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Langevin based turbulence model and its relationship with Kappa distributions. Sci Rep 2022; 12:2136. [PMID: 35136141 PMCID: PMC8827075 DOI: 10.1038/s41598-022-05996-0] [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: 10/18/2021] [Accepted: 01/14/2022] [Indexed: 11/08/2022] Open
Abstract
Kappa distributions (or \documentclass[12pt]{minimal}
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\begin{document}$$\kappa $$\end{document}κ-like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and \documentclass[12pt]{minimal}
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\begin{document}$$\kappa $$\end{document}κ-like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by \documentclass[12pt]{minimal}
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\begin{document}$$\kappa $$\end{document}κ-like distributions. We observe a robust relation between the \documentclass[12pt]{minimal}
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\begin{document}$$\kappa $$\end{document}κ parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the \documentclass[12pt]{minimal}
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\begin{document}$$\kappa $$\end{document}κ parameter; namely \documentclass[12pt]{minimal}
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\begin{document}$$\kappa \sim \text {Re}\,k^{-5/3}$$\end{document}κ∼Rek-5/3. We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.
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Verscharen D, Wicks RT, Alexandrova O, Bruno R, Burgess D, Chen CHK, D’Amicis R, De Keyser J, de Wit TD, Franci L, He J, Henri P, Kasahara S, Khotyaintsev Y, Klein KG, Lavraud B, Maruca BA, Maksimovic M, Plaschke F, Poedts S, Reynolds CS, Roberts O, Sahraoui F, Saito S, Salem CS, Saur J, Servidio S, Stawarz JE, Štverák Š, Told D. A Case for Electron-Astrophysics. EXPERIMENTAL ASTRONOMY 2021; 54:473-519. [PMID: 36915623 PMCID: PMC9998602 DOI: 10.1007/s10686-021-09761-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 05/07/2021] [Indexed: 06/18/2023]
Abstract
The smallest characteristic scales, at which electron dynamics determines the plasma behaviour, are the next frontier in space and astrophysical plasma research. The analysis of astrophysical processes at these scales lies at the heart of the research theme of electron-astrophysics. Electron scales are the ultimate bottleneck for dissipation of plasma turbulence, which is a fundamental process not understood in the electron-kinetic regime. In addition, plasma electrons often play an important role for the spatial transfer of thermal energy due to the high heat flux associated with their velocity distribution. The regulation of this electron heat flux is likewise not understood. By focussing on these and other fundamental electron processes, the research theme of electron-astrophysics links outstanding science questions of great importance to the fields of space physics, astrophysics, and laboratory plasma physics. In this White Paper, submitted to ESA in response to the Voyage 2050 call, we review a selection of these outstanding questions, discuss their importance, and present a roadmap for answering them through novel space-mission concepts.
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Affiliation(s)
- Daniel Verscharen
- Mullard Space Science Laboratory, University College London, Dorking, UK
- Space Science Center, University of New Hampshire, Durham, NH USA
| | - Robert T. Wicks
- Mullard Space Science Laboratory, University College London, Dorking, UK
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle-upon-Tyne, UK
| | - Olga Alexandrova
- Laboratoire d’Études Spatiales et d’Instrumentation en Astrophysique, Observatoire de Paris-Meudon, Paris, France
| | - Roberto Bruno
- Instituto di Astrofisica e Planetologia Spaziali, INAF, Rome, Italy
| | - David Burgess
- School of Physics and Astronomy, Queen Mary University of London, London, UK
| | | | | | - Johan De Keyser
- Royal Belgian Institute for Space Aeronomy, Brussels, Belgium
| | - Thierry Dudok de Wit
- Laboratoire de Physique et Chimie de l’Environment et de l’Espace, CNRS, University of Orléans and CNES, Orléans, France
| | - Luca Franci
- School of Physics and Astronomy, Queen Mary University of London, London, UK
- Osservatorio Astrofisico di Arcetri, INAF, Firenze, Italy
| | - Jiansen He
- School of Earth and Space Sciences, Peking University, Beijing, China
| | - Pierre Henri
- Laboratoire de Physique et Chimie de l’Environment et de l’Espace, CNRS, University of Orléans and CNES, Orléans, France
- CNRS, UCA, OCA, Lagrange, Nice, France
| | - Satoshi Kasahara
- Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan
| | | | - Kristopher G. Klein
- Lunar and Planetary Laboratory and Department of Planetary Sciences, University of Arizona, Tucson, AZ USA
| | - Benoit Lavraud
- Laboratoire d’astrophysique de Bordeaux, Université de Bordeaux, CNRS, Pessac, France
- Institut de Recherche en Astrophysique et Planétologie, CNRS, UPS, CNES, Université de Toulouse, Toulouse, France
| | - Bennett A. Maruca
- Department of Physics and Astronomy, Bartol Research Institute, University of Delaware, Newark, DE USA
| | - Milan Maksimovic
- Laboratoire d’Études Spatiales et d’Instrumentation en Astrophysique, Observatoire de Paris-Meudon, Paris, France
| | | | - Stefaan Poedts
- Centre for Mathematical Plasma Astrophysics, KU Leuven, Leuven, Belgium
- Institute of Physics, University of Maria Curie-Skłodowska, Lublin, Poland
| | | | - Owen Roberts
- Space Research Institute, Austrian Academy of Sciences, Graz, Austria
| | - Fouad Sahraoui
- Laboratoire de Physique des Plasmas, CNRS, École Polytechnique, Sorbonne Université, Observatoire de Paris-Meudon, Paris Saclay, Palaiseau, France
| | - Shinji Saito
- Space Environment Laboratory, National Institute of Information and Communications Technology, Tokyo, Japan
| | - Chadi S. Salem
- Space Sciences Laboratory, University of California, Berkeley, CA USA
| | - Joachim Saur
- Institut für Geophysik und Meteorologie, University of Cologne, Cologne, Germany
| | - Sergio Servidio
- Department of Physics, Università della Calabria, Rende, Italy
| | | | - Štěpán Štverák
- Astronomical Institute and Institute of Atmospheric Physics, Czech Academy of Sciences, Prague, Czech Republic
| | - Daniel Told
- Max Planck Institute for Plasma Physics, Garching, Germany
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Bandyopadhyay R, Matthaeus WH, Parashar TN, Yang Y, Chasapis A, Giles BL, Gershman DJ, Pollock CJ, Russell CT, Strangeway RJ, Torbert RB, Moore TE, Burch JL. Statistics of Kinetic Dissipation in the Earth's Magnetosheath: MMS Observations. PHYSICAL REVIEW LETTERS 2020; 124:255101. [PMID: 32639771 DOI: 10.1103/physrevlett.124.255101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2020] [Revised: 04/03/2020] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
A familiar problem in space and astrophysical plasmas is to understand how dissipation and heating occurs. These effects are often attributed to the cascade of broadband turbulence which transports energy from large scale reservoirs to small scale kinetic degrees of freedom. When collisions are infrequent, local thermodynamic equilibrium is not established. In this case the final stage of energy conversion becomes more complex than in the fluid case, and both pressure-dilatation and pressure strain interactions (Pi-D≡-Π_{ij}D_{ij}) become relevant and potentially important. Pi-D in plasma turbulence has been studied so far primarily using simulations. The present study provides a statistical analysis of Pi-D in the Earth's magnetosheath using the unique measurement capabilities of the Magnetospheric Multiscale (MMS) mission. We find that the statistics of Pi-D in this naturally occurring plasma environment exhibit strong resemblance to previously established fully kinetic simulations results. The conversion of energy is concentrated in space and occurs near intense current sheets, but not within them. This supports recent suggestions that the chain of energy transfer channels involves regional, rather than pointwise, correlations.
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Affiliation(s)
- Riddhi Bandyopadhyay
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - William H Matthaeus
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA and Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA
| | - Tulasi N Parashar
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Yan Yang
- Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Alexandros Chasapis
- Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, Colorado 80303, USA
| | - Barbara L Giles
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | | | | | | | | | - Roy B Torbert
- University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Thomas E Moore
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - James L Burch
- Southwest Research Institute, San Antonio, Texas 78238-5166, USA
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Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale. ATMOSPHERE 2020. [DOI: 10.3390/atmos11020203] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm’s law including a Hall current. The ion inertial length ϵ H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity—invariants in the ideal case—grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with ϵ H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, ∼ k − 2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows.
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Chen CHK, Klein KG, Howes GG. Evidence for electron Landau damping in space plasma turbulence. Nat Commun 2019; 10:740. [PMID: 30765843 PMCID: PMC6375956 DOI: 10.1038/s41467-019-08435-3] [Citation(s) in RCA: 86] [Impact Index Per Article: 17.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2018] [Accepted: 01/08/2019] [Indexed: 11/25/2022] Open
Abstract
How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas.
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Affiliation(s)
- C H K Chen
- School of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, UK.
| | - K G Klein
- Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ, 85719, USA
| | - G G Howes
- Department of Physics and Astronomy, University of Iowa, Iowa City, IA, 52242, USA
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Sorriso-Valvo L, Catapano F, Retinò A, Le Contel O, Perrone D, Roberts OW, Coburn JT, Panebianco V, Valentini F, Perri S, Greco A, Malara F, Carbone V, Veltri P, Pezzi O, Fraternale F, Di Mare F, Marino R, Giles B, Moore TE, Russell CT, Torbert RB, Burch JL, Khotyaintsev YV. Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability. PHYSICAL REVIEW LETTERS 2019; 122:035102. [PMID: 30735422 DOI: 10.1103/physrevlett.122.035102] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Revised: 12/10/2018] [Indexed: 05/20/2023]
Abstract
The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Here, for the first time, we report observations suggesting the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas.
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Affiliation(s)
- Luca Sorriso-Valvo
- Nanotec/CNR, U.O.S. di Cosenza, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy and Departamento de Física, Escuela Politécnica Nacional, 170517 Quito, Ecuador
| | - Filomena Catapano
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy and LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Alessandro Retinò
- LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Olivier Le Contel
- LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Denise Perrone
- Department of Physics, Imperial College of London, London SW7 2AZ, United Kingdom
| | - Owen W Roberts
- Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
| | - Jesse T Coburn
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Vincenzo Panebianco
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Francesco Valentini
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Silvia Perri
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Antonella Greco
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Francesco Malara
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Vincenzo Carbone
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Pierluigi Veltri
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Oreste Pezzi
- Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L'Aquila, Italy and Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Federico Fraternale
- Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, 10129 Torino, Italy
| | - Francesca Di Mare
- Department of Physics, University of Oslo, Sem Sælands Vei 26, Fysikkbygningen 0371 Oslo, Norway
| | - Raffaele Marino
- Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS, École Centrale de Lyon, Université Claude Bernard Lyon 1, INSA de Lyon, F-69134 Écully, France
| | - Barbara Giles
- NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - Thomas E Moore
- NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - Christopher T Russell
- Institute of Geophysics and Planetary Physics, and Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, California 90095-1567, USA
| | - Roy B Torbert
- Space Science Center, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Jim L Burch
- Southwest Research Institute, San Antonio, Texas 78238-5166, USA
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