A Phenomenological Model for Anisotropic Thermoelastic Type-II Superconductor in the Mixed State

Abstract

A phenomenological model is proposed in this article to study magnetothermoelastic response of anisotropic deformable type-II superconductors in the mixed state. In the model, the anisotropic effect, the vortex dynamic effect, the thermoelastic effect, and the galvanomagnetic and thermomagnetic effects in the superconductor are all taken into account self-consistently. The effect of normal conduction fluid in the superconductor is also formulated by a modified two-fluid model. It is shown that, at the London approximation, the classical London equations for rigid-body superconductors are modified in order to analyse deformable type-II superconductors in the mixed state due to the effect of vortex dynamics, the effect of mechanical motion, and the effect of inertia of superconducting electrons in the superconductor. At the linear approximation, the complete set of effective constitutive equations and field equations are formulated for analysing magnetothermoelastic behaviour of anisotropic deformable type-II superconductors in the mixed state. Illustratively, a wave solution for an anisotropic superconducting planar waveguide in DC magnetic field is derived and some discussion about the effect of anisotropy is given with the aid of this phenomenological model.