eta}{sub e}=1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of {eta}{sub e} reveals fine scale structure for {eta}{sub e} > or approx. 1, consistent with linear expectation.more » For {eta}{sub e}<1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to {eta}{sub e}. For {eta}{sub e}>1, zonal flows are weak, and TEM transport falls inversely with a power law in {eta}{sub e}. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of {eta}{sub e}=d ln T{sub e}/d ln n{sub e} values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter {eta}{sub e} for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.« less
  • Gyrokinetic {delta}f particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturationmore » phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.« less
  • It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.
  • It is argued that the usual understanding of the suppression of radial turbulent transport across a sheared zonal flow based on a reduction in effective transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, ion-temperature-gradient turbulence, it is found instead that the character of the radial transport is altered fundamentally by the presence of a sheared zonal flow, changing from diffusive to anticorrelated and subdiffusive. Furthermore, if the flows are self-consistently driven by the turbulence via the Reynolds stresses (in contrast to being induced externally), radial transport becomes non-Gaussian as well. These results warrant amore » reevaluation of the traditional description of radial transport across sheared flows in tokamaks via effective transport coefficients, suggesting that such description is oversimplified and poorly captures the underlying dynamics, which may in turn compromise its predictive capabilities.« less