Critical state analysis of orthogonal flux interactions in pinned superconductors

We show that, based on the critical state model for flux-line pinning in hard superconductors, one can assess the magnetic moment relaxation induced by the oscillations of a perpendicular magnetic field. Our theory follows a recent proposal of using phenomenological 2D modeling for the description of crossed field dynamics in high-T$_c$ superconductors [{\tt arXiv:cond-mat/0703330}]. Stationary regimes with either saturation to metastable configurations, or complete decay to the thermodynamic equilibrium are obtained. The transition between both types of response is related to the disappearance of a flux free core within the sample. As a common feature, a step-like dependence in the time relaxation is predicted for both cases. The theory may be applied to long bars of arbitrary and non homogeneous cross section, under in-plane magnetic field processes.Comment: 11 figures, submitte

Inversion mechanism for the transport current in type-II superconductors

The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical studies for general scenarios, it is shown that a remarkable inversion of the current flow in a surface layer may be predicted under a wide set of experimental conditions. Strongly inhomogeneous current density profiles, characterized by enhanced transport toward the center and reduced, or even negative, values at the periphery of the conductor, are expected when the physical mechanisms of flux depinning and consumption (via line cutting) are recalled. A number of striking collateral effects, such as local and global paramagnetic behavior, are predicted. Our geometrical description of the macroscopic material laws allows a pictorial interpretation of the physical phenomena underlying the transport backflow.Comment: 8 pages, 6 figures (Best quality pictures are available by author's contact

Log-concavity of compound distributions with applications in operational and actuarial models

We establish that a random sum of independent and identically distributed (i.i.d.) random quantities has a log-concave cumulative distribution function (cdf) if (i) the random number of terms in the sum has a log-concave probability mass function (pmf) and (ii) the distribution of the i.i.d. terms has a non-increasing density function (when continuous) or a non-increasing pmf (when discrete). We illustrate the usefulness of this result using a standard actuarial risk model and a replacement model.We apply this fundamental result to establish that a compound renewal process observed during a random time interval has a log-concave cdf if the observation time interval and the inter-renewal time distribution have log-concave densities, while the compounding distribution has a decreasing density or pmf. We use this second result to establish the optimality of a so-called (s, S) policy for various inventory models with a stock-out cost coefficient of dimension [$/unit], significantly generalizing the conditions for the demand and leadtime processes, in conjunction with the cost structure in these models. We also identify the implications of our results for various algorithmic approaches to compute optimal policy parameters. Copyrigh

Exotic magnetic response of superconducting wires subject to synchronous and asynchronous oscillating excitations

Under the terms of the Creative Commons Attribution 3.0 Unported License.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. © 2013 AIP Publishing LLC.This work was supported by the Spanish MINECO and the FEDER program (MAT2011-22719 and ENE2011-29741 projects), DGA Grant T12/2011. Funding provided by the Spanish CSIC JAE program is gratefully acknowledged.Peer Reviewe

Modelling toolkit for simulation of maglev devices

arXiv:1612.09266v1A stand-alone App has been developed, focused on obtaining information about relevant engineering properties of magnetic levitation systems. Our modelling toolkit provides real time simulations of 2D magneto-mechanical quantities for superconductor (SC)/permanent magnet structures. The source code is open and may be customised for a variety of configurations. Ultimately, it relies on the variational statement of the critical state model for the superconducting component and has been verified against experimental data for YBaCuO/NdFeB assemblies. On a quantitative basis, the values of the arising forces, induced superconducting currents, as well as a plot of the magnetic field lines are displayed upon selection of an arbitrary trajectory of the magnet in the vicinity of the SC. The stability issues related to the cooling process, as well as the maximum attainable forces for a given material and geometry are immediately observed. Due to the complexity of the problem, a strategy based on cluster computing, database compression, and real-time post-processing on the device has been implemented.Funding of this research by Spanish MINECO and FEDER programme (Project ENE2014-52105-R) and by Gobierno de Aragón (Research group T-12) is gratefully acknowledged. J Peña-Roche acknowledges a Research Grant by ICMA (PI2 programme 2015).Peer Reviewe

Vector magnetic hysteresis of hard superconductors

Critical state problems which incorporate more than one component for the magnetization vector of hard superconductors are investigated. The theory is based on the minimization of a cost functional ${\cal C}[\vec{H}(\vec{x})]$ which weighs the changes of the magnetic field vector within the sample. We show that Bean's simplest prescription of choosing the correct sign for the critical current density $J_c$ in one dimensional problems is just a particular case of finding the components of the vector $\vec{J}_c$. $\vec{J}_c$ is determined by minimizing ${\cal C}$ under the constraint $\vec{J}\in\Delta (\vec{H},\vec{x})$, with $\Delta$ a bounded set. Upon the selection of different sets $\Delta$ we discuss existing crossed field measurements and predict new observable features. It is shown that a complex behavior in the magnetization curves may be controlled by a single external parameter, i.e.: the maximum value of the applied magnetic field $H_m$.Comment: 10 pages, 9 figures, accepted in Phys. Rev.

A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors

We consider the Bean's critical state model for anisotropic superconductors. A variational problem solved by the quasi--static evolution of the internal magnetic field is obtained as the $\Gamma$-limit of functionals arising from the Maxwell's equations combined with a power law for the dissipation. Moreover, the quasi--static approximation of the internal electric field is recovered, using a first order necessary condition. If the sample is a long cylinder subjected to an axial uniform external field, the macroscopic electrodynamics is explicitly determined.Comment: 24 pages, 15 figure