Magnetomechanical Instabilities in Elastic-Plastic Cylinders, Part I: Elastic Response

Abstract

The effects of electromagnetic fields on instabilities in metal cylinders are considered in this analysis. The cylinder is assumed to be infinitely long and perfectly conducting. An axial electric current is introduced in the cylinder, giving rise to an azimuthal magnetic field in the surrounding vacuum, causing mechanical distortion in the cylinder. The current is assumed to be small so that the deformation remains elastic; in an accompanying paper (Littlefield, 1996) larger currents are considered where plastic flow becomes important. After solutions to the idealized motion of the cylinder under uniaxial strain conditions are developed, small perturbations to the motion are considered. The equations governing the motion of these disturbances are derived using linear perturbation theory. Solutions to the equations indicate that electromagnetic fields can have a substantial effect on the stability spectrum in the cylinder. In general, the frequency of oscillating perturbations is suppressed by the azimuthal magnetic field, and distending instabilities are possible if the magnetic field is above a threshold value. The underlying physical mechanisms contributing to these deviations are proposed.