Magnetohydrodynamics

Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics), is the academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water. The word magnetohydrodynamics (MHD) is derived from magneto- meaning magnetic field, and hydro- meaning fluid, and -dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in 1970.

The set of equations which describe MHD are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism. These differential equations have to be solved simultaneously. This is too complex or impossible to do symbolically in all but the most trivial cases. For real-world problems, numeric solutions are found using supercomputers. Because MHD is a fluid theory, it cannot treat kinetic phenomena, i.e., those in which the existence of discrete particles, or of a non-thermal distribution of their velocities, is important.

Contents

1 Applications 1.1 Geophysics 1.2 Astrophysics 1.3 Engineering 2 See also 3 References

Applications

Geophysics

The fluid mantle of the Earth and other planets is theorized to be a huge MHD dynamo that generates the Earth's magnetic field due to the motion of the molten rock.

Astrophysics

MHD applies quite well to astrophysics since over 99% of the matter content of the Universe is made up of plasma, including stars, interplanetary medium (the space between the planets), interstellar medium (space between the stars), nebulae and jets; however MHD is lacking when electric currents flows through these plasmas and produces filaments, double layers and plasma instabilities.

Sunspots are caused by the Sun's magnetic fields, as Joseph Larmor theorized in 1919, as is the differential solar rotation. The solar wind is also governed by MHD.

Previously, theories describing the creation of the Sun and planets could not explain how the Sun has 99% of the mass, yet only 1% of the angular momentum in the solar system. In a closed system such as the cloud of gas and dust from which the Sun was formed, mass and angular momentum are both conserved. That conservation would imply that as the mass concentrated in the center of the cloud to form the Sun, it would spin up, much like a skater pulling their arms in. The high speed of rotation predicted by early theories would have flung the proto-Sun apart before it could have formed. However, magnetohydrodynamic effects transfer the Sun's angular momentum into the outer solar system, slowing its rotation.

Engineering

MHD is related to engineering problems such as plasma confinement, liquid-metal cooling of nuclear reactors, and electromagnetic casting (among others).

In early 1990s, Mitsubishi built a boat, the 'Yamoto', which uses a magnetohydrodynamic drive, is driven by a liquid helium-cooled superconductor, and can travel at 15 km/h.

See also

• Alfvén wave
• Electromagnetic casting
• Ferrofluid
• Magnetic reconnection
• MHD generator
• Magnetohydrodynamic drive
• Nuclear reactor liquid-metal cooling
• Plasma equilibria and stability- plasma confinement
• Tokamak

References

• P. A. Davidson, "An Introduction to Magnetohydrodynamics (http://books.cambridge.org/0521794870.htm)", May 2001 452 p ISBN 0521794870
• Jordan, R.,"A statistical equilibrium model of coherent structures in magnetohydrodynamics (http://www.iop.org/EJ/abstract/-search=5216637.3/0951-7715/8/4/007)". Nonlinearity 8 (July 1995) 585-613.
• Hurricane, O. A., B. H. Fong, and S. C. Cowley, "Nonlinear magnetohydrodynamic detonation: Part I (http://content.aip.org/PHPAEN/v4/i10/3565_1.html)". Physics of Plasmas Vol 4(10) pp. 3565-3580. October 1997.
• Tabar, M. R. Rahimi, and S. Rouhani, "Turbulent Two Dimensional Magnetohydrodynamics and Conformal Field Theory (http://arxiv.org/abs/hep-th/9503005)". Department of Physics, Sharif University of Technology. Institute for Studies in Theoretical Physics and Mathematics. Tehran, Iran. arXiv:hep-th/9503005 v1 1 Mar 1995.
• Pai, Shih-I. "Magnetogasdynamics and Plasma Dynamics". Vienna: Springer-Verlag, 1962. 197 p. ASIN 0387806083
• Biskamp, Dieter. "Nonlinear Magnetohydrodynamics". Cambridge, England: Cambridge University Press, 1993. 378 p. ISBN 0521599180
• Ferraro, Vincenzo Consolato Antonio and Plumpton, Charles. "An Introduction to Magneto-Fluid Mechanics", 2nd ed.
• Roberts, P.H. "Introduction to Magnetohydrodynamics". London: Longmans Green, 1967.
• Kulikovskiy, A.G. & Lyubimov, G.A. "1965 Magnetohydrodynamics". Addison&Wesley, Massachusetts.
• Sutton, G. W., and A. Sherman, "Engineering Magnetohydrodynamics", McGraw-Hill Book Company, New York, 1965.
• "Magnetohydrodynamic Generators with Nonequilibrium Ionization", AIAA Journal, Vol. 3, April, 1965, p 591.
• Hughes, W., and F. Young, "The Electromagnetodynamics of Fluids", New York, John Wiley & Sons Inc. 1966.
• Dr. James B. Calvert, "Magnetohydrodynamics" (http://www.du.edu/~jcalvert/phys/mhd.htm), 2002-10-20
• David P. Stern, NASA, "The Sun's Magnetic Cycle" (http://pwg.gsfc.nasa.gov/earthcc/Sconct22.htm)de:Magnetohydrodynamik