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E-raamat: Practical Design of Magnetostatic Structure Using Numerical Simulation

(Institute of Electrical Engineering, Chinese Academy of Sciences, China)
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  • Ilmumisaeg: 20-Mar-2013
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118398166
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-Mar-2013
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118398166
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"Covers extensively the magnet design and computation aspects from theories to practical applications, emphasizing design methods of practical structures such as superconducting, electromagnetic and permanent magnet for use in various scientific instruments, industrial processing, biomedicine and special electrical equipments"--

Writing mainly for practicing engineers engaged in magnet design, but perhaps also graduate students conducting their research, Wang (electrical engineering, Chinese Academy of Sciences) illustrates in some detail approaches to solving several kinds of magnet design problems. Among his topics are magnetostatic equations for the magnet structure, finite element analysis for the magnetostatic field, numerical methods for solenoid coil design, a high field magnet with high homogeneity, and elecromechanical effects and forces on the magnet. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)

Covers the practical numerical method for the analysis and design of magnets

Extensively covers the magnet design and computation aspects from theories to practical applications, emphasizing design methods of practical structures such as superconducting, electromagnetic and permanent magnet for use in various scientific instruments, industrial processing, biomedicine and special electrical equipments. The computations cover a wide range of numerical techniques and analytical derivation to efficiently provide solutions to complicated problems that are often encountered in practice, where simple analytical calculations are no longer adequate.

Chapters include: Introduction of Magnet Technology, Magnetostatic Equation for the Magnet Structure, Finite Element Analysis for Magnetostatic Field, Integral Method for Magnetostatic Field, Numerical Method of Solenoid Coils Design, Series Analysis of Axially Symmetric Magnetic Field, Magnets with High Magnetic Field and High Homogeneity, Permanent Magnet and its Applications, Shimming Magnetic Field with Optimal Magnet Structure, Electro-Mechanical Effect of Magnet, Calculation Formula of Magnetic Field Vector/Recurrence Formula of Legendre Function/Magnetization Equation in Cylindrical Coordinate System.

  • Presents a clear introduction to magnet technology, followed by basic theories, numerical analysis and practical applications
  • Emphasizes the latest developments in magnet design, including MRI systems, and provides comprehensive numerical techniques that provide solutions to practical problems
  • Covers the most recent developments on magnet design and application as well as emphasizing latest computation techniques for optimising and characterising the magnetostatic structure design

Essential reading for Researchers in Magnets and Applications, Materials Scientists, Structural Engineers, Graduate students in Electrical Engineering.

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