1641:. reported the observation of highly energetic Alfvén waves combined with energetic spicules which could sustain heating the corona to its million-kelvin temperature. These observed amplitudes (20.0 km/s against 2007's observed 0.5 km/s) contained over one hundred times more energy than the ones observed in 2007. The short period of the waves also allowed more energy transfer into the coronal atmosphere. The 50,000 km-long spicules may also play a part in accelerating the solar wind past the corona. Alfvén waves are routinely observed in solar wind, in particular in fast solar wind streams. The role of Alfvénic oscillations in the interaction between fast solar wind and the Earth's
1519:
1172:
38:
3522:
105:
957:
1947:
2018: Using spectral imaging observations, non-LTE inversions and magnetic field extrapolations of sunspot atmospheres, Grant et al. found evidence for elliptically polarized Alfvén waves forming fast-mode shocks in the outer regions of the chromospheric umbral atmosphere. For the first time, these
2634:
Rivera, Yeimy J.; Badman, Samuel T.; Stevens, Michael L.; Verniero, Jaye L.; Stawarz, Julia E.; Shi, Chen; Raines, Jim M.; Paulson, Kristoff W.; Owen, Christopher J.; Niembro, Tatiana; Louarn, Philippe; Livi, Stefano A.; Lepri, Susan T.; Kasper, Justin C.; Horbury, Timothy S.; Halekas, Jasper S.;
1688:
observations, non-LTE (local thermodynamic equilibrium) inversions and magnetic field extrapolations of sunspot atmospheres, Grant et al. found evidence for elliptically polarized Alfvén waves forming fast-mode shocks in the outer regions of the chromospheric umbral atmosphere. They provided
185:
provides the restoring force. Alfvén waves propagate in the direction of the magnetic field, and the motion of the ions and the perturbation of the magnetic field are transverse to the direction of propagation. However, Alfvén waves existing at oblique incidences will smoothly change into
73:
1557:), which is only a few thousand kelvins. Intuitively, it would make sense to see a decrease in temperature when moving away from a heat source, but this does not seem to be the case even though the photosphere is denser and would generate more heat than the corona.
4682:
Grant, Samuel D. T.; Jess, David B.; Zaqarashvili, Teimuraz V.; Beck, Christian; Socas-Navarro, Hector; Aschwanden, Markus J.; Keys, Peter H.; Christian, Damian J.; Houston, Scott J.; Hewitt, Rebecca L. (2018), "Alfvén Wave
Dissipation in the Solar Chromosphere",
2578:
Grant, Samuel D. T.; Jess, David B.; Zaqarashvili, Teimuraz V.; Beck, Christian; Socas-Navarro, Hector; Aschwanden, Markus J.; Keys, Peter H.; Christian, Damian J.; Houston, Scott J.; Hewitt, Rebecca L. (2018), "Alfvén Wave
Dissipation in the Solar Chromosphere",
4635:
Srivastava, Abhishek K.; Shetye, Juie; Murawski, Krzysztof; Doyle, John Gerard; Stangalini, Marco; Scullion, Eamon; Ray, Tom; Wójcik, Dariusz Patryk; Dwivedi, Bhola N. (2017), "High-frequency torsional Alfvén waves as an energy source for coronal heating",
590:
725:. (The formula for the phase velocity assumes that the plasma particles are moving at non-relativistic speeds, the mass-weighted particle velocity is zero in the frame of reference, and the wave is propagating parallel to the magnetic field vector.)
109:
1167:{\displaystyle v_{A}\approx \left(2.18\times 10^{11}\,{\text{cm}}\,{\text{s}}^{-1}\right)\left({\frac {m_{i}}{m_{p}}}\right)^{-{\frac {1}{2}}}\left({\frac {n_{i}}{1~{\text{cm}}^{-3}}}\right)^{-{\frac {1}{2}}}\left({\frac {B}{1~{\text{G}}}}\right).}
113:
111:
108:
106:
112:
1637:., but their predictions could not conclude that the energy carried by the Alfvén waves was sufficient to heat the corona to its enormous temperatures, for the observed amplitudes of the waves were not high enough. However, in 2011, McIntosh
1652:
era in 2007 for the next 10 years, mostly fall in the realm of Alfvénic waves essentially generated as a mixed mode due to transverse structuring of the magnetic and plasma properties in the localized flux tubes. In 2009, Jess
110:
3351:
Pontieu, B. De; McIntosh, S. W.; Carlsson, M.; Hansteen, V. H.; Tarbell, T. D.; Schrijver, C. J.; Title, A. M.; Shine, R. A.; Tsuneta, S. (7 December 2007). "Chromospheric Alfvénic Waves Strong Enough to Power the Solar Wind".
3460:
Thierry
Alboussière; Philippe Cardin; François Debray; Patrick La Rizza; Jean-Paul Masson; Franck Plunian; Adolfo Ribeiro; Denys Schmitt (2011). "Experimental evidence of Alfvén wave propagation in a Gallium alloy".
666:
3281:
Okamoto, T. J.; Tsuneta, S.; Berger, T. E.; Ichimoto, K.; Katsukawa, Y.; Lites, B. W.; Nagata, S.; Shibata, K.; Shimizu, T. (7 December 2007). "Coronal
Transverse Magnetohydrodynamic Waves in a Solar Prominence".
296:
1943:
2017: 3D numerical modelling performed by
Srivastava et al. show that the high-frequency (12–42 mHz) Alfvén waves detected by the Swedish Solar Telescope can carry substantial energy to heat the Sun's inner
1582:
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
719:
1379:
501:
3222:
Cirtain, J. W.; Golub, L.; Lundquist, L.; Ballegooijen, A. van; Savcheva, A.; Shimojo, M.; DeLuca, E.; Tsuneta, S.; Sakao, T. (7 December 2007). "Evidence for Alfvén Waves in Solar X-ray Jets".
1462:
2510:
Srivastava, Abhishek Kumar; Shetye, Juie; Murawski, Krzysztof; Doyle, John Gerard; Stangalini, Marco; Scullion, Eamon; Ray, Tom; Wójcik, Dariusz Patryk; Dwivedi, Bhola N. (3 March 2017).
1257:
419:
1508:
2430:
Jess, David B.; Mathioudakis, Mihalis; Erdélyi, Robert; Crockett, Philip J.; Keenan, Francis P.; Christian, Damian J. (20 March 2009). "Alfvén Waves in the Lower Solar
Atmosphere".
898:
825:
1684:. They discovered that these high-frequency waves carry substantial energy capable of heating the Sun's corona and also originating the supersonic solar wind. In 2018, using
792:
4573:
Jess, David B.; Mathioudakis, Mihalis; Erdélyi, Robert; Crockett, Philip J.; Keenan, Francis P.; Christian, Damian J. (2009), "Alfvén Waves in the Lower Solar
Atmosphere",
853:. That is, at high field or low density, the group velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.
4174:
Nakariakov, V. M.; Ofman, L.; Deluca, E. E.; Roberts, B.; Davila, J. M. (1999), "TRACE observation of damped coronal loop oscillations: Implications for coronal heating",
226:
107:
2029:
759:
1210:
355:
2635:
Dewey, Ryan M.; De Marco, Rossana; Bale, Stuart D. (30 August 2024). "In situ observations of large-amplitude Alfvén waves heating and accelerating the solar wind".
851:
952:
925:
493:
466:
3702:
Bostick, Winston H.; Levine, Morton A. (1952), "Experimental
Demonstration in the Laboratory of the Existence of Magneto-Hydrodynamic Waves in Ionized Helium",
1887:
2007: Tomczyk et al. reported the detection of Alfvénic waves in images of the solar corona with the
Coronal Multi-Channel Polarimeter (CoMP) instrument at the
1615:
produced in the convection zone induce random motion on the photospheric surface and produce Alfvén waves. The waves then leave the surface, travel through the
1403:
1297:
1277:
324:
1669:
bright-points. They claimed first direct detection of the long-period (126–700 s), incompressible, torsional Alfvén waves in the lower solar atmosphere.
595:
4268:
Otani, N. F. (1988b), "Application of
Nonlinear Dynamical Invariants in a Single Electromagnetic Wave to the Study of the Alfvén-Ion-Cyclotron Instability",
439:
1907:. Alfvén wave signatures in the coronal atmosphere were observed by Cirtain et al., Okamoto et al., and De Pontieu et al. By estimating the observed waves'
231:
3084:
Tomczyk, S.; McIntosh, S. W.; Keil, S. L.; Judge, P. G.; Schad, T.; Seeley, D. H.; Edmondson, J. (31 August 2007). "Alfvén Waves in the Solar Corona".
671:
1314:
4543:
Vasheghani Farahani, S.; Van Doorsselaere, T.; Verwichte, E.; Nakariakov, V. M. (2009), "Propagating transverse waves in soft X-ray coronal jets",
2756:
Sonett, C. P.; Smith, E. J.; Judge, D. L.; Coleman, P. J. (15 February 1960). "Current Systems in the Vestigial Geomagnetic Field: Explorer VI".
1574:. He claimed that the sun had all the necessary criteria to support these waves and they may in turn be responsible for sun spots. He stated:
3620:
1884:), interpreted as standing kink (or "Alfvénic") oscillations of the loops. This confirms the theoretical prediction of Roberts et al. (1984).
3732:
Coleman, P. J. Jr.; Sonett, C. P.; Judge, D. L.; Smith, E. J. (1960), "Some Preliminary Results of the Pioneer V Magnetometer Experiment",
3830:
Falceta-Gonçalves, D.; Jatenco-Pereira, V. (2002), "The Effects of Alfvén Waves and Radiation Pressure in Dust Winds of Late-Type Stars",
1728:
1949: Laboratory experiments by S. Lundquist produce such waves in magnetized mercury, with a velocity that approximated Alfvén's formula.
2236:
Tomczyk, S.; McIntosh, S.W.; Keil, S.L.; Judge, P.G.; Schad, T.; Seeley, D.H.; Edmondson, J. (2007). "Alfven waves in the solar corona".
1619:
and transition zone, and interact with the ionized plasma. The wave itself carries energy and some of the electrically charged plasma.
4453:
Tomczyk, S.; McIntosh, S. W.; Keil, S. L.; Judge, P. G.; Schad, T.; Seeley, D. H.; Edmondson, J. (2007), "Waves in the Solar Corona",
1979:
1408:
3558:
2167:
2396:"Further investigation of the effect of upstream solar-wind fluctuations on solar-wind/magnetosphere coupling: Is the effect real?"
1622:
In the early 1990s, de Pontieu and Haerendel suggested that Alfvén waves may also be associated with the plasma jets known as
1570:
the existence of an electromagnetic-hydrodynamic wave which would carry energy from the photosphere to heat up the corona and the
1518:
1215:
4108:
Mancuso, S.; Spangler, S. R. (1999), "Coronal Faraday Rotation Observations: Measurements and Limits on Plasma Inhomogeneities",
3530:
368:
3674:
1689:
quantification of the degree of physical heat provided by the dissipation of such Alfvén wave modes above active region spots.
358:
2050:
2004:
2287:
McIntosh; et al. (2011). "Alfvenic waves with sufficient energy to power the quiet solar corona and fast solar wind".
4497:
Van Doorsselaere, T.; Nakariakov, V. M.; Verwichte, E. (2008), "Detection of Waves in the Solar Corona: Kink or Alfvén?",
1666:
1612:
182:
2049:
Iwai, K; Shinya, K,; Takashi, K. and Moreau, R. (2003) "Pressure change accompanying Alfvén waves in a liquid metal"
1948:
authors provided quantification of the degree of physical heat provided by the dissipation of such Alfvén wave modes.
1888:
1706:
in February 2022, and implying Alfvén waves were what kept the jet's energy high enough to match the observations.
4785:
3540:
1951:
2024: Alfvén waves are implied to be behind a smaller than expected energy loss in solar wind jets out as far as
585:{\displaystyle v={\frac {c}{\sqrt {\varepsilon }}}={\frac {c}{\sqrt {1+{\dfrac {c^{2}\mu _{0}\rho }{B^{2}}}}}}}
3672:
Berthold, W. K.; Harris, A. K.; Hope, H. J. (1960), "World-Wide Effects of Hydromagnetic Waves Due to Argus",
1872:
1999: Aschwanden et al. and Nakariakov et al. report the detection of damped transverse oscillations of solar
1471:
1680:. detected the existence of high-frequency torsional Alfvén waves in the Sun's chromospheric fine-structured
1930:
1662:
1648:
However, the above-mentioned discoveries of Alfvén waves in the complex Sun's atmosphere, starting from the
1542:
1865:
1984: Roberts et al. predict the presence of standing MHD waves in the solar corona and opens the field of
1578:
If a conducting liquid is placed in a constant magnetic field, every motion of the liquid gives rise to an
4514:
1830:
1633:
In 2007, Alfvén waves were reportedly observed for the first time traveling towards the corona by Tomczyk
1588:
142:
859:
303:
206:
1749:
1952: Additional confirmation appears in experiments by Winston Bostick and Morton Levine with ionized
1746:, detailing hydromagnetic waves, and discussing their application to both laboratory and space plasmas.
4210:
Ofman, L.; Wang, T. J. (2008), "Hinode observations of transverse waves with flows in coronal loops",
797:
4702:
4645:
4592:
4552:
4506:
4462:
4434:
4406:
4363:
4333:
4305:
4277:
4249:
4219:
4183:
4155:
4117:
4089:
4061:
4025:
3997:
3988:
Ip, W.-H.; Mendis, D. A. (1975), "The cometary magnetic field and its associated electric currents",
3967:
3931:
3885:
3849:
3803:
3773:
3741:
3713:
3683:
3645:
3584:
3480:
3424:
3361:
3301:
3231:
3156:
3093:
3042:
2990:
2935:
2890:
2843:
2800:
2791:
Sugiura, Masahisa (December 1961). "Evidence of low-frequency hydromagnetic waves in the exosphere".
2765:
2714:
2679:
2598:
2523:
2449:
2296:
2245:
2202:
2132:
2089:
1989:
1984:
1852:
1845:
1834:
4761:
4519:
3794:
Dessler, A. J. (1970), "Swedish iconoclast recognized after many years of rejection and obscurity",
764:
421:
over all species of charged plasma particles (electrons as well as all types of ions). Here species
4770:
2193:
Gerhard Haerendel (1992). "Weakly damped Alfven waves as drivers of solar chromospheric spicules".
1999:
1911:, De Pontieu et al. have shown that the energy associated with the waves is sufficient to heat the
1891:, New Mexico. However, these observations turned out to be kink waves of coronal plasma structures.
1877:
1768:
1579:
194:
76:
A cluster of double layers forming in an Alfvén wave, about a sixth of the distance from the left.
52:
211:
4718:
4692:
4624:
4582:
4532:
4486:
4391:
4379:
4135:
4041:
3947:
3921:
3901:
3865:
3839:
3661:
3600:
3496:
3470:
3442:
3393:
3333:
3291:
3263:
3125:
3066:
2959:
2738:
2614:
2588:
2489:
2439:
2320:
2269:
2218:
2148:
1956:
1898:
1892:
1866:
1699:
1649:
1626:. It was theorized these brief spurts of superheated gas were carried by the combined energy and
4425:
Sugiura, Masahisa (1961), "Some Evidence of Hydromagnetic Waves in the Earth's Magnetic Field",
4240:
Otani, N. F. (1988a), "The Alfvén ion-cyclotron instability, simulation theory and techniques",
1816:
1630:
of their own upward velocity, as well as the oscillating transverse motion of the Alfvén waves.
731:
2339:
1929:
2009: Jess et al. detect torsional Alfvén waves in the structured Sun's chromosphere using the
1607:, is sensitive to the motion of the core due to the rotation of the sun. Together with varying
1188:
4755:
4671:
4616:
4478:
4199:
3819:
3616:
3385:
3377:
3325:
3317:
3255:
3247:
3204:
3174:
3117:
3109:
3058:
3008:
2951:
2908:
2859:
2816:
2730:
2652:
2557:
2539:
2481:
2473:
2312:
2261:
2105:
1974:
1926:
uses driven wave fluctuations as a diagnostic tool to detect Alfvén waves in the solar corona.
1903:
1823:
1694:
1608:
1465:
333:
187:
158:
2978:
4710:
4661:
4653:
4608:
4600:
4560:
4556:
4524:
4470:
4442:
4414:
4371:
4367:
4341:
4313:
4285:
4257:
4227:
4223:
4191:
4163:
4125:
4097:
4069:
4033:
4005:
3975:
3939:
3893:
3857:
3811:
3781:
3749:
3721:
3691:
3653:
3592:
3575:
3488:
3432:
3369:
3309:
3239:
3164:
3101:
3050:
2998:
2943:
2898:
2851:
2808:
2773:
2722:
2687:
2644:
2606:
2547:
2531:
2465:
2457:
2407:
2374:
2304:
2253:
2210:
2140:
2097:
2024:
1698:
detailing a set of observations of what turned out to be the same jet of solar wind made by
1685:
1566:
1561:
830:
174:
130:
1603:
of the sun, the region beneath the photosphere in which energy is transported primarily by
930:
903:
4392:"Computer simulation of Alfvén waves and double layers along auroral magnetic field lines"
3704:
3026:
Aschwanden, Markus J.; Fletcher, Lyndsay; Schrijver, Carolus J.; Alexander, David (1999).
1775:
1600:
72:
2171:
4706:
4649:
4596:
4510:
4466:
4438:
4410:
4337:
4309:
4281:
4253:
4187:
4159:
4121:
4093:
4065:
4029:
4001:
3971:
3935:
3912:
Galtier, S. (2000), "A weak turbulence theory for incompressible magnetohydrodynamics",
3889:
3853:
3807:
3777:
3745:
3717:
3687:
3649:
3588:
3484:
3428:
3365:
3305:
3235:
3160:
3097:
3046:
2994:
2939:
2894:
2847:
2804:
2769:
2718:
2683:
2602:
2527:
2453:
2300:
2249:
2206:
2136:
2093:
51:
Please expand the article to include this information. Further details may exist on the
4730:
4666:
3437:
3412:
2552:
2511:
1908:
1859:
1838:
1536:
1388:
1282:
1262:
1212:
is an important timescale for wave phenomena. It is related to the Alfvén velocity by:
1182:
471:
444:
327:
309:
170:
146:
122:
2926:
Mendis, D. A.; Ip, W. -H. (March 1977). "The ionospheres and plasma tails of comets".
49:
about Alfvén wave modes (e.g., inertial and kinetic modes) and the Alfvén Mach number.
4779:
4722:
4383:
4261:
4139:
4009:
3665:
3446:
3337:
3070:
2963:
2618:
2080:
Gedalin, M. (1993). "Linear waves in relativistic anisotropic magnetohydrodynamics".
2069:(3rd ed.). Switzerland: Springer International Publishing. pp. 55, 126–131.
2009:
1960:
1873:
1812:
1961: Sugiura suggests evidence of hydromagnetic waves in the Earth's magnetic field.
1764:
1703:
1642:
1623:
4628:
4536:
4490:
4045:
3951:
3631:"Coronal Loop Oscillations Observed with the Transition Region and Coronal Explorer"
3397:
3267:
3129:
3028:"Coronal Loop Oscillations Observed with the Transition Region and Coronal Explorer"
2742:
2493:
2273:
2222:
4354:
Parker, E. N. (1973), "Extragalactic Cosmic Rays and the Galactic Magnetic Field",
4080:
Lundquist, S. (1949), "Experimental Investigations of Magneto-Hydrodynamic Waves",
3905:
3761:
3604:
3500:
2324:
2152:
1912:
1802:
1785:
1778:
1732:
1616:
1550:
1546:
424:
4565:
3869:
1781:, generated by the explosion, and traveling at speeds predicted by Alfvén formula.
4296:
Parker, E. N. (1955), "Hydromagnetic Waves and the Acceleration of Cosmic Rays",
4232:
4195:
3815:
1774:
1958: Berthold, Harris, and Hope detect Alfvén waves in the ionosphere after the
2019:
1858:
1977: Mendis and Ip suggest the existence of hydromagnetic waves in the coma of
1798:
1959: C. H. Kelley and J. Yenser produce Alfvén waves in the ambient atmosphere.
1554:
162:
134:
3192:
2512:"High-frequency torsional Alfvén waves as an energy source for coronal heating"
4714:
4446:
4324:
Parker, E. N. (1958), "Suprathermal Particle Generation in the Solar Corona",
3943:
2777:
2610:
2412:
2395:
2379:
2362:
2014:
1994:
1916:
1806:
1789:
1736:
1604:
1571:
1523:
3630:
3381:
3321:
3251:
3208:
3178:
3113:
3062:
3027:
3012:
2955:
2912:
2863:
2820:
2734:
2656:
2543:
2477:
2101:
4604:
4474:
4101:
3897:
3753:
3695:
3373:
3313:
3243:
3105:
2812:
2648:
2461:
2257:
1681:
17:
4675:
4620:
4482:
4317:
4203:
4073:
3823:
3725:
3389:
3329:
3259:
3121:
2691:
2561:
2485:
2316:
2265:
1720:
37:
4612:
2670:
Lehnert, Bo (15 May 1954). "Magneto-Hydrodynamic Waves in Liquid Sodium".
2469:
2363:"The influence of solar wind variability on magnetospheric ULF wave power"
2123:
Alfvén, Hannes (1942). "Existence of electromagnetic–hydrodynamic waves".
2109:
1936:
2011: Alfvén waves are shown to propagate in a liquid metal alloy made of
3926:
3844:
3629:
Aschwanden, M. J.; Fletcher, L.; Schrijver, C. J.; Alexander, D. (1999),
1815:
1961: Normal Alfvén modes and resonances in liquid sodium are studied by
1627:
3411:
Kaghashvili, Edisher Kh.; Quinn, Richard A.; Hollweg, Joseph V. (2009).
2308:
1587:
This would eventually turn out to be Alfvén waves. He received the 1970
661:{\displaystyle v={\frac {v_{A}}{\sqrt {1+{\dfrac {v_{A}^{2}}{c^{2}}}}}}}
4375:
2947:
2834:
Motz, Robin O. (1966). "Alfvén Wave Generation in a Spherical System".
1937:
1658:
1300:
178:
4657:
4418:
4167:
4037:
3958:
Hollweg, J. V. (1974), "Hydromagnetic waves in interplanetary space",
3573:
Alfvén, H. (1942), "Existence of electromagnetic-hydrodynamic waves",
3492:
2855:
2726:
2535:
291:{\displaystyle \varepsilon =1+{\frac {c^{2}\,\mu _{0}\,\rho }{B^{2}}}}
4289:
3596:
2214:
2144:
1851:
1974: J. V. Hollweg suggests the existence of hydromagnetic waves in
1757:
1750:
362:
4771:
EurekAlert! notification: "Scientists find solution to solar puzzle"
4146:
Motz, R. O. (1966), "Alfven Wave Generation in a Spherical System",
3786:
4697:
4528:
4346:
4130:
4052:
Lehnert, Bo (1954), "Magneto-Hydrodynamic Waves in Liquid Sodium",
3980:
3861:
3657:
3169:
3144:
3054:
3003:
2903:
2878:
2705:
JEPHCOTT, D. F. (13 June 1959). "Alfvén Waves in a Gas Discharge".
2593:
2361:
Pokhotelov, D.; Rae, I.J.; Murphy, K.R.; Mann, I.R. (8 June 2015).
2170:. Max-Planck-Institut für extraterrestrische Physik. Archived from
1801:
1960: Coleman et al. report the measurement of Alfvén waves by the
4587:
3475:
3296:
2444:
1952:
1881:
1880:(EUV) imager on board the Transition Region And Coronal Explorer (
1517:
856:
Neglecting the contribution of the electrons to the mass density,
498:
The phase velocity of an electromagnetic wave in such a medium is
103:
71:
1311:
The Alfvén wave velocity in relativistic magnetohydrodynamics is
1553:
is hot (about one million kelvins) compared to its surface (the
714:{\displaystyle v_{A}\equiv {\frac {B}{\sqrt {\mu _{0}\,\rho }}}}
3143:
Doorsselaere, T. Van; Nakariakov, V. M.; Verwichte, E. (2008).
1374:{\displaystyle v={\frac {c}{\sqrt {1+{\dfrac {e+P}{2P_{m}}}}}}}
3515:
1795:
1959: D. F. Jephcott produces Alfvén waves in a gas discharge.
166:
138:
31:
1522:
Magnetic waves, called Alfvén S-waves, flow from the base of
1279:
denotes the characteristic scale of the system. For example,
190:
when the propagation is perpendicular to the magnetic field.
4016:
Jephcott, D. F. (1959), "Alfvén waves in a gas discharge",
3876:
Fermi, E. (1949), "On the Origin of the Cosmic Radiation",
141:
oscillate in response to a restoring force provided by an
3145:"Detection of Waves in the Solar Corona: Kink or Alfvén?"
3413:"Driven Waves as a Diagnostics Tool in the Solar Corona"
1844:
1973: Eugene Parker suggests hydromagnetic waves in the
1822:
1966: R. O. Motz generates and observes Alfvén waves in
1784:
1958: Eugene Parker suggests hydromagnetic waves in the
3960:
Publications of the Astronomical Society of the Pacific
2883:
Publications of the Astronomical Society of the Pacific
1742:
1950: Alfvén publishes the first edition of his book,
474:
447:
427:
3766:
Publications of the Astronomical Society of Australia
1474:
1411:
1391:
1337:
1317:
1285:
1265:
1218:
1191:
960:
933:
906:
862:
833:
800:
767:
734:
674:
625:
598:
539:
504:
371:
336:
312:
234:
214:
2629:
2627:
2067:
Introduction to Plasma Physics and Controlled Fusion
1510:, this formula reduces to the one given previously.
157:An Alfvén wave is a low-frequency (compared to the
1502:
1456:
1397:
1373:
1291:
1271:
1251:
1204:
1166:
946:
919:
892:
845:
819:
786:
753:
713:
660:
584:
487:
460:
433:
413:
349:
318:
290:
220:
2030:Shocks and discontinuities (magnetohydrodynamics)
1837:with fruitful applications in different parts of
1756:1954: Bo Lehnert produces Alfvén waves in liquid
1385:is the total energy density of plasma particles,
1457:{\displaystyle P_{m}={\frac {B^{2}}{2\mu _{0}}}}
2977:Roberts, B.; Edwin, P. M.; Benz, A. O. (1984).
2168:"Chromospheric Spicules driven by Alfvén waves"
1692:In 2024, a paper was published in the journal
2879:"Hydromagnetic Waves in Interplanetary Space"
1537:Stellar corona § Coronal heating problem
8:
4762:EurekAlert! notification of 7 December 2007
2340:"SDO spots extra energy in the Sun's corona"
1549:. It was unclear why the temperature of the
1299:could be the minor radius of the torus in a
1252:{\displaystyle \tau _{A}={\frac {a}{v_{A}}}}
3762:"Alfvén Waves in Dusty Interstellar Clouds"
954:is the mean ion mass per particle, so that
414:{\displaystyle \rho =\sum _{s}n_{s}m_{s},}
4696:
4665:
4586:
4564:
4518:
4345:
4231:
4129:
3979:
3925:
3843:
3785:
3760:Cramer, N. F.; Vladimirov, S. V. (1997),
3559:Learn how and when to remove this message
3474:
3436:
3295:
3168:
3002:
2902:
2592:
2551:
2443:
2411:
2400:Frontiers in Astronomy and Space Sciences
2378:
2166:Bart de Pontieu (18 December 1997).
1833:for "fundamental work and discoveries in
1541:The study of Alfvén waves began from the
1494:
1473:
1445:
1431:
1425:
1416:
1410:
1390:
1358:
1336:
1324:
1316:
1284:
1264:
1241:
1232:
1223:
1217:
1196:
1190:
1149:
1137:
1121:
1117:
1101:
1096:
1082:
1076:
1059:
1055:
1043:
1033:
1027:
1008:
1003:
1001:
996:
995:
989:
965:
959:
938:
932:
911:
905:
884:
879:
873:
861:
832:
805:
799:
778:
766:
739:
733:
704:
698:
688:
679:
673:
646:
636:
631:
624:
611:
605:
597:
570:
556:
546:
538:
526:
511:
503:
479:
473:
452:
446:
426:
402:
392:
382:
370:
341:
335:
311:
280:
271:
265:
260:
254:
247:
233:
213:
4731:"Alfven wave propagation in dusty atoms"
1503:{\displaystyle P\ll e\approx \rho c^{2}}
2042:
1715:1942: Alfvén suggests the existence of
1468:. In the non-relativistic limit, where
4758:Dave Mosher 2 September 2007 Space.com
4390:Silberstein, M.; Otani, N. F. (1994),
2573:
2571:
2505:
2503:
2425:
2423:
1657:. reported the periodic variation of
1595:Experimental studies and observations
7:
1767:suggests hydromagnetic waves in the
177:. The ion mass density provides the
1735:uses Alfvén waves in his theory of
228:of a magnetized plasma is given by
1980:Computational magnetohydrodynamics
1829:1970: Hannes Alfvén wins the 1970
1405:is the total plasma pressure, and
893:{\displaystyle \rho =n_{i}\,m_{i}}
814:
365:, and the mass density is the sum
25:
4756:Mysterious Solar Ripples Detected
3149:The Astrophysical Journal Letters
2394:Borovsky, J.E. (5 January 2023).
1963:observations only two days apart.
4242:Journal of Computational Physics
3520:
820:{\displaystyle v_{A}\to \infty }
36:
4399:Journal of Geophysical Research
3734:Journal of Geophysical Research
3675:Journal of Geophysical Research
2793:Journal of Geophysical Research
1893:doi:10.1051/0004-6361/200911840
1672:After the seminal work of Jess
592:For the case of an Alfvén wave
4356:Astrophysics and Space Science
2005:Magnetohydrodynamic turbulence
1719:waves in a paper published in
927:is the ion number density and
837:
811:
787:{\displaystyle v\approx v_{A}}
1:
3543:and help improve the section.
1897:2007: A special issue on the
1717:electromagnetic-hydromagnetic
1676:. (2009), in 2017 Srivastava
1545:, a longstanding question in
4262:10.1016/0021-9991(88)90049-6
4196:10.1126/science.285.5429.862
4010:10.1016/0019-1035(75)90115-3
3816:10.1126/science.170.3958.604
3438:10.1088/0004-637x/703/2/1318
2055:39(3): pp. 245-250, page 245
1901:was released in the journal
1613:electromagnetic fluctuations
221:{\displaystyle \varepsilon }
4566:10.1051/0004-6361/200911840
1645:is currently under debate.
1531:The coronal heating problem
183:magnetic field line tension
92:= parallel electric field,
4802:
4545:Astronomy and Astrophysics
4233:10.1051/0004-6361:20079340
4212:Astronomy and Astrophysics
2338:Karen Fox (27 July 2011).
1889:National Solar Observatory
1722:Nature 150, 405–406 (1942)
1661:line-width as observed by
1534:
794:. On the other hand, when
754:{\displaystyle v_{A}\ll c}
723:Alfvén wave group velocity
4715:10.1038/s41567-018-0058-3
4499:The Astrophysical Journal
4447:10.1103/PhysRevLett.6.255
4326:The Astrophysical Journal
4110:The Astrophysical Journal
3966:(October 1974): 561–594,
3944:10.1017/S0022377899008284
3832:The Astrophysical Journal
3638:The Astrophysical Journal
3417:The Astrophysical Journal
3203:(5856). 7 December 2007.
3035:The Astrophysical Journal
2983:The Astrophysical Journal
2778:10.1103/PhysRevLett.4.161
2611:10.1038/s41567-018-0058-3
2413:10.3389/fspas.2022.975135
2380:10.5194/angeo-33-697-2015
1205:{\displaystyle \tau _{A}}
27:Low-frequency plasma wave
2102:10.1103/PhysRevE.47.4354
1899:Hinode space observatory
1744:Cosmical Electrodynamics
350:{\displaystyle \mu _{0}}
4605:10.1126/science.1168680
4557:2009A&A...498L..29V
4475:10.1126/science.1143304
4427:Physical Review Letters
4368:1973Ap&SS..24..279P
4224:2008A&A...482L...9O
4102:10.1103/PhysRev.76.1805
3898:10.1103/PhysRev.75.1169
3754:10.1029/JZ065i006p01856
3696:10.1029/JZ065i008p02233
3374:10.1126/science.1151747
3314:10.1126/science.1145447
3244:10.1126/science.1147050
3106:10.1126/science.1143304
2877:Hollweg, J. V. (1974).
2813:10.1029/jz066i012p04087
2758:Physical Review Letters
2649:10.1126/science.adk6953
2462:10.1126/science.1168680
2258:10.1126/science.1143304
1931:Swedish Solar Telescope
1805:aboard the Pioneer and
1663:Swedish Solar Telescope
1543:coronal heating problem
4318:10.1103/PhysRev.99.241
4074:10.1103/PhysRev.94.815
3726:10.1103/PhysRev.87.671
2979:"Coronal oscillations"
2692:10.1103/PhysRev.94.815
1831:Nobel Prize in physics
1589:Nobel Prize in Physics
1585:
1527:
1504:
1458:
1399:
1375:
1293:
1273:
1253:
1206:
1168:
948:
921:
894:
847:
846:{\displaystyle v\to c}
821:
788:
755:
715:
662:
586:
489:
468:and mass per particle
462:
435:
415:
351:
320:
292:
222:
118:
101:
88:= electric potential,
47:is missing information
3193:"Science: 318 (5856)"
2928:Space Science Reviews
1835:magneto-hydrodynamics
1611:beneath the surface,
1576:
1535:Further information:
1521:
1505:
1459:
1400:
1376:
1294:
1274:
1254:
1207:
1169:
949:
947:{\displaystyle m_{i}}
922:
920:{\displaystyle n_{i}}
895:
848:
822:
789:
756:
716:
663:
587:
490:
463:
436:
416:
352:
321:
304:magnetic flux density
293:
223:
207:relative permittivity
116:
75:
2052:Magnetohydrodynamics
1990:Electromagnetic pump
1985:Electrohydrodynamics
1853:interplanetary space
1846:intergalactic medium
1591:for this discovery.
1472:
1409:
1389:
1315:
1283:
1263:
1216:
1189:
958:
931:
904:
860:
831:
798:
765:
732:
672:
596:
502:
472:
445:
425:
369:
334:
310:
232:
212:
4707:2018NatPh..14..480G
4650:2017NatSR...743147S
4597:2009Sci...323.1582J
4581:(5921): 1582–1585,
4511:2008ApJ...676L..73V
4467:2007Sci...317.1192T
4461:(5842): 1192–1196,
4439:1961PhRvL...6..255S
4411:1994JGR....99.6351S
4338:1958ApJ...128..677P
4310:1955PhRv...99..241P
4282:1988PhFl...31.1456O
4254:1988JCoPh..78..251O
4188:1999Sci...285..862N
4160:1966PhFl....9..411M
4122:1999ApJ...525..195M
4094:1949PhRv...76.1805L
4066:1954PhRv...94..815L
4030:1959Natur.183.1652J
4024:(4676): 1652–1654,
4002:1975Icar...26..457I
3972:1974PASP...86..561H
3936:2000JPlPh..63..447G
3890:1949PhRv...75.1169F
3854:2002ApJ...576..976F
3808:1970Sci...170..604D
3778:1997PASA...14..170C
3746:1960JGR....65.1856C
3718:1952PhRv...87..671B
3688:1960JGR....65.2233B
3650:1999ApJ...520..880A
3615:, Holland: Reidel,
3611:Alfvén, H. (1981),
3589:1942Natur.150..405A
3485:2011PhFl...23i6601A
3429:2009ApJ...703.1318K
3366:2007Sci...318.1574D
3360:(5856): 1574–1577.
3306:2007Sci...318.1577O
3290:(5856): 1577–1580.
3236:2007Sci...318.1580C
3230:(5856): 1580–1582.
3161:2008ApJ...676L..73V
3098:2007Sci...317.1192T
3092:(5842): 1192–1196.
3047:1999ApJ...520..880A
2995:1984ApJ...279..857R
2940:1977SSRv...20..145M
2895:1974PASP...86..561H
2848:1966PhFl....9..411M
2805:1961JGR....66.4087S
2770:1960PhRvL...4..161S
2719:1959Natur.183.1652J
2713:(4676): 1652–1654.
2684:1954PhRv...94..815L
2603:2018NatPh..14..480G
2528:2017NatSR...743147S
2454:2009Sci...323.1582J
2438:(5921): 1582–1585.
2367:Annales Geophysicae
2309:10.1038/nature10235
2301:2011Natur.475..477M
2250:2007Sci...317.1192T
2244:(5842): 1192–1196.
2207:1992Natur.360..241H
2137:1942Natur.150..405A
2094:1993PhRvE..47.4354G
2065:Chen, F.F. (2016).
2000:Magnetic flow meter
1915:and accelerate the
1878:extreme ultraviolet
1788:extending into the
1769:interstellar medium
1710:Historical timeline
641:
441:has number density
117:Kinetic Alfvén wave
4638:Scientific Reports
4376:10.1007/BF00648691
2948:10.1007/bf02186863
2516:Scientific Reports
1957:Parker Solar Probe
1955:' orbit, based on
1922:2008: Kaghashvili
1876:observed with the
1867:coronal seismology
1700:Parker Solar Probe
1609:pressure gradients
1528:
1500:
1454:
1395:
1371:
1366:
1289:
1269:
1249:
1202:
1185:, the Alfvén time
1164:
944:
917:
890:
843:
817:
784:
751:
711:
658:
653:
627:
582:
577:
488:{\textstyle m_{s}}
485:
461:{\textstyle n_{s}}
458:
431:
411:
387:
347:
316:
288:
218:
205:The low-frequency
188:magnetosonic waves
119:
102:
96:= charge density,
4729:Murtaza, Ghulam.
4658:10.1038/srep43147
4419:10.1029/93JA02963
4405:(A4): 6351–6365,
4270:Physics of Fluids
4182:(5429): 862–864,
4168:10.1063/1.1761687
4148:Physics of Fluids
4088:(12): 1805–1809,
4038:10.1038/1831652a0
3914:J. Plasma Physics
3802:(3958): 604–606,
3622:978-90-277-1151-9
3583:(3805): 405–406,
3569:
3568:
3561:
3493:10.1063/1.3633090
2856:10.1063/1.1761687
2836:Physics of Fluids
2799:(12): 4087–4095.
2727:10.1038/1831652a0
2643:(6712): 962–966.
2536:10.1038/srep43147
2295:(7357): 477–480.
2201:(6401): 241–243.
2131:(3805): 405–406.
2082:Physical Review E
1466:magnetic pressure
1452:
1398:{\displaystyle P}
1369:
1368:
1365:
1307:Relativistic case
1292:{\displaystyle a}
1272:{\displaystyle a}
1247:
1155:
1152:
1148:
1129:
1111:
1099:
1094:
1067:
1049:
1006:
999:
709:
708:
656:
655:
652:
580:
579:
576:
521:
520:
378:
319:{\displaystyle c}
286:
193:Alfvén waves are
159:ion gyrofrequency
143:effective tension
114:
70:
69:
16:(Redirected from
4793:
4786:Waves in plasmas
4745:
4743:
4741:
4735:
4725:
4700:
4678:
4669:
4631:
4590:
4569:
4568:
4539:
4522:
4493:
4449:
4421:
4396:
4386:
4350:
4349:
4320:
4292:
4290:10.1063/1.866736
4276:(6): 1456–1464,
4264:
4236:
4235:
4206:
4170:
4142:
4133:
4104:
4076:
4048:
4012:
3984:
3983:
3954:
3929:
3927:astro-ph/0008148
3908:
3884:(8): 1169–1174,
3872:
3847:
3845:astro-ph/0207342
3826:
3790:
3789:
3756:
3740:(6): 1856–1857,
3728:
3698:
3682:(8): 2233–2239,
3668:
3635:
3625:
3607:
3597:10.1038/150405d0
3564:
3557:
3553:
3550:
3544:
3539:Please read the
3535:may need cleanup
3524:
3523:
3516:
3505:
3504:
3478:
3457:
3451:
3450:
3440:
3408:
3402:
3401:
3348:
3342:
3341:
3299:
3278:
3272:
3271:
3219:
3213:
3212:
3189:
3183:
3182:
3172:
3140:
3134:
3133:
3081:
3075:
3074:
3032:
3023:
3017:
3016:
3006:
2974:
2968:
2967:
2923:
2917:
2916:
2906:
2874:
2868:
2867:
2831:
2825:
2824:
2788:
2782:
2781:
2753:
2747:
2746:
2702:
2696:
2695:
2667:
2661:
2660:
2631:
2622:
2621:
2596:
2575:
2566:
2565:
2555:
2507:
2498:
2497:
2447:
2427:
2418:
2417:
2415:
2391:
2385:
2384:
2382:
2358:
2352:
2351:
2349:
2347:
2335:
2329:
2328:
2284:
2278:
2277:
2233:
2227:
2226:
2215:10.1038/360241a0
2190:
2184:
2183:
2181:
2179:
2163:
2157:
2156:
2145:10.1038/150405d0
2120:
2114:
2113:
2088:(6): 4354–4357.
2077:
2071:
2070:
2062:
2056:
2047:
2025:Plasma stability
1686:spectral imaging
1509:
1507:
1506:
1501:
1499:
1498:
1463:
1461:
1460:
1455:
1453:
1451:
1450:
1449:
1436:
1435:
1426:
1421:
1420:
1404:
1402:
1401:
1396:
1384:
1380:
1378:
1377:
1372:
1370:
1367:
1364:
1363:
1362:
1349:
1338:
1329:
1325:
1298:
1296:
1295:
1290:
1278:
1276:
1275:
1270:
1258:
1256:
1255:
1250:
1248:
1246:
1245:
1233:
1228:
1227:
1211:
1209:
1208:
1203:
1201:
1200:
1173:
1171:
1170:
1165:
1160:
1156:
1154:
1153:
1150:
1146:
1138:
1132:
1131:
1130:
1122:
1116:
1112:
1110:
1109:
1108:
1100:
1097:
1092:
1087:
1086:
1077:
1070:
1069:
1068:
1060:
1054:
1050:
1048:
1047:
1038:
1037:
1028:
1021:
1017:
1016:
1015:
1007:
1004:
1000:
997:
994:
993:
970:
969:
953:
951:
950:
945:
943:
942:
926:
924:
923:
918:
916:
915:
899:
897:
896:
891:
889:
888:
878:
877:
852:
850:
849:
844:
826:
824:
823:
818:
810:
809:
793:
791:
790:
785:
783:
782:
760:
758:
757:
752:
744:
743:
720:
718:
717:
712:
710:
703:
702:
693:
689:
684:
683:
667:
665:
664:
659:
657:
654:
651:
650:
640:
635:
626:
617:
616:
615:
606:
591:
589:
588:
583:
581:
578:
575:
574:
565:
561:
560:
551:
550:
540:
531:
527:
522:
516:
512:
494:
492:
491:
486:
484:
483:
467:
465:
464:
459:
457:
456:
440:
438:
437:
432:
420:
418:
417:
412:
407:
406:
397:
396:
386:
356:
354:
353:
348:
346:
345:
325:
323:
322:
317:
301:
297:
295:
294:
289:
287:
285:
284:
275:
270:
269:
259:
258:
248:
227:
225:
224:
219:
115:
100:= magnetic field
99:
95:
91:
87:
83:
79:
65:
62:
56:
40:
32:
21:
4801:
4800:
4796:
4795:
4794:
4792:
4791:
4790:
4776:
4775:
4752:
4739:
4737:
4733:
4728:
4681:
4634:
4572:
4542:
4520:10.1.1.460.1896
4496:
4452:
4424:
4394:
4389:
4353:
4323:
4298:Physical Review
4295:
4267:
4239:
4209:
4173:
4145:
4107:
4082:Physical Review
4079:
4054:Physical Review
4051:
4015:
3987:
3957:
3911:
3878:Physical Review
3875:
3829:
3793:
3787:10.1071/AS97170
3759:
3731:
3705:Physical Review
3701:
3671:
3633:
3628:
3623:
3610:
3572:
3565:
3554:
3548:
3545:
3538:
3531:Further reading
3525:
3521:
3514:
3512:Further reading
3509:
3508:
3459:
3458:
3454:
3410:
3409:
3405:
3350:
3349:
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2174:on 16 July 2002
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201:Alfvén velocity
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4750:External links
4748:
4747:
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4691:(5): 480–483,
4685:Nature Physics
4679:
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4505:(1): L73–L75,
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2581:Nature Physics
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3541:editing guide
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2010:MHD generator
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1562:Hannes Alfvén
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131:Hannes Alfvén
128:
124:
80:= electrons,
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48:
45:This article
43:
39:
34:
33:
30:
19:
4763:
4738:. Retrieved
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4644:: id.43147,
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4637:
4578:
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