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Richard L, Sorriso-Valvo L, Yordanova E, Graham DB, Khotyaintsev YV. Turbulence in Magnetic Reconnection Jets from Injection to Sub-Ion Scales. Phys Rev Lett 2024; 132:105201. [PMID: 38518330 DOI: 10.1103/physrevlett.132.105201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Revised: 10/02/2023] [Accepted: 02/05/2024] [Indexed: 03/24/2024]
Abstract
We investigate turbulence in magnetic reconnection jets in the Earth's magnetotail using data from the Magnetospheric Multiscale spacecraft. We show that signatures of a limited inertial range are observed in many reconnection jets. The observed turbulence develops on the timescale of a few ion gyroperiods, resulting in intermittent multifractal energy cascade from the characteristic scale of the jet down to the ion scales. We show that at sub-ion scales, the fluctuations are close to monofractal and predominantly kinetic Alfvén waves. The observed energy transfer rate across the inertial range is ∼10^{8} J kg^{-1} s^{-1}, which is the largest reported for space plasmas so far.
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Affiliation(s)
- Louis Richard
- Swedish Institute of Space Physics, Uppsala 751 21, Sweden and Department of Physics and Astronomy, Space and Plasma Physics, Uppsala University, Uppsala 751 20, Sweden
| | - Luca Sorriso-Valvo
- CNR/ISTP-Istituto per la Scienza e la Tecnologia dei Plasmi, 70126 Bari, Italy; Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm 114 28, Sweden; and Swedish Institute of Space Physics, Uppsala 751 21, Sweden
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2
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Bowen TA, Chandran BDG, Squire J, Bale SD, Duan D, Klein KG, Larson D, Mallet A, McManus MD, Meyrand R, Verniero JL, Woodham LD. In Situ Signature of Cyclotron Resonant Heating in the Solar Wind. Phys Rev Lett 2022; 129:165101. [PMID: 36306754 DOI: 10.1103/physrevlett.129.165101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 06/20/2022] [Accepted: 09/16/2022] [Indexed: 06/16/2023]
Abstract
The dissipation of magnetized turbulence is an important paradigm for describing heating and energy transfer in astrophysical environments such as the solar corona and wind; however, the specific collisionless processes behind dissipation and heating remain relatively unconstrained by measurements. Remote sensing observations have suggested the presence of strong temperature anisotropy in the solar corona consistent with cyclotron resonant heating. In the solar wind, in situ magnetic field measurements reveal the presence of cyclotron waves, while measured ion velocity distribution functions have hinted at the active presence of cyclotron resonance. Here, we present Parker Solar Probe observations that connect the presence of ion-cyclotron waves directly to signatures of resonant damping in observed proton-velocity distributions using the framework of quasilinear theory. We show that the quasilinear evolution of the observed distribution functions should absorb the observed cyclotron wave population with a heating rate of 10^{-14} W/m^{3}, indicating significant heating of the solar wind.
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Affiliation(s)
- Trevor A Bowen
- Space Sciences Laboratory, University of California, Berkeley, California 94720-7450, USA
| | - Benjamin D G Chandran
- Department of Physics and Astronomy, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Jonathan Squire
- Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016, New Zealand
| | - Stuart D Bale
- Space Sciences Laboratory, University of California, Berkeley, California 94720-7450, USA
- Physics Department, University of California, Berkeley, California 94720-7300, USA
| | - Die Duan
- School of Earth and Space Sciences, Peking University, Beijing 100871, China
| | - Kristopher G Klein
- Department of Planetary Sciences and Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721, USA
| | - Davin Larson
- Space Sciences Laboratory, University of California, Berkeley, California 94720-7450, USA
| | - Alfred Mallet
- Space Sciences Laboratory, University of California, Berkeley, California 94720-7450, USA
| | - Michael D McManus
- Space Sciences Laboratory, University of California, Berkeley, California 94720-7450, USA
- Physics Department, University of California, Berkeley, California 94720-7300, USA
| | - Romain Meyrand
- Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016, New Zealand
| | - Jaye L Verniero
- NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, Maryland 20771, USA
| | - Lloyd D Woodham
- Department of Physics, The Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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3
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Manzini D, Sahraoui F, Califano F, Ferrand R. Local energy transfer and dissipation in incompressible Hall magnetohydrodynamic turbulence: The coarse-graining approach. Phys Rev E 2022; 106:035202. [PMID: 36266803 DOI: 10.1103/physreve.106.035202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2022] [Accepted: 07/27/2022] [Indexed: 06/16/2023]
Abstract
We derive the coarse-graining (CG) equations of incompressible Hall magnetohydrodynamic (HMHD) turbulence to investigate the local (in space) energy transfer rate as a function of the filtering scale ℓ. First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to three-dimensional simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law. Furthermore, we developed an anisotropic version of CG that allows us to study the magnitude of the cascade rate along different directions with respect to the mean magnetic field. Its implementation on the numerical data with moderate background magnetic field shows a weaker cascade along the magnetic field than in the perpendicular plane, while an isotropic cascade is recovered in the absence of a background field. The strength of the CG approach is further revealed when considering the local-in-space energy transfer, which is shown theoretically and numerically to match at a given position x, when locally averaged over a neighboring region, the (quasi-)local dissipation. Prospects of exploiting this model to investigate local dissipation in spacecraft data are discussed.
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Affiliation(s)
- D Manzini
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
- Dipartimento di Fisica E. Fermi, University of Pisa, 56127 Pisa, Italy
| | - F Sahraoui
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
| | - F Califano
- Dipartimento di Fisica E. Fermi, University of Pisa, 56127 Pisa, Italy
| | - R Ferrand
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
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4
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Simon P, Sahraoui F. Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities. Phys Rev E 2022; 105:055111. [PMID: 35706285 DOI: 10.1103/physreve.105.055111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.
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Affiliation(s)
- P Simon
- Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris-Saclay, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
| | - F Sahraoui
- Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris-Saclay, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
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Parashar TN, Matthaeus WH. Observations of cross scale energy transfer in the inner heliosphere by Parker Solar Probe. Rev Mod Plasma Phys 2022; 6:41. [PMCID: PMC9684259 DOI: 10.1007/s41614-022-00097-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 10/02/2022] [Indexed: 11/27/2022]
Abstract
The solar wind, a continuous flow of plasma from the sun, not only shapes the near Earth space environment but also serves as a natural laboratory to study plasma turbulence in conditions that are not achievable in the lab. Starting with the Mariners, for more than five decades, multiple space missions have enabled in-depth studies of solar wind turbulence. Parker Solar Probe (PSP) was launched to explore the origins and evolution of the solar wind. With its state-of-the-art instrumentation and unprecedented close approaches to the sun, PSP is starting a new era of inner heliospheric exploration. In this review we discuss observations of turbulent energy flow across scales in the inner heliosphere as observed by PSP. After providing a quick theoretical overview and a quick recap of turbulence before PSP, we discuss in detail the observations of energy at various scales on its journey from the largest scales to the internal degrees of freedom of the plasma. We conclude with some open ended questions, many of which we hope that PSP will help answer.
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Affiliation(s)
- Tulasi N. Parashar
- grid.267827.e0000 0001 2292 3111School of Chemical and Physical Sciences, Victoria University of Wellington, Gate 7, Kelburn Parade, Kelburn, Wellington, 6012 New Zealand ,grid.33489.350000 0001 0454 4791Department of Physics and Astronomy, University of Delaware, Sharp Laboratory, Newark, Delaware 19711 USA
| | - William H. Matthaeus
- grid.33489.350000 0001 0454 4791Department of Physics and Astronomy, University of Delaware, Sharp Laboratory, Newark, Delaware 19711 USA
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Bandyopadhyay R, Sorriso-Valvo L, Chasapis A, Hellinger P, Matthaeus WH, Verdini A, Landi S, Franci L, Matteini L, Giles BL, Gershman DJ, Moore TE, Pollock CJ, Russell CT, Strangeway RJ, Torbert RB, Burch JL. In Situ Observation of Hall Magnetohydrodynamic Cascade in Space Plasma. Phys Rev Lett 2020; 124:225101. [PMID: 32567898 DOI: 10.1103/physrevlett.124.225101] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2019] [Revised: 04/07/2020] [Accepted: 05/01/2020] [Indexed: 05/20/2023]
Abstract
We present estimates of the turbulent energy-cascade rate derived from a Hall-magnetohydrodynamic (MHD) third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. Magnetospheric Multiscale (MMS) data accumulated in the magnetosheath and the solar wind are compared with previously established simulation results. Consistent with the simulations, we find that at large (MHD) scales, the MMS observations exhibit a clear inertial range dominated by the MHD flux. In the subion range, the cascade continues at a diminished level via the Hall term, and the change becomes more pronounced as the plasma beta increases. Additionally, the MHD contribution to interscale energy transfer remains important at smaller scales than previously thought. Possible reasons are offered for this unanticipated result.
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Affiliation(s)
- Riddhi Bandyopadhyay
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Luca Sorriso-Valvo
- Departamento de Física, Escuela Politécnica Nacional, 170517 Quito, Ecuador and Istituto per la Scienza e Tecnologia dei Plasmi, Consiglio Nazionale delle Ricerche, 87036 Bari, Italy
| | - Alexandros Chasapis
- Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, Colorado 80303, USA
| | - Petr Hellinger
- Astronomical Institute, CAS, Bocni II/1401, CZ-14100 Prague, Czech Republic and Institute of Atmospheric Physics, CAS, Bocni II/1401, CZ-14100 Prague, Czech Republic
| | - 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
| | - Andrea Verdini
- Dipartimento di Fisica e Astronomia, Universitá degli Studi di Firenze, 50125 Firenze, Italy and INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
| | - Simone Landi
- Dipartimento di Fisica e Astronomia, Universitá degli Studi di Firenze, 50125 Firenze, Italy and INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
| | - Luca Franci
- School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom and INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
| | - Lorenzo Matteini
- LESIA, Observatoire de Paris, Meudon, France and INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
| | - Barbara L Giles
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | | | - Thomas E Moore
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | | | | | | | - Roy B Torbert
- University of New Hampshire, Durham, New Hampshire 03824, USA
| | - James L Burch
- Southwest Research Institute, San Antonio, Texas 78238-5166, USA
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Ferrand R, Galtier S, Sahraoui F, Meyrand R, Andrés N, Banerjee S. On Exact Laws in Incompressible Hall Magnetohydrodynamic Turbulence. ACTA ACUST UNITED AC 2019; 881:50. [DOI: 10.3847/1538-4357/ab2be9] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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8
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David V, Galtier S. ${k}_{\perp }^{-8/3}$ Spectrum in Kinetic Alfvén Wave Turbulence: Implications for the Solar Wind. ACTA ACUST UNITED AC 2019; 880:L10. [DOI: 10.3847/2041-8213/ab2fe6] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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9
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Banerjee S, Hadid LZ, Sahraoui F, Galtier S. SCALING OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE IN THE FAST SOLAR WIND. ACTA ACUST UNITED AC 2016; 829:L27. [DOI: 10.3847/2041-8205/829/2/l27] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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10
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Coburn JT, Forman MA, Smith CW, Vasquez BJ, Stawarz JE. Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer. Philos Trans A Math Phys Eng Sci 2015; 373:rsta.2014.0150. [PMID: 25848079 PMCID: PMC4394682 DOI: 10.1098/rsta.2014.0150] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/12/2015] [Indexed: 05/29/2023]
Abstract
We review some aspects of solar wind turbulence with an emphasis on the ability of the turbulence to account for the observed heating of the solar wind. Particular attention is paid to the use of structure functions in computing energy cascade rates and their general agreement with the measured thermal proton heating. We then examine the use of 1 h data samples that are comparable in length to the correlation length for the fluctuations to obtain insights into local inertial range dynamics and find evidence for intermittency in the computed energy cascade rates. When the magnetic energy dominates the kinetic energy, there is evidence of anti-correlation in the cascade of energy associated with the outward- and inward-propagating components that we can only partially explain.
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Affiliation(s)
- Jesse T Coburn
- Physics Department and Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH, USA
| | - Miriam A Forman
- Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, NY, USA
| | - Charles W Smith
- Physics Department and Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH, USA
| | - Bernard J Vasquez
- Physics Department and Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH, USA
| | - Julia E Stawarz
- Department of Astrophysical and Planetary Sciences, University of Colorado at Boulder, Boulder, CO, USA
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12
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Osman KT, Matthaeus WH, Kiyani KH, Hnat B, Chapman SC. Proton kinetic effects and turbulent energy cascade rate in the solar wind. Phys Rev Lett 2013; 111:201101. [PMID: 24289672 DOI: 10.1103/physrevlett.111.201101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2013] [Indexed: 06/02/2023]
Abstract
The first observed connection between kinetic instabilities driven by proton temperature anisotropy and estimated energy cascade rates in the turbulent solar wind is reported using measurements from the Wind spacecraft at 1 AU. We find enhanced cascade rates are concentrated along the boundaries of the (β∥, T⊥/T∥) plane, which includes regions theoretically unstable to the mirror and firehose instabilities. A strong correlation is observed between the estimated cascade rate and kinetic effects such as temperature anisotropy and plasma heating, resulting in protons 5-6 times hotter and 70%-90% more anisotropic than under typical isotropic plasma conditions. These results offer new insights into kinetic processes in a turbulent regime.
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Affiliation(s)
- K T Osman
- Centre for Fusion, Space, and Astrophysics, University of Warwick, Coventry CV4 7AL, United Kingdom
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Wan M, Matthaeus WH, Karimabadi H, Roytershteyn V, Shay M, Wu P, Daughton W, Loring B, Chapman SC. Intermittent dissipation at kinetic scales in collisionless plasma turbulence. Phys Rev Lett 2012; 109:195001. [PMID: 23215389 DOI: 10.1103/physrevlett.109.195001] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2012] [Indexed: 06/01/2023]
Abstract
High resolution kinetic simulations of collisionless plasma driven by shear show the development of turbulence characterized by dynamic coherent sheetlike current density structures spanning a range of scales down to electron scales. We present evidence that these structures are sites for heating and dissipation, and that stronger current structures signify higher dissipation rates. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform and patchy.
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Affiliation(s)
- M Wan
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
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14
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Osman KT, Matthaeus WH, Hnat B, Chapman SC. Kinetic signatures and intermittent turbulence in the solar wind plasma. Phys Rev Lett 2012; 108:261103. [PMID: 23004954 DOI: 10.1103/physrevlett.108.261103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2012] [Indexed: 06/01/2023]
Abstract
A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.
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Affiliation(s)
- K T Osman
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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Abstract
Evidence for nonuniform heating in the solar wind plasma near current sheets dynamically generated by magnetohydrodynamic (MHD) turbulence is obtained using measurements from the ACE spacecraft. These coherent structures only constitute 19% of the data, but contribute 50% of the total plasma internal energy. Intermittent heating manifests as elevations in proton temperature near current sheets, resulting in regional heating and temperature enhancements extending over several hours. The number density of non-Gaussian structures is found to be proportional to the mean proton temperature and solar wind speed. These results suggest magnetofluid turbulence drives intermittent dissipation through a hierarchy of coherent structures, which collectively could be a significant source of coronal and solar wind heating.
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Affiliation(s)
- K T Osman
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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Yoshimatsu K. Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 85:066313. [PMID: 23005212 DOI: 10.1103/physreve.85.066313] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2011] [Indexed: 06/01/2023]
Abstract
The four-fifths law for third-order longitudinal moments is examined, using direct numerical simulation (DNS) data on three-dimensional (3D) forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a periodic box. The magnetic Prandtl number is set to one, and the number of grid points is 512(3). A generalized Kármán-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of r. Here, r is a separation vector. The viscous, forcing, anisotropic and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.
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Affiliation(s)
- Katsunori Yoshimatsu
- Department of Computational Science and Engineering, Nagoya University, Nagoya, 464-8603, Japan.
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