The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework, by using a variational theory supported by well established physical principles. The equivalence between the variational statement and more conventional treatments, based on the solution of the differential Maxwell equations together with appropriate conductivity laws is shown. Advantages of the variational method are emphasized, focusing on its numerical performance, that allows to explore new physical scenarios. In particular, we present the extension of the so-called double critical state model to three dimensional configurations in which only flux transport (T-states), cutting (C-states) or both mechanisms (CT-states) occur. The theory is applied to several problems. First, we show the features of the transition from T to CT states. Second, we give a generalized expression for the flux cutting threshold in 3-D and show its relevance in the slab geometry. In addition, several models that allow to treat flux depinning and cutting mechanisms are compared. Finally, the longitudinal transport problem (current is applied parallel to the external magnetic field) is analyzed both under T and CT conditions. The complex interaction between shielding and transport is solved.Comment: 21 figures, submitted for publicatio

Numerical simulations of a type-II superconducting wire subject to an ac transport current and oscillating transverse magnetic field are performed using the theory of the critical state. Time-dependent distributions of the current and the density of magnetic flux, the local power dissipation, and cycles of the magnetic moment are displayed. Noticeable inhomogeneous dissipation and field distortions are exposed. Results for hysteretic ac losses are reported too, and significant differences to predictions of available approximate formulae identified. Finally, a distinct low-pass filtering effect intrinsic to the wire’s magnetic response is revealed.

Abstract. A theory for the electromagnetic response of type-II superconductors close beyond the critical state is presented. Our formulation relies on general physical principles applied to the superconductor as a thermodynamic system. Equilibrium critical states, externally driven steady solutions, and transient relaxation are altogether described in terms of free energy and entropy production. This approach allows a consistent macroscopic statement that incorporates the intricate vortex dynamic effects, revealed in non-idealized experimental configurations. Magnetically anisotropic critical currents and flux stirring resistivities are straightforwardly included in three dimensional scenarios.Starting from a variational form of our postulate, a numerical implementation for practical configurations is shown. In particular, several results are provided for the infinite strip geometry: voltage generation in multicomponent experiments, and magnetic relaxation towards the critical state under applied field and transport current. Explicitly, we show that for a given set of external conditions, the well established critical states may be utterly obtained as diffusive final profiles.

The time-dependent local electromagnetic properties of a type-II superconducting wire subject to the concomitant action of an ac transport current and an oscillating transverse magnetic field in synchronous and asynchronous regimes are thoroughly studied under the critical state approach. Relative double frequency effects between the electromagnetic excitations have been explored for the asynchronous cases. Outstandingly, the occurrence of this event can drastically alter the efficiency of the superconducting wire by increasing the ac losses, contrary to the prediction of a reduction in the ac losses when a relative phase shifting is considered. Likewise, striking magnetization loops and remarkable differences to the ac losses predicted by simplified analytical approaches are reported. For cyclic regime, the time-dependent distribution of local current density, the density of power dissipation, and the components of the magnetic flux density are shown in a wide number of cases. Multiply connected domains are revealed for the flux front profiles via the time-dependent consumption of the magnetization currents by effect of the injected transport current lines. Finally, we have shown that the strong localization of the power density and the recently envisaged low pass filtering effect in the wire's magnetic response is only affordable when both electromagnetic excitations evolve synchronous. V C 2013 AIP Publishing LLC. [http://dx.