Elastic Wave Motion and a Nonuniform Magnetic Field in Electrical Conductors

An applied magnetic field will perturb an elastic wave that is passing through an electrical conductor. Nonuniformity in the applied field introduces an extra dissipative effect that is not present for a uniform applied field. In this paper one case of the interaction of elastic wave motion with a nonuniform field is solved by means of series expansions in the two dimensionless perturbation parameters involved. The effect of the nonuniform field dominates the effect of the uniform field in regions where the local field strength is less than half of the change in field strength per wavelength. For seismic waves in the core of the earth, the effect would be most important for long-wavelength standing modes of free vibration. However, taking accepted values for the conductivity and field strength in the core, the effect of the nonuniform field is found to be insignificant, as is the uniform field effect.