Ac Loss and Macroscopic Theory of Superconductors

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ISBN: 9780415267977 | 0415267978
Cover: Hardcover
Copyright: 7/5/2001

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Through the 'magic' of averages it is shown that Maxwell's equations can be used in a simple way to describe filamentary composites as well as pure bulk superconductors. The second edition of AC Loss and Macroscopic Theory of Superconductors, like the first edition, is written for both physicists and engineers. It starts with a rigorous and partially new derivation of Maxwell's equations as they apply to superconductors, and the remainder of the book is devoted to loss approximations for a wide range of applications. The chapters on high-Tc materials were updated and include a change to SI units and the addition of some historical perspective.

Preface to Second Edition

xiii

Part I Introduction to Applied Superconductivity and Macroscopic Theory

Introduction

(14)

Focus of the Book

(1)

Applications of Superconductors and their Limitations

(1)

High Tc Superconductors

(1)

Loss in a Superconductor

(1)

Critical Current Density

(2)

The Bean Model and its History

(1)

Hysteresis Loss in the Bean Model

(1)

Magnitude of the Electric Field

(1)

Multifilament Conductors, Stability and Eddy Current Loss

(3)

Viewpoint and Scope of the Book

(1)

The ``Magic'' of Volume Averaging

(1)

Units

(3)

References

(3)

Survey of Type-II Superconductivity

(12)

Type-I and Type-II Superconductors

(3)

Vortex Magnetization

(1)

Flux Penetration and Bulk Current Density in a Hard Superconductor

(3)

Extended Bean Models

(1)

Flux Pinning and Critical Current Density

(1)

Origin of the Internal Heat

(3)

References

(2)

Macroscopic Description of Type-II Superconductors

(12)

The Macroscopic Equations in Superconductors and Normal Materials

(1)

The Maxwell-Lorentz Equations

(1)

Derivation of Maxwell's Equations

(2)

Calculation of the Average Charge and Current Density

(2)

Maxwell's Equations in SI Units

(1)

The Family of Maxwell Equations

(1)

True Magnetization and Effective Magnetization

(1)

The Magnetic Moment Under Static Conditions

(1)

The Magnetic Moment of a Long Wire

(1)

Constitutive Equations

(1)

Summary of the Meaning of the Maxwell Variables in Normal Materials and Superconductors

(3)

Notation

(1)

References

(1)

Expressions for the Loss Per Cycle

(10)

The Various Ways of Computing Cyclic Loss

(1)

The Microscopic Applied Field Loss

(1)

The Macroscopic Applied Field Loss

(1)

Loss Per Cycle in SI Units and Approximation for Ordinary Superconductors

(1)

Loss in Terms of the Poynting Vector

(1)

Calculation of the Loss From the Effective Magnetization and Applied Magnetic Field

(1)

Computation of Loss From the Flux for a One-Dimensional Problem

(1)

Loss in a Superconducting Wire with External Leads Attached

(1)

Loss Density

(1)

The Electric Field at a Discontinuity in Tangential Current Density

(1)

Summary

(4)

Part II Hysteresis in Ordinary Bulk Superconductors

Instantaneous Power Loss in a Sheet in the Bean Approximation

(16)

Introduction

(2)

Solution of Maxwell Equations

(2)

Electric Field Near the Surface

(1)

Field Penetration into a Flux-Free Sheet Due to Establishment of a Transport Current and Transverse Applied Field

(1)

Instantaneous Power Loss

(1)

Partial Penetration Power Loss for a Virgin and a Cyclic State

(3)

Above Complete Penetration

(1)

Field Profiles

(2)

Summary of the More Important Loss Expressions

(3)

Notation

(2)

Cyclical Hysteresis in a Sheet

(12)

Loss Per Cycle for No Transport Current

(1)

Effect of a DC Transport Current

(2)

Alternating Current Loss with No Applied Magnetic Field

(1)

Combined Alternating Current and Transverse Field

(1)

Loss Due to a Field Applied Normal to a Strip

(1)

Calculation of Hp

(1)

Effect of a Constant Bias Field

(1)

Improved Loss Expressions

(1)

Summary

(5)

Notation

(1)

References

(2)

Hysteresis Loss in Circular Wires in the Bean Approximation

(30)

Introduction

(1)

Transverse Field Loss for Weak Partial Penetration

(4)

Loss for Full Penetration

(1)

Approximations for the Transverse Field Loss Over the Complete Range of Field

(1)

Longitudinal Field Loss

(3)

Alternating Current Loss

(2)

Dynamic Resistance for Full Penetration

(5)

Dynamic Resistance for Modified Bean Models

(1)

Cyclic Loss for a Combined Alternating Transverse Field and Transport Current

(3)

Transverse Field Loss in Hollow and Concentric Cylinders

(4)

Loss for a Large Transverse Rotating Field

101

(1)

Loss for a Field Having Both Transverse and Longitudinal Components and the Problem of Critical-Current Anisotropy

101

(1)

Summary of Loss Formulas

102

(7)

Notation

105

(1)

References

106

(3)

Part III Multifilament Superconductors

Theory of Filamentary Superconductors

109

(16)

Introduction and History

109

(1)

Coupling Current Models and Coupled Filaments

110

(1)

The Anisotropic Continuum Model

111

(2)

Symmetry of the Continuum

113

(1)

Constitutive Equations

114

(1)

Conductivity for a Single Component Matrix

115

(3)

The Applied Field for a Conductor

118

(1)

The Local Field Applied to a Filament

119

(1)

Values for the Permeability

120

(1)

Expressions for the Loss in a Composite Conductor

121

(1)

Summary

122

(3)

Notation

123

(2)

Transverse Field Loss in Multifilament Conductors

125

(26)

Introduction

125

(1)

Loss for a Slowly Changing Magnetic Field

126

(2)

The Boundary Layer

128

(1)

Shielding Effects and Loss at Higher Frequencies Below the Skin Effect Region

129

(3)

Frequency Dependence in the Skin-Effect Range

132

(1)

Critical Frequencies and Relaxation Times

132

(3)

Loss in the Saturated Region and General Loss Expression for Frequencies Below the Skin-Effect Range

135

(3)

Comparison of the Hysteresis Loss in a Twisted Composite With that of a Solid Superconductor at Low Frequencies

138

(1)

Loss for Periodic Ramped or Pulsed Fields

139

(2)

Effect of a DC Transport Current

141

(1)

Rectangular Multifilament Conductor

141

(1)

Effect of a Sheath

142

(2)

Loss in a Solenoid

144

(1)

Summary

144

(7)

Notation

147

(1)

References

148

(3)

Cables, Longitudinal Field Loss and Miscellaneous Topics

151

(10)

Cables

151

(2)

Ultrafine Filaments

153

(1)

In Situ Superconductors

154

(2)

Effects of Surface Roughness and DC Longitudinal Fields

156

(1)

AC Longitudinal Field Loss for Twisted Filaments

157

(2)

Loss Due to Alternating Transport Current in a Multifilament Conductor

159

(2)

Additional References

159

(2)

Part IV High-Tc Superconductors

161

(34)

Loss in High-Tc Superconductors Exhibiting Granularity

163

(18)

Introduction

163

(1)

Loss from Maxwell Equations for High-Tc Superconductors

164

(2)

The N-Power Law and Loss for a DC Current

166

(1)

Microscopic Model for DC Loss

167

(2)

General Loss Expressions in the Microscopic Picture

169

(2)

Macroscopic Loss Expressions

171

(2)

Hysteresis and the Power Law

173

(1)

Multifilament Conductors

174

(1)

Discussion and Summary

175

(6)

General References

178

(1)

Notation

179

(2)

High-Tc Coated Conductors

181

(14)

Introduction

181

(1)

AC Loss

182

(1)

Ideas for Reducing the AC Loss

182

(2)

Coordinates for a Twisted Strip

184

(1)

Limit on the Twist

185

(1)

Anisotropic Continuum Model for Filamentary Strips on a Substrate

186

(1)

Calculation of the Electric Field for a Transverse Magnetic Field

186

(1)

Transverse Current Density

187

(1)

Perpendicular Field Loss in Twisted Strip Conductor

188

(4)

Transport Current Loss

192

(1)

Transverse Field Combined with Applied Transport Current

192

(1)

Summary and Discussion

193

(2)

Notation

193

(1)

Additional References

194

(1)

Appendix A: Critique of SI Units

195

(3)

Appendix B: Evaluation of Average Charge and Current Density

198

(5)

Appendix C: Data on Resistivity and Critical Current Density

203

(4)

Index

207

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Ac Loss and Macroscopic Theory of Superconductors

Summary

Table of Contents

Supplemental Materials