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The classical boundary problem of the transition of a spherical type-I superconductor to the normal state with increasing of the applied uniform magnetic field

A complicated boundary value problem of the transition of a macroscopic massive spherical type-I superconductor to the intermediate and normal state with increasing of the applied uniform magnetic field has been solved. Taking into account a penetration effect and exact boundary conditions the boundary problem has been solved completely and rigorously within the framework of the classical (non-quantum) electrodynamics of continuous mediums and the modified (simplified) nonlocal Pippard electrodynamics of spatially homogenous type-I superconductors.

The principal object of this work is a self-consistent and exact setting of the boundary value problem and also its mathematically rigorous solution taking into account surface effects and nonlocality of Pippard type-I superconductors.

The solution novelty is a description of the surface effects within the framework the modified (simplified) nonlocal Pippard electrodynamics.

It is shown that disregarding for the surface effects in a theory of low-temperature superconductors can lead not only to computational mistakes, but also to incorrect qualitative conclusions.

The conclusions about nature of a macroscopic spherical type-I superconductor to the intermediate and normal state have been drawn on the ground of a rigorous solution of the boundary problem and determination of the total magnetic field distribution in the whole space (inside and outside the superconducting sphere). These conclusions are in agreement with those, which have been drawn earlier by other authors on the ground of different approximate models and methods.

Since the scientific results have been obtained by the authors on the basis of rigorous and self-consistent solution of the exactly set boundary problem, the work is undoubtedly of theoretical and methodical interest.