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E-raamat: Channeling and Radiation in Periodically Bent Crystals

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The development of coherent radiation sources for sub-angstrom wavelengths - i.e. in the hard X-ray and gamma-ray range - is a challenging goal of modern physics. The availability of such sources will have many applications in basic science, technology and medicine and in particular, they may have a revolutionary impact on nuclear and solid state physics, as well as on the life sciences. The present state-of-the-art lasers are capable of emitting electromagnetic radiation from the infrared to the ultraviolet, while free electron lasers (X-FELs) are now entering the soft X-ray region. Moving further, i.e. into the hard X and/or gamma ray band, however, is not possible without new approaches and technologies.

In this book we introduce and discuss one such novel approach -the radiation formed in a Crystalline Undulator - whereby electromagnetic radiation is generated by a bunch of ultra-relativistic particles channeling through a periodically bent crystalline structure. Under certain conditions, such a device can emit intensive spontaneous monochromatic radiation and even reach the coherence of laser light sources.

Readers will be presented with the underlying fundamental physics and be familiarized with the theoretical, experimental and technological advances made during the last one and a half decades in exploring the various features of investigations into crystalline undulators. This research draws upon knowledge from many research fields - such as materials science, beam physics, the physics of radiation, solid state physics and acoustics, to name but a few. Accordingly, much care has been taken by the authors to make the book as self-contained as possible in this respect, so as to also provide a useful introduction to this emerging field to a broad readership of researchers and scientist with various backgrounds.

This new edition has been revised and extended to take recent developments in the field into account. 
1 Introduction 1(12)
1.1 Crystalline Undulator: Basic Ideas
1(3)
1.2 Why a Crystalline Undulator?
4(3)
1.3 Is This Realistic?
7(6)
1.3.1 Feasibility of CU
8(1)
1.3.2 Methods of Preparation of CU
9(4)
2 Related Phenomena 13(34)
2.1 Radiation from Relativistic Charges: Classical, Quantum and Quasiclassical Approaches
13(5)
2.1.1 Classical Description
14(1)
2.1.2 Quantum Description
15(1)
2.1.3 Quasi-Classical Description of Radiation Emission
16(2)
2.2 UR from an Ideal Planar Undulator
18(8)
2.2.1 General Formalism
18(4)
2.2.2 Spectral Distribution in the Forward Direction
22(2)
2.2.3 Spectral Distribution Integrated Over the Emission Angles
24(2)
2.3 Channeling in Straight Crystals
26(9)
2.3.1 Crystallographic Axes and Planes
27(1)
2.3.2 Continuous Potential Model
28(4)
2.3.3 Positron Versus Electron Channeling
32(2)
2.3.4 Classical Versus Quantum Description
34(1)
2.4 Channeling in Bent Crystals
35(3)
2.5 Radiative Processes in Crystals
38(9)
2.5.1 Bremsstrahlung
38(4)
2.5.2 ChR in Straight and Bent Crystals
42(5)
3 Schemes for Periodic Bending of Crystals 47(26)
3.1 Periodic Bending with AW
48(3)
3.2 Growing of Crystals with PBCh
51(3)
3.3 Periodic Surface Deformations
54(4)
3.3.1 Diamond-Blade Scratching
54(1)
3.3.2 Laser-Ablation Technique
55(2)
3.3.3 Tensile Strips Deposition
57(1)
3.4 Imperfectness of Crystalline Structure Bending
58(15)
3.4.1 Introductory Remarks
59(1)
3.4.2 Periodic Deformations in Bulk: Model and Formalism
60(5)
3.4.3 Periodic Deformations in Bulk: Numerical Results
65(8)
4 Feasibility of a Positron-Based Crystalline Undulator 73(40)
4.1 Channeling Condition in PBCr
73(2)
4.2 Large and Small Amplitude Regimes
75(4)
4.2.1 Influence of Channeling Oscillations on the CU Radiation
77(2)
4.3 Dechanneling and Photon Attenuation
79(16)
4.3.1 Dechanneling Process
80(8)
4.3.2 Photon Attenuation
88(1)
4.3.3 UR in Presence of Dechanneling and Photon Attenuation
88(7)
4.4 Energy Losses
95(9)
4.4.1 Quasi-Classical Formalism for the Radiative Energy Loss in CU
95(4)
4.4.2 Calculation of Radiative Energy Losses in PBCr
99(2)
4.4.3 Undulator Effect in the High-Energy Regime
101(3)
4.5 Feasibility of a Positron-Based CU: Summary of the Necessary Conditions
104(4)
4.6 Feasibility of a Positron-Based CU: Historical Survey
108(5)
5 Positron-Based CU: Illustrative Material 113(40)
5.1 Brief Description of the Computer Algorithms
114(2)
5.1.1 Computation of Positron Trajectories in PBCr
114(1)
5.1.2 Computation of Characteristics of the Emitted Radiation
115(1)
5.1.3 Test Calculation of the ChR Spectrum
116(1)
5.2 CUR for 0.5 GeV Positrons
116(5)
5.3 CUR for 5 GeV Positrons
121(5)
5.4 Estimation of Brilliance of CUR
126(7)
5.4.1 Optimal Length of CU
127(1)
5.4.2 Numerical Results for Brilliance
128(5)
5.5 Emission from Imperfect CU
133(8)
5.5.1 Emission from CU with a Varied Amplitude: Formalism
133(2)
5.5.2 Averaged Spectra: Numerical Results
135(5)
5.5.3 Concluding Remarks
140(1)
5.6 Channeling of Ultra-Relativistic Projectiles Simulated with MBN Explorer
141(12)
5.6.1 Description of the Algorithm
143(3)
5.6.2 Positron Channeling in Si(110) and Si(111)
146(2)
5.6.3 ChR and CUR by Positrons in Straight and Periodically Bent Si(110) and Si(111) Channels
148(5)
6 CUs for Electrons and Heavy Particles 153(38)
6.1 Electron-Based CU
153(23)
6.1.1 Electron-Based Versus Positron-Based CU
153(5)
6.1.2 Electron-Based CU: High-Energy Regime
158(5)
6.1.3 Electron-Based CU: Low-Energy Regime
163(13)
6.2 Crystalline Undulators for Heavy Projectiles
176(15)
6.2.1 Dechanneling and Energy Losses
176(2)
6.2.2 Photon Attenuation, Channeling Condition and Large-Amplitude Regime
178(13)
7 Experimental Studies of CUR 191(16)
7.1 Experiments with Positrons
192(8)
7.1.1 Experiments at IHEP
192(5)
7.1.2 Planned Experiments at CERN and INFN
197(1)
7.1.3 Perspectives of the Experiments at DANE BTF
198(2)
7.2 Experiments with Electrons at MAMI
200(7)
7.2.1 Experiments with 855 and 1,508 MeV Electrons
200(3)
7.2.2 Experiments with E = 195-855 MeV Electrons
203(4)
8 Stimulated Emission from CU 207(30)
8.1 Introduction
207(2)
8.2 'Naive' Approach to the CU-Based Gamma-Laser
209(11)
8.2.1 Crude Estimate of the Gamma-Laser Gain
210(3)
8.2.2 One-Crystal Gamma-Ray Amplifier
213(7)
8.3 Gamma-klystron
220(4)
8.3.1 Multicascade Amplifier
223(1)
8.4 Beam Demodulation in CU
224(9)
8.4.1 Diffusion Equation and Its Solution
225(4)
8.4.2 Demodulation Length
229(4)
8.5 A Scheme for CUL
233(4)
9 Conclusion 237(4)
Appendix A: Motion in Periodically Bent Channel 241(10)
Appendix B: Estimation of the Undulator Parameter Due to Channeling Oscillations 251(2)
Appendix C: Poschl-Teller Potential 253(6)
Appendix D: Interplanar Potential Within the Moliere Approximation 259(4)
Appendix E: Classical Scattering of an Ultra-Relativistic Projectile from a "Snapshot" Atom 263(6)
References 269(14)
Index 283