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.

Ideal MHD

The most common simplification of MHD is to assume that the fluid is a perfect conductor with little or no resistivity; this simplification is called ideal MHD. In ideal MHD, Lenz's law dictates that magnetic field lines cannot move through the fluid, instead remaining attached to the same small piece of fluid at all times. Under such conditions, most electric currents tend to be compressed into thin, nearly-two-dimensional ribbons termed current sheets. This has the effect of dividing the fluid into magnetic domains, each of which may carry a small electric current in the direction of the magnetic field lines themselves, with most current contained in current sheets between the domains.

Related Topics:
Perfect conductor - Resistivity - Lenz's law - Current sheet

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The connection between magnetic field lines and fluid in ideal MHD fixes the topology of the magnetic field in the fluid -- for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection that releases the stored energy from the magnetic field.

Related Topics:
Topology - Magnetic reconnection

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Limits of ideal MHD

There are no perfect conductors and hence ideal MHD is not a perfect description of any physical system. In reality, that is not the case, and in any physical system there is non-ideal behavior. In particular, the magnetic field can generally move through the plasma, following a diffusion law with the resistivity of the plasma serving as a diffusion constant. This means that solutions to the ideal MHD equations are only applicable for a limited time before diffusion becomes too important to ignore. Solar active regions, for example, have diffusion times of hundreds to thousands of years, much longer than the actual lifetime of a sunspot -- so they can be treated as ideal MHD systems. By contrast, a meter-sized volume of seawater has a magnetic diffusion time measured in milliseconds.

Related Topics:
Perfect conductor - Diffusion law - Diffusion constant

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Under ideal MHD all current sheets are infinitely thin and have infinitely high current density. In reality, the thickness of a current sheet is limited both by the resistivity of the plasma and by the density of the individual charge carrrier particles (such as electrons) in the plasma, and by the Larmor radius of those particles' motion in the magnetic field. Current sheets in the solar corona are thought to be between a few meters and a few kilometers in thickness, which is quite thin compared to the magnetic domains (which are thousands to hundreds of thousands of kilometers across).

Related Topics:
Charge carrrier - Larmor radius

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Alfvén described MHD as a "magnetic field description". But based on his experimental work, Alfvén's also applied an "electric current description" to plasmas, whose properties are less well-known, such as Birkeland currents (field-align currents), double layers (charge separation regions), certain classes of plasma instabilities, and chemical separation in space plasmas. An extended version of MHD encompassing an electric field description and some of these more complex phenomena is called Hall-magnetohydrodynamics (Hall-MHD or HMHD).

Related Topics:
Birkeland current - Double layer

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Breakdown of ideal MHD

Even in physical systems that can be treated as ideal, the assumptions of MHD can break down. Many instabilities exist that can increase the effective resistivity of the plasma by factors of more than a billion. When this happens, the electric current sheets that separate different magnetic domains can collapse rapidly, causing magnetic reconnection in the plasma and releasing stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration, and heat.

Related Topics:
Instabilities - Magnetic reconnection - Energy - Wave - Acceleration - Particle acceleration - Heat

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Magnetic reconnection in near-ideal MHD systems is important because it concentrates energy in time and space, so that gentle forces applied to a plasma for long periods of time can cause violent explosions and bursts of radiation.

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Additionally, MHD "completely excludes the possibility of field aligned potentials for the simple reason that electrons travelling along the field lines would be accelerated by such potentials and quickly redistribute the charge" .

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Hannes Alfvén, who won the Nobel Prize for his development of magnetohydrodynamics, and co-author Carl-Gunne Fälthammar, wrote in their book Cosmical Electrodynamics (1952, 2nd Ed.): "It should be noted that the fundamental equations of magnetohydrodynamics rest on the assumption that the conducting medium can be considered as a fluid. This is an important limitation, for if the medium is a plasma it is sometimes necessary to use a microscopic description in which the motion of the constituent particles is taken into account. Examples of plasma phenomena invalidating a hydromagnetic description are ambipolar diffusion, electron runaway, and generation of microwaves". In other words, MHD may not lead to correct results when applied to low-density cosmic plasmas.

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