Macroscopic Superconducting Phenomena

Name: Macroscopic Superconducting Phenomena | An interactive guide
Brand: Institute of Physics Publishing
Price: 92.99 EUR
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An interactive guide

Antonio Badía-Majós(Autor*in)

Institute of Physics Publishing

Erschienen am 18. November 2021

170 Seiten

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978-0-7503-2711-4 (ISBN)

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Inhalt

Intro
Preface
How to use this book
Acknowledgements
Author biography
Antonio Badía-Majós
Chapter 1 Elements of electromagnetic theory
1.1 Low frequency electrodynamics: fundamentals
1.1.1 Maxwell equations
1.1.2 The field H and the magnetisation M
1.2 The MQS regime
1.2.1 Magnetic diffusion in conductors
1.2.2 Magnetic diffusion: thermodynamic background
1.2.3 A simple mechanical analogue
1.2.4 MQS quasi-steady states: thermodynamic background
1.2.5 Physical interpretation
1.3 Review exercises
References
Chapter 2 Basic superconductivity: observations and theories
2.1 Basic phenomenology
2.2 The London equations
2.3 From classical to quantum
2.4 Wave functions: the Ginzburg-Landau theory
2.4.1 Gauge invariance: the current density ?
2.4.2 On the nature of ? and ?: wave functions
2.4.3 Ginzburg-Landau equations
2.5 The characteristic lengths
2.6 Flux vortices
2.6.1 Structure of an isolated vortex
2.6.2 Interaction between vortices
2.6.3 The vortex lattice: average of b
2.6.4 Equilibrium magnetisation curve of a type-II superconductor
2.6.5 Vortex dynamics: dissipation
2.6.6 Vortex dynamics: flux pinning
2.7 Representative superconducting materials
2.8 Review exercises
References
Chapter 3 Idealised models and equations: examples
3.1 Flux expulsion: Meissner state of a sphere
3.2 The resistive transition: fundamentals
3.3 The critical state
3.4 Josephson junctions
3.4.1 Josephson relations
3.4.2 The SQUID magnetometer
3.4.3 Josephson effect in extended junctions
References
Chapter 4 Some revealing experiments with superconductors
4.1 Transport measurements
Resistivity measurements
Critical current measurements
4.2 Inductive measurements
Basic experiment: quantitative analysis
Interpretation of results
Some final remarks on inductive measurements
4.3 Magneto-optics
4.3.1 Basic experiment: analysis
4.3.2 Quantitative aspects
4.3.3 Interpretation of results
4.4 Force measurements
4.4.1 Macroscopic force measurements
4.4.2 Magnetic force microscopy: experiment
Other techniques
References
Chapter 5 Some useful mathematical resources
5.1 Variational calculus
5.1.1 The basic problem: concept of variation
5.1.2 Constrained variations
5.1.3 Non-smooth solutions
5.2 Discrete formulation
5.2.1 Grids and regions
5.2.2 Vectors and matrices
References
Chapter 6 Introduction to computational methods
6.1 MATLAB: some basics
6.1.1 User's interface
6.1.2 Features of the language
6.1.3 Graphics
6.1.4 Mathematical analysis tools
6.2 GNU Octave
Chapter 7 The resistive transition
7.1 The broadening of the resistive transition
7.2 Evaluation of resistance and activation energies
7.3 Extensions
7.3.1 Influence of the applied current
7.3.2 Activation energies from experimental R(T) data
7.4 Review exercises and challenges
7.4.1 Review exercises
7.4.2 Challenges
References
Chapter 8 Flux transport in type-II superconductors
8.1 The penetration of magnetic fields in superconductors
8.1.1 Variational statement
8.1.2 Discrete formulation
8.2 The critical state model: transport problem
8.2.1 Geometry and circuits
8.2.2 Inductance matrix
8.2.3 Dissipation mechanism
8.2.4 Experimental process
8.2.5 Minimisation
8.2.6 Application and analysis
8.3 The critical state problem: magnetisation
8.3.1 Geometry and circuits
8.3.2 Inductance matrix
8.3.3 Dissipation mechanism
8.3.4 Experimental process
8.3.5 Minimisation
8.3.6 Application and analysis
8.4 Response to non-uniform magnetic fields
8.4.1 The permanent magnet's vector potential
8.4.2 Application and analysis
8.5 Finite resistivity: piece-wise approximation
8.5.1 Minimisation
8.5.2 Application and analysis
8.6 Finite resistivity: power-law approximation
8.6.1 Minimisation
8.6.2 Application and analysis
8.7 Review exercises and challenges
8.7.1 Review exercises
8.7.2 Challenges
References
Chapter 9 Shape effects: demagnetising fields
9.1 Statement of the problem
9.2 The Meissner state in finite samples: ellipsoids and cylinders
9.3 The critical state in finite samples
9.3.1 Bean's model in ellipsoids and cylinders
9.3.2 Analytical approximations for extreme geometries
9.3.3 The internal magnetic field: Jc(B) versus Jc(µ0Ha)
9.4 Review exercises and challenges
9.4.1 Review exercises
9.4.2 Challenges
References
Chapter 10 Thin superconductors: the stream function method
10.1 Statement of the problem
10.1.1 The stream function formalism
10.1.2 The critical state in thin samples
10.1.3 Stream functions: discrete formulation
10.2 Response to applied magnetic fields
10.2.1 Perpendicular fields
10.2.2 Magnetic hysteresis
10.2.3 On-surface magnetic flux density
10.2.4 Application of inclined magnetic fields
10.3 Description of the numerical resources
10.4 Review exercises and challenges
10.4.1 Review exercises
10.4.2 Challenges
References
Chapter 11 Magneto-optical imaging of superconductors
11.1 Magneto-optics in the Meissner state
11.1.1 Physical modelling
11.1.2 Quantification of the MOI signal
11.2 Magneto-optics in the critical state
11.2.1 Thin sample limit: long strips
11.2.2 Thin sample limit: square platelet
11.3 Review exercises and challenges
11.3.1 Review exercises
11.3.2 Challenges
References
Chapter 12 Interaction with magnets: force microscopies
12.1 Forward problem: prediction of the force
12.1.1 Point dipole approximation
12.1.2 Finite size effects
12.2 Inverse problem: prediction of ?L
12.3 Review exercises and challenges
12.3.1 Review exercises
12.3.2 Challenges
References
Chapter 13 Interaction with magnets: levitation
13.1 Levitation in the Meissner state
13.1.1 Meissner state: analytical solutions
13.1.2 Meissner state: numerical solution
13.2 Levitation in the critical state
13.2.1 The issue of mechanical stability
13.2.2 Critical state: analytical solution
13.2.3 Critical state: numerical solutions
13.3 Review exercises and challenges
13.3.1 Review exercises
13.3.2 Challenges
References
Chapter 14 Superconductors and magnets: cloaking devices
14.1 Pre-cloaking: magnetic shielding
14.1.1 Shielding with paramagnets
14.1.2 Shielding with superconductors
14.2 Cloaking bilayers: magnets and superconductors
14.2.1 Cloaking in the Meissner state
14.2.2 Cloaking in the critical state
14.3 Review exercises and challenges
14.3.1 Review exercises
14.3.2 Challenges
References
Chapter 15 Intermediate Josephson junctions
15.1 Critical currents in planar Josephson junctions
15.1.1 Constitutive equations
15.1.2 The integrated current density
15.1.3 The field dependence Ic(B)
15.2 Resistive transitions in the shunted model
15.2.1 The shunted RCSJ model
15.2.2 v(?) relations: overdamped regime
15.2.3 v(?) relations: underdamped regime
15.3 Review exercises and challenges
15.3.1 Review exercises
15.3.2 Challenges
References
Chapter
Outline placeholder
Chapter 6: Introduction to computational methods
Chapter 7: The resistive transition
Chapter 8: Flux transport in type-II superconductors
Chapter 9: Shape effects: demagnetizing fields
Chapter 10: Thin superconductors: the stream function method
Chapter 11: Magneto-optical imaging of superconductors
Chapter 12: Interaction with magnets: force microscopies
Chapter 13: Interaction with magnets: levitation
Chapter 14: Magnets and superconductors: cloaking devices
Chapter 15: Intermediate Josephson junctions
Reference
Chapter
Notation

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