| Preface |
|
xv | |
| Notation |
|
xix | |
|
|
|
1 | (48) |
|
The Large hadron Collider |
|
|
2 | (5) |
|
|
|
7 | (9) |
|
Superconductor Technology |
|
|
16 | (11) |
|
Critical Current Density of Superconductors |
|
|
16 | (3) |
|
|
|
19 | (3) |
|
|
|
22 | (5) |
|
|
|
27 | (2) |
|
Superfluid Helium Physics and Cryogenic Engineering |
|
|
29 | (3) |
|
Cryostat Design and Cryogenic Temperature Levels |
|
|
32 | (1) |
|
|
|
33 | (2) |
|
Powering and Electrical Quality Assurance |
|
|
35 | (3) |
|
Electromagnetic Design Challenges |
|
|
38 | (11) |
|
The CERN Field Computation Program ROXIE |
|
|
42 | (2) |
|
Analytical and Numerical Field Computation |
|
|
44 | (2) |
|
|
|
46 | (3) |
|
Algebraic Structures and Vector Fields |
|
|
49 | (36) |
|
|
|
49 | (1) |
|
Groups, Rings, and Fields |
|
|
50 | (1) |
|
|
|
51 | (3) |
|
Linear Independence and Basis |
|
|
53 | (1) |
|
|
|
54 | (2) |
|
|
|
56 | (4) |
|
|
|
58 | (2) |
|
|
|
60 | (6) |
|
|
|
62 | (1) |
|
|
|
63 | (1) |
|
The Erhard Schmidt Orthogonalization |
|
|
64 | (2) |
|
|
|
66 | (2) |
|
A Glimpse on Topological Concepts |
|
|
68 | (4) |
|
|
|
69 | (1) |
|
|
|
70 | (2) |
|
|
|
72 | (3) |
|
Identities of Vector Algebra |
|
|
75 | (1) |
|
|
|
75 | (2) |
|
|
|
77 | (3) |
|
The Physical Dimension System |
|
|
80 | (5) |
|
|
|
84 | (1) |
|
Classical Vector Analysis |
|
|
85 | (52) |
|
|
|
86 | (7) |
|
The Frenet Frame of Space Curves |
|
|
88 | (5) |
|
The Directional Derivative |
|
|
93 | (1) |
|
Gradient, Divergence, and Curl |
|
|
94 | (2) |
|
Identities of Vector Analysis |
|
|
96 | (1) |
|
|
|
96 | (2) |
|
|
|
98 | (4) |
|
Differential Operators on Scalar and Vector Fields in r and r |
|
|
102 | (1) |
|
The Path Integral of a Vector Field |
|
|
103 | (1) |
|
Coordinate-Free Definitions of the Differential Operators |
|
|
104 | (2) |
|
|
|
106 | (5) |
|
The Kelvin-Stokes Theorem |
|
|
106 | (1) |
|
Green's Theorem in the plane |
|
|
107 | (1) |
|
The Gauss-Ostrogradski Divergence Theorem |
|
|
108 | (1) |
|
A Variant of the gauss Theorem |
|
|
108 | (1) |
|
|
|
109 | (1) |
|
Green's Second Identity (Green's Theorem) |
|
|
110 | (1) |
|
Vector Form of Green's Theorem |
|
|
110 | (1) |
|
Generalization of the Integration-by-Parts Rule |
|
|
110 | (1) |
|
|
|
111 | (1) |
|
|
|
111 | (4) |
|
Components of a Vector Field |
|
|
113 | (1) |
|
Contravariant Coefficients |
|
|
114 | (1) |
|
|
|
115 | (1) |
|
Integration on Space Elements |
|
|
115 | (2) |
|
Orthogonal Coordinate Systems |
|
|
117 | (2) |
|
|
|
119 | (6) |
|
|
|
121 | (1) |
|
|
|
122 | (3) |
|
|
|
125 | (1) |
|
|
|
126 | (3) |
|
|
|
129 | (8) |
|
|
|
136 | (1) |
|
Maxwell's Equations and Boundary Value Problems in Magnetostatics |
|
|
137 | (50) |
|
|
|
138 | (5) |
|
|
|
138 | (1) |
|
|
|
139 | (2) |
|
|
|
141 | (1) |
|
Maxwell's Original Set of Equations |
|
|
142 | (1) |
|
|
|
143 | (1) |
|
Conversion of Energy in Electromagnetic Fields |
|
|
143 | (1) |
|
|
|
144 | (2) |
|
Boundary and Interface Conditions |
|
|
146 | (5) |
|
|
|
151 | (14) |
|
|
|
152 | (3) |
|
Measurement of Hysteresis Curves |
|
|
155 | (4) |
|
Magnetic Anisotropy in Laminated Iron Yokes |
|
|
159 | (1) |
|
|
|
160 | (1) |
|
|
|
161 | (2) |
|
Magnetization Currents and Fictitious Magnetic Charges |
|
|
163 | (2) |
|
Classification Diagrams for Electromagnetism |
|
|
165 | (2) |
|
|
|
167 | (4) |
|
Classification of Electromagnetic Field Problems |
|
|
167 | (4) |
|
Boundary Value Problems 1: Magnetostatic |
|
|
171 | (9) |
|
Scalar-Potential Formulations |
|
|
171 | (2) |
|
Vector-Potential Formulations |
|
|
173 | (6) |
|
The Scalar Laplace Equation in 2D |
|
|
179 | (1) |
|
Boundary Value Problems 2: Magnetic Diffusion Problems |
|
|
180 | (7) |
|
|
|
184 | (3) |
|
Fields and Potentials of Line-Currents |
|
|
187 | (50) |
|
|
|
188 | (1) |
|
Potentials on Bounded Domains |
|
|
189 | (2) |
|
Properties of Harmonic Fields |
|
|
191 | (2) |
|
|
|
193 | (4) |
|
Field of a Straight Line-Current Segment |
|
|
197 | (3) |
|
|
|
200 | (3) |
|
The Magnetic Dipole Moment |
|
|
203 | (2) |
|
The Magnetic Double Layer |
|
|
205 | (4) |
|
|
|
206 | (2) |
|
Approximating the Solid Angle of a Current Loop |
|
|
208 | (1) |
|
|
|
209 | (7) |
|
|
|
211 | (2) |
|
|
|
213 | (3) |
|
Stored Energy in a Magnetostatic Field |
|
|
216 | (8) |
|
Self and Mutual Inductance |
|
|
218 | (2) |
|
The geometric Mean Distance |
|
|
220 | (2) |
|
|
|
222 | (2) |
|
Magnetic Energy in Nonlinear Circuits |
|
|
224 | (3) |
|
|
|
224 | (3) |
|
Magnetic Forces and the Maxwell Stress Tensor |
|
|
227 | (3) |
|
Fields and Potentials of Magentization Currents |
|
|
230 | (2) |
|
|
|
232 | (5) |
|
|
|
235 | (2) |
|
|
|
237 | (32) |
|
|
|
238 | (19) |
|
Determining the Multipole Coefficients |
|
|
240 | (13) |
|
Magnetic Shielding; Permeable Cylindrical Shell in a Uniform Field |
|
|
253 | (2) |
|
Integrated Multipoles in Accelerator Magnets |
|
|
255 | (2) |
|
|
|
257 | (8) |
|
Legendre Series Expression for the Vector Potential |
|
|
262 | (1) |
|
Determining the Zonal Harmonics |
|
|
263 | (2) |
|
Separation in Cartesian Coordinates |
|
|
265 | (4) |
|
|
|
268 | (1) |
|
|
|
269 | (24) |
|
|
|
270 | (1) |
|
|
|
271 | (1) |
|
Ohmic Losses in Dipole and Quadrupole Coils |
|
|
272 | (1) |
|
Magnetic Circuit with Varying Yoke Width |
|
|
272 | (2) |
|
|
|
274 | (1) |
|
Ideal Pole Shapes of Iron-Dominated Magnets |
|
|
275 | (3) |
|
|
|
277 | (1) |
|
|
|
278 | (3) |
|
Combined-Function Magnets |
|
|
281 | (1) |
|
Permanent Magnet Excitation |
|
|
282 | (5) |
|
Cooling of Normal-Conducting Magnets |
|
|
287 | (6) |
|
|
|
291 | (2) |
|
|
|
293 | (34) |
|
|
|
294 | (15) |
|
Generation of Pure Multipole Fields |
|
|
295 | (10) |
|
Sensitivity to Coil-Block Positioning Errors |
|
|
305 | (1) |
|
|
|
305 | (1) |
|
Margins in the LHC Main Dipole |
|
|
306 | (3) |
|
Combined-Function Magnets and the Unipolar Current Dipole |
|
|
309 | (1) |
|
Rectangular Block-Coil Structures |
|
|
310 | (1) |
|
Field Enhancement in Coil Ends of Accelerator Magnets |
|
|
311 | (1) |
|
Magnetic Force Distribution in the LHC Dipole Coil Ends |
|
|
312 | (2) |
|
|
|
314 | (1) |
|
|
|
315 | (12) |
|
Helmholtz and Maxwell Coils |
|
|
315 | (2) |
|
|
|
317 | (4) |
|
|
|
321 | (3) |
|
|
|
324 | (1) |
|
|
|
325 | (2) |
|
Complex Analysis Methods for Magnet Design |
|
|
327 | (36) |
|
The Field of Complex Numbers |
|
|
328 | (1) |
|
Holomorphic Functions and the Cauchy-Riemann Equations |
|
|
329 | (2) |
|
|
|
331 | (2) |
|
The Complex Form of the Discrete Fourier Transform |
|
|
333 | (2) |
|
|
|
335 | (1) |
|
|
|
336 | (2) |
|
Complex Representation of Field Quality in Accelerator Magnets |
|
|
338 | (6) |
|
|
|
338 | (4) |
|
|
|
342 | (1) |
|
Reflection about the Vertical Axis |
|
|
343 | (1) |
|
|
|
344 | (5) |
|
Cauchy's Theorem and the Integral Formula |
|
|
345 | (1) |
|
Properties of Holomorphic Functions |
|
|
346 | (2) |
|
|
|
348 | (1) |
|
The Field and Potential of a Line Current |
|
|
349 | (2) |
|
Series Expansion of the Line-Current Field |
|
|
350 | (1) |
|
|
|
351 | (1) |
|
Multipoles Generated by a Magnetic Dipole Moment |
|
|
351 | (1) |
|
Beth's Current-Sheet Theorem |
|
|
352 | (2) |
|
Electromagnetic Forces on the Dipole Coil |
|
|
354 | (2) |
|
The Field of a Polygonal Conductor |
|
|
356 | (2) |
|
Magnetic Flux Density Inside Elliptical Conductors |
|
|
358 | (5) |
|
|
|
362 | (1) |
|
|
|
363 | (20) |
|
Time Constants and Penetration Depths |
|
|
363 | (2) |
|
|
|
365 | (5) |
|
Conductive Slab in a Time-Transient Applied Field |
|
|
370 | (6) |
|
The Step-Excitation Function |
|
|
371 | (2) |
|
Linear Ramp of the Applied Field |
|
|
373 | (2) |
|
|
|
375 | (1) |
|
Eddy Currents in the LHC Cold Bore and Beam Screen |
|
|
376 | (7) |
|
|
|
382 | (1) |
|
Elementary Beam Optics and Field Requirements |
|
|
383 | (32) |
|
The Equations of Charged Particle Motion in a Magnetic Field |
|
|
383 | (4) |
|
Magnetic Rigidity and the Bending Magnets |
|
|
387 | (2) |
|
The Linear Equations of Motion |
|
|
389 | (1) |
|
|
|
390 | (2) |
|
|
|
392 | (1) |
|
|
|
393 | (2) |
|
Strong Focusing and the FODO Cell |
|
|
395 | (2) |
|
The Beta Function, Tune, and Transverse Resonances |
|
|
397 | (10) |
|
|
|
407 | (8) |
|
|
|
408 | (2) |
|
|
|
410 | (2) |
|
Field Error Specifications |
|
|
412 | (1) |
|
|
|
413 | (2) |
|
Reference Frames and Magnet Polarities |
|
|
415 | (18) |
|
Magnet Polarity Conventions |
|
|
416 | (4) |
|
|
|
418 | (1) |
|
Twin-Aperture and Two-in-One Magnets |
|
|
418 | (2) |
|
|
|
420 | (6) |
|
|
|
421 | (1) |
|
|
|
421 | (2) |
|
The Local Reference Frame of Beam 1 |
|
|
423 | (1) |
|
Definition of Field Errors in the Accelerator Design Program MAD |
|
|
424 | (1) |
|
Transformation between the Magnet and the Beam 1 Frames |
|
|
424 | (2) |
|
|
|
426 | (1) |
|
Position of the Connection Terminals |
|
|
426 | (1) |
|
Turned Magnets and Magnet Assemblies |
|
|
427 | (2) |
|
Electrical Circuits in the LHC Machine |
|
|
429 | (4) |
|
|
|
432 | (1) |
|
Finite-Element Formulations |
|
|
433 | (22) |
|
One-Dimensional Finite-Element Analysis |
|
|
434 | (7) |
|
|
|
439 | (2) |
|
FEM with the Vector-Potential (Curl-Curl) Formulation |
|
|
441 | (4) |
|
|
|
443 | (1) |
|
|
|
444 | (1) |
|
Complementary Formulations |
|
|
445 | (10) |
|
FEM with Reduced vector-Potential Formulation |
|
|
445 | (4) |
|
FEM, Employing the Vector Poisson Equation |
|
|
449 | (2) |
|
The A-Ø Formulation for Eddy-Current Problems |
|
|
451 | (2) |
|
|
|
453 | (2) |
|
|
|
455 | (26) |
|
Quadrilateral Mesh Generation |
|
|
456 | (9) |
|
|
|
457 | (1) |
|
|
|
458 | (1) |
|
|
|
459 | (1) |
|
Meshing of Simple Domains |
|
|
460 | (1) |
|
|
|
461 | (1) |
|
|
|
462 | (3) |
|
Finite-Element Shape Functions |
|
|
465 | (16) |
|
The Linear Triangular Element, 2D |
|
|
466 | (3) |
|
|
|
469 | (1) |
|
|
|
470 | (1) |
|
|
|
471 | (3) |
|
Generation of the Shape Functions |
|
|
474 | (2) |
|
Transformation of Differential Operators |
|
|
476 | (3) |
|
|
|
479 | (2) |
|
Coupling of Boundary and Finite Elements |
|
|
481 | (22) |
|
The Boundary-Element Method |
|
|
482 | (5) |
|
The Node Collocation Method |
|
|
486 | (1) |
|
|
|
487 | (2) |
|
BEM-FEM Coupling using the Total Scalar-Potential |
|
|
489 | (2) |
|
|
|
491 | (1) |
|
|
|
492 | (11) |
|
|
|
492 | (3) |
|
Saturation Effects in the Iron Yoke |
|
|
495 | (1) |
|
|
|
496 | (6) |
|
|
|
502 | (1) |
|
Superconductor Magnetization |
|
|
503 | (40) |
|
Superconductor Magnetization |
|
|
507 | (2) |
|
Critical Surface Modeling |
|
|
509 | (4) |
|
|
|
513 | (3) |
|
The Ellipse on a Cylinder Model |
|
|
516 | (3) |
|
Nested Intersecting Circles and Ellipses |
|
|
519 | (2) |
|
|
|
521 | (6) |
|
Magnet Field Errors due to the Superconducting Filament Magnetization |
|
|
527 | (3) |
|
|
|
530 | (2) |
|
|
|
532 | (1) |
|
Applications to Magnet Design |
|
|
532 | (11) |
|
Compensation of Multipole Field Errors |
|
|
534 | (3) |
|
|
|
537 | (3) |
|
|
|
540 | (3) |
|
Interstrand Coupling Currents |
|
|
543 | (32) |
|
Analysis of Linear Networks |
|
|
544 | (11) |
|
The Linear U(I) Relation in a Branch |
|
|
545 | (2) |
|
|
|
547 | (1) |
|
The Branch/Node Incidence Matrix and the Node-Potential Method |
|
|
548 | (3) |
|
The Mesh Matrix and the Mesh-Current Method |
|
|
551 | (2) |
|
|
|
553 | (2) |
|
A Network Model for the Interstrand Coupling Currents |
|
|
555 | (2) |
|
Steady-State Calculations |
|
|
557 | (3) |
|
Spectral Analysis of the Solution |
|
|
559 | (1) |
|
|
|
560 | (2) |
|
Spectral Analysis of the Solution |
|
|
561 | (1) |
|
The M(B) Iteration Scheme for ISCCs |
|
|
562 | (1) |
|
Approximation for the Interstrand Coupling Currents |
|
|
563 | (1) |
|
Interfilament Coupling Currents |
|
|
564 | (2) |
|
Applications to Magnet Design |
|
|
566 | (9) |
|
|
|
566 | (1) |
|
|
|
567 | (5) |
|
|
|
572 | (3) |
|
|
|
575 | (34) |
|
The Heat Balance Equation |
|
|
577 | (3) |
|
Electrical Network Models of Superconductors |
|
|
580 | (2) |
|
|
|
582 | (2) |
|
Winding Schemes and Equivalent Electrical Circuit Diagrams |
|
|
584 | (1) |
|
|
|
585 | (1) |
|
|
|
586 | (3) |
|
Numerical Quench Simulation |
|
|
589 | (6) |
|
|
|
591 | (3) |
|
External Electrical Circuits |
|
|
594 | (1) |
|
The Time-Stepping Algorithm |
|
|
595 | (1) |
|
|
|
596 | (13) |
|
|
|
598 | (3) |
|
|
|
601 | (6) |
|
|
|
607 | (2) |
|
Differential Geometry Applied to Coil-End Design |
|
|
609 | (28) |
|
Constant-Perimeter Coil Ends |
|
|
612 | (3) |
|
Differential Geometry of the Strip Surfaces |
|
|
615 | (6) |
|
The Frenet-Serret Equations for Strips |
|
|
616 | (2) |
|
|
|
618 | (3) |
|
Discrete Theory of the Strip Surface |
|
|
621 | (6) |
|
Optimization of the Strip Surface |
|
|
627 | (3) |
|
|
|
630 | (1) |
|
Corrector Magnet Coil End with Ribbon Cables |
|
|
631 | (2) |
|
|
|
633 | (1) |
|
|
|
634 | (3) |
|
|
|
636 | (1) |
|
Mathematical Optimization Techniques |
|
|
637 | (108) |
|
Mathematical Formulation of the Optimization Problem |
|
|
639 | (2) |
|
Optimality Criteria for Unconstrained Problems |
|
|
641 | (1) |
|
Karush-Kuhn-Tucker Conditions |
|
|
642 | (2) |
|
|
|
644 | (2) |
|
Methods for Decision Making |
|
|
646 | (8) |
|
|
|
646 | (4) |
|
The Pareto-Strength Algorithm |
|
|
650 | (1) |
|
Constraint Formulation and Sensitivity Analysis |
|
|
651 | (2) |
|
|
|
653 | (1) |
|
|
|
654 | (1) |
|
Treatment of Nonlinear Constraints |
|
|
655 | (1) |
|
Deterministic Optimization Algorithms |
|
|
655 | (12) |
|
|
|
656 | (3) |
|
Multidimensional Search Methods |
|
|
659 | (1) |
|
|
|
660 | (7) |
|
Genetic Optimization Algorithms |
|
|
667 | (14) |
|
|
|
669 | (1) |
|
|
|
669 | (2) |
|
|
|
671 | (7) |
|
|
|
678 | (3) |
|
|
|
681 | (22) |
|
Conceptual Coil Design with Genetic Algorithms |
|
|
683 | (2) |
|
Deterministic Optimization of Coil Cross Sections |
|
|
685 | (3) |
|
Yoke Design as a Material-Distribution Problem |
|
|
688 | (1) |
|
Shape Optimization of the Iron Yoke |
|
|
689 | (2) |
|
Payoff Tables for Dipole Designs |
|
|
691 | (2) |
|
Lagrange Multiplier Estimation |
|
|
693 | (1) |
|
|
|
694 | (2) |
|
|
|
696 | (1) |
|
Tracing of Manufacturing Errors |
|
|
697 | (3) |
|
|
|
700 | (3) |
|
|
|
|
Material Property Data for Quench Simulations |
|
|
703 | (14) |
|
|
|
703 | (2) |
|
|
|
705 | (3) |
|
|
|
708 | (3) |
|
|
|
711 | (4) |
|
|
|
715 | (2) |
|
|
|
717 | (12) |
|
|
|
717 | (9) |
|
Normal-Conducting Magnets |
|
|
726 | (3) |
|
|
|
729 | (2) |
|
|
|
731 | (4) |
|
|
|
735 | (2) |
|
|
|
737 | (8) |
| Index |
|
745 | |
Lisainfo e-raamatute kohta