Magneto-hydrodynamic Oscillations of a Perfectly Conducting Fluid Sphere Placed in a Uniform Magnetic Field

Abstract

An attempt to improve theories of magneto-hydrodynamic oscillations of a conducting fluid sphere in a uniform magnetic field is made. Unlike the previous theories which have been developed by M. Schwarzschild and T. Rikitake, analytical expressions for zonal oscillations are obtained rigorously in this paper. It turns out that no eigen-periods are determined accurately. However, they are approximately obtained with drastic simplifications. Two fundamental normal modes of oscillation are also approximately obtained and illustrated.