Material Laws and Numerical Methods in Applied Superconductivity

TL;DR

This comprehensive study develops and applies variational and computational methods to analyze the electromagnetic behavior and material laws of type II superconductors, including anisotropy effects and applications to superconducting wires.

Contribution

It introduces a variational framework for critical state problems in superconductors with magnetic anisotropy and extends computational methods to complex 3D configurations.

Findings

Validated variational models for anisotropic critical states

Analyzed electromagnetic responses of superconducting wires under AC excitations

Provided insights into magnetic anisotropy effects in superconductor behavior

Abstract

Contents Preface I Electromagnetism of type II superconductors 1 General Statements Of The Critical State 1.1 The CS In The Maxwell Equations Formalism 1.2 The CS Regime And The MQS Limit 2 Variational Theory for CS Problems 2.1 General Principles Of The Variational Method 2.2 The Material Law: SCs with magnetic anisotropy 2.2.1 Onto the 1D Critical States 2.2.2 Towards The 3D Critical States 3 Computational Method Conclusions I References I II Critical State Problems:Effects & Applications 4 Type-II SCs With Intrinsic Magnetic Anisotropy 4.1 3D variational statement in slab geometry 4.2 Isotropic predictions in -3D- configurations 4.3 T-states in -3D- configurations 4.4 CT-states in -3D- configurations 4.5 Smooth critical states in -3D- configurations Appendix I Critical angle gradient in -3D- configurations 5 The Longitudinal Transport Problem 5.1 Simplified analytical models and beyond 5.1.1 The simplest analytical model 5.1.2 The SDCST statement and the BM's approach 5.2 Magnetic anisotropy and the uncommon effects 5.2.1 Extremal case: The T-states model 5.2.2 Material laws with magnetic anisotropy: CT\chi - models 6 Electromagnetism For Superconducting Wires 6.1 Theoretical framework and general considerations 6.2 SC wires subjected to isolated external sources 6.2.1 Wires with an injected AC transport current 6.2.2 Wires under an external AC magnetic flux 6.2.3 Ultimate considerations on the AC losses 6.3 SC wires under simultaneous AC excitations (B_{0},I_{tr}) 6.3.1 Synchronous excitations 6.3.2 Asynchronous excitations Conclusions II References II Supplementary Material II III Microscopical aspects also analyzed 7 E-Ph Theory And The Nodal Kink Effect In HTSC 8 Is it necessary to go beyond the E-Ph mode? Conclusions III References III Supplementary Material III IV Addenda