This articleis missing information about Alfvén wave modes (e.g., inertial and kinetic modes) and the Alfvén Mach number. Please expand the article to include this information. Further details may exist on thetalk page.(September 2022)
Schematic illustration of the excitation of large-scale thermospheric gravity waves by Alfvén waves carried by a high-speed solar wind stream emanating from a coronal hole.[1]
An Alfvén wave is a low-frequency (compared to theion gyrofrequency) travellingoscillation of theions andmagnetic field in aplasma. The ion mass density provides theinertia and themagnetic field line tension 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 intomagnetosonic waves when the propagation is perpendicular to the magnetic field.
A cluster of double layers forming in an Alfvén wave, about a sixth of the distance from the left.Red = electrons,Green = ions,Yellow = electric potential,Orange = parallel electric field,Pink = charge density,Blue = magnetic field
The low-frequencyrelative permittivity of a magnetized plasma is given by[3]whereB is themagnetic flux density, is thespeed of light, is thepermeability of thevacuum, and the mass density is the sumover all species of charged plasma particles (electrons as well as all types of ions).Here species has number densityand mass per particle.
The phase velocity of an electromagnetic wave in such a medium isFor the case of an Alfvén wavewhereis theAlfvén wave group velocity.(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.)
If, then. On the other hand, when,. That is, at high field or low density, thegroup velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.
Neglecting the contribution of the electrons to the mass density,, where is the ionnumber density and is the mean ion mass per particle, so that
Inplasma physics, the Alfvén time is an important timescale for wave phenomena. It is related to the Alfvén velocity by:where denotes the characteristic scale of the system. For example, could be the minor radius of the torus in atokamak.
The Alfvén wave velocity in relativistic magnetohydrodynamics is[4]wheree is the total energy density of plasma particles, is the total plasma pressure, andis themagnetic pressure. In the non-relativistic limit, where, this formula reduces to the one given previously.
The study of Alfvén waves began from thecoronal heating problem, a longstanding question inheliophysics. It was unclear why the temperature of thesolar corona is hot (about one million kelvins) compared to its surface (thephotosphere), 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.
In 1942,Hannes Alfvén proposed inNature the existence of an electromagnetic-hydrodynamic wave which would carry energy from the photosphere to heat up the corona and thesolar wind. 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:
If a conducting liquid is placed in a constant magnetic field, every motion of the liquid gives rise to anE.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.[5]
This would eventually turn out to be Alfvén waves. He received the 1970Nobel Prize in Physics for this discovery.
Theconvection zone of the Sun, the region beneath the photosphere in which energy is transported primarily byconvection, is sensitive to the motion of the core due to the rotation of the Sun. Together with varyingpressure gradients beneath the surface,electromagnetic fluctuations produced in the convection zone induce random motion on the photospheric surface and produce Alfvén waves. The waves then leave the surface, travel through thechromosphere and transition zone, and interact with the ionized plasma. The wave itself carries energy and some of the electrically charged plasma.
In the early 1990s, de Pontieu[6] and Haerendel[7] suggested that Alfvén waves may also be associated with the plasma jets known asspicules. It was theorized these brief spurts of superheated gas were carried by the combined energy andmomentum of their own upward velocity, as well as the oscillating transverse motion of the Alfvén waves.
In 2007, Alfvén waves were reportedly observed for the first time traveling towards the corona by Tomczyket al., 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.[8] However, in 2011, McIntoshet al. 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.[9] 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.[10] 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'smagnetosphere is currently under debate.[11][12]
However, the above-mentioned discoveries of Alfvén waves in the complex Sun's atmosphere, starting from theHinode 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, Jesset al.[13] reported the periodic variation ofH-alpha line-width as observed bySwedish Solar Telescope (SST) abovechromospheric bright-points. They claimed first direct detection of the long-period (126–700 s), incompressible, torsional Alfvén waves in the lower solar atmosphere.
After the seminal work of Jesset al. (2009), in 2017 Srivastavaet al.[14] detected the existence of high-frequency torsional Alfvén waves in the Sun's chromospheric fine-structuredflux tubes. 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, usingspectral imaging observations, non-LTE (local thermodynamic equilibrium) inversions and magnetic field extrapolations of sunspot atmospheres, Grant et al.[15] found evidence for elliptically polarized Alfvén waves forming fast-mode shocks in the outer regions of the chromospheric umbral atmosphere. They provided quantification of the degree of physical heat provided by the dissipation of such Alfvén wave modes above active region spots.
In 2024, a paper was published in the journalScience detailing a set of observations of what turned out to be the same jet of solar wind made byParker Solar Probe andSolar Orbiter in February 2022, and implying Alfvén waves were what kept the jet's energy high enough to match the observations.[16]
1950: Alfvén publishes the first edition of his book,Cosmical Electrodynamics, detailing hydromagnetic waves, and discussing their application to both laboratory and space plasmas.
1952: Additional confirmation appears in experiments by Winston Bostick and Morton Levine with ionizedhelium.
1954: Bo Lehnert produces Alfvén waves in liquidsodium.[17]
1958: Berthold, Harris, and Hope detect Alfvén waves in the ionosphere after theArgusnuclear test, generated by the explosion, and traveling at speeds predicted by Alfvén formula.
1958: Eugene Parker suggests hydromagnetic waves in theSolar corona extending into theSolar wind.
1959: D. F. Jephcott produces Alfvén waves in a gas discharge.[18]
1959: C. H. Kelley and J. Yenser produce Alfvén waves in the ambient atmosphere.
1960: Coleman et al. report the measurement of Alfvén waves by themagnetometer aboard the Pioneer andExplorer satellites.[19]
1977: Mendis and Ip suggest the existence of hydromagnetic waves in the coma ofComet Kohoutek.[23]
1984: Roberts et al. predict the presence of standing MHD waves in the solar corona[24] and opens the field ofcoronal seismology.
1999: Aschwanden et al.[25] and Nakariakov et al. report the detection of damped transverse oscillations of solarcoronal loops observed with theextreme ultraviolet (EUV) imager on board the Transition Region And Coronal Explorer (TRACE), interpreted as standing kink (or "Alfvénic") oscillations of the loops. This confirms the theoretical prediction of Roberts et al. (1984).
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 theNational Solar Observatory, New Mexico.[26] However, these observations turned out to be kink waves of coronal plasma structures.[27]doi:10.1051/0004-6361/200911840
2007: A special issue on theHinode space observatory was released in the journalScience.[28] Alfvén wave signatures in the coronal atmosphere were observed by Cirtain et al.,[29] Okamoto et al.,[30] and De Pontieu et al.[31] By estimating the observed waves'energy density, De Pontieu et al. have shown that the energy associated with the waves is sufficient to heat thecorona and accelerate thesolar wind.
2008: Kaghashviliet al. uses driven wave fluctuations as a diagnostic tool to detect Alfvén waves in the solar corona.[32]
2009: Jess et al. detect torsional Alfvén waves in the structured Sun's chromosphere using theSwedish Solar Telescope.[13]
2011: Alfvén waves are shown to propagate in a liquid metal alloy made ofGallium.[33]
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 corona.[14]
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 authors provided quantification of the degree of physical heat provided by the dissipation of such Alfvén wave modes.[15]
2024: Alfvén waves are implied to be behind a smaller than expected energy loss in solar wind jets out as far asVenus' orbit, based onParker Solar Probe andSolar Orbiter observations only two days apart.[16]
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^Chen, F.F. (2016).Introduction to Plasma Physics and Controlled Fusion (3rd ed.). Switzerland: Springer International Publishing. pp. 55,126–131.
^abGrant, 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",Nature Physics,14 (5):480–483,arXiv:1810.07712,Bibcode:2018NatPh..14..480G,doi:10.1038/s41567-018-0058-3,S2CID119089600
^abRivera, 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.; 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".Science.385 (6712):962–966.arXiv:2409.00267.Bibcode:2024Sci...385..962R.doi:10.1126/science.adk6953.ISSN0036-8075.PMID39208109.
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^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".Phys. Fluids.23 (9): 096601.arXiv:1106.4727.Bibcode:2011PhFl...23i6601A.doi:10.1063/1.3633090.S2CID2234120.
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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",Scientific Reports,7: id.43147,Bibcode:2017NatSR...743147S,doi:10.1038/srep43147,PMC5335648,PMID28256538
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