Synchrotron Radiation and Free-Electron Lasers: Principles of Coherent X-Ray Generation

Contents
Preface
Conventions and Notation
1 Preliminary Concepts
	1.1 Particle (Electron) Beams
		1.1.1 Electron Beam Phase Space
		1.1.2 Beam Transport and Linear Optics
		1.1.3 Beam Emittance and Envelope Functions
		1.1.4 Beam Properties under Simple Transport
		1.1.5 Electron Distribution Function on Phase Space
	1.2 Radiation Beams
		1.2.1 Diffraction of Paraxial Beams
		1.2.2 The Paraxial Wave Equation and Energy Transport
		1.2.3 Phase Space Methods in Wave Optics
		1.2.4 Transverse Coherence
		1.2.5 Temporal Coherence
		1.2.6 Bunching and Intensity Enhancement
	References
2 Synchrotron Radiation
	2.1 Radiation by Relativistic Electrons
	2.2 The Driven Paraxial Wave Equation
	2.3 Bending Magnet Radiation
	2.4 Undulator Radiation
		2.4.1 Electron Trajectory and a Qualitative Discussion of Undulator Radiation
		2.4.2 Paraxial Analysis of Undulator Radiation
		2.4.3 Frequency Integrated Power
		2.4.4 Polarization Control
		2.4.5 Undulator Brightness and the Effects of the Electron Beam Distribution
		2.4.6 From Undulator Radiation to Free-Electron Lasers
	2.5 Future Directions of Synchrotron Radiation Sources
		2.5.1 Multi-Bend Achromat Lattices for Smaller Storage Ring Emittances
		2.5.2 Energy Recovery Linacs
		2.5.3 Superconducting Undulators
		2.5.4 Laser Undulator
	References
3 Basic FEL Physics
	3.1 Introduction
		3.1.1 Coherent Radiation Sources
		3.1.2 What Is an FEL?
	3.2 Electron Equations of Motion: The Pendulum Equations
		3.2.1 Derivation of the Equations
		3.2.2 Motion in Phase Space
	3.3 Low-Gain Regime
		3.3.1 Derivation of Gain
		3.3.2 Particle Trapping and Low-Gain Saturation
	3.4 High-Gain Regime
		3.4.1 Maxwell Equation
		3.4.2 FEL Equations and Energy Conservation
		3.4.3 Dimensionless FEL Scaling Parameter ρ
		3.4.4 1D Solution Using Collective Variables
		3.4.5 Qualitative Description of Self-Amplified Spontaneous Emission (SASE)
	References
4 1D FEL Analysis
	4.1 Coupled Maxwell–Klimontovich Equations for the 1D FEL
	4.2 Pertubative Solution for Small FEL Gain
	4.3 Solution via Laplace Transformation for Arbitrary FEL Gain
		4.3.1 Spontaneous Radiation and the Low-Gain Limit
		4.3.2 Exponential Growth Regime
		4.3.3 Temporal Fluctuation and Correlation of SASE
	4.4 Quasilinear Theory and Saturation
	4.5 Undulator Tapering after Gain Saturation
	4.6 Superradiance
	References
5 3D FEL Analysis
	5.1 Qualitative Discussion
		5.1.1 Diffraction and Guiding
		5.1.2 Beam Emittance and Focusing
	5.2 Electron Trajectory
		5.2.1 Natural Focusing in an Undulator
		5.2.2 Betatron Motion in an External Focusing Lattice
	5.3 3D Equations of the FEL
		5.3.1 Maxwell Equation
		5.3.2 3D Pendulum Equations for the Electron Motion
		5.3.3 Coupled Maxwell–Klimontovich Equations
	5.4 Solution in the Low-Gain Regime
		5.4.1 Low-Gain Expression for No Transverse Focusing
	5.5 Solution in the High-Gain Regime
		5.5.1 Van Kampen’s Normal Mode Expansion
		5.5.2 Dispersion Relation with Four Scaled Parameters
		5.5.3 Gain Guiding and Transverse Coherence
		5.5.4 Numerically Solving the Dispersion Relation
		5.5.5 Variational Solution and Fitting Formulas
	References
6 Harmonic Generation in High-Gain FELs
	6.1 Nonlinear Harmonic Generation
	6.2 High-Gain Harmonic Generation
	6.3 Echo-Enabled Harmonic Generation
	6.4 Recent Developments in Harmonic Generation
	References
7 FEL Oscillators and Coherent Hard X-Rays
	7.1 FEL Oscillator Principles
		7.1.1 Power Evolution and Saturation
		7.1.2 Qualitative Description of Longitudinal Mode Development
		7.1.3 Longitudinal Supermodes of the FEL Oscillator
		7.1.4 Transverse Physics of the Optical Cavity
	7.2 X-Ray Cavity Configurations
		7.2.1 Four-Crystal, Wavelength-Tunable XFELO Cavity
		7.2.2 Diamond Crystals for XFELO
	7.3 XFELO Parameters and Performance
	7.4 X-Ray Frequency Combs from a Mode-Locked FEL Oscillator
	7.5 A Hard X-Ray Master–Oscillator–Power Amplifier (MOPA)
	References
8 Practical Considerations and Experimental Results for High-Gain FELs
	8.1 Undulator Tolerances and Wakefields
		8.1.1 Undulator Errors and Tolerances
		8.1.2 Beam Trajectory Errors
		8.1.3 Wakefield Effects, Energy Loss, and Undulator Tapering
	8.2 FEL Experimental Results
		8.2.1 SASE FELs
		8.2.2 Seeded FEL
		8.2.3 Short-Pulse Generation
	References
Appendix A Hamilton’s Equations of Motion on Phase Space
	A.1 FEL Particle Equations from Transformation Theory
	A.2 Motion of a Test Electron in a High-Gain FEL
	References
Appendix B Simulation Methods for FELs
	B.1 The Design of FEL Simulation Codes
	B.2 Existing FEL Codes
	References
Appendix C Quantum Considerations for the FEL
	C.1 The Quantum Formulation
	C.2 Quantum Noise in the FEL Amplifier
	C.3 Madey’s Theorem
	References
Appendix D Transverse Gradient Undulators
	D.1 Low-Gain Analysis
	D.2 High-Gain Analysis
	References
Further Reading
Index