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Lukin AS, Artemyev AV, Vainchtein DL, Petrukovich AA. Regimes of ion dynamics in current sheets: The machine learning approach. Phys Rev E 2022; 106:065205. [PMID: 36671165 DOI: 10.1103/physreve.106.065205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 11/28/2022] [Indexed: 12/24/2022]
Abstract
Current sheets are spatially localized almost-one-dimensional (1D) structures with intense plasma currents. They play a key role in storing the magnetic field energy and they separate different plasma populations in planetary magnetospheres, the solar wind, and the solar corona. Current sheets are primary regions for the magnetic field line reconnection responsible for plasma heating and charged particle acceleration. One of the most interesting and widely observed types of 1D current sheets is the rotational discontinuity, which can be force-free or include plasma compression. Theoretical models of such 1D current sheets are based on the assumption of adiabatic motion of ions, i.e., ion adiabatic invariants are conserved. We focus on three current sheet configurations, widely observed in the Earth magnetopause and magnetotail and in the near-Earth solar wind. The magnetic field in such current sheets is supported by currents carried by transient ions, which exist only when there is a sufficient number of invariants. In this paper, we apply a machine learning approach, AI Poincaré, to determine parametrical domains where adiabatic invariants are conserved. For all three current sheet configurations, these domains are quite narrow and do not cover the entire parametrical range of observed current sheets. We discuss possible interpretation of obtained results indicating that 1D current sheets are dynamical rather than static plasma equilibria.
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Affiliation(s)
- A S Lukin
- Space Research Institute RAS, Moscow 117997, Russia.,Faculty of Physics, National Research University Higher School of Economics, Moscow 101000, Russia
| | - A V Artemyev
- Space Research Institute RAS, Moscow 117997, Russia.,Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA
| | - D L Vainchtein
- Space Research Institute RAS, Moscow 117997, Russia.,Nyheim Plasma Institute, Drexel University, Camden, New Jersey 08103, USA
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2
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Durrive JB, Changmai M, Keppens R, Lesaffre P, Maci D, Momferatos G. Swift generator for three-dimensional magnetohydrodynamic turbulence. Phys Rev E 2022; 106:025307. [PMID: 36109980 DOI: 10.1103/physreve.106.025307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Magnetohydrodynamic turbulence is central to laboratory and astrophysical plasmas, and is invoked for interpreting many observed scalings. Verifying predicted scaling law behavior requires extreme-resolution direct numerical simulations (DNS), with needed computing resources excluding systematic parameter surveys. We here present an analytic generator of realistically looking turbulent magnetic fields, that computes three-dimensional (3D) O(1000^{3}) solenoidal vector fields in minutes to hours on desktop computers. Our model is inspired by recent developments in 3D incompressible fluid turbulence theory, where a Gaussian white noise vector subjected to a nonlinear transformation results in an intermittent, multifractal random field. Our B×C model has only few parameters that have clear geometric interpretations. We directly compare a (costly) DNS with a swiftly B×C-generated realization, in terms of its (1) characteristic sheetlike structures of current density, (2) volume-filling aspects across current intensity, (3) power-spectral behavior, (4) probability distribution functions of increments for magnetic field and current density, structure functions, and spectra of exponents, and (5) partial variance of increments. The model even allows to mimic time-evolving magnetic and current density distributions and can be used for synthetic observations on 3D turbulent data cubes.
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Affiliation(s)
- Jean-Baptiste Durrive
- Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium
| | - Madhurjya Changmai
- Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium
| | - Rony Keppens
- Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium
| | - Pierre Lesaffre
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Daniela Maci
- Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium
| | - Georgios Momferatos
- Environmental Research Laboratory, National Center for Scientific Research Demokritos, Agia Paraskevi 15341, Greece
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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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Verscharen D, Klein KG, Maruca BA. The multi-scale nature of the solar wind. LIVING REVIEWS IN SOLAR PHYSICS 2019; 16:5. [PMID: 31929769 PMCID: PMC6934245 DOI: 10.1007/s41116-019-0021-0] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Accepted: 11/09/2019] [Indexed: 05/29/2023]
Abstract
The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.
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Affiliation(s)
- Daniel Verscharen
- Mullard Space Science Laboratory, University College London, Dorking, RH5 6NT UK
- Space Science Center, University of New Hampshire, Durham, NH 03824 USA
| | - Kristopher G. Klein
- Lunar and Planetary Laboratory and Department of Planetary Sciences, University of Arizona, Tucson, AZ 85719 USA
| | - Bennett A. Maruca
- Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 USA
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Hoppock IW, Chandran BDG, Klein KG, Mallet A, Verscharen D. Stochastic proton heating by kinetic-Alfvén-wave turbulence in moderately high- β plasmas. JOURNAL OF PLASMA PHYSICS 2018; 84:905840615. [PMID: 30948860 PMCID: PMC6443259 DOI: 10.1017/s0022377818001277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are much smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the heating of the solar wind. Using phenomenological arguments, we derive the stochastic-proton-heating rate in plasmas in which β p ∼ 1 - 30, where β p is the ratio of the proton pressure to the magnetic pressure. (We do not consider the β p ≳ 30 regime, in which KAWs at the proton gyroscale become non-propagating.) We test our formula for the stochastic-heating rate by numerically tracking test-particle protons interacting with a spectrum of randomly phased AWs and KAWs. Previous studies have demonstrated that at β p ≲1, particles are energized primarily by time variations in the electrostatic potential and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the electrostatic potential. In contrast, at β p ≳ 1, particles are energized primarily by the solenoidal component of the electric field and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the magnetic field.
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Affiliation(s)
- Ian W. Hoppock
- Space Science Center, University of New Hampshire, Durham, NH, 03824, USA
| | | | - Kristopher G. Klein
- Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ, 85719, USA
- CLASP, University of Michigan, Ann Arbor, MI, 48109, USA
| | - Alfred Mallet
- Space Science Center, University of New Hampshire, Durham, NH, 03824, USA
- Space Sciences Laboratory, University of California, Berkeley, CA, 94720, USA
| | - Daniel Verscharen
- Space Science Center, University of New Hampshire, Durham, NH, 03824, USA
- Mullard Space Science Laboratory, University College London, Dorking, RH5 6NT, UK
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Self-consistent Energetic Particle Acceleration by Contracting and Reconnecting Small-scale Flux Ropes: The Governing Equations. ACTA ACUST UNITED AC 2018. [DOI: 10.3847/1538-4357/aad8b3] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Howes GG. A dynamical model of plasma turbulence in the solar wind. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:20140145. [PMID: 25848075 PMCID: PMC4394677 DOI: 10.1098/rsta.2014.0145] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/05/2015] [Indexed: 06/01/2023]
Abstract
A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.
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Affiliation(s)
- G G Howes
- Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA
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Chasapis A, Retinò A, Sahraoui F, Vaivads A, Khotyaintsev YV, Sundkvist D, Greco A, Sorriso-Valvo L, Canu P. THIN CURRENT SHEETS AND ASSOCIATED ELECTRON HEATING IN TURBULENT SPACE PLASMA. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/2041-8205/804/1/l1] [Citation(s) in RCA: 77] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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le Roux JA, Zank GP, Webb GM, Khabarova O. A KINETIC TRANSPORT THEORY FOR PARTICLE ACCELERATION AND TRANSPORT IN REGIONS OF MULTIPLE CONTRACTING AND RECONNECTING INERTIAL-SCALE FLUX ROPES. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/0004-637x/801/2/112] [Citation(s) in RCA: 107] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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10
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Schaffner DA, Wan A, Brown MR. Observation of turbulent intermittency scaling with magnetic helicity in an MHD plasma wind tunnel. PHYSICAL REVIEW LETTERS 2014; 112:165001. [PMID: 24815655 DOI: 10.1103/physrevlett.112.165001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Indexed: 06/03/2023]
Abstract
The intermittency in turbulent magnetic field fluctuations has been observed to scale with the amount of magnetic helicity injected into a laboratory plasma. An unstable spheromak injected into the MHD wind tunnel of the Swarthmore Spheromak Experiment displays turbulent magnetic and plasma fluctuations as it relaxes into a Taylor state. The level of intermittency of this turbulence is determined by finding the flatness of the probability distribution function of increments for magnetic pickup coil fluctuations B˙(t). The intermittency increases with the injected helicity, but spectral indices are unaffected by this variation. While evidence is provided which supports the hypothesis that current sheets and reconnection sites are related to the generation of this intermittent signal, the true nature of the observed intermittency remains unknown.
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Affiliation(s)
- D A Schaffner
- Swarthmore College, Swarthmore, Pennsylvania 19081, USA
| | - A Wan
- Swarthmore College, Swarthmore, Pennsylvania 19081, USA
| | - M R Brown
- Swarthmore College, Swarthmore, Pennsylvania 19081, USA
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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. PHYSICAL REVIEW LETTERS 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] [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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Greco A, Valentini F, Servidio S, Matthaeus WH. Inhomogeneous kinetic effects related to intermittent magnetic discontinuities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066405. [PMID: 23368057 DOI: 10.1103/physreve.86.066405] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2012] [Revised: 11/13/2012] [Indexed: 06/01/2023]
Abstract
A connection between kinetic processes and two-dimensional intermittent plasma turbulence is observed using direct numerical simulations of a hybrid Vlasov-Maxwell model, in which the Vlasov equation is solved for protons, while the electrons are described as a massless fluid. During the development of turbulence, the proton distribution functions depart from the typical configuration of local thermodynamic equilibrium, displaying statistically significant non-Maxwellian features. In particular, temperature anisotropy and distortions are concentrated near coherent structures, generated as the result of the turbulent cascade, such as current sheets, which are nonuniformly distributed in space. Here, the partial variance of increments (PVI) method has been employed to identify high magnetic stress regions within a two-dimensional turbulent pattern. A quantitative association between non-Maxwellian features and coherent structures is established.
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Affiliation(s)
- A Greco
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
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Osman KT, Matthaeus WH, Hnat B, Chapman SC. Kinetic signatures and intermittent turbulence in the solar wind plasma. PHYSICAL REVIEW LETTERS 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] [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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Osman KT, Matthaeus WH, Wan M, Rappazzo AF. Intermittency and local heating in the solar wind. PHYSICAL REVIEW LETTERS 2012; 108:261102. [PMID: 23004953 DOI: 10.1103/physrevlett.108.261102] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2011] [Indexed: 06/01/2023]
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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