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Magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature titled "Existence of Electromagnetic–Hydrodynamic Waves" which outlined his discovery of what are now referred to as Alfvén waves. Alfvén initially referred to these waves as "electromagnetic–hydrodynamic waves"; however, in a later paper he noted, "As the term 'electromagnetic–hydrodynamic waves' is somewhat complicated, it may be convenient to call this phenomenon 'magneto–hydrodynamic' waves." In MHD, motion in the fluid is described using linear combinations of the mean motions of the individual species: the current density and the center of mass velocity . In a given fluid, each species has a number density , mass , electric charge , and a mean velocity . The fluid's total mass density is then , and the motion of the fluid can be described by the current density expressed as and the center of mass velocity expressed as: MHD can be described by a set of equations consisting of a continuity equation, an equation of motion, an equation of state, Ampère's Law, Faraday's law, and Ohm's law. As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation. This is often accomplished with approximations to the heat flux through a condition of adiabaticity or isothermality.