Flux Pinning in Superconductors

Description

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 3rd 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. Preface to the Third Edition Preface to the Second Edition Preface to the First Edition Contents 1 Introduction Abstract 1.1 Superconducting Phenomena 1.2 Kinds of Superconductors 1.3 London Theory 1.4 Ginzburg-Landau Theory 1.5 Magnetic Properties 1.5.1 Quantization of Magnetic Flux 1.5.2 Vicinity of Lower Critical Field 1.5.3 Vicinity of Upper Critical Field 1.6 Surface Superconductivity 1.7 Josephson Effect 1.8 Critical Current Density 1.8.1 Depairing Current Density 1.8.2 Meissner Current Density 1.8.3 Critical Current Density by Flux Pinning 1.9 Flux Pinning Effect 1.10 Exercises References 2 Fundamental Electromagnetic Phenomena in Superconductors Abstract 2.1 Equations of Electromagnetism 2.2 Flux Flow 2.3 Mechanism of Hysteresis Loss 2.4 Characteristic of the Critical State Model and Its Applicable Range 2.5 Irreversible Phenomena 2.6 Effect of Diamagnetism 2.7 AC Losses 2.8 Exercises References 3 Various Electromagnetic Phenomena Abstract 3.1 Geometrical Effect 3.1.1 Loss in Superconducting Wire Due to AC Current 3.1.2 Loss in Superconducting Wire of Ellipsoidal Cross Section and Thin Strip Due to AC Current 3.1.3 Transverse Magnetic Field 3.1.4 Rotating Magnetic Field 3.1.5 AC Loss in a Thin Superconducting Strip in Normal Magnetic Field 3.2 Dynamic Phenomena 3.3 Superposition of AC Magnetic Field 3.3.1 Rectifying Effect 3.3.2 Reversible Magnetization 3.3.3 Abnormal Transverse Magnetic Field Effect 3.4 Flux Jump 3.5 Surface Irreversibility 3.6 DC Susceptibility 3.7 Reversible Flux Motion 3.8 Flux Creep 3.9 Exercises References 4 Critical State Theory Abstract 4.1 Pinning Loss 4.2 Critical State Theory 4.3 Minimum Energy Dissipation 4.4 Exercises References 5 Longitudinal Magnetic Field Effect Abstract 5.1 Outline of Longitudinal Magnetic Field Effect 5.2 Flux-Cutting Model 5.3 Stability of the Force-Free State 5.4 Motion of Flux Lines 5.5 Critical Current Density 5.6 Generalized Critical State Model 5.7 Resistive State 5.8 On the Flux Cutting 5.9 Exercises References 6 Measurement Methods for Critical Current Density Abstract 6.1 Four-Terminal Method 6.2 DC Magnetization Method 6.3 Campbell’s Method 6.4 Other AC Inductive Methods 6.4.1 Third Harmonic Analysis 6.4.2 AC Susceptibility Measurement 6.5 Exercises References 7 Flux Pinning Mechanisms Abstract 7.1 Elementary Pinning and the Summation Problem 7.2 Elementary Pinning Force 7.3 Condensation Energy Interaction 7.3.1 Normal Precipitates 7.3.2 Grain Boundary 7.4 Elastic Interaction 7.5 Magnetic Interaction 7.6 Kinetic Energy Interaction 7.7 Improvement of Pinning Characteristics 7.8 Exercises References 8 Flux Pinning Characteristics Abstract 8.1 Flux Pinning Characteristics 8.2 Elastic Moduli of Flux Line Lattice 8.3 Summation Problem 8.3.1 Statistical Theory 8.3.2 Dynamic Theory 8.3.3 Larkin-Ovchinnikov Theory 8.3.4 Coherent Potential Approximation Theory 8.4 Comparison with Experiments 8.4.1 Qualitative Comparison 8.4.2 Quantitative Comparison 8.4.3 Problems in Summation Theories 8.5 Saturation Phenomenon 8.5.1 Saturation and Nonsaturation 8.5.2 Kramer Model 8.5.3 Model of Evetts et al. 8.5.4 Comparison Between Models and Experiments 8.5.5 Avalanching Flux Flow Model 8.6 Peak Effect and Related Phenomena 8.7 Upper Limit of Critical Current Density 8.8 Pinning Potential Energy 8.9 Exercises References 9 High-Temperature Superconductors Abstract 9.1 Anisotropy of Superconductors 9.2 Phase Diagram of Flux Lines 9.2.1 Melting Transition 9.2.2 Vortex Glass-Liquid Transition 9.2.3 Order-Disorder Transition 9.2.4 Phase Diagram of Flux Lines in Each Superconductor 9.2.5 Size Effect 9.2.6 Other Theoretical Predictions 9.3 Weak Links of Grain Boundaries 9.4 Electromagnetic Properties 9.4.1 Anisotropy 9.4.2 Differences in the Size Effect Due to the Dimensionality 9.4.3 Flux Creep 9.4.4 E-J Curve 9.4.5 Josephson Plasma 9.5 Irreversibility Field 9.5.1 Analytic Solution of Irreversibility Field 9.5.2 Effect of Distribution of Pinning Strength 9.5.3 Comparison with Flux Creep-Flow Model 9.5.4 Relation with G-L Transition 9.6 Flux Pinning Properties 9.6.1 RE-123 9.6.2 Bi-2223 9.6.3 Bi-2212 9.7 Upper Limit of Critical Current Density 9.8 Exercises References 10 MgB2 Abstract 10.1 Superconducting Properties 10.2 Critical Current Properties 10.2.1 Wires and Bulk Materials 10.2.2 Thin Films 10.3 Flux Pinning Properties 10.3.1 Pinning Property in the Low Magnetic Field Region 10.3.2 Pinning Properties in the High Magnetic Field Region 10.4 Upper Limit of Critical Current Density 10.5 Exercises References Appendix A.1 Tinkham’s Critical Current Density A.2 Description of Equilibrium State A.3 Magnetic Properties of a Small Superconductor A.4 Partition of Pinning Energy A.5 Comments on the Nonlocal Theory of the Elasticity of the Flux Line Lattice A.6 Avalanching Flux Flow Model A.7 Josephson Penetration Depth A.8 On the Transverse Flux Bundle Size References Answers to Exercises Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 References Index