Modelling of Elastic Superconductors

In this paper, we build a phenomenological model for elastic superconductors which relies on rigorous thermodynamics. The basic postulate is the dependence of the free energy of the medium on the electric current density vector and on an objective time derivative of the magnetic field. The entropy flux retains its usual, simple form. A wave type equation is obtained for the magnetic field that may be used to investigate wave propagation in superconductors. We study in some details the penetration of electromagnetic plane waves in the medium to get a dispersion relation between the penetration depth, frequency and phase velocity of the wave. It is shown, in Particular, that the penetration depth is frequency-independent for frequencies of the electromagnetic field much smaller than 10 13 s −1 . For a simple form of the free energy, we obtain a set of coupled, nonlinear equations for the displacement and magnetic field vector components. These will be solved, under the proper boundary conditions, in a forthcoming publication to investigate the propagation of surface acoustic waves in superconductors.