Alfvén wave

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An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.

An Alfvén wave in a plasma is a traveling 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. 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. The motion of the ions and the perturbation of the magnetic field are in the same direction and transverse to the direction of propagation. The wave is dispersionless with a speed of

$v_A = \frac{B}{\sqrt{\mu_0 n_i m_i}}\,$ in SI

$v_A = \frac{B}{\sqrt{4 \pi n_i m_i}}\,$ in cgs

$\qquad \ = (2.18\times10^{11}\,\mbox{cm/s})\,(m_i/m_p)^{-1/2}\,(n_i/{\rm cm}^{-3})^{-1/2}\,(B/{\rm gauss})$

where $v_A\,$ is the velocity of the Alfvén wave, B is the magnetic field strength, $\mu_0\,$ is the permeability of the plasma, $n_i\,$ is the ion number density, and $m_i\,$ is the ion mass. At high field or low density, the Alfvén speed approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.

[edit] History

1942: Alfvén theorises the existence of electromagnetic-hydromagnetic waves in a paper published in Nature.
1949: Laboratory experiments by S. Lundquist produce such waves in magnetised mercury, with a velocity that approximated Alfvén's formula.
1949: Enrico Fermi uses Alfvén waves in his theory of cosmic rays. 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".
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 ionized helium
1954: Bo Lehnert produces Alfvén waves in liquid sodium
1958: Eugene Parker suggests hydromagnetic waves in the interstellar medium
1958: Berthold, Harris, and Hope detect Alfvén waves in the ionosphere after the Argus nuclear test, generated by the explosion, and travelling at speeds predicted by Alfvén formula.
1958: Eugene Parker suggests hydromagnetic waves in the Solar corona extending into the Solar wind.
1959: D. F. Jephcott produces Alfvén waves in a gas discharge
1960: Coleman, et al, report the measurement of Alfvén waves by the magnetometer aboard the Pioneer and Explorer satellites
1960: Sugiura suggests evidence of hydromagnetic waves in the Earth's magnetic field
1966: R.O.Motz generates and observes Alfven waves in mercury
1970 Hannes Alfvén wins the 1970 Nobel Prize in physics for "for fundamental work and discoveries in magneto-hydrodynamics with fruitful applications in different parts of plasma physics"
1973: Eugene Parker suggests hydromagnetic waves in the intergalactic medium
1974: Hollweg suggests the existence of hydromagnetic waves in interplanetary space
1974: Ip and Mendis suggests the existence of hydromagnetic waves in the coma of Comet Kohoutek.
2007: Tomczyk, et al, report the detection of Alfvén waves in images of the solar corona with the Coronal Multi-Channel Polarimeter (CoMP) instrument at the National Solar Observatory, New Mexico.
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 also shows 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.

[edit] Further reading

Alfvén, H. "Cosmic Plasma". Holland. 1981.
Alfvén, H. "Existence of electromagnetic-hydrodynamic waves", Nature (1942) Vol. 150, pp. 405
Berthold, W. K.; Harris, A. K.; Hope, H. J., "World-Wide Effects of Hydromagnetic Waves Due to Argus" (1960), Journal of Geophysical Research, Vol. 65, p.2233
Bostick, Winston H.; Levine, Morton A., "Experimental Demonstration in the Laboratory of the Existence of Magneto-Hydrodynamic Waves in Ionized Helium", Physical Review (1952), vol. 87, Issue 4, pp. 671-671
Coleman, P. J., Jr.; Sonett, C. P.; Judge, D. L.; Smith, E. J., "Some Preliminary Results of the Pioneer V Magnetometer Experiment", Journal of Geophysical Research (1960), Vol. 65, p.1856
Dessler, A. J., "Swedish iconoclast recognized after many years of rejection and obscurity," Science (1970) , vol. 170, p. 604
Fermi, E., "On the Origin of the Cosmic Radiation", Physical Review (1949), vol. 75, Issue 8, pp. 1169-1174
Hollweg, J. V., "Hydromagnetic waves in interplanetary space", Astronomical Society of the Pacific, Publications (1974), vol. 86, Oct. 1974, p. 561-594.
Ip, W.-H.; Mendis, D. A., "The cometary magnetic field and its associated electric currents", Icarus (1975), vol. 26, Dec. 1975, p. 457-461.
Jephcott, D.F., "Alfvén waves in a gas discharge", Nature, (1959) vol.183, p.1653
Lehnert, Bo, "Magneto-Hydrodynamic Waves in Liquid Sodium", Physical Review (1954), vol. 94, Issue 4, pp. 815-824
Lundquist, S., "Experimental Investigations of Magneto-Hydrodynamic Waves", Physical Review (1949), vol. 76, Issue 12, pp. 1805-1809
Otani, N. F., "Application of Nonlinear Dynamical Invariants in a Single Electromagnetic Wave to the Study of the Alfvén-Ion-Cyclotron Instability", Physics of Fluids 31, 1456-1464 (1988).
Parker, E. N.,

"Suprathermal Particle Generation in the Solar Corona", Astrophysical Journal (1958), vol. 128, p.677
"Hydromagnetic Waves and the Acceleration of Cosmic Rays", Physical Review (1955), vol. 99, Issue 1, pp. 241-253
"Extragalactic Cosmic Rays and the Galactic Magnetic Field", Astrophysics and Space Science (1973), Vol. 24, p.279

Silberstein, M., and N. F. Otani, "Computer simulation of Alfvén waves and double layers along auroral magnetic field lines", Journal of Geophysical Research 99, 6351-6365 (1994). (PDF)
Sugiura, Masahisa, "Some Evidence of Hydromagnetic Waves in the Earth's Magnetic Field", Physical Review Letters (1961), vol. 6, Issue 6, pp. 255-257
Cramer, N. F., and S. V. Vladimirov, "Alfvén Waves in Dusty Interstellar Clouds". PASA, 14 (2).
Otani, N. F., "The Alfvén ion-cyclotron instability, simulation theory and techniques". Journal of Computational Physics 78, 251-277 (1988).
Falceta-Gonçalves, D. and Jatenco-Pereira, V., "The Effects of Alfvén Waves and Radiation Pressure in Dust Winds of Late-Type Stars". Astrophysical Journal, 576, 976 (2002).
Motz, R.O., "Alfven Wave Generation in a Spherical System", Physics of Fluids, 9, 411-412, (1966)
S. Tomczyk, S. W. McIntosh, S. L. Keil, P. G. Judge, T. Schad, D. H. Seeley and J. Edmondson, "Waves in the Solar Corona", Science Magazine, Vol. 317. no. 5842, pp. 1192-1196, (2007)