Practical Design of Magnetostatic Structure Using Numerical Simulation.

By: Wang, QiuliangPublisher: Somerset : John Wiley & Sons, Incorporated, 2013Copyright date: ©2013Edition: 1st edDescription: 1 online resource (498 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118398166Subject(s): Superconductors -- Magnetic properties.;Magnetic instruments -- Design and construction -- Mathematics.;Magnetic instruments -- Mathematical models.;Superconducting magnetsGenre/Form: Electronic books. Additional physical formats: Print version:: Practical Design of Magnetostatic Structure Using Numerical SimulationDDC classification: 621.3/5 LOC classification: QC611.97.M34 -- W36 2013ebOnline resources: Click to View
Contents:
Practical Design of Magnetostatic Structure Using Numerical Simulation -- Contents -- Foreword -- Preface -- 1 Introduction to Magnet Technology -- 1.1 Magnet Classification -- 1.2 Scientific Discoveries in High Magnetic Field -- 1.3 High Field Magnets for Applications -- 1.3.1 Magnets in Energy Science -- 1.3.2 Magnets in Condensed Matter Physics -- 1.3.3 Magnets in NMR and MRI -- 1.3.4 Magnets in Scientific Instruments and Industry -- 1.4 Structure of Magnets -- 1.4.1 Configuration of Solenoid Magnet -- 1.4.2 Racetrack and Saddle-Shaped Magnets -- 1.4.3 Structure of Other Complicated Magnets -- 1.5 Development Trends in High Field Magnets -- 1.6 Numerical Methods for Magnet Design -- 1.7 Summary -- References -- 2 Magnetostatic Equations for the Magnet Structure -- 2.1 Basic Law of Macroscopic Electromagnetic Phenomena -- 2.1.1 Biot-Savart Law -- 2.1.2 Faraday's Law -- 2.2 Mathematical Basis of Classical Electromagnetic Theory -- 2.2.1 Gauss's Theorem -- 2.2.2 Stokes' Theorem -- 2.2.3 Green's Theorem -- 2.2.4 Helmholtz's Theorem -- 2.3 Equations of Magnetostatic Fields -- 2.3.1 Static Magnetic Field Generated by Constant Current in Free Space -- 2.3.2 Basic Properties of Static Magnetic Field -- 2.3.3 Magnetic Media in Static Magnetic Field -- 2.3.4 Boundary Conditions of Magnetostatic Field -- 2.3.5 Boundary-Value Problem of Static Magnetic Field -- 2.3.6 Summary of Equations of Magnetostatic Problem -- 2.4 Summary -- References -- 3 Finite Element Analysis for the Magnetostatic Field -- 3.1 Introduction -- 3.1.1 Basic Concept of the FEM -- 3.1.2 Basic Steps of the FEM -- 3.2 Functional Construction for Static Magnetic Field -- 3.3 Discretization and Interpolation Function of Solution Domain -- 3.3.1 Principle of Selecting Subdivisions in the Domain -- 3.3.2 Selection of Interpolation Function.
3.3.3 Unified Expressions of Interpolation Function -- 3.4 Formulation of System Equations -- 3.4.1 Two-Dimensional Cartesian Coordinate System -- 3.4.2 Three-Dimensional Cartesian Coordinate System -- 3.4.3 Axially Symmetric Scalar Potential System -- 3.5 Solution of System Equation for the FEM -- 3.6 Applied FEM for Magnet Design -- 3.6.1 Magnetic Field for a Superconducting Magnet with LTS and HTS -- 3.6.2 Magnetic Field for a Superferric Dipole Magnet -- 3.6.3 Force Characteristics of a Superconducting Ball in Magnetic Field -- 3.7 Summary -- References -- 4 Integral Method for the Magnetostatic Field -- 4.1 Integral Equation of Static Magnetic Field -- 4.2 Magnetic Field from Current-Carrying Conductor -- 4.2.1 Magnetic Field Generated by Rectangular Conductor -- 4.2.2 Magnetic Field of Arc-Shaped Winding -- 4.2.3 Magnetic Field Generated by Solenoid Coil -- 4.2.4 Magnetic Field of Elliptical Cross-Section Winding -- 4.2.5 Parallel Plane Field -- 4.2.6 Magnetic Field ofWedge-Shaped Current Block with Triangular Cross-Section -- 4.2.7 Magnetic Field of Wedge-Shaped Structure with Rectangular Cross-Section -- 4.3 Magnetic Field with Anisotropic Magnetization -- 4.3.1 Subdivision of Three-Dimensional Ferromagnetic Media -- 4.3.2 Magnetic Field in the Cylindrical Symmetrical System -- 4.4 Case Studies of Complex Coil Structures -- 4.4.1 Magnetic Field Distribution of Superconducting Magnet in Space -- 4.4.2 Superconducting Magnet with Very Small Stray Magnetic Field for an Energy Storage System -- 4.5 Summary -- References -- 5 Numerical Methods for Solenoid Coil Design -- 5.1 Magnet Materials and Performance -- 5.1.1 Basic Properties of Superconducting Materials -- 5.1.2 Material Properties of Copper, Aluminum, and their Alloys -- 5.2 Magnetic Field of the Superconducting Solenoid -- 5.2.1 Solenoid Coils with Uniform Current Density.
5.2.2 Current Density Graded by Multisolenoid Coils -- 5.2.3 Design of High Temperature Superconducting Coils -- 5.3 Design of Resistive Magnets -- 5.3.1 Resistive Magnet with Nonuniform Current Distribution -- 5.3.2 Structure of Bitter Resistive Magnets -- 5.3.3 Resistive Magnet with Iron Yoke -- 5.4 Engineering Design for Superconducting Magnets -- 5.4.1 10 T Cryogen-Free Superconducting Magnet -- 5.4.2 Split Superconducting Magnet System with Large Crossing Warm Bore -- 5.4.3 Superconducting Magnet with Persistent Current Switch -- 5.4.4 Ultrahigh Field Superconducting Magnet -- 5.4.5 A Bi2223 Split Pair Superconducting Magnet for a Propulsion Experiment -- 5.5 Summary -- References -- 6 Series Analysis of Axially Symmetric Magnetic Field -- 6.1 Laplace's Equation in Spherical Coordinates -- 6.1.1 Legendre Equation and Polynomial -- 6.1.2 Orthogonality of the Legendre Polynomial -- 6.1.3 Associated Legendre Function and Spherical Harmonics Ylm(θ,φ) -- 6.1.4 Addition Theorem of Spherical Harmonic Functions -- 6.1.5 Magnetic Vector of Loop Current with Series Expression -- 6.1.6 Magnetic Scalar Potential of Loop Current with Series Expression -- 6.1.7 Magnetic Field of Zonal Current with Series Expression -- 6.2 Series Expression of the Boundary-Value Problem -- 6.2.1 Expansion of Magnetic Induction of Circular Current Filaments -- 6.2.2 Expansion of the Magnetic Induction for Solenoid Coils -- 6.2.3 Expansion of Magnetic Induction of Solenoid at any Position on the z-Axis -- 6.2.4 Expansion of Magnetic Fields with Multi-Current Filaments -- 6.2.5 Expansion of Magnetic Field of Magnetization Loop -- 6.2.6 Calculation of Expansion Coefficients of Arc-Type Coils -- 6.3 Magnetic Induction of Helical Coils -- 6.3.1 Magnetic Field Calculation of Helical Current Filaments -- 6.3.2 Magnetic Induction Generated by Helical Coils.
6.4 Magnetic Field of Multi-Coil Combination -- 6.4.1 Configuration of Highly Homogeneous Field -- 6.4.2 Determination Methods for Parameters of Multi-Section Magnets -- 6.5 Applied Magnetic Field Series Expansion -- 6.5.1 Magnetic Field for a Surgical Magnetic Navigation System -- 6.5.2 Force of Superconducting Sphere in the Magnetic Field -- 6.5.3 Design of Superconducting Magnet Shim Coils -- 6.6 Summary -- References -- 7 High Field Magnet with High Homogeneity -- 7.1 Definition of Magnetic Field Homogeneity -- 7.2 Requirements for Magnets with High Homogeneity -- 7.2.1 Large-Bore MRI Magnet System for Medical Research and Clinical Applications -- 7.2.2 Electronic Cyclotron and Focused Magnet System -- 7.2.3 High Homogeneity Magnet for Scientific Instruments -- 7.2.4 Main Constraint Conditions of Inverse Problem for High Homogeneity Magnet -- 7.3 Design of High Homogeneity Magnet -- 7.3.1 Review of Inverse Problem -- 7.3.2 Continuous Current Distribution Method -- 7.3.3 Solving Nonlinear Equations for the Coil Design -- 7.3.4 Combined Linear and Nonlinear Method for Inverse Problem -- 7.3.5 Regularization Method for Inverse Problem -- 7.3.6 Ferromagnetic Shielding of Superconducting Coil -- 7.3.7 Solving the Magnet Structure by the Fredholm Equation -- 7.3.8 Nonlinear Optimization with Preset Coil Number -- 7.4 Design Example of High Homogeneity Magnet -- 7.4.1 Active-Shield Cylindrical Magnet -- 7.4.2 Openness of MRI Magnet -- 7.4.3 Short-Length Active-Shield MRI Magnet -- 7.5 Design of High Field and High Homogeneity Magnet -- 7.5.1 Minimum Volume Method -- 7.5.2 One-Step Nonlinear Optimal Method -- 7.6 Engineering Designs and Applications -- 7.7 Summary -- References -- 8 Permanent Magnets and their Applications -- 8.1 Introduction to Magnetic Materials -- 8.1.1 Basic Parameters of Magnetism -- 8.1.2 Progress in Magnetic Materials.
8.2 Classification and Characteristics of Permanent Magnets -- 8.2.1 Selection of Permanent Materials -- 8.2.2 Selection of Soft Magnetic Materials -- 8.3 Permanent Magnet Structure Design -- 8.3.1 Magnetic Circuit Design of Permanent Magnet -- 8.3.2 Numerical Methods of Permanent Magnet Design -- 8.4 Design of Magnet for Engineering Applications -- 8.4.1 MRI Permanent Magnets -- 8.4.2 AMS with Permanent Magnet -- 8.4.3 Structure of Six-Pole Permanent Magnet -- 8.4.4 Magnetic Resonance Imaging Logging -- 8.4.5 Q&A Vacuum Birefringence Experimental Magnet -- 8.4.6 Permanent Magnets for Magnetic Resonance Molecular Imaging -- 8.5 Summary -- References -- 9 Shimming Magnetic Field -- 9.1 Magnetostatic Principle for Shimming Magnetic Field -- 9.2 Design Method for Active Shimming Coil -- 9.2.1 Axial Shim Design -- 9.2.2 Radial Coil Design -- 9.2.3 Shim Design by Arbitrary Current Distribution -- 9.2.4 Target-Field Method for MRI Shim Coils -- 9.3 Current Calculation for Active Shim Coils -- 9.4 Passive Shimming Design Method -- 9.4.1 Magnetic Field Produced by Magnetic Material -- 9.4.2 Mathematical Optimization Model -- 9.5 Summary -- References -- 10 Electromechanical Effects and Forces on the Magnet -- 10.1 Magnetostatic Electromechanical Effects on the Solenoid -- 10.1.1 Analytical Method for the Stress Problem in a Solenoid -- 10.1.2 Semi-Analytical Method for the Stress in a Solenoid -- 10.2 Averaged Model of the Magnet -- 10.2.1 Basic Theory of the FEM -- 10.2.2 Averaged Model for FEM -- 10.2.3 Stress Solution for a High Field Magnet -- 10.2.4 Equivalent Elastic Material of Magnet -- 10.3 Detailed FEM for the Ultrahigh Field Solenoid -- 10.3.1 Establishment of the Detailed FEM -- 10.3.2 Mesh Construction in the Detailed Model -- 10.3.3 Analysis Method of the Detailed Model -- 10.3.4 Equivalent Treatment of Electromagnetic Force Loading.
10.3.5 Finite Element Equation of Detailed FEM.
Summary: Qiuliang WangInstitute of electrical Engineering, Chinese Academy of Sciences, China.
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Practical Design of Magnetostatic Structure Using Numerical Simulation -- Contents -- Foreword -- Preface -- 1 Introduction to Magnet Technology -- 1.1 Magnet Classification -- 1.2 Scientific Discoveries in High Magnetic Field -- 1.3 High Field Magnets for Applications -- 1.3.1 Magnets in Energy Science -- 1.3.2 Magnets in Condensed Matter Physics -- 1.3.3 Magnets in NMR and MRI -- 1.3.4 Magnets in Scientific Instruments and Industry -- 1.4 Structure of Magnets -- 1.4.1 Configuration of Solenoid Magnet -- 1.4.2 Racetrack and Saddle-Shaped Magnets -- 1.4.3 Structure of Other Complicated Magnets -- 1.5 Development Trends in High Field Magnets -- 1.6 Numerical Methods for Magnet Design -- 1.7 Summary -- References -- 2 Magnetostatic Equations for the Magnet Structure -- 2.1 Basic Law of Macroscopic Electromagnetic Phenomena -- 2.1.1 Biot-Savart Law -- 2.1.2 Faraday's Law -- 2.2 Mathematical Basis of Classical Electromagnetic Theory -- 2.2.1 Gauss's Theorem -- 2.2.2 Stokes' Theorem -- 2.2.3 Green's Theorem -- 2.2.4 Helmholtz's Theorem -- 2.3 Equations of Magnetostatic Fields -- 2.3.1 Static Magnetic Field Generated by Constant Current in Free Space -- 2.3.2 Basic Properties of Static Magnetic Field -- 2.3.3 Magnetic Media in Static Magnetic Field -- 2.3.4 Boundary Conditions of Magnetostatic Field -- 2.3.5 Boundary-Value Problem of Static Magnetic Field -- 2.3.6 Summary of Equations of Magnetostatic Problem -- 2.4 Summary -- References -- 3 Finite Element Analysis for the Magnetostatic Field -- 3.1 Introduction -- 3.1.1 Basic Concept of the FEM -- 3.1.2 Basic Steps of the FEM -- 3.2 Functional Construction for Static Magnetic Field -- 3.3 Discretization and Interpolation Function of Solution Domain -- 3.3.1 Principle of Selecting Subdivisions in the Domain -- 3.3.2 Selection of Interpolation Function.

3.3.3 Unified Expressions of Interpolation Function -- 3.4 Formulation of System Equations -- 3.4.1 Two-Dimensional Cartesian Coordinate System -- 3.4.2 Three-Dimensional Cartesian Coordinate System -- 3.4.3 Axially Symmetric Scalar Potential System -- 3.5 Solution of System Equation for the FEM -- 3.6 Applied FEM for Magnet Design -- 3.6.1 Magnetic Field for a Superconducting Magnet with LTS and HTS -- 3.6.2 Magnetic Field for a Superferric Dipole Magnet -- 3.6.3 Force Characteristics of a Superconducting Ball in Magnetic Field -- 3.7 Summary -- References -- 4 Integral Method for the Magnetostatic Field -- 4.1 Integral Equation of Static Magnetic Field -- 4.2 Magnetic Field from Current-Carrying Conductor -- 4.2.1 Magnetic Field Generated by Rectangular Conductor -- 4.2.2 Magnetic Field of Arc-Shaped Winding -- 4.2.3 Magnetic Field Generated by Solenoid Coil -- 4.2.4 Magnetic Field of Elliptical Cross-Section Winding -- 4.2.5 Parallel Plane Field -- 4.2.6 Magnetic Field ofWedge-Shaped Current Block with Triangular Cross-Section -- 4.2.7 Magnetic Field of Wedge-Shaped Structure with Rectangular Cross-Section -- 4.3 Magnetic Field with Anisotropic Magnetization -- 4.3.1 Subdivision of Three-Dimensional Ferromagnetic Media -- 4.3.2 Magnetic Field in the Cylindrical Symmetrical System -- 4.4 Case Studies of Complex Coil Structures -- 4.4.1 Magnetic Field Distribution of Superconducting Magnet in Space -- 4.4.2 Superconducting Magnet with Very Small Stray Magnetic Field for an Energy Storage System -- 4.5 Summary -- References -- 5 Numerical Methods for Solenoid Coil Design -- 5.1 Magnet Materials and Performance -- 5.1.1 Basic Properties of Superconducting Materials -- 5.1.2 Material Properties of Copper, Aluminum, and their Alloys -- 5.2 Magnetic Field of the Superconducting Solenoid -- 5.2.1 Solenoid Coils with Uniform Current Density.

5.2.2 Current Density Graded by Multisolenoid Coils -- 5.2.3 Design of High Temperature Superconducting Coils -- 5.3 Design of Resistive Magnets -- 5.3.1 Resistive Magnet with Nonuniform Current Distribution -- 5.3.2 Structure of Bitter Resistive Magnets -- 5.3.3 Resistive Magnet with Iron Yoke -- 5.4 Engineering Design for Superconducting Magnets -- 5.4.1 10 T Cryogen-Free Superconducting Magnet -- 5.4.2 Split Superconducting Magnet System with Large Crossing Warm Bore -- 5.4.3 Superconducting Magnet with Persistent Current Switch -- 5.4.4 Ultrahigh Field Superconducting Magnet -- 5.4.5 A Bi2223 Split Pair Superconducting Magnet for a Propulsion Experiment -- 5.5 Summary -- References -- 6 Series Analysis of Axially Symmetric Magnetic Field -- 6.1 Laplace's Equation in Spherical Coordinates -- 6.1.1 Legendre Equation and Polynomial -- 6.1.2 Orthogonality of the Legendre Polynomial -- 6.1.3 Associated Legendre Function and Spherical Harmonics Ylm(θ,φ) -- 6.1.4 Addition Theorem of Spherical Harmonic Functions -- 6.1.5 Magnetic Vector of Loop Current with Series Expression -- 6.1.6 Magnetic Scalar Potential of Loop Current with Series Expression -- 6.1.7 Magnetic Field of Zonal Current with Series Expression -- 6.2 Series Expression of the Boundary-Value Problem -- 6.2.1 Expansion of Magnetic Induction of Circular Current Filaments -- 6.2.2 Expansion of the Magnetic Induction for Solenoid Coils -- 6.2.3 Expansion of Magnetic Induction of Solenoid at any Position on the z-Axis -- 6.2.4 Expansion of Magnetic Fields with Multi-Current Filaments -- 6.2.5 Expansion of Magnetic Field of Magnetization Loop -- 6.2.6 Calculation of Expansion Coefficients of Arc-Type Coils -- 6.3 Magnetic Induction of Helical Coils -- 6.3.1 Magnetic Field Calculation of Helical Current Filaments -- 6.3.2 Magnetic Induction Generated by Helical Coils.

6.4 Magnetic Field of Multi-Coil Combination -- 6.4.1 Configuration of Highly Homogeneous Field -- 6.4.2 Determination Methods for Parameters of Multi-Section Magnets -- 6.5 Applied Magnetic Field Series Expansion -- 6.5.1 Magnetic Field for a Surgical Magnetic Navigation System -- 6.5.2 Force of Superconducting Sphere in the Magnetic Field -- 6.5.3 Design of Superconducting Magnet Shim Coils -- 6.6 Summary -- References -- 7 High Field Magnet with High Homogeneity -- 7.1 Definition of Magnetic Field Homogeneity -- 7.2 Requirements for Magnets with High Homogeneity -- 7.2.1 Large-Bore MRI Magnet System for Medical Research and Clinical Applications -- 7.2.2 Electronic Cyclotron and Focused Magnet System -- 7.2.3 High Homogeneity Magnet for Scientific Instruments -- 7.2.4 Main Constraint Conditions of Inverse Problem for High Homogeneity Magnet -- 7.3 Design of High Homogeneity Magnet -- 7.3.1 Review of Inverse Problem -- 7.3.2 Continuous Current Distribution Method -- 7.3.3 Solving Nonlinear Equations for the Coil Design -- 7.3.4 Combined Linear and Nonlinear Method for Inverse Problem -- 7.3.5 Regularization Method for Inverse Problem -- 7.3.6 Ferromagnetic Shielding of Superconducting Coil -- 7.3.7 Solving the Magnet Structure by the Fredholm Equation -- 7.3.8 Nonlinear Optimization with Preset Coil Number -- 7.4 Design Example of High Homogeneity Magnet -- 7.4.1 Active-Shield Cylindrical Magnet -- 7.4.2 Openness of MRI Magnet -- 7.4.3 Short-Length Active-Shield MRI Magnet -- 7.5 Design of High Field and High Homogeneity Magnet -- 7.5.1 Minimum Volume Method -- 7.5.2 One-Step Nonlinear Optimal Method -- 7.6 Engineering Designs and Applications -- 7.7 Summary -- References -- 8 Permanent Magnets and their Applications -- 8.1 Introduction to Magnetic Materials -- 8.1.1 Basic Parameters of Magnetism -- 8.1.2 Progress in Magnetic Materials.

8.2 Classification and Characteristics of Permanent Magnets -- 8.2.1 Selection of Permanent Materials -- 8.2.2 Selection of Soft Magnetic Materials -- 8.3 Permanent Magnet Structure Design -- 8.3.1 Magnetic Circuit Design of Permanent Magnet -- 8.3.2 Numerical Methods of Permanent Magnet Design -- 8.4 Design of Magnet for Engineering Applications -- 8.4.1 MRI Permanent Magnets -- 8.4.2 AMS with Permanent Magnet -- 8.4.3 Structure of Six-Pole Permanent Magnet -- 8.4.4 Magnetic Resonance Imaging Logging -- 8.4.5 Q&A Vacuum Birefringence Experimental Magnet -- 8.4.6 Permanent Magnets for Magnetic Resonance Molecular Imaging -- 8.5 Summary -- References -- 9 Shimming Magnetic Field -- 9.1 Magnetostatic Principle for Shimming Magnetic Field -- 9.2 Design Method for Active Shimming Coil -- 9.2.1 Axial Shim Design -- 9.2.2 Radial Coil Design -- 9.2.3 Shim Design by Arbitrary Current Distribution -- 9.2.4 Target-Field Method for MRI Shim Coils -- 9.3 Current Calculation for Active Shim Coils -- 9.4 Passive Shimming Design Method -- 9.4.1 Magnetic Field Produced by Magnetic Material -- 9.4.2 Mathematical Optimization Model -- 9.5 Summary -- References -- 10 Electromechanical Effects and Forces on the Magnet -- 10.1 Magnetostatic Electromechanical Effects on the Solenoid -- 10.1.1 Analytical Method for the Stress Problem in a Solenoid -- 10.1.2 Semi-Analytical Method for the Stress in a Solenoid -- 10.2 Averaged Model of the Magnet -- 10.2.1 Basic Theory of the FEM -- 10.2.2 Averaged Model for FEM -- 10.2.3 Stress Solution for a High Field Magnet -- 10.2.4 Equivalent Elastic Material of Magnet -- 10.3 Detailed FEM for the Ultrahigh Field Solenoid -- 10.3.1 Establishment of the Detailed FEM -- 10.3.2 Mesh Construction in the Detailed Model -- 10.3.3 Analysis Method of the Detailed Model -- 10.3.4 Equivalent Treatment of Electromagnetic Force Loading.

10.3.5 Finite Element Equation of Detailed FEM.

Qiuliang WangInstitute of electrical Engineering, Chinese Academy of Sciences, China.

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