Nonlinear Optics, Quantum Optics, and Ultrafast Phenomena with X-Rays: Physics with X-Ray Free-Elect

1 X-Ray Sources.- 1 Introduction.- 2 X-Ray Tubes.- 3 Laser-Driven Sources.- 4 Synchrotrons and Storage Rings.- 5 Pulse Slicing and Ultrafast Thomson Scattering.- 6 Energy-Recovering Linacs.- 7 X-Ray Free-Electron Lasers.- 7.1 The Physics of the FEL Process.- 7.2 Hard X-Ray FEL Facilities in Planning.- 7.3 The Quantum FEL.- 7.4 Lasing without Inversion.- 8 Comparison of Sources.- 2 Nonlinear Optics of Free Electrons.- 1 Introduction.- 2 Relativistic Electrons in Electromagnetic Waves.- 2.1 Single Plane Wave Packet.- 2.2 Multiple Parallel Plane Waves.- 2.3 Multiple Plane Waves, Nonrelativistic Approximation.- 2.4 Relativistic Electrons in Two Plane Wave Packets.- 2.4.1 Discussion.- 2.5 Laser Acceleration of Electrons.- 3 Dynamical Diffraction.- 1 Introduction.- 2 Linear Perfect Crystal Theory.- 2.1 Perfect Lattice, Fourier and Bloch Sums.- 2.2 The System of Linear Equations.- 2.3 The Dispersion Surface.- 2.4 Phase and Group Velocity, Beam Direction.- 2.5 Extinction and Boundary Conditions.- 3 Extended Takagi-Taupin Theory.- 3.1 Disturbed Lattice, Fourier and Bloch Sums.- 3.2 The System of Differential Equations.- 3.3 Comparison with the Takagi-Taupin Theory.- 3.3.1 Differential Equations.- 3.3.2 Generalized Wave Fields.- 3.4 Comparison with Kato's Eikonal Theory.- 3.5 Numerical Solution of the Differential Equations.- 3.6 The Dispersion Surface.- 3.6.1 Propagation of the Field Amplitudes.- 3.7 Beams, Adiabatic Change and Interbranch Scattering.- 3.8 Obtaining Qualitative Information.- 3.8.1 Example: Optical Phonons, Frequency Shifts.- 3.8.2 Example: Static Distortion, Guided Waves.- 3.9 From Boundary to Transition Conditions.- 3.10 Summary and Discussion.- 4 Nonlinear Dynamical Diffraction from Free Electrons.- 4.1 Multiple Bloch Waves.- 4.2 The System of Nonlinear Equations.- 4.3 An Example: Parametric Down Conversion.- 5 Appendix.- 5.1 Dynamical Diffraction in Macroscopic Form.- 5.2 The Longitudinal Current.- 5.3 Applicability of Macroscopic Electromagnetism.- 5.4 The Position of a Tie Point in Reciprocal Space.- 5.5 The Direction of the Poynting Vector.- 5.6 Details of Derivations.- 5.6.1 Amplitude Ratio, Equation (3.15).- 5.6.2 Equation (3.27).- 5.6.3 An Integral.- 4 Ultrafast Diffractive X-Ray Optics.- 1 Introduction.- 2 Laser-Induced Changes in Crystal Diffractive Properties.- 3 Bragg Reflection.- 4 Laue Transmission.- 4.1 Redirection of the Poynting Vector.- 4.2 An X-Ray Optical Femtosecond Streak Camera.- 4.2.1 Grazing Incidence.- 4.2.2 Swept Laser Excitation.- 4.2.3 An Example.- 4.2.4 Discussion.- 4.3 An Ultrafast Phase Retarder.- 4.4 Spectral Concentration of X-Rays.- 4.5 A Fast Borrmann Shutter.- 5 Parametric Down Converion.- 1 Introduction.- 1.1 Nonlinear Medium.- 1.2 Wave Vector and Frequency Matching.- 1.3 Strength of the Effect.- 2 Experiments.- 2.1 The Classical Experiment by Eisenberger and McCall.- 2.2 The First Synchrotron Results, Yoda et al.- 2.3 Energy Discrimination and Time Correlation.- 2.4 High Event Rate.- 2.5 High Pump Photon Energy - 98.9 keV.- 2.6 Suppression of the Pump Photons with a Mirror.- 2.7 Small Angles.- 2.7.1 The First Small-Angle Experiment.- 2.7.2 APS, 1-ID.- 2.7.3 APS, 7-ID.- 2.7.4 Suppression of Down Conversion at Small Angles.- 2.8 Wave Vector Matching by Dynamical Diffraction.- 3 Potential Applications.- 3.1 Tests of the Quantum Theory.- 3.2 Sub-Poisson Absorption Spectroscopy.- 3.3 Integration into a Beam Line.- 4 Experimental Issues.- 4.1 Background Suppression.- 4.2 Electric Noise.- 4.3 Stray Radiation.- 4.4 Energy Resolution.- 4.5 Time Resolution.- 4.6 Time Structure of the Source.- 4.7 Choice of Sample Material.- 5 Summary.- 6 Appendix.- 6.1 The Virtual Power Density of Vacuum Fluctuations.- 6.2 Cross Section.- 6.3 Amplitude Growth.- 6.4 Wave Vector Matching.- 6.4.1 Without Dynamical Diffraction.- 6.4.2 With Dynamical Diffraction of the Pump Only.- 6.5 Electronics.- 6.5.1 The Correlation Circuit.- 6.5.2 The Event Logger.- 6 Laser Pump, X-Ray Probe Spectroscopy on GaAs.- 1 In