Accelerator XRay SourcesISBN: 9783527405909
494 pages
July 2006

Description
Written primarily for general, high energy and radiation physicists, the systematic treatment adopted by the work makes it equally suitable as an advanced textbook for young researchers.
Table of Contents
Preface XIII
1 Beams of Electrons or Photons 1
1.1 Preview 1
1.2 Coordinate Definitions 2
1.3 Onedimensional Transverse Propagation Equations 4
1.4 Transfer Matrices for Simple Elements 7
1.4.1 Drift Space 7
1.4.2 Thin Lens 7
1.4.3 Thick Lens 9
1.4.4 Erect Quadrupole Lens 11
1.5 Elliptical (in Phase Space) Beams 13
1.6 Beam Envelope E(s) 15
1.7 Gaussian Beams: their Variances and Covariances 17
1.8 Pseudoharmonic Trajectory Description 18
1.9 Transfer Matrix Parametrization 21
1.10 Reconciliation of Beam and Lattice Parameters 23
1.10.1 Beam Evolution Through a Drift Section 23
1.10.2 Beam Evolution Through a Thin Lens 24
References 25
2 Beams Treated as Waves 27
2.1 Preview 27
2.2 Scalar Wave Equation 28
2.3 The Short Wavelength, Geometric Optics Limit 30
2.3.1 Determination of Rays from Wavefronts 31
2.3.2 The Ray Equation in Geometric Optics 32
2.3.3 Obtaining Phase Information from Intensity Measurement 34
2.4 Wave Description of Gaussian Beams 36
2.4.1 Gaussian Beam in a Focusing Medium 37
2.4.2 Spatial Dependence of a Wave Near a Free Space Focus 39
2.4.3 The ABCD Law 40
2.4.4 Optics Using Mirrors 42
2.4.5 Wave Particle Duality for Electrons 44
2.5 Synchrotron Radiation: Waves or Particles? 45
2.6 Xray Holography and Phase Contrast and Lensfree Imaging 46
References 48
3 Synchrotron Radiation From Accelerator Magnets 49
3.1 Capsule History of Synchrotron Light Sources 49
3.2 Generalities 51
3.3 Potentials and Fields 53
3.4 Relations Between Observation Time and Retarded Time 54
3.5 Evaluation of Electric and Magnetic Fields 58
3.5.1 Radial Field Approximation 60
3.6 Total Power Radiated and its Angular Distribution 62
3.7 Spectral Power Density of the Radiation 65
3.7.1 Estimate of Frequency Spectrum from Pulse Duration 65
3.7.2 Radial Approximation 67
3.7.3 Accurate Formula for Spectral Power Density 68
3.8 Radiation from Multiple Charges 70
3.9 The Terminology of “Intensity” Measures 71
3.10 Photon Beam Features “Inherited from” the Electron Beam 74
3.11 Intensity Estimates for Bending Magnet beams 75
References 81
4 Simple Storage Rings 83
4.1 Preview 83
4.2 The Uniform Field Ring 84
4.3 Horizontal Stability 85
4.4 Vertical Stability 87
4.5 Simultaneous Horizontal and Vertical Stability 88
4.6 Dispersion 89
4.7 Momentum Compaction 90
4.8 Chromaticity 91
4.9 Strong Focusing 92
5 The Influence of Synchrotron Radiation on a Storage Ring 95
5.1 Preview 95
5.2 Statistical Properties of Synchrotron Radiation 96
5.2.1 Total Energy Radiated 96
5.2.2 The Distribution of Photon Energies; “Regularized Treatment” 99
5.2.3 Randomness of the Radiation 103
5.3 The Damping Rate Sum Rule: Robinson’s Theorem 105
5.3.1 Vertical Damping 110
5.3.2 Longitudinal Damping 111
5.3.3 Horizontal Damping and Partition Numbers 119
5.4 Equilibrium between Damping and Fluctuation. 120
5.5 Horizontal Equilibrium and Beam Width 121
5.6 Longitudinal Bunch Distributions 128
5.6.1 Energy Spread 128
5.6.2 Bunch Length 131
5.7 “Thermodynamics” of Wigglerdominated Storage Rings 132
5.7.1 Emittance of Pure Wiggler Lattice 132
5.7.2 Thermodynamic Analogy 137
References 140
6 Elementary Theory Of Linacs 141
6.1 Acknowledgement and Preview 141
6.2 The Nonrelativistic Linac 142
6.2.1 Transit Time Factor 142
6.2.2 Shunt Impedance 143
6.2.3 Cavity Q, R/Q, and Decay Time 144
6.2.4 Phase Stability and Adiabatic Damping 145
6.2.5 Transverse Defocusing 151
6.3 The Relativistic Electron Linac 153
6.3.1 Introduction 153
6.3.2 Particle Acceleration by a Wave 154
6.3.3 Wave Confined by Parallel Planes 155
6.3.4 Circular Waveguide 161
6.3.5 Cylindrical “Pillbox” Resonator 163
6.3.6 Lumped Constant Model for One Cavity Resonance 164
6.3.7 Cavity Excitation 166
6.3.8 Wave Propagation in Coupled Resonator Chain 168
6.3.9 Periodically Loaded Structures 172
6.3.10 Space Harmonics 174
7 Undulator Radiation 179
7.1 Preview 179
7.2 Introduction 180
7.3 Electron Orbit in a Wiggler or Undulator 184
7.4 Energy Radiated From one Wiggler Pole 187
7.5 Spectral Analysis for Arbitrary Longitudinal Field Profile 188
7.6 Spectrum of the Radiation from a Single Pole 191
7.6.1 Orbit Treated as Arc of Circle 191
7.6.2 Radiation from a Single, Short, Isolated, Magnet, K _ 1 192
7.7 Coherence from Multiple Deflections 196
7.8 Phasor Summation for K _ 1 199
7.9 Photon Energy Distributions 203
7.9.1 Energy Distribution from the n = 1 Undulator Fundamental 203
7.10 Undulator Radiation for Arbitrary K Value 204
7.10.1 Analytic Formulation 204
7.10.2 Diffraction Grating Analogy 212
7.10.3 Numerical/Graphical Representation of Undulator Radiation 213
7.10.4 Approximation of the Integrals by Special Functions 220
7.10.5 Practical Evaluation of the Series 222
7.11 Postmonochromator Profile 223
7.11.1 Monochromatic Annular Rings 225
7.11.2 Numerical Investigation of Undulator Rings 227
7.11.3 Is the Forward Undulator Peak Subject to Angular Narrowing? 227
References 230
8 Undulator Magnets 231
8.1 Preview 231
8.2 Considerations Governing Undulator Parameters 232
8.3 Simplified Radiation Formulas 234
8.4 A Hybrid, Electopermanent, Asymmetric Undulator 237
8.4.1 Electromagnet Design 239
8.4.2 Permanent Magnet Design—Small Gap Limit 244
8.4.3 Combined Electro/Permanent magnet Design 246
8.4.4 Estimated Xray Flux 247
References 248
9 XRay Beam Line Design 249
9.1 Preview 249
9.2 Beam Line Generalities 250
9.3 Accelerator Parameters 252
9.4 Bragg Scattering and Darwin Width 254
9.5 Aperturedefined Beam Line Design 257
9.5.1 Undulator Radiation, n = 1, Negligible Electron Divergence 257
9.5.2 Effect of Electron Beam Emittances on Flux and Brilliance 261
9.5.3 Brilliance with K > 1 and n > 1 263
9.6 Xray Mirrors 266
9.6.1 Specular Reflection of Xrays 266
9.6.2 Elliptical Mirrors 266
9.6.3 Hyperbolic Mirrors 267
9.7 Xray Lenses 270
9.7.1 Monochromatic Xray Lens 270
9.7.2 Focusing a Monochromatic Undulator Radiation Ring 270
9.7.3 Undulatorspecific Xray Lens 272
9.7.4 Lens Quality 278
9.8 Beam cameras 279
9.8.1 The Pinhole Camera 279
9.8.2 Imaging the Beam with Visible Light 280
9.8.3 Practicality of Lensbased, Xray Beam Camera? 283
9.9 Aperturefree Xray Beam Line Design 286
9.9.1 Aperturefree Rationale 286
9.9.2 Aperturefree Microbeam Line Based on Lenses 287
9.9.3 Effective Lens Stop Caused by Absorption 291
9.9.4 Choice of Undulator Parameter K 292
9.9.5 Estimated Flux 293
9.9.6 Estimated Brilliance and Qualifying Comments 295
References 296
10 The Energy Recovery Linac XRay Source 299
10.1 Preview 299
10.2 Introduction 300
10.3 Emittance Evolution in a DC Electron Gun 301
10.4 Qualitative Description of Lattice Design Issues 306
10.5 Isochronous Arc Design 309
10.6 Evolution of Betatron Amplitudes through the Linac Sections 314
10.6.1 Deceleration through Linac Section to Dump 314
10.6.2 Triplet Design 318
10.6.3 Acceleration through the High Energy Linac Section 319
10.7 Emittance Growth Due to CSR and Space Charge 321
References 325
11 A Fourth Generation, Fast Cycling, Conventional Light Source 327
11.1 Preview 327
11.2 Low Emittance Lattices 328
11.3 Production of High Quality Xray Beams 333
11.3.1 A Formula for Brilliance B 333
11.3.2 A Strategy to Maximize B 334
11.3.3 Hypothetical Utilization of an Existing Large Ring 335
11.4 Acceleration Scenario 338
11.5 Power Considerations 342
11.5.1 Average Power 342
11.5.2 Instantaneous Power 343
11.6 Critical Components and Parameter Dependencies 344
11.7 TrbojevicCourant Minimum Emittance Cells 346
11.7.1 Basic Formulas 346
11.7.2 Thin Lens Treatment 348
11.7.3 Thick Lens Treatment 353
11.7.4 Zero Dispersion Straight Sections 355
11.7.5 Nonlinearity and Dynamic Aperture 357
11.8 Emittance Evolution During Acceleration 359
11.9 Touschek Lifetime Estimate 362
11.10 Performance as Xray Source 363
11.10.1 Brilliance from Short Undulator 363
11.10.2 Refinement of Brilliance Calculation 365
References 368
12 Compton Scattered Beams And “Laser Wire” Diagnostics 369
12.1 Preview 369
12.2 Compton Scattering Kinematics 370
12.3 Some Specialized Laser, Electron Beam Configurations 373
12.3.1 Backscattered Photons 373
12.3.2 Orthogonal Photon Incidence in the Laboratory 374
12.3.3 Orthogonal Electron Frame Incidence 375
12.4 Total Compton Cross Section 380
12.5 The Photon Beam Treated as an Electromagnetic Wave 381
12.5.1 Determination of the Electron’s Velocity Modulation 382
12.5.2 Undulator Parametrization of Electron Motion in a Wave 386
12.6 Undulator Fields in Electron Rest Frame 388
12.6.1 Some Formulas from Special Relativity [7] 389
12.6.2 Treatment of an Undulator Magnet as an Electromagnetic Wave 389
12.7 Classical Derivation of Thomson Scattering 391
12.7.1 Introduction 391
12.7.2 Free Electron Oscillating in Electromagnetic Wave [5] 392
12.7.3 Electric Dipole Radiation [6] 392
12.7.4 Scattering Rate Expressed as a Total Cross Section 394
12.8 Transformation of Photon Distributions to the Laboratory 395
12.8.1 Solid Angle Transformation 395
12.8.2 Photon Energy Distribution in the Laboratory 396
12.8.3 A Theorem Applicable to Isotropic Distributions 398
12.8.4 Energy Distribution of Undulator Radiation 399
12.9 Rate Estimates for a Laser Wire Diagnostic Apparatus 401
12.9.1 The Nonrelativistic Limit 403
12.9.2 Laser Wire Treated as Undulator 403
12.9.3 Laser Wire Treated via Electron Rest Frame 405
12.9.4 Invariant Cross Section Applied to Laser Wire 406
12.9.5 Bunched Beam Rates 408
References 411
13 Space Charge Effects and Coherent Radiation 413
13.1 Acknowledgement and Preview 413
13.2 Introduction to the String Space Charge Formalism 414
13.3 Selfforce of Moving Straight Charged String 418
13.4 Selfforce of Moving Straight Charged Ribbon 423
13.5 Curve End Point Determination 430
13.6 Field Calculation 434
13.7 “Regularization” of the Longitudinal Force 438
13.8 Coherent Synchrotron Radiation 440
13.9 Evaluation of Integrals 442
13.10 Calculational Practicalities 443
13.11 Suppression of CSR by Wall Shielding 444
13.12 Effects of Entering and Leaving Magnets 445
13.13 Space Charge Calculations Using Unified Accelerator Libraries 447
13.13.1 Numerical Procedures Used by UAL 448
13.13.2 Program Architecture 450
13.13.3 Numerical Procedures 452
13.13.4 Comparison with TRAFIC4 [24] 453
References 456
14 The Xray FEL 457
14.1 Absorption and Spontaneous and Stimulated Emission 457
14.2 Closed and Open FELs 458
14.3 Interpretation of Undulator Radiation as Compton Scattering 459
14.4 Applicability Condition for SemiClassical Treatment 461
14.5 Comparison of Storage Ring, ERL, and FEL 462
References 465
Index 467
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