This comprehensive book provides fundamentals of magnetic field design in accelerators as well as detailed coverage of analytical and numerical field computation, mathematical optimization and multiphysics simulations.
Table of Contents
VOLUME 1: FOUNDATIONS OF FIELD COMPUTATION AND MAGNETIC MEASUREMENTS1 Algebraic Structures and Vector Fields
1.1 Groups, Rings, and Fields
1.2 Mappings
1.3 Real functions
1.4 Vector Spaces
1.5 Linear Transformations
1.6 Affine Space
1.7 Inner Product Space
1.8 Orientation
1.9 A Glimpse on Topological Concepts
1.10 Exterior Products
1.11 Identities of Vector Algebra
1.12 Vector Fields
1.13 Phase Portraits
1.14 Matrix Algebra
1.15 The Physical Dimension System
2 Classical Vector Analysis
2.1 Space Curves
2.2 The Directional Derivative
2.3 Gradient, Divergence, and Curl
2.4 Identities of Vector Analysis
2.5 Surfaces in E3
2.6 The Differential
2.7 Differential Operators on Scalar and Vector Fields in r and r 0
2.8 The Path Integral of a Vector Field
2.9 Coordinate-Free Definitions of the Differential Operators
2.10 Integral Theorems
2.11 Curvilinear Coordinates
2.12 Integration on Space Elements
2.13 Orthogonal Coordinate Systems
2.14 The Lemmata of Poincaré
2.15 De Rham Cohomology
2.16 Fourier Series
3 Maxwell?s Equations and Boundary-Value Problems in Magnetostatics
3.1 Maxwell?s Equations
3.2 Kirchhoff?s Laws
3.3 Constitutive Equations
3.4 Energy in Electromagnetic Fields
3.5 Boundary and Interface Conditions
3.6 Magnetic Materials
3.7 Classification Diagrams for Electromagnetism
3.8 Field Lines
3.9 Boundary-Value Problems 1: Magnetostatics
3.10 Boundary-Value Problems 2: Magnetic Diffusion
4 Fields and Potentials of Line-Currents
4.1 Green Functions
4.2 Potentials on Bounded Domains
4.3 The Direct Boundary-Element Formulation
4.4 Properties of Harmonic Fields
4.5 The Biot-Savart Law
4.6 Field Contribution of a Straight Line-Current Segments
4.7 Field of a Ring Current
4.8 The Magnetic Dipole Moment
4.9 Magnetic Double Layers
4.10 The Image-Current Method
4.11 Stored Energy in a Magnetostatic Field
4.12 Magnetic Energy in Nonlinear Circuits
4.13 Magnetic Forces and the Maxwell Stress Tensor
4.14 Fields and Potentials of Magnetization Currents
4.15 The Torque on a Magnetic Dipole Moment
4.16 Magnetic Levitation
5 Field Harmonics
5.1 Circular Harmonics
5.2 Zonal Harmonics
5.3 Cartesian Coordinates
5.4 The General Case
5.5 Plane Elliptic Coordinates
5.6 Bipolar Coordinates
5.7 Integrated Multipoles in Accelerator Magnets
5.8 3D Field Harmonics -
Generalized Gradients
6 Complex Analysis Methods for Magnet Design
6.1 The Field of Complex Numbers
6.2 Holomorphic Functions and the Cauchy-Riemann Equations
6.3 Power Series
6.4 The Complex Form of the Discrete Fourier-Series Expansion
6.5 The Fourier Transform of Non-Periodic Functions
6.6 Complex Potentials
6.7 Complex Representation of Field Quality in Accelerator Magnets
6.8 Complex Integration
6.9 The Field and Potential of a Line Current
6.10 Multipoles Generated by a Magnetic Dipole Moment
6.11 Beth?s Current-Sheet Theorem
6.12 Electromagnetic Forces on the Dipole Coil
6.13 The Field of a Polygonal Conductor
6.14 Magnetic Flux Density Inside Elliptical Conductors
7 Faraday?s Law of Induction
7.1 The Electromotive Force
7.2 Definitions of the Electromotive Force
7.3 EMF Formulas
7.4 Faraday Paradoxes
8 Field Diffusion
8.1 Time Constants and Penetration Depths
8.2 The Laplace Transform
8.3 Conductive Slab in a Time-Transient Applied Field
8.4 Eddy Currents in the LHC Cold Bore and Beam Screen
9 Synchrotron Radiation
9.1 The Wave Equation in Free Space
9.2 The Liénard-Wichert Potentials
9.3 The Fields of Moving Charges
9.4 Power Radiated by an Accelerated Charge
9.5 Nonrelativistic Motion
9.6 Bremsstrahlung
9.7 Synchrotron Radiation
10 The Theory of the Coil Magnetometer
10.1 Terminology for Magnetic Field Transducers
10.2 Coil-Sensitivity Factors
10.3 Reparametrization to the Arc-Length
10.4 The Sensitivity Factor as a Convolution Kernel
10.5 Polarity Convention and Calibration of Rotating-Coil Magnetometers
10.6 Alternative Calibration Procedures
10.7 The Transversal-Multipole Mapper
10.8 The Harmonic Field Scanner
10.9 The Translating-Coil Magnetometer
10.10 The Solenoidal-Field Transducer
11 Stretched-Wire Field Measurements
11.1 The System Architecture of CERN?s Stretched-Wire Systems
11.2 Caternaries and Sag Parameters of a Taut String
11.3 The Single Stretched-Wire Method
11.4 The Vibrating-Wire Method
11.5 The Oscillating-Wire Technique
11.6 The Frequency-Response Method
11.7 Magnetic-Center Location
VOLUME 2: FIELD COMPUTATION FOR MAGNET DESIGN AND OPTIMIZATION
12 Magnets for Accelerators
12.1 The Large Hadron Collider
12.2 A Magnet Metamorphosis
12.3 Superconductor Technology
12.4 The LHC Dipole Coldmass
12.5 Superfluid Helium Physics and Cryogenic Engineering
12.6 Cryostat Design and Cryogenic Temperature Levels
12.7 Vacuum Technology
12.8 Powering and Electrical Quality Assurance
12.9 Electromagnetic Design Challenges
13 Elementary Beam Optics and Field Requirements
13.1 The Equations of Charged Particle Motion in a Magnetic Field
13.2 Magnetic Rigidity and the Bending Magnets
13.3 The Linear Equations of Motion
13.4 Weak Focusing
13.5 Thin-Lens Approximations
13.6 Transfer Matrices
13.7 Strong Focusing and the FODO Cell
13.8 The Beta Function, Tune, and Transverse Resonances
13.9 Off-Momentum Particles
13.10 Field Error Specifications
14 Iron-Dominated Magnets
14.1 C-Shaped Dipoles
14.2 Quadrupoles
14.3 Ohmic Losses in Dipole and Quadrupole Coils
14.4 Magnetic Circuit with Varying Yoke Width
14.5 Ideal Pole Shapes of Iron-Dominated Magnets
14.6 The Mass of the Iron Yoke
14.7 Rogowski Profiles
14.8 Combined-Function Magnets
14.9 Permanent Magnet Excitation
14.10 Wigglers and Undulators
14.11 Cooling of Normal-Conducting Magnets
15 Coil-Dominated Magnets
15.1 Accelerator Magnets
15.2 Combined-Function Magnets and the Unipolar Current Dipole
15.3 Rectangular Block-Coil Structures
15.4 Field Enhancement in Coil Ends of Accelerator Magnets
15.5 Magnetic Force Distribution in the LHC Dipole Coil Ends
15.6 Nested Helices
15.7 Helmholtz and Maxwell Coils
15.8 Solenoids
16 Reference Frames and Magnet Polarities
16.1 Magnet Polarity Conventions
16.2 Reference Frames
16.3 Multipole Expansions
16.4 Orbit Correctors
16.5 Position of the Connection Terminals
16.6 Turned Magnets and Magnet Assemblies
16.7 Electrical Circuits in the LHC Machine
17 Finite-Element Formulations
17.1 One-Dimensional Finite-Element Analysis
17.2 FEM with the Vector-Potential (Curl-Curl) Formulation
17.3 Complementary Formulations
18 Discretization
18.1 Quadrilateral Mesh Generation
18.2 Finite-Element Shape Functions
19 Coupling of Boundary and Finite Elements
19.1 The Boundary-Element Method
19.2 BEM-FEM Coupling
19.3 BEM-FEM Coupling using the Total Scalar-Potential
19.4 The M(B) Iteration
19.5 Applications
20 Superconductor Magnetization
20.1 Superconductor Magnetization
20.2 Critical Surface Modeling
20.3 The Critical State Model
20.4 The Ellipse on a Cylinder Model
20.5 Nested Intersecting Circles and Ellipses
20.6 Hysteresis Modeling
20.7 Magnet Field Errors due to the Superconducting Filament Magnetization
20.8 The M(B) Iteration
20.9 Software Implementation
20.10 Applications to Magnet Design
20.11 Nested Magnets
21 Interstrand Coupling Currents
21.1 Analysis of Linear Networks
21.2 A Network Model for the Interstrand Coupling Currents
21.3 Steady-State Calculations
21.4 Time-Transient Analysis
21.5 The M(B) Iteration Scheme for ISCCs
21.6 Approximation for the Interstrand Coupling Currents
21.7 Interfilament Coupling Currents
21.8 Applications to Magnet Design
22 Quench Simulation
22.1 The Heat Balance Equation
22.2 Electrical Network Models of Superconductors
22.3 Current Sharing
22.4 Winding Schemes and Equivalent Electrical Circuit Diagrams
22.5 Quench Detection
22.6 Magnet Protection
22.7 Numerical Quench Simulation
22.8 The Time-Stepping Algorithm
22.9 Applications
23 Differential Geometry Applied to Coil-End Design
23.1 Constant-Perimeter Coil Ends
23.2 Differential Geometry of the Strip Surfaces
23.3 Discrete Theory of the Strip Surface
23.4 Optimization of the Strip Surface
23.5 Coil-End Transformations
23.6 Corrector Magnet Coil End with Ribbon Cables
23.7 End-Spacer Manufacturing
23.8 Splice Configuration
24 Mathematical Optimization Techniques
24.1 Mathematical Formulation of the Optimization Problem
24.2 Optimality Criteria for Unconstrained Problems
24.3 Karush-Kuhn-Tucker Conditions
24.4 Pareto Optimality
24.5 Methods for Decision Making
24.6 Box Constraints
24.7 Treatment of Nonlinear Constraints
24.8 Deterministic Optimization Algorithms
24.9 Genetic Optimization Algorithms
24.10 Applications
A Material-Property Data for Quench Simulations
A.1 Mass Density
A.2 Electrical Resistivity
A.3 Thermal Conductivity
A.4 Heat Capacity
B The LHC Magnet Zoo
B.1 Superconducting Magnets
B.2 Normal-Conducting Magnets
C Ramping the LHC Dipoles
D The Vibration of the Taut String
D.1 The Inhomogeneous Wave Equation
D.2 Energy in Vibrating Wires
D.3 Numerical Solution of the Wave Equation
E The Dirac delta
F Detailed Calculation of the Field of Moving Charges
G Uncertainty in Measurement and Approximation
G.1 Sample Mean, Standard Deviation, and Confidence Interval
G.2 Random Numbers as a Vector-Space, Error Norms
H Orthogonal-Array Testing
I SI (MKSA) Units
J Glossary
