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Alfvén's Theorem and the Frozen Flux Approximation

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Encyclopedia of Geomagnetism and Paleomagnetism

History

In 1942, Hannes Alfvén (q.v.) published a paper that announced the discovery of the wave that now bears his name (Alfvén, 1942; see Alfvén waves ), and that is now often regarded as marking the birth of magnetohydrodynamics or “MHD” for short (see Magnetohydrodynamics ). In interpreting the waves in an associated paper (Alfvén, 1943, §4), he enunciated a result that has become known as “Alfvén's theorem”:

Suppose that we have a homogeneous magnetic field in a perfectly conducting fluid…  . In view of the infinite conductivity, every motion (perpendicular to the field) of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. Thus the matter of the liquid is “fastened” to the lines of force…

Here, one understands “in relation” to mean “relative.” Also the term “frozen” instead of “fastened” has been thought more appealing, and the theorem is frequently referred to as “the frozen flux theorem.” It is now more often stated in terms...

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Roberts, P.H. (2007). Alfvén's Theorem and the Frozen Flux Approximation. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_5

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