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

Title: Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

Abstract

A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeitmore » in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.« less

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1272650
Alternate Identifier(s):
OSTI ID: 1272651; OSTI ID: 1326679
Grant/Contract Number:  
FG02-04ER54742
Resource Type:
Published Article
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Name: New Journal of Physics Journal Volume: 18 Journal Issue: 7; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United Kingdom
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; gyrokinetics; pseudospectra; non-modal; plasma turbulence; Landau damping; Hermite polynomials

Citation Formats

Hatch, D. R., Jenko, F., Navarro, A. Bañón, Bratanov, V., Terry, P. W., and Pueschel, M. J.. Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra. United Kingdom: N. p., 2016. Web. https://doi.org/10.1088/1367-2630/18/7/075018.
Hatch, D. R., Jenko, F., Navarro, A. Bañón, Bratanov, V., Terry, P. W., & Pueschel, M. J.. Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra. United Kingdom. https://doi.org/10.1088/1367-2630/18/7/075018
Hatch, D. R., Jenko, F., Navarro, A. Bañón, Bratanov, V., Terry, P. W., and Pueschel, M. J.. Fri . "Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra". United Kingdom. https://doi.org/10.1088/1367-2630/18/7/075018.
@article{osti_1272650,
title = {Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra},
author = {Hatch, D. R. and Jenko, F. and Navarro, A. Bañón and Bratanov, V. and Terry, P. W. and Pueschel, M. J.},
abstractNote = {A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.},
doi = {10.1088/1367-2630/18/7/075018},
journal = {New Journal of Physics},
number = 7,
volume = 18,
place = {United Kingdom},
year = {2016},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1088/1367-2630/18/7/075018

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Gyrokinetic simulation of collisionless trapped-electron mode turbulence
journal, July 2005

  • Dannert, Tilman; Jenko, Frank
  • Physics of Plasmas, Vol. 12, Issue 7
  • DOI: 10.1063/1.1947447

Multiscale features of density and frequency spectra from nonlinear gyrokinetics
journal, October 2008

  • Görler, T.; Jenko, F.
  • Physics of Plasmas, Vol. 15, Issue 10
  • DOI: 10.1063/1.3006086

Role of subdominant stable modes in plasma microturbulence
journal, May 2011

  • Hatch, D. R.; Terry, P. W.; Jenko, F.
  • Physics of Plasmas, Vol. 18, Issue 5
  • DOI: 10.1063/1.3563536

Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales
journal, July 2011


Gyrokinetic study of ASDEX Upgrade inter-ELM pedestal profile evolution
journal, May 2015


Measurement of the Electric Fluctuation Spectrum of Magnetohydrodynamic Turbulence
journal, June 2005


Measurements of the cross-phase angle between density and electron temperature fluctuations and comparison with gyrokinetic simulations
journal, May 2010

  • White, A. E.; Peebles, W. A.; Rhodes, T. L.
  • Physics of Plasmas, Vol. 17, Issue 5
  • DOI: 10.1063/1.3323084

Possible Evidence of AlfvÉN-Cyclotron Waves in the Angle Distribution of Magnetic Helicity of Solar wind Turbulence
journal, March 2011


The Slow-Mode Nature of Compressible wave Power in Solar wind Turbulence
journal, June 2012


A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence
journal, December 2014

  • Görler, T.; White, A. E.; Told, D.
  • Physics of Plasmas, Vol. 21, Issue 12
  • DOI: 10.1063/1.4904301

A gyro-Landau-fluid transport model
journal, July 1997

  • Waltz, R. E.; Staebler, G. M.; Dorland, W.
  • Physics of Plasmas, Vol. 4, Issue 7
  • DOI: 10.1063/1.872228

A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas
journal, November 2007

  • Bourdelle, C.; Garbet, X.; Imbeaux, F.
  • Physics of Plasmas, Vol. 14, Issue 11
  • DOI: 10.1063/1.2800869

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

Validating a quasi-linear transport model versus nonlinear simulations
journal, July 2009


Quasilinear transport modelling at low magnetic shear
journal, June 2012

  • Citrin, J.; Bourdelle, C.; Cottier, P.
  • Physics of Plasmas, Vol. 19, Issue 6
  • DOI: 10.1063/1.4719697

Transition between Landau and Van Kampen Treatments of the Vlasov Equation
journal, January 1967


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


Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality
journal, April 2004

  • Watanabe, T. -H.; Sugama, H.
  • Physics of Plasmas, Vol. 11, Issue 4
  • DOI: 10.1063/1.1669393

Two-dimensional gyrokinetic turbulence
journal, October 2010


Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas
journal, October 2011

  • Zocco, Alessandro; Schekochihin, Alexander A.
  • Physics of Plasmas, Vol. 18, Issue 10
  • DOI: 10.1063/1.3628639

Fast Collisionless Reconnection and Electron Heating in Strongly Magnetized Plasmas
journal, July 2013


Transition between Saturation Regimes of Gyrokinetic Turbulence
journal, October 2013


Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence
journal, May 2014


Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
journal, September 2014


Irreversible energy flow in forced Vlasov dynamics
journal, October 2014


Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit
journal, February 2015


Role of stable eigenmodes in saturated local plasma turbulence
journal, February 2006

  • Terry, P. W.; Baver, D. A.; Gupta, Sangeeta
  • Physics of Plasmas, Vol. 13, Issue 2
  • DOI: 10.1063/1.2168453

Reduction of inward momentum flux by damped eigenmodes
journal, December 2009

  • Terry, P. W.; Baver, D. A.; Hatch, D. R.
  • Physics of Plasmas, Vol. 16, Issue 12
  • DOI: 10.1063/1.3271158

Damped eigenmode saturation in plasma fluid turbulence
journal, January 2011

  • Makwana, K. D.; Terry, P. W.; Kim, J. -H.
  • Physics of Plasmas, Vol. 18, Issue 1
  • DOI: 10.1063/1.3530186

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

Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011


The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
journal, January 1993


Spatiotemporal multiscaling analysis of impurity transport in plasma turbulence using proper orthogonal decomposition
journal, April 2009

  • Futatani, S.; Benkadda, S.; del-Castillo-Negrete, D.
  • Physics of Plasmas, Vol. 16, Issue 4
  • DOI: 10.1063/1.3095865

Origin of Magnetic Stochasticity and Transport in Plasma Microturbulence
journal, June 2012


The effect of weak collisionality on damped modes and its contribution to linear mode coupling in gyrokinetic simulation
journal, August 2013

  • Hilscher, P. P.; Imadera, K.; Li, J. Q.
  • Physics of Plasmas, Vol. 20, Issue 8
  • DOI: 10.1063/1.4819033

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


Mode-space energy distribution in instability-driven plasma turbulence
journal, December 2014

  • Terry, P. W.; Makwana, K. D.; Pueschel, M. J.
  • Physics of Plasmas, Vol. 21, Issue 12
  • DOI: 10.1063/1.4903207

Hydrodynamic Stability Without Eigenvalues
journal, July 1993


Pseudospectra of Linear Operators
journal, January 1997


Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition
journal, June 2012

  • Hatch, D. R.; del-Castillo-Negrete, D.; Terry, P. W.
  • Journal of Computational Physics, Vol. 231, Issue 11
  • DOI: 10.1016/j.jcp.2012.02.007

Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma
journal, September 1999


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

Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958


On the theory of stationary waves in plasmas
journal, January 1955


Plasma oscillations
journal, July 1959


Aspects of linear Landau damping in discretized systems
journal, February 2013

  • Bratanov, Vasil; Jenko, Frank; Hatch, David
  • Physics of Plasmas, Vol. 20, Issue 2
  • DOI: 10.1063/1.4792163

Kinetic theory of shear Alfvén waves
journal, January 1984


Radial fluctuation scale of ion temperature gradient driven turbulence
journal, January 1988

  • Terry, P. W.; Leboeuf, J. N.; Diamond, P. H.
  • Physics of Fluids, Vol. 31, Issue 10
  • DOI: 10.1063/1.867023

The pseudospectrum of the resistive magnetohydrodynamics operator: Resolving the resistive Alfvén paradox
journal, October 1994

  • Borba, D.; Riedel, K. S.; Kerner, W.
  • Physics of Plasmas, Vol. 1, Issue 10
  • DOI: 10.1063/1.870468

Effect of coupling and linear transformation of waves in shear flows
journal, June 1996

  • Chagelishvili, G. D.; Rogava, A. D.; Tsiklauri, D. G.
  • Physical Review E, Vol. 53, Issue 6
  • DOI: 10.1103/PhysRevE.53.6028

Nonmodal energetics of resistive drift waves
journal, September 1998

  • Camargo, Suzana J.; Tippett, Michael K.; Caldas, Iberê L.
  • Physical Review E, Vol. 58, Issue 3
  • DOI: 10.1103/PhysRevE.58.3693

Robust control of resistive wall modes using pseudospectra
journal, May 2009


Transient growth in stable collisionless plasma
journal, March 2009

  • Camporeale, Enrico; Burgess, David; Passot, Thierry
  • Physics of Plasmas, Vol. 16, Issue 3
  • DOI: 10.1063/1.3094759

Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas
journal, April 2012


Linear Technique to Understand Non-Normal Turbulence Applied to a Magnetized Plasma
journal, July 2014


A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model
journal, January 2015

  • Friedman, B.; Carter, T. A.
  • Physics of Plasmas, Vol. 22, Issue 1
  • DOI: 10.1063/1.4905863

Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995

  • Goldreich, P.; Sridhar, S.
  • The Astrophysical Journal, Vol. 438
  • DOI: 10.1086/175121

Evidence of critical balance in kinetic Alfvén wave turbulence simulations
journal, May 2012

  • TenBarge, J. M.; Howes, G. G.
  • Physics of Plasmas, Vol. 19, Issue 5
  • DOI: 10.1063/1.3693974

Critically Balanced Ion Temperature Gradient Turbulence in Fusion Plasmas
journal, September 2011


Landau damping in a turbulent setting
journal, March 2013


Optimizing Stellarators for Turbulent Transport
journal, August 2010


    Works referencing / citing this record:

    Linear theory of electron-plasma waves at arbitrary collisionality
    journal, April 2019


    Saturation and nonlinear electromagnetic stabilization of ITG turbulence
    journal, August 2019

    • Whelan, G. G.; Pueschel, M. J.; Terry, P. W.
    • Physics of Plasmas, Vol. 26, Issue 8
    • DOI: 10.1063/1.5096252

    Saturation scalings of toroidal ion temperature gradient turbulence
    journal, January 2018

    • Terry, P. W.; Faber, B. J.; Hegna, C. C.
    • Physics of Plasmas, Vol. 25, Issue 1
    • DOI: 10.1063/1.5007062

    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

    Role of stable modes in driven shear-flow turbulence
    journal, December 2018

    • Fraser, A. E.; Pueschel, M. J.; Terry, P. W.
    • Physics of Plasmas, Vol. 25, Issue 12
    • DOI: 10.1063/1.5049580

    Flow shear suppression of pedestal ion temperature gradient turbulence-A first principles theoretical framework
    journal, June 2018

    • Hatch, D. R.; Hazeltine, R. D.; Kotschenreuther, M. K.
    • Plasma Physics and Controlled Fusion, Vol. 60, Issue 8
    • DOI: 10.1088/1361-6587/aac7a7

    A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality
    journal, November 2017