Magnetic field in type II superconductors cylindrical geometry

The purpose of this paper is to establish a particular mathematical basis for study of electromagnetic fields and forces in a spherical gyro based on the new high-temperature superconducting oxides. In the process of designing various instruments with superconductors, we must analyze the static and transient electromagnetic effects which occur as the penetration of the field into the device part takes place. While a thorough understanding of superconductivity is only possible through quantum mechanics, the modified London's equations, in conjunction with Maxwell's field equations provide a convenient means for insight into the mechanics of superconducting devices. Accurate and very efficient finite difference methods for the approximate solution of nonlinear boundary value problems have been studied recently by the author for the case of a superconducting cylinder located in a magnetic field. The numerical methods generally have advantages over other methods such as analytical modelling since they are able to handle problems not only with complicated geometry, but also with a material property (magnetic susceptibility) which varies with position within the device analyzed. Moreover, they offer acceptable results with a reasonable effect. To keep the presentation simple, we confine our attention to a second order nonlinear ordinary differential equation of the form, derived in terms of flux density, subject to boundary conditions. Extension of the result to a nonlinear equation is not difficult