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Existence of Purely Alvén Waves in Magnetic Flux Tubes with Arbitrary Cross-Sections. PHYSICS 2022. [DOI: 10.3390/physics4030055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
We study linear torsional Alfvén waves in a magnetic flux tube with an arbitrary cross-section. We assume that the equilibrium magnetic field is propagating in the z-direction in Cartesian coordinates x,y, and z. The tube cross-section is bounded by a smooth closed curve. Both plasma and magnetic field are homogeneous outside this curve. The magnetic field magnitude is a function of x and y, while the density is a product of two functions: one dependent on z and the other dependent on x and y. As a result, the Alfvén speed is also equal to V0(x,y) times a function of z. We define Alfvén waves as waves that do not disturb plasma density. We show that these waves can exist only when the magnetic field magnitude is a function of V0. When the condition of existence of Alfvén waves is satisfied, the waves are polarised in the directions tangent to the level lines of V0(x,y) and orthogonal to the equilibrium magnetic field. We found that the Alfvén wave amplitude has a specific form that depends on a particular coordinate system.
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How Transverse Waves Drive Turbulence in the Solar Corona. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Oscillatory power is pervasive throughout the solar corona, and magnetohydrodynamic (MHD) waves may carry a significant energy flux throughout the Sun’s atmosphere. As a result, over much of the past century, these waves have attracted great interest in the context of the coronal heating problem. They are a potential source of the energy required to maintain the high-temperature plasma and may accelerate the fast solar wind. Despite many observations of coronal waves, large uncertainties inhibit reliable estimates of their exact energy flux, and as such, it remains unclear whether they can contribute significantly to the coronal energy budget. A related issue concerns whether the wave energy can be dissipated over sufficiently short time scales to balance the atmospheric losses. For typical coronal parameters, energy dissipation rates are very low and, thus, any heating model must efficiently generate very small-length scales. As such, MHD turbulence is a promising plasma phenomenon for dissipating large quantities of energy quickly and over a large volume. In recent years, with advances in computational and observational power, much research has highlighted how MHD waves can drive complex turbulent behaviour in the solar corona. In this review, we present recent results that illuminate the energetics of these oscillatory processes and discuss how transverse waves may cause instability and turbulence in the Sun’s atmosphere.
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Khiar B, Revet G, Ciardi A, Burdonov K, Filippov E, Béard J, Cerchez M, Chen SN, Gangolf T, Makarov SS, Ouillé M, Safronova M, Skobelev IY, Soloviev A, Starodubtsev M, Willi O, Pikuz S, Fuchs J. Laser-Produced Magnetic-Rayleigh-Taylor Unstable Plasma Slabs in a 20 T Magnetic Field. PHYSICAL REVIEW LETTERS 2019; 123:205001. [PMID: 31809120 DOI: 10.1103/physrevlett.123.205001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 10/02/2019] [Indexed: 06/10/2023]
Abstract
Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the "classical," fluidlike magnetized Rayleigh-Taylor instability.
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Affiliation(s)
- B Khiar
- Sorbonne Université, Observatoire de Paris, PSL Research University, LERMA, CNRS UMR 8112, F-75005 Paris, France
- Flash Center for Computational Science, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA
| | - G Revet
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - A Ciardi
- Sorbonne Université, Observatoire de Paris, PSL Research University, LERMA, CNRS UMR 8112, F-75005 Paris, France
| | - K Burdonov
- Sorbonne Université, Observatoire de Paris, PSL Research University, LERMA, CNRS UMR 8112, F-75005 Paris, France
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - E Filippov
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
- Joint Institute for High Temperatures, RAS, 125412 Moscow, Russia
| | - J Béard
- LNCMI, UPR 3228, CNRS-UGA-UPS-INSA, 31400 Toulouse, France
| | - M Cerchez
- Institute for Laser and Plasma Physics, University of Düsseldorf, 40225 Düsseldorf, Germany
| | - S N Chen
- ELI-NP, "Horia Hulubei" National Institute for Physics and Nuclear Engineering, 30 Reactorului Street, RO-077125 Bucharest-Magurele, Romania
| | - T Gangolf
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
- Institute for Laser and Plasma Physics, University of Düsseldorf, 40225 Düsseldorf, Germany
| | - S S Makarov
- Joint Institute for High Temperatures, RAS, 125412 Moscow, Russia
| | - M Ouillé
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
| | - M Safronova
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - I Yu Skobelev
- Joint Institute for High Temperatures, RAS, 125412 Moscow, Russia
- National Research Nuclear University, MEPhI, 115409 Moscow, Russia
| | - A Soloviev
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - M Starodubtsev
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - O Willi
- Institute for Laser and Plasma Physics, University of Düsseldorf, 40225 Düsseldorf, Germany
| | - S Pikuz
- Joint Institute for High Temperatures, RAS, 125412 Moscow, Russia
- National Research Nuclear University, MEPhI, 115409 Moscow, Russia
| | - J Fuchs
- LULI - CNRS, CEA, Sorbonne Université, Ecole Polytechnique, Institut Polytechnique de Paris - F-91128 Palaiseau cedex, France
- Institute of Applied Physics, RAS, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
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Relevant heating of the quiet solar corona by Alfvén waves: a result of adiabaticity breakdown. Sci Rep 2019; 9:14274. [PMID: 31582798 PMCID: PMC6776755 DOI: 10.1038/s41598-019-50820-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Accepted: 09/19/2019] [Indexed: 11/15/2022] Open
Abstract
Ion heating by Alfvén waves has been considered for long as the mechanism explaining why the solar corona has a temperature several orders of magnitude higher than the photosphere. Unfortunately, as the measured wave frequencies are much smaller than the ion cyclotron frequency, particles were expected to behave adiabatically, impeding a direct wave-particle energy transfer to take place, except through decorrelating stochastic mechanisms related to broadband wave spectra. This paper proposes a new paradigm for this mechanism by showing it is actually much simpler, more general, and very efficient. Indeed, for measured wave amplitudes in the quiet corona, ion orbits are shown to cross quasi-periodically one or several slowly pulsating separatrices in phase space. Now, a separatrix is an orbit with an infinite period, thus much longer than the pulsation one. Therefore, each separatrix crossing cancels adiabatic invariance, and yields a very strong energy transfer from the wave, and thus particle heating. This occurs whatever be the wave spectrum, even a monochromatic one. The proposed mechanism is so efficient that it might lead to a self-organized picture of coronal heating: all Alfvén waves exceeding a threshold are immediately quenched and transfer their energy to the ions.
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Vickers E, Ballai I, Erdélyi R. Propagation of Leaky MHD Waves at Discontinuities with Tilted Magnetic Field. SOLAR PHYSICS 2018; 293:139. [PMID: 30956361 PMCID: PMC6413887 DOI: 10.1007/s11207-018-1359-5] [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: 09/25/2017] [Accepted: 09/21/2018] [Indexed: 06/09/2023]
Abstract
We investigate the characteristics of magneto-acoustic surface waves propagating at a single density interface, in the presence of an inclined magnetic field. For linear wave propagation, the dispersion relation is obtained and analytical solutions are derived for small inclination angle. The inclination of the field renders the frequency of the waves complex, where the imaginary part describes wave attenuation, due to lateral energy leakage.
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Affiliation(s)
- E. Vickers
- Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield, S3 7RH UK
| | - I. Ballai
- Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield, S3 7RH UK
| | - R. Erdélyi
- Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield, S3 7RH UK
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Del Zanna G, Mason HE. Solar UV and X-ray spectral diagnostics. LIVING REVIEWS IN SOLAR PHYSICS 2018; 15:5. [PMID: 30872982 PMCID: PMC6390902 DOI: 10.1007/s41116-018-0015-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 07/12/2018] [Indexed: 06/04/2023]
Abstract
X-ray and ultraviolet (UV) observations of the outer solar atmosphere have been used for many decades to measure the fundamental parameters of the solar plasma. This review focuses on the optically thin emission from the solar atmosphere, mostly found at UV and X-ray (XUV) wavelengths, and discusses some of the diagnostic methods that have been used to measure electron densities, electron temperatures, differential emission measure (DEM), and relative chemical abundances. We mainly focus on methods and results obtained from high-resolution spectroscopy, rather than broad-band imaging. However, we note that the best results are often obtained by combining imaging and spectroscopic observations. We also mainly focus the review on measurements of electron densities and temperatures obtained from single ion diagnostics, to avoid issues related to the ionisation state of the plasma. We start the review with a short historical introduction on the main XUV high-resolution spectrometers, then review the basics of optically thin emission and the main processes that affect the formation of a spectral line. We mainly discuss plasma in equilibrium, but briefly mention non-equilibrium ionisation and non-thermal electron distributions. We also summarise the status of atomic data, which are an essential part of the diagnostic process. We then review the methods used to measure electron densities, electron temperatures, the DEM, and relative chemical abundances, and the results obtained for the lower solar atmosphere (within a fraction of the solar radii), for coronal holes, the quiet Sun, active regions and flares.
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Affiliation(s)
- Giulio Del Zanna
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA UK
| | - Helen E. Mason
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA UK
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De Moortel I, Browning P. Recent advances in coronal heating. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:20140269. [PMID: 25897095 PMCID: PMC4410557 DOI: 10.1098/rsta.2014.0269] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/03/2015] [Indexed: 05/08/2023]
Abstract
The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.
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Affiliation(s)
- Ineke De Moortel
- School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
| | - Philippa Browning
- Jodrell Bank Centre for Astrophysics, University of Manchester, Manchester M13 9PL, UK
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