Magnetohydrodynamics

magnetohydrodynamics (măgnē'tōhī'drōdīnăm`ĭks), study of the motions of electrically conducting fluids and their interactions with magnetic fields. The principles of magnetohydrodynamics are of particular importance in plasma physics. See nuclear energy.

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Magnetohydrodynamics

The interaction of electrically conducting fluids with magnetic fields. The fluids can be ionized gases (commonly called plasmas) or liquid metals. Magnetohydrodynamic (MHD) phenomena occur naturally in the Earth's interior, constituting the dynamo that produces the Earth's magnetic field; in the magnetosphere that surrounds the Earth; and in the Sun and throughout astrophysics. In the laboratory, magnetohydrodynamics is important in the magnetic confinement of plasmas in experiments on controlled thermonuclear fusion. Magnetohydrodynamic principles are also used in plasma accelerators for ion thrusters for spacecraft propulsion, for light-ion-beam powered inertial confinement, and for magnetohydrodynamic power generation. See Nuclear fusion, Plasma (physics)

The conducting fluid and magnetic field interact through electric currents that flow in the fluid. The currents are induced as the conducting fluid moves across the magnetic field lines. In turn, the currents influence both the magnetic field and the motion of the fluid. Qualitatively, the magnetohydrodynamic interactions tend to link the fluid and the field lines so as to make them move together. See Electric current

The generation of the currents and their subsequent effects are governed by the familiar laws of electricity and magnetism. The motion of a conductor across magnetic lines of force causes a voltage drop or electric field at right angles to the direction of the motion and the field lines; the induced voltage drop causes a current to flow as in the armature of a generator.

The currents themselves create magnetic fields which tend to loop around each current element. The currents heat the conductor and also give rise to mechanical ponderomotive forces when flowing across a magnetic field. (These are the forces which cause the armature of an electric motor to turn.) In a fluid, the ponderomotive forces combine with the pressure forces to determine the fluid motion. See Electricity, Magnetism

Magnetohydrodynamic phenomena involve two well-known branches of physics, electrodynamics and hydrodynamics, with some modifications to account for their interplay. The basic laws of electrodynamics as formulated by J. C. Maxwell apply without any change. However, Ohm's law, which relates the current flow to the induced voltage, has to be modified for a moving conductor. See Electrodynamics, Hydrodynamics, Maxwell's equations, Ohm's law

It is useful to consider first the extreme case of a fluid with a very large electrical conductivity. Maxwell's equations predict, according to H. Alfvén, that for a fluid of this kind the lines of the magnetic field move with the material. The picture of moving lines of force is convenient but must be used with care because such a motion is not observable. It may be defined, however, in terms of observable consequences by either of the following statements: (1) a line moving with the fluid, which is initially a line of force, will remain one; or (2) the magnetic flux through a closed loop moving with the fluid remains unchanged.

If the conductivity is low, this is not true and the fluid and the field lines slip across each other. This is similar to a diffusion of two gases across one another and is governed by similar mathematical laws.

As in ordinary hydrodynamics, the dynamics of the fluid obeys theorems expressing the conservation of mass, momentum, and energy. These theorems treat the fluid as a continuum. This is justified if the mean free path of the individual particles is much shorter than the distances that characterize the structure of the flow. Although this assumption does not generally hold for plasmas, one can gain much insight into magnetohydrodynamics from the continuum approximation. The ordinary laws of hydrodynamics can then easily be extended to cover the effect of magnetic and electric fields on the fluid by adding a magnetic force to the momentum-conservation equation and electric heating and work to the energy-conservation equation.