https://en.formulasearchengine.com/w/index.php?action=history&feed=atom&title=Source-synchronousSource-synchronous - Revision history2026-09-29T07:34:55ZRevision history for this page on the wikiMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Source-synchronous&diff=6934&oldid=preven>Iyulaev: PCI Express is not really source-synchronous, it's isochornous.2014-01-23T07:12:36Z<p>PCI Express is not really source-synchronous, it's isochornous.</p>
<p><b>New page</b></p><div>{{Use dmy dates|date=June 2013}}<br />
{{Technical|date=October 2012}}<br />
<br />
In [[plasma physics]], an '''Alfvén wave''', named after [[Hannes Alfvén]], is a type of [[Magnetohydrodynamics|magnetohydrodynamic]] [[wave]] in which [[ion]]s oscillate in response to a restoring force provided by an [[Magnetic tension force|effective tension]] on the [[magnetic field]] lines.<ref>Iwai, K; Shinya, K,; Takashi, K. and Moreau, R. (2003) "Pressure change accompanying Alfvén waves in a liquid metal" [[Magnetohydrodynamics (journal)|''Magnetohydrodynamics'']] 39(3): pp. 245-250, page 245</ref><br />
<br />
==Definition==<br />
An '''Alfvén wave''' in a [[Plasma (physics)|plasma]] is a low-frequency (compared to the [[ion]] [[cyclotron frequency]]) travelling [[oscillation]] of the ions and the [[magnetic field]]. The ion mass density provides the [[inertia]] and the [[magnetic field]] line tension provides the restoring force.<br />
<br />
The wave propagates in the direction of the magnetic field, although waves exist at oblique incidence and smoothly change into the [[magnetosonic wave]] when the propagation is perpendicular to the magnetic field.<br />
<br />
The motion of the ions and the [[perturbation]] of the magnetic field are in the same direction and [[transverse wave|transverse]] to the direction of propagation. The wave is [[dispersion relation|dispersionless]].<br />
<br />
==Alfvén velocity==<br />
<!-- linked from redirect [[Alfvén velocity]] --><br />
<!-- linked from redirect [[Alfven velocity]] --><br />
<br />
The low-frequency [[relative permittivity]] <math>\epsilon\,</math> of a magnetized plasma is given by<br />
<br />
:<math>\epsilon = 1 + \frac{1}{B^2}c^2 \mu_0 \rho</math><br />
<br />
where <math>B\,</math> is the [[magnetic field strength]], <math>c\,</math> is the [[speed of light]], <math>\mu_0\,</math> is the [[Permeability (electromagnetism)|permeability]] of the [[vacuum]], and <math>\rho = \Sigma n_s m_s\,</math> is the total mass density of the charged plasma particles. Here, <math>s\,</math> goes over all plasma species, both electrons and (few types of) ions.<br />
<br />
Therefore, the phase velocity of an electromagnetic wave in such a medium is<br />
<br />
:<math>v = \frac{c}{\sqrt{\epsilon}} = \frac{c}{\sqrt{1 + \frac{1}{B^2}c^2 \mu_0 \rho}}</math><br />
<br />
or<br />
<br />
:<math>v = \frac{v_A}{\sqrt{1 + \frac{1}{c^2}v_A^2}}</math><br />
<br />
where<br />
:<math>v_A = \frac{B}{\sqrt{\mu_0 \rho}}</math><br />
<br />
is the '''Alfvén velocity'''. If <math>v_A \ll c</math>, then <math>v \approx v_A</math>. On the other hand, when <math>v_A \gg c</math>, then <math>v \approx c</math>. That is, at high field or low density, the velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.<br />
<br />
Neglecting the contribution of the electrons to the mass density and assuming that there is a single ion species, we get<br />
<br />
:<math>v_A = \frac{B}{\sqrt{\mu_0 n_i m_i}}~~</math> in SI<br />
:<math>v_A = \frac{B}{\sqrt{4 \pi n_i m_i}}~~</math> in CGS<br />
:<math>v_A \approx (2.18\times10^{11}\,\mbox{cm/s})\,(m_i/m_p)^{-1/2}\,(n_i/{\rm cm}^{-3})^{-1/2}\,(B/{\rm gauss})</math><br />
<br />
where <math>n_i\,</math> is the ion number density and <math>m_i\,</math> is the ion mass.<br />
<br />
==Alfvén time==<br />
In [[plasma physics]], the Alfvén time <math> \tau_A </math> is an important timescale for wave phenomena. It is related to the Alfvén velocity by:<br />
:<math>\tau_A = \frac{a}{v_A}</math><br />
<br />
where <math> a </math> denotes the characteristic scale of the system, for example <math> a </math> is the minor radius of the torus in a [[tokamak]].<br />
<br />
==Relativistic case==<br />
The general Alfvén wave velocity is defined by Gedalin (1993):<ref>{{Citation |last=Gedalin |first=M. |title=Linear waves in relativistic anisotropic magnetohydrodynamics |journal=Physical Review E |volume=47 |issue=6 |pages=4354–4357 |year=1993 |doi=10.1103/PhysRevE.47.4354 |bibcode = 1993PhRvE..47.4354G }}</ref><br />
<br />
:<math>v = \frac{c}{\sqrt{1 + \frac{e + P}{2 P_m}}}</math><br />
<br />
where<br />
<br />
<math>e\,</math> is the total energy density of plasma particles, <math>P\,</math> is the total plasma pressure, and <math>P_m = \frac{1}{2\mu_0}B^2\,</math> is the [[magnetic field pressure]]. In the non-relativistic limit <math>P \ll e \approx \rho c^2</math>, and we immediately get the expression from the previous section.<br />
<br />
==Heating the Corona==<br />
The [[Coronal heating problem]] is a longstanding question in astrophysics. It is unknown why the sun's corona lives in a temperature range higher than one million degrees while the sun's surface (photosphere) is only a few thousand degrees in temperature. Natural intuition would predict a decrease in temperature while getting farther away from a heat source, but it is theorized that the photosphere, influenced by the sun's magnetic fields, emits certain waves which carry energy (i.e. heat) to the corona and solar wind. It is important to note that because the density of the corona is quite smaller than the photosphere, the heat and energy level of the photosphere is much higher than the corona. Temperature is only the average speed of a species, and less energy is required to heat fewer particles to higher temperatures in the coronal atmosphere. <br />
Alfven first proposed the existence of an electromagnetic-hydrodynamic wave in 1942 in Nature. He claimed the sun had all necessary criteria to support these waves and that they may in turn be responsible for sun spots. From his paper:<br />
<br />
{{Quote|text=If a conducting liquid is placed in a constant magnetic field, every motion of the liquid gives rise to an E.M.F. which produces electric currents. Owing to the magnetic field, these currents give mechanical forces which change the state of motion of the liquid. Thus a kind of combined electromagnetic-hydrodynamic wave is produced.|sign=Hannes Alfvén, ''Existence of Electromagnetic-Hydrodynamic Waves'' |source=<ref>{{cite journal |title=Existence of Electromagnetic-Hydrodynamic Waves |author=Hannes Alfvén|journal=Nature |volume=150 |issue=3805 |pages=405–406 |year=1942 |bibcode = 1942Natur.150..405K |doi = 10.1038/150405a0}}</ref>}}<br />
<br />
Beneath the sun's photosphere lies the convection zone. The rotation of the sun, as well as varying pressure gradients beneath the surface, produces the periodic electromagnetism in the convection zone which can be observed on the sun's surface. This random motion of the surface gives rise to Alfven waves. The waves travel through the chromosphere and transition zone and interact with much of the ionized plasma. The wave itself carries energy as well as some of the electrically charged plasma. De Pointe<ref>{{cite web |url = http://www.mpe.mpg.de/Highlights/FB1997/h97-10-02.html.|title = Chromospheric Spicules driven by Alfvén waves |author = Bart de Pontieu |publisher = Max-Planck-Institut für extraterrestrische Physik |date = 18 December 1997 |accessdate= 1 April 2012 }}</ref> and Haerendel <ref>{{cite journal |title=Weakly damped Alfven waves as drivers of solar chromospheric spicules|author=Gerhard Haerendel|journal=Nature |volume=360 |pages=241–243 |year=1992 |bibcode = 1992Natur.360..241H |doi = 10.1038/360241a0 }}</ref> suggested in the early 1990s that Alfven waves may also be associated with the plasma jets known as spicules. It was theorized these short lasting spurts of superheated gas were carried by the combined energy and momentum of their own upward velocity as well as the oscillating transverse motion of the Alfven waves. In 2007, Alfven waves were reportedly observed for the first time traveling towards the corona by Tomcyzk et al., but their predictions could not conclude that the energy carried by the Alfven waves were sufficient enough to heat the corona to its enormous temperatures, for the observed amplitudes of the waves were not high enough.<ref>{{cite journal |title=Alfven waves in the solar corona |author=Tomczyk, S., McIntosh, S.W., Keil, S.L., Judge, P.G., Schad, T., Seeley, D.H., Edmondson, J.|journal=Science |volume=31 |issue=5842 |pages=1192–1196 |year=2007 }}</ref> However, in 2011, McIntosh et al. reported the observation of highly energetic Alfven waves combined with energetic spicules which could sustain heating the corona to its million Kelvin temperature. These observed amplitudes (20.0&nbsp;km/s against 2007's observed 0.5&nbsp;km/s) contained over one hundred times more energy than the ones observed in 2007.<ref>{{cite journal |title=Alfvenic waves with sufficient energy to power the quiet solar corona and fast solar wind. |author=McIntosh, et al.|journal=Nature |volume=475 |issue=7357 |page=477 |year=2011 |bibcode = 2011Natur.475..477M |doi = 10.1038/nature10235 }}</ref> The short period of the waves also allowed more energy transfer into the coronal atmosphere. The 50,000&nbsp;km long spicules may also play a part in accelerating the solar wind past the corona.<ref>{{cite web |url = http://www.nasa.gov/mission_pages/sdo/news/alfven-waves.html|title = SDO Spots Extra Energy in the Sun's Corona. |author = Karen Fox |publisher = NASA |date = 27 July 2011 |accessdate= 2 April 2012 }}</ref><br />
<br />
==History==<br />
How this phenomenon became understood<br />
*1942: Alfvén suggests the existence of ''electromagnetic-hydromagnetic'' waves in a paper published in ''Nature''.<br />
*1949: Laboratory experiments by S. Lundquist produce such waves in magnetized mercury, with a velocity that approximated Alfvén's formula.<br />
*1949: [[Enrico Fermi]] uses Alfvén waves in his theory of [[cosmic ray]]s. According to Alex Dessler in a 1970 ''Science'' journal article, Fermi had heard a lecture at the University of Chicago, Fermi nodded his head exclaiming "of course" and the next day, the physics world said "of course".<br />
*1950: Alfvén publishes the first edition of his book, ''Cosmical Electrodynamics'', detailing hydromagnetic waves, and discussing their application to both laboratory and space plasmas.<br />
*1952: Additional confirmation appears in experiments by Winston Bostick and Morton Levine with ionized helium<br />
*1954: [[Bo Lehnert]] produces Alfvén waves in liquid sodium<br />
*1958: [[Eugene Parker]] suggests hydromagnetic waves in the [[interstellar medium]]<br />
*1958: Berthold, Harris, and Hope detect Alfvén waves in the ionosphere after the [[Operation Argus|Argus]] [[nuclear test]], generated by the explosion, and traveling at speeds predicted by Alfvén formula.<br />
*1958: Eugene Parker suggests hydromagnetic waves in the [[Solar corona]] extending into the [[Solar wind]].<br />
*1959: D. F. Jephcott produces Alfvén waves in a gas discharge<br />
*1959: C. H. Kelley and J. Yenser produce Alfvén waves in the ambient atmosphere.<br />
*1960: Coleman, ''et al.'', report the measurement of Alfvén waves by the [[magnetometer]] aboard the Pioneer and Explorer satellites<br />
*1960: Sugiura suggests evidence of hydromagnetic waves in the Earth's magnetic field<br />
*1961: Normal Alfvén modes and resonances in liquid sodium are studied by [http://aero-comlab.stanford.edu/jameson/publication_list.html Jameson]<br />
*1966: R.O.Motz generates and observes Alfven waves in mercury<br />
*1970 Hannes Alfvén wins the 1970 [[Nobel Prize in physics]] for "fundamental work and discoveries in [[Magnetohydrodynamics|magneto-hydrodynamics]] with fruitful applications in different parts of [[plasma physics]]"<br />
*1973: Eugene Parker suggests hydromagnetic waves in the [[intergalactic medium]]<br />
*1974: Hollweg suggests the existence of hydromagnetic waves in [[interplanetary space]]<br />
*1974: Ip and Mendis suggests the existence of hydromagnetic waves in the coma of [[Comet Kohoutek]].<br />
*1999: Aschwanden, ''et al.'' and Nakariakov, ''et al.'' report the detection of damped transverse oscillations of solar [[coronal loops]] observed with the [[Extreme ultraviolet|EUV]] imager on board the Transition Region And Coronal Explorer ([[TRACE]]), interpreted as standing kink (or "Alfvénic") oscillations of the loops.<br />
*2007: Tomczyk, ''et al.'', report the detection of Alfvénic waves in images of the solar corona with the Coronal Multi-Channel Polarimeter (CoMP) instrument at the [[National Solar Observatory]], New Mexico. These waves were interpreted as propagating kink waves by Van Doorsselaere et al. (2008)<br />
*2007: Alfvén wave discoveries appear in articles by Jonathan Cirtain and colleagues, Takenori J. Okamoto and colleagues, and Bart De Pontieu and colleagues. De Pontieu's team proposed that the energy associated with the waves is sufficient to heat the [[corona]] and accelerate the [[solar wind]]. These results appear in a special collection of 10 articles, by scientists in Japan, [[Europe]] and the United States, in the 7 December issue of the journal ''[[Science (journal)|Science]]''. It was demonstrated that those waves should be interpreted in terms of kink waves of coronal plasma structures by Van Doorsselaere, ''et al.'' (2008); Ofman and Wang (2008); and Vasheghani Farahani, ''et al.'' (2009).<br />
*2011: Experimental evidence of Alfvén wave propagation in a Gallium alloy<ref>{{cite journal |title=Experimental evidence of Alfvén wave propagation in a Gallium alloy |author=Thierry Alboussière, Philippe Cardin, François Debray, Patrick La Rizza, Jean-Paul Masson, Franck Plunian, Adolfo Ribeiro, Denys Schmitt |journal=Phys. Fluids |volume=23 |issue=9 |page=096601 |year=2011 |doi=10.1063/1.3633090|bibcode = 2011PhFl...23i6601A |arxiv = 1106.4727 }}</ref><br />
<br />
==See also==<br />
*[[Electrohydrodynamics]]<br />
*[[Plasma stability]]<br />
*[[Shocks and discontinuities (magnetohydrodynamics)]]<br />
*[[Computational magnetohydrodynamics]]<br />
*[[Ferrofluid]]<br />
*[[MHD generator]]<br />
*[[MHD sensor]]<br />
*[[Magnetic flow meter]]<br />
*[[Magnetohydrodynamic turbulence]]<br />
*[[Molten salt]]<br />
*[[Electromagnetic pump]]<br />
*[[List of plasma (physics) articles]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==Further reading==<br />
*{{Citation |last=Alfvén |first=H. |title=Existence of electromagnetic-hydrodynamic waves |journal=[[Nature (journal)|Nature]] |year=1942 |volume=150 |issue=3805 |pages=405–406 |doi=10.1038/150405d0 |bibcode = 1942Natur.150..405A }}<br />
*{{Citation |last=Alfvén |first=H. |author-mask=——— |title=Cosmic Plasma |location=Holland |publisher=Reidel |year=1981 |isbn=90-277-1151-8 }}<br />
*{{Citation |last=Aschwanden |first=M. J. |last2=Fletcher |first2=L. |last3=Schrijver |first3=C. J. |last4=Alexander |first4=D. |title=Coronal Loop Oscillations Observed with the Transition Region and Coronal Explorer |journal=The Astrophysical Journal |volume=520 |issue=2 |pages=880–894 |year=1999 |doi=10.1086/307502 |bibcode=1999ApJ...520..880A}}<br />
*{{Citation |last=Berthold |first=W. K. |last2=Harris |first2=A. K. |last3=Hope |first3=H. J. |title=World-Wide Effects of Hydromagnetic Waves Due to Argus |year=1960 |journal=[[Journal of Geophysical Research]] |volume=65 |issue=8 |pages=2233–2239 |doi=10.1029/JZ065i008p02233 |bibcode=1960JGR....65.2233B}}<br />
*{{Citation |last=Bostick |first=Winston H. |last2=Levine |first2=Morton A. |title=Experimental Demonstration in the Laboratory of the Existence of Magneto-Hydrodynamic Waves in Ionized Helium |journal=[[Physical Review]] |year=1952 |volume=87 |issue=4 |pages=671 |doi=10.1103/PhysRev.87.671 |bibcode = 1952PhRv...87..671B }}<br />
*{{Citation |last=Coleman |first=P. J., Jr. |last2=Sonett |first2=C. P. |last3=Judge |first3=D. L. |last4=Smith |first4=E. J. |title=Some Preliminary Results of the Pioneer V Magnetometer Experiment |journal=Journal of Geophysical Research |year=1960 |volume=65 |issue=6 |pages=1856–1857 |doi=10.1029/JZ065i006p01856 |bibcode=1960JGR....65.1856C}}<br />
*{{Citation |last=Cramer |first=N. F. |last2=Vladimirov |first2=S. V. |title=Alfvén Waves in Dusty Interstellar Clouds |year=1997 |journal=Publications of the Astronomical Society of Australia |volume=14 |issue=2 |pages=170–178 |url=http://www.atnf.csiro.au/pasa/14_2/cramer/paper/ |bibcode = 1997PASA...14..170C |doi = 10.1071/AS97170 }}<br />
*{{Citation |last=Dessler |first=A. J. |title=Swedish iconoclast recognized after many years of rejection and obscurity |journal=Science |year=1970 |volume=170 |issue=3958 |pages=604–606 |doi=10.1126/science.170.3958.604 |bibcode = 1970Sci...170..604D }}<br />
*{{Citation |last=Falceta-Gonçalves |first=D. |last2=Jatenco-Pereira |first2=V. |title=The Effects of Alfvén Waves and Radiation Pressure in Dust Winds of Late-Type Stars |journal=Astrophysical Journal |volume=576 |issue=2 |pages=976–981 |year=2002 |doi=10.1086/341794 |bibcode=2002ApJ...576..976F|arxiv = astro-ph/0207342 }}<br />
*{{Citation |last=Fermi |first=E. |title=On the Origin of the Cosmic Radiation |journal=Physical Review |year=1949 |volume=75 |issue=8 |pages=1169–1174 |doi=10.1103/PhysRev.75.1169 |bibcode = 1949PhRv...75.1169F }}<br />
*{{Citation |last=Galtier |first=S. |title=A weak turbulence theory for incompressible magnetohydrodynamics |journal=J. Plasma Physics |year=2000 |volume=63 |issue=5 |pages=447–488 |doi=10.1017/S0022377899008284 |bibcode = 2000JPlPh..63..447G |arxiv = astro-ph/0008148 }}<br />
*{{Citation |last=Hollweg |first=J. V. |title=Hydromagnetic waves in interplanetary space |journal=Astronomical Society of the Pacific, Publications |year=1974 |volume=86 |issue=October 1974 |pages=561–594 |doi=10.1086/129646 |bibcode=1974PASP...86..561H}}<br />
*{{Citation |last=Ip |first=W.-H. |last2=Mendis |first2=D. A. |title=The cometary magnetic field and its associated electric currents |journal=Icarus |year=1975 |volume=26 |issue=4 |pages=457–461 |doi=10.1016/0019-1035(75)90115-3 |bibcode=1975Icar...26..457I}}<br />
*{{Citation |last=Jephcott |first=D. F. |title=Alfvén waves in a gas discharge |journal=Nature |year=1959 |volume=183 |issue=4676 |pages=1652–1654 |doi=10.1038/1831652a0 |bibcode = 1959Natur.183.1652J }}<br />
*{{Citation |last=Lehnert |first=Bo |title=Magneto-Hydrodynamic Waves in Liquid Sodium |journal=Physical Review |year=1954 |volume=94 |issue=4 |pages=815–824 |doi=10.1103/PhysRev.94.815 |bibcode = 1954PhRv...94..815L }}<br />
*{{Citation |last=Lundquist |first=S. |title=Experimental Investigations of Magneto-Hydrodynamic Waves |journal=Physical Review |year=1949 |volume=76 |issue=12 |pages=1805–1809 |doi=10.1103/PhysRev.76.1805 |bibcode = 1949PhRv...76.1805L }}<br />
*{{Citation |last=Mancuso |first=S. |last2=Spangler |first2=S. R. |title=Coronal Faraday Rotation Observations: Measurements and Limits on Plasma Inhomogeneities |year=1999 |journal=The Astrophysical Journal |volume=525 |issue=1 |pages=195–208 |bibcode = 1999ApJ...525..195M |doi = 10.1086/307896 }}<br />
*{{Citation |last=Motz |first=R. O. |title=Alfven Wave Generation in a Spherical System |journal=Physics of Fluids |volume=9 |issue=2 |pages=411–412 |year=1966 |doi=10.1063/1.1761687 |bibcode = 1966PhFl....9..411M }}<br />
*{{Citation |last=Nakariakov |first=V. M. |last2=Ofman |first2=L. |last3=Deluca |first3=E. E. |last4=Roberts |first4=B. |last5=Davila |first5=J. M. |title=TRACE observation of damped coronal loop oscillations: Implications for coronal heating |journal=Science |volume=285 |issue=5429 |pages=862–864 |year=1999 |doi=10.1126/science.285.5429.862 |pmid=10436148 |bibcode=1999Sci...285..862N}}<br />
*{{Citation |last=Ofman |first=L.|last2=Wang |first2=T. J. |title=Hinode observations of transverse waves with flows in coronal loops |journal=Astronomy and Astrophysics |volume=482 |issue=2 |pages=L9-L12 |year=2008 |doi=10.1051/0004-6361:20079340 |bibcode=2008A&A...482L...9O}}<br />
*{{Citation |last=Otani |first=N. F. |title=The Alfvén ion-cyclotron instability, simulation theory and techniques |journal=Journal of Computational Physics |volume=78 |issue=2 |pages=251–277 |year=1988a |doi=10.1016/0021-9991(88)90049-6 |bibcode = 1988JCoPh..78..251O }}<br />
*{{Citation |last=Otani |first=N. F. |author-mask=——— |title=Application of Nonlinear Dynamical Invariants in a Single Electromagnetic Wave to the Study of the Alfvén-Ion-Cyclotron Instability |journal=Physics of Fluids |volume=31 |issue=6 |pages=1456–1464 |year=1988b |doi=10.1063/1.866736 |bibcode = 1988PhFl...31.1456O }}<br />
*{{Citation |last=Parker |first=E. N. |title=Hydromagnetic Waves and the Acceleration of Cosmic Rays |journal=Physical Review |year=1955 |volume=99 |issue=1 |pages=241–253 |doi=10.1103/PhysRev.99.241 |bibcode = 1955PhRv...99..241P }}<br />
*{{Citation |last=Parker |first=E. N. |author-mask=——— |title=Suprathermal Particle Generation in the Solar Corona |journal=Astrophysical Journal |year=1958 |volume=128 |issue= |pages=677 |doi=10.1086/146580 |bibcode=1958ApJ...128..677P}}<br />
*{{Citation |last=Parker |first=E. N. |author-mask=——— |title=Extragalactic Cosmic Rays and the Galactic Magnetic Field |journal=Astrophysics and Space Science |year=1973 |volume=24 |issue=1 |pages=279–288 |doi=10.1007/BF00648691 |bibcode=1973Ap&SS..24..279P}}<br />
*{{Citation |last=Silberstein |first=M. |last2=Otani |first2=N. F. |title=Computer simulation of Alfvén waves and double layers along auroral magnetic field lines |journal=Journal of Geophysical Research |volume=99 |issue=A4 |pages=6351–6365 |year=1994 |url=http://otani.vet.cornell.edu/papers/silberstein_otani_1994.pdf |doi=10.1029/93JA02963 |bibcode=1994JGR....99.6351S}}<br />
*{{Citation |last=Sugiura |first=Masahisa |title=Some Evidence of Hydromagnetic Waves in the Earth's Magnetic Field |journal=Physical Review Letters |year=1961 |volume=6 |issue=6 |pages=255–257 |doi=10.1103/PhysRevLett.6.255 |bibcode=1961PhRvL...6..255S}}<br />
*{{Citation |last=Tomczyk |first=S. |last2=McIntosh |first2=S. W. |last3=Keil |first3=S. L. |last4=Judge |first4=P. G. |last5=Schad |first5=T. |last6=Seeley |first6=D. H. |last7=Edmondson |first7=J. |title=Waves in the Solar Corona |journal=Science |volume=317 |issue=5842 |pages=1192–1196 |year=2007 |doi=10.1126/science.1143304 |bibcode = 2007Sci...317.1192T }}<br />
*{{Citation |last=Van Doorsselaere |first=T. |last2=Nakariakov |first2=V. M. |last3=Verwichte |first3=E.|title=Detection of Waves in the Solar Corona: Kink or Alfvén? |journal=The Astrophysical Journal |volume=676 |issue=1 |pages=L73-L75 |year=2008 |doi= 10.1086/587029 |bibcode=2008ApJ...676L..73V}}<br />
*{{Citation |last=Vasheghani Farahani |first=S. |last2=Van Doorsselaere |first2=T. |last3=Verwichte |first3=E. |last4=Nakariakov |first4=V. M. |title=Propagating transverse waves in soft X-ray coronal jets |journal=Astronomy and Astrophysics |volume=498 |issue=2 |pages=L29-L32 |year=2009 |doi= 10.1051/0004-6361/200911840 |bibcode=2009A&A...498L..29V}}<br />
<br />
==External links==<br />
*[http://www.space.com/scienceastronomy/070830_sun_waves.html Mysterious Solar Ripples Detected] Dave Mosher 2 September 2007 Space.com<br />
*[http://www.eurekalert.org/pub_releases/2007-12/aaft-hmd113007.php EurekAlert! notification of 7 December 2007 ''Science'' special issue]<br />
*[http://www.eurekalert.org/pub_releases/2009-03/uos-sfs032009.php EurekAlert! notification: "Scientists find solution to solar puzzle"]<br />
<br />
{{DEFAULTSORT:Alfven Wave}}<br />
[[Category:Waves in plasmas]]</div>en>Iyulaev