Flux in Motion under the Influence of a Field Gradient

Abstract

Chapter 16 has dealt with the critical state primarily as the static condition of a magnetized irreversible type-II superconductor. The critical state is, of course, attained in the first place by the motion of flux into the superconductor and the establishment of a flux density gradient whose magnitude at any place is controlled by the local pinning forces. When the applied field stops increasing or decreasing, the internal flux density gradient rests at its critical value, poised ready to move in response to any subsequent change, in either direction, of the external field. Numerous authors have inquired into the permanence of the critical state, as defined by the equality of a fluxoid driving force, F, to the aggregate or bulk pinning force, Fp. It seems that, although the critical state can for all practical purposes be regarded as permanent, it does undergo a slow logarithmic decay by a thermally activated process of flux creep. Similarly, if the sample is in its shielding critical state and the field increase is reinstated in the form of a small step, more flux will creep into the sample. In this chapter, flux creep is to be treated both as a thermally activated process and as an example of electromagnetic diffusion. If pinning is relatively weak, flux flow is able to take place. But since in the weak-pinning situation the critical flux-density gradient is necessarily small, flux flow usually occurs under the influence of a transport-current instigated Lorentz force.