简介
This unique book, written by one of the world's foremost specialists in the field, is devoted to the design of low and medium field electromagnets whose field level and quality (uniformity) are dominated by the pole shape and saturation characteristics of the iron yoke.The wide scope covers material ranging from the physical requirements for typical high performance accelerators, through the mathematical relationships which describe the shape of two-dimensional magnetic fields, to the mechanical fabrication, assembly, installation, and alignment of magnets in a typical accelerator lattice. In addition, stored energy concepts are used to develop magnetic force relationships and expressions for magnets with time varying fields.The material in the book is derived from lecture notes used in a course at the Lawrence Livermore National Laboratory and subsequently expanded for the U.S. Particle Accelerator School, making this text an invaluable reference for students planning to enter the field of high energy physics.Mathematical relationships tying together magnet design and measurement theory are derived from first principles, and chapters are included that describe mechanical design, fabrication, installation, and alignment. Some fabrication and assembly practices are reviewed to ensure personnel and equipment safety and operational reliability of electromagnets and their power supply systems. This additional coverage makes the book an important resource for those already in the particle accelerator business as well as those requiring the design and fabrication of low and medium field level magnets for charged particle beam transport in ion implantation and medical applications.
目录
Basic Concepts p. 1
Introduction p. 1
Magnet Types p. 2
Pictures p. 2
Conventions p. 6
The Field from a Line Current (Biot-Savart law) p. 6
Magnetic Force on a Line Current p. 7
MKS Units p. 7
Force Directions p. 8
Dipole Magnet p. 8
Quadrupole Magnet p. 8
Sextupole Magnet p. 9
Corrector Magnets p. 10
Specialized Magnets p. 11
More Polarity p. 14
Alternate Polarity Convention p. 15
Chapter Closure p. 15
Problems p. 17
Solutions of the Magnet Equations p. 19
Introduction p. 19
Maxwell's Magnet Equations p. 19
Continuity p. 19
Units p. 20
The Function of a Complex Variable p. 20
The Two-Dimensional Fields p. 21
Fields from the Two-Dimensional Function of a Complex Variable p. 22
Two Dimensional Fields in a Vacuum p. 22
Multipoles p. 22
Laplace's Equation p. 23
Solutions to Laplace's Equation p. 23
Two-Dimensional Vector and Scalar Potentials p. 24
Magnetic Fields from the Two-Dimensional Potentials p. 24
A Particular Function of the Complex Variable, F = C[subscript n]z[superscript n] p. 25
Ideal Two-Dimensional Multipole Magnets p. 26
Two-Dimensional Flux Lines and Poles p. 26
Pole Contours p. 30
Complex Extrapolation p. 30
Magnetic Fields Using the Function of the Complex Variable p. 31
n=1, the Dipole Magnet p. 32
n=2, the Quadrupole Magnet p. 32
n=3, the Sextupole Magnet p. 33
Multipole Errors p. 34
The Error Spectrum p. 34
"Allowed" or Systematic Multipole Errors p. 34
Multipole Field Errors p. 36
Simple Conformal Maps p. 37
Mapping Functions p. 37
Quadrupole to Dipole Map p. 38
Dipole to Quadrupole Map p. 38
Sextupole to Dipole Map p. 38
Dipole to Sextupole Map p. 39
Gradient Magnet to Dipole Map p. 39
Dipole to Gradient Magnet Map p. 40
Chapter Closure p. 40
Problems p. 41
Pole Tip Design p. 43
Understanding the Dipole Magnet p. 43
The Orthogonal Analog Model p. 43
The Orthogonal Analog Model and the Quadrupole p. 46
The "H" Dipole Geometry p. 48
H-Magnet Uniformity p. 50
Understanding the Quadrupole Magnet p. 53
Quadrupole Uniformity p. 53
Understanding the Gradient Magnet p. 56
Gradient Magnet Uniformity p. 56
Mapping an Existing Gradient Magnet Design p. 60
Baseline Optimized Pole p. 62
New Unoptimized Pole p. 63
Baseline Mapped Pole p. 63
New Mapped Unoptimized Pole p. 63
Scaling and Shifting p. 64
Center Expansion p. 65
Mapping Back into the Quadrupole Space p. 67
Chapter Closure p. 67
Problems p. 70
Perturbations p. 73
Introduction p. 73
Algorithms and Tables p. 74
Quadrupole Pole Error Coefficients, N=2 p. 74
Sextupole Pole Error Pole Error Coefficients, N=3 p. 75
Computing Error Multipoles p. 75
Two Piece Quadrupole p. 77
Magnet Assymetry p. 78
Differences in Lengths of the Upper and Lower Halves p. 80
Sorting p. 83
Two Piece Quadrupole Errors p. 83
Tolerances (Examples of Computations) p. 84
Alignment Error p. 85
Excitation Error p. 87
Random Multipole Error p. 87
Sextupole Trim Windings p. 89
Orthogonality p. 90
Horizontal Steering Trim p. 90
Vertical Steering and Skew Quadrupole Trim p. 91
Trim Excitations p. 93
Chapter Closure p. 94
Problems p. 96
Magnetic Excitation and Coil Design p. 97
Introduction p. 97
Maxwell's Inhomogeneous Equation p. 97
Continuity p. 98
Magnet Excitations p. 99
Magnet Efficiency p. 99
Dipole Magnets p. 100
Quadrupole Magnet p. 106
Sextupole Magnet p. 108
Coil Design p. 109
Coil Power p. 110
Coil Cooling p. 113
Pressure Drop p. 113
Flow Velocity p. 114
Units p. 115
Coil Cooling p. 119
Calculations p. 120
Sensitivities p. 121
Chapter Closure p. 126
Problems p. 128
Poisson p. 131
Elements of the Family of Codes p. 133
Documentation p. 134
Problem Flow p. 134
AutoMesh p. 136
Boundary Conditions and Constraints p. 136
Geometry p. 139
Setting Up and Testing the Geometry p. 141
Symmetries p. 141
Example - Collins or Figure Eight Quadrupole p. 142
Coil Geometry p. 143
Yoke Geometry p. 145
The Vector Potential Boundary Condition p. 146
Simple Dipole p. 147
The Simple Dipole with Vector Potential Boundary Conditions p. 147
The Vector Potential Boundary Condition for Optimizing the Quadrupole Pole p. 153
Other Applications of the Vector Potential Boundary Conditions p. 164
Chapter Closure p. 165
Problems p. 169
Stored Energy, Magnetic Forces and Dynamic Effects p. 171
Force on Coils p. 171
Force on a Pole p. 173
Units p. 173
A Reference Point p. 174
Magnet Stored Energy p. 174
Inductance p. 175
Eddy Currents p. 177
Field Attenuation due to Eddy Currents in a Semi-infinite Conductive Horizontal Plate p. 178
Field Attenuation due to Eddy Currents in a Pair of Semi-infinite Conductive Vertical Plates p. 182
Field Attenuation due to Eddy Currents in a Closed Rectangular Chamber p. 183
Field Amplification p. 184
Chapter Closure p. 191
Problems p. 192
Magnetic Measurements p. 195
The Vector Potential p. 196
Fourier Analysis p. 198
Output Voltage p. 200
The Compensated Coil p. 201
The Quadrupole Coil p. 203
The Dipole Coil p. 203
The Sextupole Coil p. 204
"Spilldown" and Magnetic Center p. 204
Quadrupole Magnetic Center p. 206
Sextupole Magnetic Center p. 207
Rotating Coil Magnetic Measurements p. 208
The Measurement System p. 209
Fourier Analysis p. 211
Uncompensated Signal p. 212
Compensated Signal p. 213
Expressions for the Integrated Multipole Fields p. 213
Excitation and Transfer Function p. 214
Relative Phases p. 215
Units p. 216
Measurements and Output p. 216
Measurement Plan p. 216
Raw Data Output p. 217
Bucking Ratio p. 217
Normalized Multipole Errors p. 218
Error Spectrum Normalized to the Required Good Field Radius p. 219
Magnetic Center p. 219
Measurement Output p. 220
Tabular Output p. 221
Analog Output (Iso-Error Plots) p. 221
Chapter Closure p. 224
Problems p. 225
Magnet Yoke Design and Fabrication p. 229
Introduction p. 229
Saturation p. 229
Two Dimensional Design p. 231
Three Dimensional Design p. 232
Dipole Fringe Field p. 232
Quadrupole Fringe Field p. 234
Solid Iron or Steel Laminations p. 238
Reproducibility and Symmetry p. 238
Solid Iron Cores p. 238
Laminated Steel Cores p. 239
Economics p. 240
Laminated Yoke Fabrication p. 241
Yoke Assembly/Fabrication Techniques p. 242
Gluing p. 244
Welded Laminated Yokes p. 251
Mechanically Assembled Laminated Yokes p. 253
Core Grounding p. 261
Chapter Closure p. 261
Chapter Appendix p. 264
Magnet Coil Fabrication p. 267
Introduction p. 267
Conductor Size and Turn to Turn Insulation p. 267
Coil Winding p. 268
Coil Potting (Encapsulation) p. 271
Coil Failures p. 278
Specifications p. 278
Measurements and Tests p. 279
Chapter Closure p. 284
Magnet Assembly p. 285
Introduction p. 285
Coil Supports and Bussing p. 285
Bussing p. 286
Magnet Tests p. 293
Chapter Closure p. 295
Magnet Installation and Alignment p. 297
Introduction p. 297
Magnet Support p. 298
Predetermined Alignment p. 298
Generic Fiducialization p. 299
Adjusted Alignment p. 300
Adjustable Struts p. 303
Adjustable Support Blocks p. 306
Pedigreed Fiducialization p. 308
Chapter Closure p. 310
Solutions p. 313
References p. 327
Index p. 329
Introduction p. 1
Magnet Types p. 2
Pictures p. 2
Conventions p. 6
The Field from a Line Current (Biot-Savart law) p. 6
Magnetic Force on a Line Current p. 7
MKS Units p. 7
Force Directions p. 8
Dipole Magnet p. 8
Quadrupole Magnet p. 8
Sextupole Magnet p. 9
Corrector Magnets p. 10
Specialized Magnets p. 11
More Polarity p. 14
Alternate Polarity Convention p. 15
Chapter Closure p. 15
Problems p. 17
Solutions of the Magnet Equations p. 19
Introduction p. 19
Maxwell's Magnet Equations p. 19
Continuity p. 19
Units p. 20
The Function of a Complex Variable p. 20
The Two-Dimensional Fields p. 21
Fields from the Two-Dimensional Function of a Complex Variable p. 22
Two Dimensional Fields in a Vacuum p. 22
Multipoles p. 22
Laplace's Equation p. 23
Solutions to Laplace's Equation p. 23
Two-Dimensional Vector and Scalar Potentials p. 24
Magnetic Fields from the Two-Dimensional Potentials p. 24
A Particular Function of the Complex Variable, F = C[subscript n]z[superscript n] p. 25
Ideal Two-Dimensional Multipole Magnets p. 26
Two-Dimensional Flux Lines and Poles p. 26
Pole Contours p. 30
Complex Extrapolation p. 30
Magnetic Fields Using the Function of the Complex Variable p. 31
n=1, the Dipole Magnet p. 32
n=2, the Quadrupole Magnet p. 32
n=3, the Sextupole Magnet p. 33
Multipole Errors p. 34
The Error Spectrum p. 34
"Allowed" or Systematic Multipole Errors p. 34
Multipole Field Errors p. 36
Simple Conformal Maps p. 37
Mapping Functions p. 37
Quadrupole to Dipole Map p. 38
Dipole to Quadrupole Map p. 38
Sextupole to Dipole Map p. 38
Dipole to Sextupole Map p. 39
Gradient Magnet to Dipole Map p. 39
Dipole to Gradient Magnet Map p. 40
Chapter Closure p. 40
Problems p. 41
Pole Tip Design p. 43
Understanding the Dipole Magnet p. 43
The Orthogonal Analog Model p. 43
The Orthogonal Analog Model and the Quadrupole p. 46
The "H" Dipole Geometry p. 48
H-Magnet Uniformity p. 50
Understanding the Quadrupole Magnet p. 53
Quadrupole Uniformity p. 53
Understanding the Gradient Magnet p. 56
Gradient Magnet Uniformity p. 56
Mapping an Existing Gradient Magnet Design p. 60
Baseline Optimized Pole p. 62
New Unoptimized Pole p. 63
Baseline Mapped Pole p. 63
New Mapped Unoptimized Pole p. 63
Scaling and Shifting p. 64
Center Expansion p. 65
Mapping Back into the Quadrupole Space p. 67
Chapter Closure p. 67
Problems p. 70
Perturbations p. 73
Introduction p. 73
Algorithms and Tables p. 74
Quadrupole Pole Error Coefficients, N=2 p. 74
Sextupole Pole Error Pole Error Coefficients, N=3 p. 75
Computing Error Multipoles p. 75
Two Piece Quadrupole p. 77
Magnet Assymetry p. 78
Differences in Lengths of the Upper and Lower Halves p. 80
Sorting p. 83
Two Piece Quadrupole Errors p. 83
Tolerances (Examples of Computations) p. 84
Alignment Error p. 85
Excitation Error p. 87
Random Multipole Error p. 87
Sextupole Trim Windings p. 89
Orthogonality p. 90
Horizontal Steering Trim p. 90
Vertical Steering and Skew Quadrupole Trim p. 91
Trim Excitations p. 93
Chapter Closure p. 94
Problems p. 96
Magnetic Excitation and Coil Design p. 97
Introduction p. 97
Maxwell's Inhomogeneous Equation p. 97
Continuity p. 98
Magnet Excitations p. 99
Magnet Efficiency p. 99
Dipole Magnets p. 100
Quadrupole Magnet p. 106
Sextupole Magnet p. 108
Coil Design p. 109
Coil Power p. 110
Coil Cooling p. 113
Pressure Drop p. 113
Flow Velocity p. 114
Units p. 115
Coil Cooling p. 119
Calculations p. 120
Sensitivities p. 121
Chapter Closure p. 126
Problems p. 128
Poisson p. 131
Elements of the Family of Codes p. 133
Documentation p. 134
Problem Flow p. 134
AutoMesh p. 136
Boundary Conditions and Constraints p. 136
Geometry p. 139
Setting Up and Testing the Geometry p. 141
Symmetries p. 141
Example - Collins or Figure Eight Quadrupole p. 142
Coil Geometry p. 143
Yoke Geometry p. 145
The Vector Potential Boundary Condition p. 146
Simple Dipole p. 147
The Simple Dipole with Vector Potential Boundary Conditions p. 147
The Vector Potential Boundary Condition for Optimizing the Quadrupole Pole p. 153
Other Applications of the Vector Potential Boundary Conditions p. 164
Chapter Closure p. 165
Problems p. 169
Stored Energy, Magnetic Forces and Dynamic Effects p. 171
Force on Coils p. 171
Force on a Pole p. 173
Units p. 173
A Reference Point p. 174
Magnet Stored Energy p. 174
Inductance p. 175
Eddy Currents p. 177
Field Attenuation due to Eddy Currents in a Semi-infinite Conductive Horizontal Plate p. 178
Field Attenuation due to Eddy Currents in a Pair of Semi-infinite Conductive Vertical Plates p. 182
Field Attenuation due to Eddy Currents in a Closed Rectangular Chamber p. 183
Field Amplification p. 184
Chapter Closure p. 191
Problems p. 192
Magnetic Measurements p. 195
The Vector Potential p. 196
Fourier Analysis p. 198
Output Voltage p. 200
The Compensated Coil p. 201
The Quadrupole Coil p. 203
The Dipole Coil p. 203
The Sextupole Coil p. 204
"Spilldown" and Magnetic Center p. 204
Quadrupole Magnetic Center p. 206
Sextupole Magnetic Center p. 207
Rotating Coil Magnetic Measurements p. 208
The Measurement System p. 209
Fourier Analysis p. 211
Uncompensated Signal p. 212
Compensated Signal p. 213
Expressions for the Integrated Multipole Fields p. 213
Excitation and Transfer Function p. 214
Relative Phases p. 215
Units p. 216
Measurements and Output p. 216
Measurement Plan p. 216
Raw Data Output p. 217
Bucking Ratio p. 217
Normalized Multipole Errors p. 218
Error Spectrum Normalized to the Required Good Field Radius p. 219
Magnetic Center p. 219
Measurement Output p. 220
Tabular Output p. 221
Analog Output (Iso-Error Plots) p. 221
Chapter Closure p. 224
Problems p. 225
Magnet Yoke Design and Fabrication p. 229
Introduction p. 229
Saturation p. 229
Two Dimensional Design p. 231
Three Dimensional Design p. 232
Dipole Fringe Field p. 232
Quadrupole Fringe Field p. 234
Solid Iron or Steel Laminations p. 238
Reproducibility and Symmetry p. 238
Solid Iron Cores p. 238
Laminated Steel Cores p. 239
Economics p. 240
Laminated Yoke Fabrication p. 241
Yoke Assembly/Fabrication Techniques p. 242
Gluing p. 244
Welded Laminated Yokes p. 251
Mechanically Assembled Laminated Yokes p. 253
Core Grounding p. 261
Chapter Closure p. 261
Chapter Appendix p. 264
Magnet Coil Fabrication p. 267
Introduction p. 267
Conductor Size and Turn to Turn Insulation p. 267
Coil Winding p. 268
Coil Potting (Encapsulation) p. 271
Coil Failures p. 278
Specifications p. 278
Measurements and Tests p. 279
Chapter Closure p. 284
Magnet Assembly p. 285
Introduction p. 285
Coil Supports and Bussing p. 285
Bussing p. 286
Magnet Tests p. 293
Chapter Closure p. 295
Magnet Installation and Alignment p. 297
Introduction p. 297
Magnet Support p. 298
Predetermined Alignment p. 298
Generic Fiducialization p. 299
Adjusted Alignment p. 300
Adjustable Struts p. 303
Adjustable Support Blocks p. 306
Pedigreed Fiducialization p. 308
Chapter Closure p. 310
Solutions p. 313
References p. 327
Index p. 329
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