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Qi L. Energy transfer of trapped electron turbulence in tokamak fusion plasmas. Sci Rep 2022; 12:5042. [PMID: 35322113 PMCID: PMC8942984 DOI: 10.1038/s41598-022-08932-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/15/2022] [Indexed: 11/09/2022] Open
Abstract
The first principle gyrokinetic simulations of trapped electron turbulence in tokamak fusion plasmas demonstrate the energy transfers from the most linearly unstable modes at high [Formula: see text] to intermediate [Formula: see text] via parametric decay process in a short period of linear-nonlinear transition phase. Dominant nonlinear wave-wave interactions occur near the mode rational surface [Formula: see text]. In fully nonlinear turbulence, inverse energy cascade occurs between a cutoff wave number [Formula: see text] and [Formula: see text] with a power law scaling [Formula: see text], while modes with [Formula: see text] are suppressed. The numerical findings show fair agreement with both the weak turbulence theory and realistic experiments on Tore Supra tokamak.
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Affiliation(s)
- Lei Qi
- Korea Institute of Fusion Energy, Daejeon, 169-148, South Korea.
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2
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Kim CB, An CY, Min B. Intermittent strong transport of the quasi-adiabatic plasma state. Sci Rep 2018; 8:8622. [PMID: 29872085 PMCID: PMC5988669 DOI: 10.1038/s41598-018-26793-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Accepted: 05/17/2018] [Indexed: 11/09/2022] Open
Abstract
The dynamics of the fluctuating electrostatic potential and the plasma density couched in the resistive-drift model at nearly adiabatic state are simulated. The linear modes are unstable if the phase difference between the potential and the density are positive. Exponential growth of the random small perturbations slows down due to the nonlinear E × B flows that work in two ways. They regulate the strength of the fluctuations by transferring the energy from the energy-producing scale to neighboring scales and reduce the cross phase at the same time. During quasi-steady relaxation sporadic appearance of very strong turbulent particle flux is observed that is characterized by the flat energy spectrum and the broad secondary peak in the mesoscale of the order of the gyro-radius. Such boost of the transport is found to be caused by presence of relatively large cross phase as the E × B flows are not effective in cancelling out the cross phase.
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Affiliation(s)
- Chang-Bae Kim
- Physics Department and Research Institute for Origin of Matter and Evolution of Galaxies, Soongsil University, Seoul, 156-743, Korea.
| | - Chan-Yong An
- Physics Department and Research Institute for Origin of Matter and Evolution of Galaxies, Soongsil University, Seoul, 156-743, Korea
| | - Byunghoon Min
- Physics Department and Research Institute for Origin of Matter and Evolution of Galaxies, Soongsil University, Seoul, 156-743, Korea
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3
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Sabot R, Hennequin P, Colas L. Fluctuation Measurements and Their Link with Transport on Tore Supra. FUSION SCIENCE AND TECHNOLOGY 2017. [DOI: 10.13182/fst09-a9176] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- R. Sabot
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - P. Hennequin
- Laboratoire de Physique des Plasmas, CNRS, Ecole Polytechnique, 91128 Palaiseau, France
| | - L. Colas
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
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4
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Gürcan ÖD, Morel P, Kobayashi S, Singh R, Xu S, Diamond PH. Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence. Phys Rev E 2016; 94:033106. [PMID: 27739713 DOI: 10.1103/physreve.94.033106] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2016] [Indexed: 11/07/2022]
Abstract
A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with nonlocal interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seem to dominate over the dual cascade, which is a common problem of two-dimensional shell models.
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Affiliation(s)
- Ö D Gürcan
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.,CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.,Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.,Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France
| | - P Morel
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.,CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.,Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.,Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France
| | - S Kobayashi
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.,CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France
| | - Rameswar Singh
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.,CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France
| | - S Xu
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.,Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France
| | - P H Diamond
- CASS and Department of Physics, University of California San Diego, La Jolla, California 92093-0424, USA
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Guo ZB, Diamond PH, Kosuga Y, Gürcan ÖD. Elasticity in drift-wave-zonal-flow turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:041101. [PMID: 24827182 DOI: 10.1103/physreve.89.041101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2013] [Indexed: 06/03/2023]
Abstract
We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉'|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉'| is the ZF shearing rate and Δωk is the turbulence decorrelation rate. For |〈v〉'|/Δωk>1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ΩZF=±γd1/2γmodu1/2, where γd is the ZF friction coefficient and γmodu is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.
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Affiliation(s)
- Z B Guo
- WCI Center for Fusion Theory, NFRI, Daejeon 305-333, South Korea
| | - P H Diamond
- WCI Center for Fusion Theory, NFRI, Daejeon 305-333, South Korea and CMTFO and CASS, University of California, San Diego, La Jolla, California 92093, USA
| | - Y Kosuga
- IAS and RIAM, Kyushu University, Kasuga 816-8580, Japan
| | - Ö D Gürcan
- LPP, Ecole Polytechnique, CNRS, Palaiseau Cedex 91128, France
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Meyrand R, Galtier S. Anomalous k⊥(-8/3) spectrum in electron magnetohydrodynamic turbulence. PHYSICAL REVIEW LETTERS 2013; 111:264501. [PMID: 24483798 DOI: 10.1103/physrevlett.111.264501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2013] [Indexed: 06/03/2023]
Abstract
Electron magnetohydrodynamic turbulence is investigated under the presence of a relatively strong external magnetic field b0e∥ and through three-dimensional direct numerical simulations. Our study reveals the emergence of a k⊥(-8/3) scaling for the magnetic energy spectrum at scales k∥(D)≤k⊥≤k⊥(D), where k∥(D) and k⊥(D) are, respectively, the typical largest dissipative scales along and transverse to the b0 direction. Unlike standard magnetohydrodynamic, this turbulence regime is characterized by filaments of electric currents parallel to b0. The anomalous scaling is in agreement with a heuristic model in which the transfer in the parallel direction is negligible. Implications for solar wind turbulence are discussed.
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Affiliation(s)
- Romain Meyrand
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France
| | - Sébastien Galtier
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France
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Bratanov V, Jenko F, Hatch DR, Wilczek M. Nonuniversal power-law spectra in turbulent systems. PHYSICAL REVIEW LETTERS 2013; 111:075001. [PMID: 23992072 DOI: 10.1103/physrevlett.111.075001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2013] [Indexed: 06/02/2023]
Abstract
Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be observed. As a simple model for such situations, a modified version of the Kuramoto-Sivashinsky equation is studied. By means of semianalytical and numerical studies, one finds power laws with nonuniversal exponents in the spectral range for which the ratio of nonlinear and linear time scales is (roughly) scale independent.
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Affiliation(s)
- V Bratanov
- Max-Planck-Institut für Plasmaphysik, EURATOM Association, 85748 Garching, Germany
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