Foreword |
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xi | |
Preface |
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xiii | |
1 Introduction to Magnet Technology |
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1 | (16) |
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1.1 Magnet Classification |
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1 | (2) |
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1.2 Scientific Discoveries in High Magnetic Field |
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3 | (1) |
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1.3 High Field Magnets for Applications |
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3 | (4) |
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1.3.1 Magnets in Energy Science |
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4 | (1) |
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1.3.2 Magnets in Condensed Matter Physics |
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4 | (1) |
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1.3.3 Magnets in NMR and MRI |
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5 | (1) |
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1.3.4 Magnets in Scientific Instruments and Industry |
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6 | (1) |
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7 | (3) |
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1.4.1 Configuration of Solenoid Magnet |
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7 | (1) |
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1.4.2 Racetrack and Saddle-Shaped Magnets |
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7 | (3) |
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1.4.3 Structure of Other Complicated Magnets |
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10 | (1) |
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1.5 Development Trends in High Field Magnets |
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10 | (2) |
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1.6 Numerical Methods for Magnet Design |
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12 | (2) |
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14 | (1) |
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14 | (3) |
2 Magnetostatic Equations for the Magnet Structure |
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17 | (22) |
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2.1 Basic Law of Macroscopic Electromagnetic Phenomena |
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17 | (3) |
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17 | (1) |
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18 | (2) |
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2.2 Mathematical Basis of Classical Electromagnetic Theory |
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20 | (5) |
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20 | (1) |
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20 | (1) |
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21 | (1) |
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2.2.4 Helmholtz's Theorem |
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21 | (4) |
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2.3 Equations of Magnetostatic Fields |
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25 | (12) |
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2.3.1 Static Magnetic Field Generated by Constant Current in Free Space |
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25 | (1) |
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2.3.2 Basic Properties of Static Magnetic Field |
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26 | (3) |
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2.3.3 Magnetic Media in Static Magnetic Field |
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29 | (3) |
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2.3.4 Boundary Conditions of Magnetostatic Field |
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32 | (2) |
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2.3.5 Boundary-Value Problem of Static Magnetic Field |
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34 | (1) |
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2.3.6 Summary of Equations of Magnetostatic Problem |
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35 | (2) |
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37 | (1) |
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37 | (2) |
3 Finite Element Analysis for the Magnetostatic Field |
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39 | (50) |
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39 | (2) |
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3.1.1 Basic Concept of the FEM |
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39 | (1) |
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3.1.2 Basic Steps of the FEM |
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40 | (1) |
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3.2 Functional Construction for Static Magnetic Field |
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41 | (3) |
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3.3 Discretization and Interpolation Function of Solution Domain |
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44 | (24) |
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3.3.1 Principle of Selecting Subdivisions in the Domain |
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45 | (1) |
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3.3.2 Selection of Interpolation Function |
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45 | (22) |
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3.3.3 Unified Expressions of Interpolation Function |
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67 | (1) |
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3.4 Formulation of System Equations |
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68 | (6) |
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3.4.1 Two-Dimensional Cartesian Coordinate System |
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69 | (1) |
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3.4.2 Three-Dimensional Cartesian Coordinate System |
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70 | (1) |
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3.4.3 Axially Symmetric Scalar Potential System |
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71 | (3) |
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3.5 Solution of System Equation for the FEM |
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74 | (2) |
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3.6 Applied FEM for Magnet Design |
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76 | (11) |
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3.6.1 Magnetic Field for a Superconducting Magnet with LTS and HTS |
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76 | (2) |
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3.6.2 Magnetic Field for a Superferric Dipole Magnet |
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78 | (3) |
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3.6.3 Force Characteristics of a Superconducting Ball in Magnetic Field |
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81 | (6) |
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87 | (1) |
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87 | (2) |
4 Integral Method for the Magnetostatic Field |
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89 | (56) |
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4.1 Integral Equation of Static Magnetic Field |
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89 | (2) |
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4.2 Magnetic Field from Current-Carrying Conductor |
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91 | (37) |
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4.2.1 Magnetic Field Generated by Rectangular Conductor |
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91 | (5) |
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4.2.2 Magnetic Field of Arc-Shaped Winding |
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96 | (18) |
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4.2.3 Magnetic Field Generated by Solenoid Coil |
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114 | (5) |
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4.2.4 Magnetic Field of Elliptical Cross-Section Winding |
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119 | (3) |
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4.2.5 Parallel Plane Field |
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122 | (1) |
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4.2.6 Magnetic Field of Wedge-Shaped Current Block with Triangular Cross-Section |
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123 | (3) |
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4.2.7 Magnetic Field of Wedge-Shaped Structure with Rectangular Cross-Section |
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126 | (2) |
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4.3 Magnetic Field with Anisotropic Magnetization |
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128 | (11) |
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4.3.1 Subdivision of Three-Dimensional Ferromagnetic Media |
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129 | (4) |
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4.3.2 Magnetic Field in the Cylindrical Symmetrical System |
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133 | (6) |
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4.4 Case Studies of Complex Coil Structures |
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139 | (3) |
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4.4.1 Magnetic Field Distribution of Superconducting Magnet in Space |
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139 | (1) |
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4.4.2 Superconducting Magnet with Very Small Stray Magnetic Field for an Energy Storage System |
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140 | (2) |
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142 | (1) |
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142 | (3) |
5 Numerical Methods for Solenoid Coil Design |
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145 | (60) |
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5.1 Magnet Materials and Performance |
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145 | (11) |
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5.1.1 Basic Properties of Superconducting Materials |
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146 | (7) |
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5.1.2 Material Properties of Copper, Aluminum, and their Alloys |
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153 | (3) |
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5.2 Magnetic Field of the Superconducting Solenoid |
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156 | (25) |
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5.2.1 Solenoid Coils with Uniform Current Density |
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158 | (9) |
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5.2.2 Current Density Graded by Multisolenoid Cons |
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167 | (10) |
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5.2.3 Design of High Temperature Superconducting Coils |
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177 | (4) |
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5.3 Design of Resistive Magnets |
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181 | (5) |
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5.3.1 Resistive Magnet with Nonuniform Current Distribution |
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183 | (1) |
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5.3.2 Structure of Bitter Resistive Magnets |
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184 | (2) |
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5.3.3 Resistive Magnet with Iron Yoke |
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186 | (1) |
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5.4 Engineering Design for Superconducting Magnets |
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186 | (15) |
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5.4.1 10 T Cryogen-Free Superconducting Magnet |
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186 | (2) |
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5.4.2 Split Superconducting Magnet System with Large Crossing Warm Bore |
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188 | (4) |
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5.4.3 Superconducting Magnet with Persistent Current Switch |
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192 | (2) |
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5.4.4 Ultrahigh Field Superconducting Magnet |
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194 | (1) |
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5.4.5 A Bi2223 Split Pair Superconducting Magnet for a Propulsion Experiment |
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195 | (6) |
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201 | (1) |
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201 | (4) |
6 Series Analysis of Axially Symmetric Magnetic Field |
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205 | (58) |
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6.1 Laplace's Equation in Spherical Coordinates |
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205 | (18) |
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6.1.1 Legendre Equation and Polynomial |
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206 | (2) |
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6.1.2 Orthogonality of the Legendre Polynomial |
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208 | (2) |
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6.1.3 Associated Legendre Function and Spherical Harmonics Ylm(θ,φ) |
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210 | (2) |
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6.1.4 Addition Theorem of Spherical Harmonic Functions |
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212 | (2) |
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6.1.5 Magnetic Vector of Loop Current with Series Expression |
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214 | (2) |
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6.1.6 Magnetic Scalar Potential of Loop Current with Series Expression |
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216 | (2) |
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6.1.7 Magnetic Field of Zonal Current with Series Expression |
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218 | (5) |
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6.2 Series Expression of the Boundary-Value Problem |
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223 | (19) |
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6.2.1 Expansion of Magnetic Induction of Circular Current Filaments |
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224 | (2) |
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6.2.2 Expansion of the Magnetic Induction for Solenoid Coils |
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226 | (1) |
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6.2.3 Expansion of Magnetic Induction of Solenoid at any Position on the z-Axis |
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227 | (5) |
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6.2.4 Expansion of Magnetic Fields with Multi-Current Filaments |
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232 | (1) |
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6.2.5 Expansion of Magnetic Field of Magnetization Loop |
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233 | (2) |
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6.2.6 Calculation of Expansion Coefficients of Arc-Type Coils |
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235 | (7) |
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6.3 Magnetic Induction of Helical Coils |
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242 | (5) |
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6.3.1 Magnetic Field Calculation of Helical Current Filaments |
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242 | (1) |
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6.3.2 Magnetic Induction Generated by Helical Coils |
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243 | (4) |
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6.4 Magnetic Field of Multi-Coil Combination |
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247 | (2) |
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6.4.1 Configuration of Highly Homogeneous Field |
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247 | (1) |
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6.4.2 Determination Methods for Parameters of Multi-Section Magnets |
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248 | (1) |
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6.5 Applied Magnetic Field Series Expansion |
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249 | (12) |
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6.5.1 Magnetic Field for a Surgical Magnetic Navigation System |
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249 | (3) |
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6.5.2 Force of Superconducting Sphere in the Magnetic Field |
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252 | (7) |
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6.5.3 Design of Superconducting Magnet Shim Coils |
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259 | (2) |
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261 | (1) |
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261 | (2) |
7 High Field Magnet with High Homogeneity |
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263 | (58) |
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7.1 Definition of Magnetic Field Homogeneity |
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263 | (1) |
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7.2 Requirements for Magnets with High Homogeneity |
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264 | (7) |
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7.2.1 Large-Bore MRI Magnet System for Medical Research and Clinical Applications |
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264 | (3) |
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7.2.2 Electronic Cyclotron and Focused Magnet System |
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267 | (1) |
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7.2.3 High Homogeneity Magnet for Scientific Instruments |
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267 | (2) |
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7.2.4 Main Constraint Conditions of Inverse Problem for High Homogeneity Magnet |
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269 | (2) |
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7.3 Design of High Homogeneity*Magnet |
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271 | (19) |
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7.3.1 Review of Inverse Problem |
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271 | (2) |
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7.3.2 Continuous Current Distribution Method |
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273 | (4) |
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7.3.3 Solving Nonlinear Equations for the Coil Design |
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277 | (2) |
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7.3.4 Combined Linear and Nonlinear Method for Inverse Problem |
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279 | (2) |
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7.3.5 Regularization Method for Inverse Problem |
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281 | (3) |
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7.3.6 Ferromagnetic Shielding of Superconducting Coil |
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284 | (2) |
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7.3.7 Solving the Magnet Structure by the Fredholm Equation |
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286 | (1) |
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7.3.8 Nonlinear Optimization with Preset Coil Number |
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287 | (3) |
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7.4 Design Example of High Homogeneity Magnet |
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290 | (15) |
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7.4.1 Active-Shield Cylindrical Magnet |
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290 | (11) |
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7.4.2 Openness of MRI Magnet |
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301 | (1) |
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7.4.3 Short-Length Active-Shield MRI Magnet |
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302 | (3) |
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7.5 Design of High Field and High Homogeneity Magnet |
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305 | (4) |
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7.5.1 Minimum Volume Method |
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305 | (2) |
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7.5.2 One-Step Nonlinear Optimal Method |
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307 | (2) |
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7.6 Engineering Designs and Applications |
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309 | (8) |
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317 | (1) |
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318 | (3) |
8 Permanent Magnets and their Applications |
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321 | (46) |
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8.1 Introduction to Magnetic Materials |
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321 | (3) |
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8.1.1 Basic Parameters of Magnetism |
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321 | (1) |
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8.1.2 Progress in Magnetic Materials |
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322 | (2) |
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8.1 Classification and Characteristics of Permanent Magnets |
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324 | (7) |
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8.2.1 Selection of Permanent Materials |
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324 | (2) |
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8.2.2 Selection of Soft Magnetic Materials |
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326 | (5) |
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8.3 Permanent Magnet Structure Design |
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331 | (10) |
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8.3.1 Magnetic Circuit Design of Permanent Magnet |
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331 | (3) |
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8.3.2 Numerical Methods of Permanent Magnet Design |
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334 | (7) |
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8.4 Design of Magnet for Engineering Applications |
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341 | (23) |
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8.4.1 MRI Permanent Magnets |
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341 | (8) |
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8.4.2 AMS with Permanent Magnet |
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349 | (5) |
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8.4.3 Structure of Six-Pole Permanent Magnet |
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354 | (1) |
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8.4.4 Magnetic Resonance Imaging Logging |
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354 | (5) |
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8.4.5 Q&A Vacuum Birefringence Experimental Magnet |
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359 | (3) |
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8.4.6 Permanent Magnets for Magnetic Resonance Molecular Imaging |
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362 | (2) |
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364 | (1) |
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365 | (2) |
9 Shimming Magnetic Field |
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367 | (56) |
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9.1 Magnetostatic Principle for Shimming Magnetic Field |
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367 | (5) |
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9.2 Design Method for Active Shimming Coil |
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372 | (39) |
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372 | (10) |
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382 | (15) |
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9.2.3 Shim Design by Arbitrary Current Distribution |
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397 | (3) |
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9.2.4 Target-Field Method for MRI Shim Coils |
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400 | (11) |
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9.3 Current Calculation for Active Shim Coils |
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411 | (3) |
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9.4 Passive Shimming Design Method |
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414 | (6) |
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9.4.1 Magnetic Field Produced by Magnetic Material |
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415 | (1) |
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9.4.2 Mathematical Optimization Model |
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416 | (4) |
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420 | (1) |
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420 | (3) |
10 Electromechanical Effects and Forces on the Magnet |
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423 | (54) |
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10.1 Magnetostatic Electromechanical Effects on the Solenoid |
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423 | (12) |
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10.1.1 Analytical Method for the Stress Problem in a Solenoid |
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423 | (2) |
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10.1.2 Semi-Analytical Method for the Stress in a Solenoid |
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425 | (10) |
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10.2 Averaged Model of the Magnet |
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435 | (10) |
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10.2.1 Basic Theory of the FEM |
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435 | (1) |
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10.2.2 Averaged Model for FEM |
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436 | (1) |
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10.2.3 Stress Solution for a High Field Magnet |
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437 | (6) |
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10.2.4 Equivalent Elastic Material of Magnet |
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443 | (2) |
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10.3 Detailed FEM for the Ultrahigh Field Solenoid |
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445 | (14) |
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10.3.1 Establishment of the Detailed FEM |
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445 | (8) |
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10.3.2 Mesh Construction in the Detailed Model |
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453 | (3) |
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10.3.3 Analysis Method of the Detailed Model |
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456 | (1) |
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10.3.4 Equivalent Treatment of Electromagnetic Force Loading |
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456 | (2) |
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10.3.5 Finite Element Equation of Detailed FEM |
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458 | (1) |
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10.4 Mutual Inductance and Force Calculations |
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459 | (3) |
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10.5 Detailed Model for Electromechanical Stress Analysis |
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462 | (10) |
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10.5.1 Electromagnetic Stress Analysis of 11.75 T NMR Magnet |
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462 | (4) |
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10.5.2 Stress Analysis of a 19 T Insert |
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466 | (4) |
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10.5.3 Stress Analysis of a 9.4 T/800 mm MRI Magnet |
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470 | (2) |
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472 | (1) |
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473 | (4) |
Index |
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477 | |