On the possibility of localized wave propagation using a classical two-fluid model of superconductors

Abstract

In this paper, the classical two-fluid model for superconductors is used to determine the time-dependent partial differential equations (PDEs) which govern wave propagation in superconducting media. These equations are then solved exactly in both two and three dimensions using localized wave solutions rather than the traditional eigenfunction solutions. We have applied these localized wave solutions to the problem of a symmetric superconducting slab, neglecting the normally conducting current density, and found that the resultant focus wave mode magnetic field solution expels flux from the interior of the slab and can regain its initial amplitude as it travels along the surface of the slab. A comparison of the transverse part of the localized wave solution with the transverse part of the more usual plane wave solution shows remarkable agreement.