Magnetohydrodynamics, or MHD, is a branch of the science of the dynamics of matter moving in an electromagnetic field, especially where currents established in the matter by induction modify the field, so that the field and dynamics equations are coupled. It treats, in particular, conducting fluids, whether liquid or gaseous, in which certain simplifying postulates are accepted. These are, generally, that the Maxwell displacement current is neglected, and the fluid may be treated as a continuum, without mean-free-path effects. It is distinguished from the closely related plasma dynamics in which these postulates are relaxed, but there is still a large intermediate area in which similar treatment is possible.
Solid matter is generally excluded from MHD, but it should be realized that the same principles apply. Electrical conduction in metals, and the Hall Effect, are two examples. In an electric motor, the magnetic field produced by the armature current affects the operation of the motor in an important way, so that the mechanical and electrical analyses are coupled, just as in MHD. Electromagnetic forces are an essential part of motors and generators, though they generally do not produce significant elastic deformations, and the motions occur with the help of rotating and sliding contacts. Homopolar generators (ones that produce DC currents) are, indeed, closely related to MHD analogues.
MHD was originally applied to astrophysical and geophysical problems, where it is still very important, but more recently to the problem of fusion power, where the application is the creation and containment of hot plasmas by electromagnetic forces, since material walls would be destroyed. Astrophysical problems include solar structure, especially in the outer layers, the solar wind bathing the earth and other planets, and interstellar magnetic fields. The primary geophysical problem is planetary magnetism, produced by currents deep in the planet, a problem that has not been solved to any degree of satisfaction.
The purpose of this article is to explain the fundamental principles of MHD as best I understand them, and not to treat any of the applications in detail. This requires an acquaintance with several areas of theoretical physics, including electromagnetism and fluid mechanics, which are discussed in other areas of this website. I will use the index notation freely, in addition to the usual vector notation. Index notation is explained in Euclidean Tensors. The electromagnetic units used will be Gaussian. Much MHD literature is in emu (which is like Gaussian without the c's), while modern references will probably sink to MKSA. I shall relate all quantities to practical units, anyway. |
