Experiments in magneto‐fluid dynamics

DEC 01, 1960

R. A. Alpher

Magneto‐fluid dynamics deals with the motion of electrically conducting gases and liquids in the presence of magnetic fields. The macroscopic description of such motions involves the coupling of the equations of hydrodynamics and Maxwell’s equations. For velocities small compared to that of light, and if one neglects displacement and charge convection currents, the coupling in the equations of motion occurs through a Lorentz body force term—a term involving the current density j and the magnetic induction, B, viz., $j \times B /c.$ The requirement of Lorentz invariance effects the introduction of the coupling into Maxwell’s equations, so that one calculates j from the generalized Ohm’s law $j = σ(E + V \times B /c),$ where σ is the fluid conductivity, E the electric field intensity and V the fluid velocity. Both $j \times B$ and $V \times B$ are basically nonlinear terms, whence the already uncomfortable situation with nonlinearities in hydrodynamics is quite considerably aggravated. Linearization on the one hand and “simple” experiments on the other must be invoked to convey a physical feeling for the phenomena to be expected from this coupling.

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More about the authors

R. A. Alpher, General Electric Research Laboratory, Schenectady, N.Y..