Synchrotron Radiation

280 Pages·2003·7.266 MB·English

by  Professor Helmut Wiedemann (auth.)

Synchrotron Radiation
Advanced Texts in Physics
This program of advanced texts covers a broad spectrum of topics which are of
current and emerging interest in physics. Each book provides a comprehensive and
yet accessible introduction to a field at the forefront of modern research. As such,
these texts are intended for senior undergraduate and graduate students at the MS
and PhD level; however, research scientists seeking an introduction to particular
areas of physics will also benefit from the titles in this collection.
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LIBRARY
Physics and Astronomy
http://www.springer.de/phys/
Helmut Wiedemann
Synchrotron
Radiation
With 89 Figures, 7 Tables,
100 Exercises and 55 Selected Solutions
t
Springer
Professor Helmut Wiedemann
Applied Physics Department
and SSRLlSLAC
Stanford University
P.O. Box 20450
Stanford, CA 94309
USA
E-mail: wiedemann(\)SLAC. Stanford. edu
Cover picture:
Distortion of electrical field lines due to transverse acceleration of a charge (Figure 2.6)
ISSN 1439-2674
Library of Congress Cataloging-in-Publication Data
Wiedemann, Helmut, 1938-
Synchrotron radiation / Helmut Wiedemann.
p.cm. - (Advanced texts in physics)
Includes bibliographical references and index.
ISBN 978-3-642-07777-7 ISBN 978-3-662-05312-6 (eBook)
DOI 10.1007/978-3-662-05312-6
1. Synchrotron radiation. I. Title. II. Series.
QC793.5.E627 W4 5 2002 539.7'35-dc21 2002021668
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To my family and students
Preface
This book covers the physical aspects of synchrotron radiation generation and
is designed as a textbook and reference for graduate students, teachers and
scientists utilizing synchrotron radiation. It is my hope that this text may
help especially students and young researchers entering this exciting field to
gain insight into the characteristics of synchrotron radiation.
Discovered in 1945, synchrotron radiation has become the source of pho
tons from the infrared to hard x-rays for a large community of researchers in
basic and applied sciences. This process was particularly supported by the
development of electron accelerators for basic research in high energy physics.
Specifically, the development of the storage ring and associated technologies
resulted in the availability of high brightness photon beams far exceeding
other sources.
In this text, the physics of synchrotron radiation for a variety of magnets
is derived from first principles resulting in useful formulas for the practitioner.
Since the characteristics and quality of synchrotron radiation are intimately
connected with the accelerator and electron beam producing this radiation,
a short overview of relevant accelerator physics is included.
In the first four chapters radiation phenomena in general and synchrotron
radiation in particular are introduced based on more visual and basic phys
ical concepts. Where exact formulas are required, we borrow results from
rigorous derivations in Chaps. 9 and 10. This way the physics of synchrotron
radiation can be discussed without extensive deviations into mathematical
manipulations, which can be quite elaborate although straightforward. The
consequence for the reader, of this dual approach to synchrotron radiation is
that, here and there, one will find some repetitive discussions, which the au
thor hopes will provide easier reading and continuity in the train of thought.
Chapters 5 to 8 give an overview of beam dynamics in storage rings and
guidance for the optimization of a storage ring for synchrotron radiation pro
duction. The theory of synchrotron radiation is derived rigorously in Chap.
9 and that of undulator or insertion device radiation in Chap. 10. Finally, in
Chap. 11 the physics of a free electron laser is discussed.
Each chapter includes a set of exercises. For those exercises which are
marked with the argument (S), solutions are provided in Appendix A. In
support of the practitioner utilizing synchrotron radiation most relevant for-
VIII Preface
mulas together with useful mathematical and physical formulae and constants
are compiled in Appendices B - D.
The author would like to thank the editorial staff at Springer Verlag and
especially Drs. H. Lotsch and C. Ascheron for suggesting the writing of this
book. The trained eyes of Dr. A. Lahee and Mrs. Dimler contributed much to
minimize typographical errors and to greatly improve the overall appearance
of the book. Special thanks goes to Professors J. Dorfan and K. Hodgson at
Stanford University for granting a sabbatical and to Professor T. Vilaithong
at the Chiang Mai University in Thailand for providing a quiet and peaceful
environment during the final stages of writing this book.
Chiang Mai, Helmut Wiedemann
July 2002
Contents
1. Charges and Fields .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Radiation from Moving Charges . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Why do Charged Particles Radiate? ................ 2
1.1. 2 Spontaneous Synchrotron Radiation .. . . . . . . . . . . . . . . 2
1.1.3 Stimulated Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.4 Electron Beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Maxwell's Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Conversion from cgs to MKS Units. . . . . . . . . . . . . . . . . 6
1.2.2 Lorentz Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 The Lorentz Transformations ............................ 10
1.3.1 Lorentz Transformation of Coordinates. . . . . . . . . . . . .. 11
1.3.2 Energy and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14
2. Fundamental Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
2.1 Conservation Laws and Radiation. . . . . . . . . . . . . . . . . . . . . . .. 17
2.1.1 Cherenkov Radiation ............................. 18
2.1.2 Compton Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
2.2 The Poynting Vector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
2.3 Electromagnetic Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
2.3.1 Coulomb Regime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
2.3.2 Radiation Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.4 Spatial and Spectral Properties of Radiation. . . . . . . . . . . . . .. 26
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3. Overview of Synchrotron Radiation. . . . . . . . . . . . . . . . . . . . . .. 31
3.1 Radiation Power ....................................... 32
3.2 Spectrum.............................................. 36
3.3 Spatial Photon Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41
3.4 Fraunhofer Diffraction .................................. 42
3.5 Spatial Coherence ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45
3.6 Temporal Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
3.7 Spectral Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
3.7.1 Matching ........................................ 51
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
X Contents
4. Radiation Sources ........................................ 55
4.1 Bending Magnet Radiation .............................. 55
4.2 Superbends............................................ 56
4.3 Wavelength Shifter ..................................... 57
4.4 Wiggler Magnet Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
4.5 Undulator Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
4.6 Back Scattered Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
4.6.1 Photon Flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 70
5. Accelerator Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73
Exercise ................................................... 76
6. Particle Beam Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
6.1 Deflection in Bending Magnets. . . . . . . . . . . . . . . . . . . . . . . . . .. 77
6.2 Beam Focusing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
6.2.1 Principle of Focusing ............................. 80
6.2.2 Quadrupol Magnet ............................... 80
6.3 Equation of Motion .................................... , 82
6.3.1 Solutions of the Equations of Motion. . . . . . . . . . . . . . .. 84
6.3.2 Matrix Formalism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
6.3.3 FODO Lattice " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
6.4 Betatron Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
6.4.1 Betatron Phase and TUne. . . . . . . . . . . . . . . . . . . . . . . .. 87
6.4.2 Beam Envelope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88
6.5 Phase Ellipse .......................................... 88
6.6 Beam Emittance ....................................... 89
6.6.1 Variation of the Phase Ellipse. . . . . . . . . . . . . . . . . . . . .. 90
6.6.2 Transformation of Phase Ellipse. . . . . . . . . . . . . . . . . . .. 91
6.7 Dispersion Function .................................... 92
6.8 Periodic Lattice Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93
6.8.1 Periodic Betatron Function in a FODO Lattice. . . . . .. 93
6.8.2 Periodic Dispersion or 1J-Function .................. 95
6.8.3 Beam Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96
7. Radiation Effects '" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
7.1 Synchrotron Oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
7.1.1 Longitudinal Phase Space Motion .................. 103
7.2 Damping .............................................. 104
7.3 Quantum Effects ....................................... 105
7.4 Equilibrium Beam Parameters ........................... 106
7.4.1 Equilibrium Energy Spread ........................ 106
7.4.2 Bunch Length .................................... 107
7.4.3 Horizontal Beam Emittance ....................... 108
7.4.4 Vertical Beam Emittance .......................... 109
Contents XI
7.5 Transverse Beam Parameters ............................. 110
7.5.1 Beam Sizes ...................................... 111
7.5.2 Beam Divergence ................................. 112
7.6 Beam Emittance and Wiggler Magnets .................... 112
7.6.1 Damping Wigglers ................................ 115
7.6.2 Variation of the Damping Distribution .............. 117
7.6.3 Can we Eliminate the Beam Energy Spread? ......... 119
7.7 Photon Source Parameters ............................... 121
Exercises ................................................... 122
8. Storage Ring Design as a Synchrotron Light Source ...... 125
8.1 Storage Ring Lattices ................................... 126
8.1.1 FODO Lattice ................................... 126
8.2 Optimization of a Storage Ring Lattice .................... 127
8.2.1 Minimum Beam Emittance ........................ 128
8.2.2 The Double Bend Achromat (dba) Lattice ........... 131
8.2.3 The Triple Bend Achromat (tba) Lattice ............ 134
8.2.4 Limiting Effects .................................. 134
9. Theory of Synchrotron Radiation ......................... 137
9.1 Radiation Field ........................................ 137
9.2 Total Radiation Power and Energy Loss ................... 144
9.2.1 Transition Radiation .............................. 144
9.2.2 Synchrotron Radiation Power ...................... 147
9.3 Radiation Lobes ........................................ 150
9.4 Synchrotron Radiation Spectrum ......................... 155
9.5 Radiation Field in the Frequency Domain ................. 155
9.5.1 Spectral Distribution in Space and Polarization ...... 160
9.5.2 Spectral and Spatial Photon Flux .................. 163
9.5.3 Harmonic Representation .......................... 165
9.6 Spatial Radiation Power Distribution ..................... 165
9.6.1 Asymptotic Solutions ............................. 167
9.7 Angle-Integrated Spectrum .............................. 168
9.7.1 Statistical Radiation Parameters ................... 174
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 176
10. Insertion Device Radiation ............................... 177
10.1 Periodic Magnetic Field ................................. 178
10.1.1 Periodic Field Configuration ....................... 179
10.1.2 Particle Dynamics in a Periodic Field Magnet ........ 182
10.1.3 Focusing in a Wiggler Magnet ..................... 183
10.1.4 Hard Edge Wiggler Model ......................... 186