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Accelerator Physics: Example Problems with Solutions
출판사 : World Scientific
저 자 : Conte
ISBN : 9789814295994
발행일 : 2011-6
도서종류 : 외국도서
발행언어 : 영어
페이지수 : 288
판매가격 : 49,000원
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   Accelerator Physics: Example Problems with Solutions 목차
Preface vii

1 Problems of Chapter 1: Introduction 1

1.1 Problem 1-1: Luminosity of Gaussian bunches 1

1.2 Problem 1-2: Brightness of laser beam 4

1.3 Problem 1-3: Equations of motion 5

1.4 Problem 1-4: Decay of a pion to a muon 7

1.5 Problem 1-5: Collider vs fixed-target energies 9

1.6 Problem 1-6: HERA center-of-mass system 10

1.7 Problem 1-7: SLAC rf voltage and power 11

1.8 Problem 1-8: Fixed-target interaction rate 12

2 Problems of Chapter 2: Equations of Motion for Weak Focusing 13

2.1 Problem 2-1: Equations of motion with dispersion 13

2.2 Problem 2-2: Horizontal transport matrix with dispersion 16

2.3 Problem 2-3: Betatron's momentum compaction 18

2.4 Problem 2-4: Combining two dipoles 19

2.5 Problem 2-5: RHIC ion parameters 20

3 Problems of Chapter 3: Mechanics of Trajectories 23

3.1 Problem 3-1: Canonical transformation to local system 23

3.2 Problem 3-2: Inverse of a symplectic matrix 25

3.3 Problem 3-3: Definition of a group 26

3.4 Problem 3-4: Unitary similarity transformations of Sp(2n) 28

3.5 Problem 3-5: Drift matrix 31

3.6 Problem 3-6: Symplectic constraints of a bend matrix 32

3.7 Problem 3-7: Quadrupole matrix 35

3.8 Problem 3-8: Solenoid matrix 38

3.9 Problem 3-9: Matrix for a tall rectangular solenoid 43

3.10 Problem 3-10: Zassenhaus formula 45

3.11 Problem 3-11: Cayley factorization 46

4 Problems of Chapter 4: Optical Elements and Static Fields 47

4.1 Problem 4-1: Lithium lens 47

4.2 Problem 4-2: Multipoles from scalar potential 49

4.3 Problem 4-3: Dipole C-magnet 52

4.4 Problem 4-4: Nonlinear drift equations 56

4.5 Problem 4-5: Path length through thick-lens quad 58

4.6 Problem 4-6: Sector magnet transport functions 60

4.7 Problem 4-7: Vector potential for multipole expansion 64

4.8 Problem 4-8: cos θ dipole magnet 67

4.9 Problem 4-9: cos (nθ) multipole magnet 69

4.10 Problem 4-10: cos (nθ) multipole magnet (Oops!) 71

4.11 Problem 4-11: Deflectors: electric vs magnetic 73

4.12 Problem 4-12: Dipole magnet design considerations 75

4.13 Problem 4-13: Pole-face profiles of gradient dipole 79

4.14 Problem 4-14: Helical dipolar field 80

4.15 Problem 4-15: Multipole vector potential 82

4.16 Problem 4-16: Symplecticity and solenoid fringes 85

4.17 Problem 4-17: Solenoid rotational decomposition 89

4.18 Problem 4-18: Principal planes of a thick quadrupole 91

5 Problems of Chapter 5: Strong Focusing 93

5.1 Problem 5-1: Twiss version of de Moivre's theorem 93

5.2 Problem 5-2: Hill's equations from Hamiltonian 95

5.3 Problem 5-3: Courant-Snyder ellipse properties 97

5.4 Problem 5-4: Floquet transformation to a circle 100

5.5 Problem 5-5: Propagation of envelope parameters 106

5.6 Problem 5-6: Eigenvalues of the envelope propagation matrix 107

5.7 Problem 5-7: Differential equations of the envelope functions 110

5.8 Comments on the Lie group and algebra of Twiss parameter propagation: 114

5.9 Problem 5-8: Integral representation of dispersion 118

5.10 Problem 5-9: Betatron phase advance 122

5.11 Problem 5-10: Conversion of emittances 123

5.12 Problem 5-11: Emittance growth in foils 124

6 Problems of Chapter 6: Lattice Exercises 129

6.1 Problem 6-1: Maximum phase of drift and FODO cell 129

6.2 Problem 6-2: Design of a FODO lattice 131

6.2.1 Listing of Octave functions for transport matrices 133

6.2.2 Listing of the Octave program 134

6.2.3 Commands for gnuplot 138

6.3 Problem 6-3: Momentum compaction from a matrix 140

6.4 Problem 6-4: CESR luminosity 142

6.5 Problem 6-5: Teng-Edwards decoupling 144

6.6 Problem 6-6: Determinant of a symplectic matrix 147

6.7 Problem 6-7: Correction of natural chromaticity 148

6.8 Problem 6-8: Chromaticity for FODO cell 150

7 Problems of Chapter 7: Synchrotron Oscillations 153

7.1 Problem 7-1: Longitudinal scaling relations 153

7.2 Problem 7-2: Dispersion function with rf 157

7.3 Problem 7-3: RHIC longitudinal parameters with Au 159

7.4 Longitudinal coordinates and synchrobetatron coupling 162

7.4.1 Variations of the longitudinal canonical variables 168

7.4.2 Transport matrices for a few elements 170

8 Problems of Chapter 8: Synchrotron Radiation 171

8.1 Problem 8-1: D for a simple lattice 171

8.2 Problem 8-2: Damping time for 6-d volume 172

8.3 Problem 8-3: Double-bend achromat 173

8.4 Problem 8-4: Light source ring damping times 177

8.5 Problem 8-5: LHC synchrotron radiation 179

9 Problems of Chapter 9: RF Linear Accelerators 181

9.1 Problem 9-1: Acceleration via a plane wave 181

9.2 Problem 9-2: Power loss in cavity walls 183

9.3 Problem 9-3: Lowest TM mode of rectangular cavity 185

9.4 Problem 9-4: Impedance of coupling loop 191

9.5 Problem 9-5: RFQ potential 193

9.6 Problem 9-6: RFQ phase oscillations 195

10 Problems of Chapter 10: Resonances 197

10.1 Problem 10-1: Skew multipole driven resonances 199

10.2 Problem 10-2: Sextupole driven quarter-integer resonance 204

10.2.1 Perturbation approach 204

10.2.2 Maxima code to evaluate Kn up to n = 6 209

10.2.3 Simulation approach 210

10.2.4 Listing of C program for the simulation 212

10.3 Problem 10-3: Sextupole driven third-integer resonance 216

10.3.1 Listing of the Octave program 219

10.4 Problem 10-4: Synchrotron modulated coupling 222

10.4.1 Nonlinear function listings 225

10.4.2 Listing of nonlinear FODO lattice simulation 227

11 New Problem for Chapter 11 : Space-Charge Effects 231

11.1 New Problem 11-1: Beam-beam shift for unequal species 231

12 Problems of Chapter 12: How to Baffle Liouville 233

12.1 Problem 12-1: New cooling ideas 233

13 Problems of Chapter 13: Spin Dynamics 235

13.1 Problem 13-1: Translation invariance of spin 235

13.2 Problem 13-2: Rapidity: hyperbolic rotation angle 237

13.3 Problem 13-3: Lorentz boost matrix Λμν (→β) 239

13.4 Problem 13-4: Thomas precession 244

13.5 Problem 13-5: Covariant Thomas-Frenkel-BMT equation 249

13.6 Problem 13-6: Spin tune with 2½ snakes 254

13.7 Problem 13-7: Spin tune with two snakes 257

13.8 Problem 13-8: Spin-1 rotation matrices 260

14 Problems of Chapter 14: Position Measurements and Spectra 263

14.1 Problem 14-1: Signal from a ring pickup 263

14.2 Problem 14-2: Longitudinal Schottky spectrum 265

Bibliography 267

Index 271
   도서 상세설명   

This manual provides solutions to the problems given in the second edition of the textbook entitled An Introduction to the Physics of Particle Accelerators. Simple-to-solve problems play a useful role as a first check of the student's level of knowledge whereas difficult problems will test the student's capacity to find the bearing of the problems in an interdisciplinary environment. The solutions to several problems will require the strong engagement of the student, not only in accelerator physics but also in more general physical subjects, such as the profound approach to classical mechanics (discussed in Chapter 3) and the subtleties of spin dynamics (Chapter 13).

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