Alfvén waves

Any movement within a conducting fluid that is in the presence of a magnetic field will generate electrical currents. These currents will then interact with the field to produce mechanical forces which act back on the fluid. In 1942, Hannes Alfvén noted that in this scenario "a kind of combined electromagnetic-hydrodynamic wave is produced which… so far as I know, has as yet attracted no attention". Alfvén calculated the properties of such waves, suggesting that they could be important in solar physics. Today, Alfvén waves and other related magnetohydrodynamic waves take centre stage in the study of laboratory, space and astrophysical plasmas.

Nature 150, 405–406 (1942)
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Existence of Electromagnetic-Hydrodynamic Waves

H. ALFVÉN

Kgl. Tekniska Högskolan, Stockholm.

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 which, so far as I know, has as yet attracted no attention.

The phenomenon may be described by the electrodynamic equations

together with the hydrodynamic equation

where s is the electric conductivity, m the permeability, d the mass density of the liquid, i the electric current, v the velocity of the liquid, and p the pressure.

Consider the simple case when s = ¥, m = 1 and the imposed constant magnetic field H₀ is homogeneous and parallel to the z-axis. In order to study a plane wave we assume that all variables depend upon the time t and z only. If the velocity v is parallel to the x-axis, the current i is parallel to the y-axis and produces a variable magnetic field H 2 in the x-direction. By elementary calculation we obtain

which means a wave in the direction of the z-axis with the velocity

Waves of this sort may be of importance in solar physics. As the sun has a general magnetic field, and as solar matter is a good conductor, the conditions for the existence of electromagnetic-hydrodynamic waves are satisfied. If in a region of the sun we have H₀ = 15 gauss and d = 0·005 gm. cm.^-3, the velocity of the waves amounts to

This is about the velocity with which the sunspot zone moves towards the equator during the sunspot cycle. The above values of H₀ and d refer to a distance of about 10₁₀ cm. below the solar surface where the original cause of the sunspots may be found. Thus it is possible that the sunspots are associated with a magnetic and mechanical disturbance proceeding as an electromagnetic-hydrodynamic wave.

The matter is further discussed in a paper which will appear in Arkiv för matematik, astronomi och fysik.

H. ALFVÉN

Kgl. Tekniska Högskolan, Stockholm.
Aug. 24.

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