The interaction between elastic wave motions and a magnetic field in electrical conductors

The propagation of elastic waves in an electrically conducting solid permeated by a uniform, static magnetic field is discussed. In the case of plane wave motions, two systems of waves arise: simple uncoupled systems and a trimodal coupled system of waves. In the uncoupled case, in which polarizations are unaltered, two dispersive, complex phase velocities exist. For a weak impressed magnetic field, one of these velocities is close to the elastic wave velocity of the polarized wave in the absence of the field. The other wave, called an eddy current wave, although strongly attenuated, cannot be neglected in the solution of boundary value problems. When the theory of magnetoelastic interactions is applied to seismic motions in the conducting core of the earth, it is found that compressional waves are virtually unattenuated in the core for the pertinent values of frequency, conductivity, and magnetic intensity. It is concluded that magnetoelastic interactions are not a significant mechanism in the earth's core.