Theory of Flux-Line Cutting and the Critical State in Type-Ii Superconductors.

This thesis is divided into four related sections, each one dealing with an aspect of the response of type -II superconducting materials subjected to applied magnetic fields which change in magnitude and orientation. A general critical-state theory, which includes both flux pinning and flux-line cutting, is presented. In Section I, the electromagnetic response of a type-II superconducting slab subjected to a parallel, constant magnetic field whose direction undergoes either continuous rotation or periodic oscillation is investigated. In Section II, (')B, (')J, and (')E field distributions during the approach to quasi-steady state of a slab subjected to a parallel rotating magnetic field are calculated. It is shown that, regardless of the specimen's magnetic history, flux-line-cutting B-consumption leads to a final state in which B has a diamagnetic profile near the surface of the specimen. In Section III, hysteretic losses in samples subjected to an oscillating magnetic field oriented at an arbitrary angle with respect to a bias field, both fields being parallel to the surface, are discussed. Analytic expressions for the ac losses are obtained for the case that the amplitude of the oscillating field is small compared with the bias field. The calculations of Sections I-III are generalized, in Section IV, for the case of arbitrary B dependence of the parameters of the theory, and for arbitrarily large amplitude of the ac field. In this section, numerical solutions to the equations describing the theory are presented.