Flux Pinning in Superconductors

by Teruo Matsushita

Overview

This book covers the flux pinning mechanisms and properties and the electromagnetic phenomena caused by the flux pinning common for metallic, high-Tc and MgB2 superconductors. The condensation energy interaction known for normal precipitates or grain boundaries and the kinetic energy interaction proposed for artificial Nb pins in Nb-Ti, etc., are introduced for the pinning mechanism. Summation theories to derive the critical current density are discussed in detail. Irreversible magnetization and AC loss caused by the flux pinning are also discussed. The loss originally stems from the ohmic dissipation of normal electrons in the normal core driven by the electric field induced by the flux motion.

The influence of the flux pinning on the vortex phase diagram in high Tc superconductors is discussed, and the dependencies of the irreversibility field are also described on other quantities such as anisotropy of superconductor, specimen size and electric field strength. Recent developments of critical current properties in various high-Tc superconductors and MgB2 are introduced.

The 3^rd edition has been thoroughly updated, with a new chapter on critical state model. The mechanism of irreversible properties is discussed in detail. The author provides calculations of pinning loss by the equation of motion of flux lines in the pinning potential and hysteresis loss.

The readers will learn why the resultant loss is of hysteresis type in spite of such mechanism. This book aims for graduate students and researchers studying superconductivity as well as engineers working in electric utility industry.

Product Details

ISBN-13:	9783030946418
Publisher:	Springer International Publishing
Publication date:	09/01/2022
Series:	Springer Series in Solid-State Sciences , #198
Edition description:	3rd ed. 2022
Pages:	493
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Teruo Matsushita is professor emeritus in the Faculty of Computer Science and Systems Engineering at the Kyushu Institute of Technology, Japan, having served as Vice President of the institute from 1999 to 2003. His research area is wide, ranging from fundamental physics to applications associated with flux pinning phenomena in superconductors. In 2014 he published the Springer undergraduate textbook Electricity and Magnetism, which now boasts close to 2 million downloads.

Table of Contents

Introduction     1
Superconducting Phenomena     1
Kinds of Superconductors     3
London Theory     6
Ginzburg-Landau Theory     9
Magnetic Properties     16
Quantization of Magnetic Flux     16
Vicinity of Lower Critical Field     17
Vicinity of Upper Critical Field     24
Surface Superconductivity     30
Josephson Effect     32
Critical Current Density     34
Flux Pinning Effect     38
References     40
Fundamental Electromagnetic Phenomena in Superconductors     41
Equations of Electromagnetism     41
Flux Flow     45
Mechanism of Hysteresis Loss     51
Characteristic of the Critical State Model and its Applicable Range     54
Irreversible Phenomena     55
Effect of Diamagnetism     66
AC Losses     76
References     82
Various Electromagnetic Phenomena     85
Geometrical Effect     85
Loss in Superconducting Wire due to AC Current     85
Loss in Superconducting Wire of Ellipsoidal Cross Section and Thin Strip due to AC Current     89
Transverse Magnetic Field     90
Rotating Magnetic Field     92
Dynamic Phenomena     95
Superposition of AC Magnetic Field     97
Rectifying Effect     97
Reversible Magnetization     100
Abnormal Transverse Magnetic Field Effect     102
Flux Jump     103
Surface Irreversibility     108
DC Susceptibility     119
Reversible Flux Motion     125
Flux Creep     138
References     152
Longitudinal Magnetic Field Effect     155
Outline of Longitudinal Magnetic Field Effect     155
Flux-Cutting Model     161
Stability of the Force-Free State     168
Motion of Flux Lines     175
Critical Current Density     186
Generalized Critical State Model     191
Resistive State     194
References     207
Measurement Methods for Critical Current Density     209
Four Terminal Method     209
DC Magnetization Method     212
Campbell's Method     213
Other AC Inductive Methods     221
Third Harmonic Analysis     221
AC Susceptibility Measurement     225
References     231
Flux Pinning Mechanisms     233
Elementary Pinning and the Summation Problem     233
Elementary Pinning Force     234
Condensation Energy Interaction     237
Normal Precipitates     237
Grain Boundary     245
Elastic Interaction     253
Magnetic Interaction     258
Kinetic Energy Interaction     259
Improvement of Pinning Characteristics     261
References     264
Flux Pinning Characteristics     267
Flux Pinning Characteristics     267
Elastic Moduli of Flux Line Lattice     271
Summation Problem     275
Statistical Theory     275
Dynamic Theory     283
Larkin-Ovchinnikov Theory     286
Coherent Potential Approximation Theory     292
Comparison with Experiments     297
Qualitative Comparison     298
Quantitative Comparison     306
Problems in Summation Theories     307
Saturation Phenomenon     310
Saturation and Nonsaturation     310
The Kramer Model     313
Model of Evetts et al      316
Comparison Between Models and Experiments     316
Avalanching Flow Model     320
Peak Effect and Related Phenomena     322
Pinning Potential Energy     331
References     337
High-Temperature Superconductors     341
Anisotropy of Superconductors     341
Phase Diagram of Flux Lines     345
Melting Transition     345
Vortex Glass-Liquid Transition     346
Order-Disorder Transition     352
Phase Diagram of Flux Lines in Each Superconductor     357
Size Effect     359
Other Theoretical Predictions     360
Weak Links of Grain Boundaries     361
Electromagnetic Properties     365
Anisotropy     365
Differences in the Size Effect due to the Dimensionality     367
Flux Creep     372
E-J Curve     374
Josephson Plasma     378
Irreversibility Field     380
Analytic Solution of Irreversibility Field     380
Effect of Distribution of Pinning Strength     381
Comparison with Flux Creep-Flow Model     383
Relation with G-L Transition     391
Flux Pinning Properties     394
Y-123     394
Bi-2223     402
Bi-2212     406
References     409
MgB[subscript 2]     413
Superconducting Properties     413
Flux Pinning Properties     415
Wires and Bulk Materials     415
Thin Films     428
Possibility of Improvements in the Future     430
References     433
Appendix     435
Description of Equilibrium State     435
Magnetic Properties of a Small Superconductor     437
Minimization of Energy Dissipation     439
Partition of Pinning Energy     440
Comments on the Nonlocal Theory of the Elasticity of the Flux Line Lattice     441
Avalanching Flux Flow Model     448
Josephson Penetration Depth     452
On the Transverse Flux Bundle Size     452
References     461
Answers to Exercises     463
Index     499