An Analog Solution for the Static London Equations of Superconductivity

Growing interest in the theoretical as well as applied aspects of superconductivity has focused considerable attention upon the static London equations. These macroscopic relationships describe the spatial distribution of magnetic fields and currents in superconductors. In this paper a novel analog method of obtaining solutions in complicated geometries is discussed. The method makes use of the similarity in form of the static London equations and the dynamic skin-effect equations of normal conduction under exponentially-growing steady-state conditions. Conveniently scaled copper models of superconducting geometries of interest can be constructed and excited from a growing-exponential function generator. Field distributions measured in the space around the normal conductors of the model correspond with the desired distributions in the analogous superconductor geometry. Fields within conductors themselves cannot be determined directly by this method, but the surface fields are generally most important. The method is particularly useful in studying thin films which are appreciably penetrated by magnetic fields. The experimental setup and the measurement technique are discussed. Illustrative results from a copper model of a long rectangular superconducting strip, 1830 penetration depths wide and 3.81 penetration depths thick are presented.