ISBN: 3-540-66266-9
TITLE: The Physics of Free Electron Lasers
AUTHOR: Saldin, E.L.; Schneidmiller, E.V.; Yurkov, M.V.
TOC:

1. Introduction 1
1.1 Advantages of FELs Over Quantum Lasers 3
1.2 Principle of FEL Operation 4
1.3 Suggested Bibliography 11
2. One-Dimensional Theory of the FEL Amplifier 13
2.1 Linear Mode of Operation 15
2.1.1 Effective Hamiltonian 15
2.1.2 Self-Consistent Equations 18
2.1.3 Solution of the Initial-Value Problem by the Laplace Technique 22
2.1.4 General Solution of the Initial-Value Problem 38
2.1.5 Linear Theory of the FEL Amplifier with a Planar Undulator 41
2.2 Saturation Effects 48
2.2.1 Self-Consistent Equations 49
2.2.2 Numerical Simulation Algorithm 51
2.2.3 Power Balance 51
2.2.4 Saturation in the High-Gain FEL Amplifier 52
2.2.5 Space Charge Effects 59
2.2.6 Energy Spread Effects 61
2.2.7 FEL Amplifier with a Planar Undulator 63
2.3 FEL Amplifier with Tapered Undulator 65
2.3.1 Low-Efficiency Approximation 66
2.3.2 The High-Efficiency FEL Amplifier 76
2.3.3 Some Generalizations 79
2.4 Concluding Remarks 82
2.5 Suggested Bibliography 86
3. One-Dimensional Theory of the FEL Oscillator 87
3.1 Small-Signal Gain 89
3.1.1 Basic Relations 89
3.1.2 Cold Electron Beam 91
3.1.3 Gaussian Energy Spread 92
3.1.4 Space Charge Effects 94
3.2 Saturation Effects in the FEL Oscillator 96
3.2.1 Self-Consistent Equations 97
3.2.2 Nonlinear Simulation Algorithm 98
3.2.3 Resonator Losses and Efficiency Optimization 99
3.2.4 Space Charge and FEL Efficiency 104
3.2.5 Energy Spread and FEL Efficiency 106
3.2.6 Some Generalizations 107
3.3 FEL Oscillator with Nonuniform Undulator 111
3.3.1 Basic Equations 113
3.3.2 Optical Klystron 118
3.3.3 FEL Oscillator with a Prebuncher and a Tapered Main Undulator 126
3.4 Start-Up from Shot Noise in the FEL Oscillator 134
3.4.1 Basic Equations 135
3.4.2 General Results 139
3.4.3 Operation Below Threshold 144
3.4.4 Operation Above Threshold 146
3.5 Concluding Remarks 149
3.6 Suggested Bibliography 152
4. Diffraction Effects in the FEL Amplifier 155
4.1 Self-Consistent Equations 159
4.2 Power Balance 164
4.3 Linear Theory of the FEL Amplifier with a Sheet Electron Beam 168
4.3.1 Eigenvalue Problem for a Stepped Profile 170
4.3.2 Analysis of the Beam Radiation Modes 178
4.3.3 Initial-Value Problem for a Stepped Profile 187
4.3.4 Epstein Profile 194
4.3.5 Parabolic Profile 205
4.3.6 Arbitrary Gradient Profile 209
4.4 Linear Theory of the FEL Amplifier with an Axisymmetric Electron Beam 214
4.4.1 Eigenvalue Problem for a Stepped Profile 214
4.4.2 Analysis of the Solutions 216
4.4.3 Initial-Value Problem for a Stepped Profile 225
4.4.4 Parabolic Profile 234
4.4.5 Arbitrary Gradient Profile 238
4.4.6 Numerical Solution of Initial-Value Problem 243
4.5 Nonlinear Mode of Operation 245
4.5.1 Nonlinear Simulation Algorithm 246
4.5.2 Some Results of Numerical Simulations 248
4.5.3 Planar Undulator 258
4.6 Concluding Remarks 259
4.7 Suggested Bibliography 261
5. Waveguide FELs 263
5.1 Self-Consistent Equations 265
5.1.1 Integro-Differential Equation for the Field 266
5.1.2 Integro-Differential Equation for the Beam Modulation 268
5.2 Power Balance 272
5.3 Beam Radiation Modes in a Circular Waveguide 276
5.3.1 Stepped Profile of Electron Beam 278
5.3.2 Parabolic Profile 303
5.3.3 Arbitrary Gradient Profile 307
5.4 Initial-Value Problem 309
5.4.1 Analytical Solution 309
5.4.2 Effective Potential for a Circular Waveguide 320
5.4.3 Numerical Solution 328
5.5 Nonlinear Mode of Operation 330
5.6 Rectangular Waveguide 340
5.7 Wall Resistance Effects 342
5.8 Concluding Remarks 350
5.9 Suggested Bibliography 351
6. FEL Amplifier Start-up from Shot Noise 353
6.1 Shot Noise in the Electron Beam 357
6.2 One-Dimensional Theory of SASE FEL 360
6.2.1 Analytical Description of the Linear Regime 360
6.2.2 Numerical Simulation Algorithm 380
6.2.3 Numerical Simulations of the Main Characteristics of a SASE FEL 385
6.3 Three-Dimensional Simulations of SASE FEL 402
6.3.1 Numerical Simulation Algorithm 402
6.3.2 Transverse Coherence 407
6.4 SASE FEL: Experiment and Theory 414
6.4.1 Region of Physical Parameters 415
6.4.2 Numerical Analysis of the Experiment 419
6.5 Suggested Bibliography 424
Appendices 425
A.1 The Extended Hamiltonian Formalism 425
A.2 Longitudinal Space Charge Field of a Modulated Electron Beam with Finite Transverse Size 428
A.3 Green's Function for a Homogeneous Waveguide 429
A.4 Eigenfunctions of a Passive Circular Waveguide 435
A.5 Calculation of the Sums in (5.119) 437
A.6 List of Symbols 441
Suggested Further Reading 449
References 453
Index 457 
END
