Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra
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-driv...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/18/7/075018 |
| _version_ | 1797750961594171392 |
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| author | D R Hatch F Jenko A Bañón Navarro V Bratanov P W Terry M J Pueschel |
| author_facet | D R Hatch F Jenko A Bañón Navarro V Bratanov P W Terry M J Pueschel |
| author_sort | D R Hatch |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:41:23Z |
| format | Article |
| id | doaj.art-558bd2f604ba4033b474d9e43b5de7ce |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:41:23Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-558bd2f604ba4033b474d9e43b5de7ce2023-08-08T14:29:33ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118707501810.1088/1367-2630/18/7/075018Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectraD R Hatch0F Jenko1A Bañón Navarro2V Bratanov3P W Terry4M J Pueschel5Institute for Fusion Studies, University of Texas at Austin , Austin, TX 78712, USADepartment of Physics and Astronomy, University of California , Los Angeles, CA 90095, USADepartment of Physics and Astronomy, University of California , Los Angeles, CA 90095, USAMax-Planck-Institut für Plasmaphysik , Boltzmannstr. 2, D-85748 Garching, GermanyUniversity of Wisconsin-Madison , Madison, WI 53706, USAUniversity of Wisconsin-Madison , Madison, WI 53706, USAA 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.https://doi.org/10.1088/1367-2630/18/7/075018gyrokineticspseudospectranon-modalplasma turbulenceLandau dampingHermite polynomials |
| spellingShingle | D R Hatch F Jenko A Bañón Navarro V Bratanov P W Terry M J Pueschel Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra New Journal of Physics gyrokinetics pseudospectra non-modal plasma turbulence Landau damping Hermite polynomials |
| title | Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra |
| title_full | Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra |
| title_fullStr | Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra |
| title_full_unstemmed | Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra |
| title_short | Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra |
| title_sort | linear signatures in nonlinear gyrokinetics interpreting turbulence with pseudospectra |
| topic | gyrokinetics pseudospectra non-modal plasma turbulence Landau damping Hermite polynomials |
| url | https://doi.org/10.1088/1367-2630/18/7/075018 |
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