Critical state theory for nonparallel flux line lattices in type-II superconductors

Coarse-grained flux density profiles in type-II superconductors with non-parallel vortex configurations are obtained by a proposed phenomenological least action principle. We introduce a functional $C[H(x)]$, which is minimized under a constraint of the kind $J$ belongs to $Delta$ for the current density vector, where $Delta$ is a bounded set. This generalizes the concept of critical current density introduced by C. P. Bean for parallel vortex configurations. In particular, we choose the isotropic case ($Delta$ is a circle), for which the field penetration profiles $H(x,t)$ are derived when a changing external excitation is applied. Faraday's law, and the principle of minimum entropy production rate for stationary thermodynamic processes dictate the evolution of the system. Calculations based on the model can reproduce the physical phenomena of flux transport and consumption, and the striking effect of magnetization collapse in crossed field measurements.Comment: The compiled TeX document length is 10 pages. Two figures (one page each) are also included The paper is accepted for publication in Phys. Rev. Let

Systems of Differential Algebraic Equations in Computational Electromagnetics

Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept