Magnetohydrodynamics of Conducting Fluids

Abstract

Ionized gases or plasmas and liquid metals such as mercury or liquid sodium are electrically conducting fluids. The outer core of the earth is believed to be molten iron. Magnetospheres of planets and stars, tails of comets, ex-ragalactic jets, accretion disks and many other astrophysical objects are studied by treating them as electrically conducting fluids. The study of magnetohydrodynamics (MHD) draws from two well known branches of physics, electrodynamics and hydrodynamics, along with a provision to include their coupling. The basic laws of electrodynamics described in the form of Maxwell’s Equations supplemented by the generalized Ohm’s law are sufficient for the purpose. The hydrodynamics of a fluid is expressed in the form of conservation laws of mass, momentum and energy These laws treat the fluid as a continuum. The continuum description is valid if the mean free path of the constituent particles is much shorter than the spatial scales on which the flow is visualized. Thus, according to this criterion, any substance can be treated as a continuum at some spatial scale. The magne-tohydrodynamic phenomena are a consequence of the mutual interaction of the fluid flow and the magnetic field. As is well known, a conductor crossing magnetic field lines gives rise to an induced electric field, which drives an electric current in the conducting fluid. The resulting Lorentz force accelerates the fluid across the magnetic field, which in turn creates another induced electric field and currents which modify the initial magnetic field. Thus, the bulk motion of a conducting fluid and a magnetic field influence each other and must be determined self-consistently