Part 1 book “An introduction to x- ray physics, optics, and applications” has contents: Introduction, a case study - nuclear medicine, thermal sources and plasmas, characteristic radiation, x- ray tubes, and x- ray fluorescence spectroscopy, source intensity, divergence, and coherence, bremsstrahlung radiation and x- ray tubes, synchrotron radiation,… and other contents.
AN INTRODUCTION TO X-Ray Physics, Optics, and Applications AN INTRODUCTION TO X-Ray Physics, Optics, and Applications C A R O LY N A M A C D O N A L D P R I NC E TON UN I V E R S I TY PR E SS P rin ce to n a nd Oxfo rd Copyright © 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket images (top, left to right): Fig Courtesy of Michael Flynn, University of Michigan Fig From Journal of Analytical Atomic Spectrometry (2011) / The Royal Society of Chemistry Fig. 3 From Proceedings of the 46th Annual Denver X-ray Conference (1997) / Courtesy of Scott Rohrbach (Bottom) Fig. 4 © American and Science Engineering, Inc All Rights Reserved ISBN 978-0-691-13965-4 Library of Congress Control Number 2017935618 British Library Cataloging-in-Publication Data is available This book has been composed in Minion Pro and Gotham Narrow Printed on acid-free paper ∞ Printed in the United States of America 10 In memory of my father Harry Edward MacDonald and my mentor Walter Maxwell Gibson CONTENTS Preface xiii Acknowledgments xv List of Constants and Variables xvii PART I FOUNDATIONS INTRODUCTION 1.1 The discovery 1.2 What is an x ray? 1.3 What makes x rays useful? 1.4 The layout of the text 1.5 The elusive hyphen Problems Further reading A CASE STUDY: NUCLEAR MEDICINE 2.1 Metastable emitters and half-life 2.2 A brief introduction to nuclear decay 2.3 Nuclear medicine 2.4 Photon detection and scatter rejection 2.5 Photon statistics 2.6 SPECT Problems Further reading 3 8 10 10 13 14 20 22 24 27 29 PART II X-RAY GENERATION THERMAL SOURCES AND PLASMAS 3.1 Blackbody radiation 3.2 Generation of very hot plasmas 3.3 Plasma frequency 33 33 35 37 viii ■ Contents 3.4 Debye length 3.5 Screening and the Debye length 3.6 Fluctuations and the Debye length Problems Further reading CHARACTERISTIC RADIATION, X-RAY TUBES, AND X-RAY FLUORESCENCE SPECTROSCOPY 4.1 Introduction 4.2 Core atomic levels 4.3 Characteristic spectra 4.4 Emission rates and intensity 4.5 Auger emission 4.6 Line widths 4.7 X-ray fluorescence Problems Further reading SOURCE INTENSITY, DIVERGENCE, AND COHERENCE 5.1 Intensity and angular intensity 5.2 Photon intensity and photon angular intensity 5.3 Brightness and brilliance 5.4 Global divergence 5.5 Local divergence 5.6 X-ray tube design 5.7 Coherence 5.8 Spatial coherence 5.9 Temporal coherence 5.10 In-line phase imaging Problems Further reading BREMSSTRAHLUNG RADIATION AND X-RAY TUBES SYNCHROTRON RADIATION 6.1 Field from a moving charge 6.2 Radiation from an accelerating (or decelerating) charge 6.3 Emission from a very thin anode 6.4 Emission from a thick anode 6.5 Efficiency 6.6 Thick-target photon emission rate modeling 6.7 Spectral shaping Problems Further reading 7.1 Classical (nonrelativistic) orbits 7.2 Semiclassical analysis 40 41 42 42 43 44 44 45 48 50 52 53 55 65 67 68 68 73 75 79 80 82 84 86 90 92 93 94 95 95 95 98 101 101 102 105 106 107 108 108 112 Contents ■ 7.3 Relativistic bremsstrahlung 7.4 Synchrotrons 7.5 Pulse time and spectrum 7.6 Insertion devices 7.7 Collimation and coherence Problems Further reading 114 117 117 121 125 126 126 X-RAY LASERS 127 127 130 131 131 133 135 135 136 8.1 Stimulated and spontaneous emission 8.2 Laser cavities 8.3 Highly ionized plasmas 8.4 High-harmonic generation 8.5 Free-electron lasers 8.6 Novel sources Problems Further reading PART III X-RAY INTERACTIONS WITH MATTER PHOTOELECTRIC ABSORPTION, ABSORPTION SPECTROSCOPY, IMAGING, AND DETECTION 9.1 Absorption coefficients 9.2 Attenuation versus absorption 9.3 Index of refraction 9.4 Absorption coefficient of compounds and broadband radiation 9.5 Absorption edges 9.6 Absorption spectroscopy 9.7 Filtering 9.8 Imaging 9.8.1 Contrast 9.8.2 Dose 9.8.3 Noise 9.9 Detectors 9.10 Tomosynthesis and tomography Problems Further reading 10 COMPTON SCATTERING 10.1 Conservation laws 10.2 Compton cross section 10.3 Inverse Compton sources 10.4 Scatter in radiography 10.5 Contrast with scatter 10.6 Scatter reduction 139 139 144 145 147 148 149 151 152 152 154 154 156 160 161 162 163 164 165 166 168 169 170 ix 122 ■ Chapter Radiation from an insertion device N S Electron beam S S N S N N S N Radiation S N Magnet poles FIGURE 7-14 Wiggler device From S L Hulbert and G P Williams, Synchrotron Sources, chap 55, Handbook of Optics, 3rd ed., vol 5, McGraw-Hill, 2010 Radiation xo – d + – FIGURE 7-15 Sinusoidal path of the electron past a sinusoidal magnetic field represented by magnets with their fields into and out of the page Radiation is emitted from the regions of highest curvature and v⊥ ≈ 2πc 2π ⎞ x cos ⎛ ct ⎝ d ⎠ d o (7-45) The transverse momentum is then p⊥ ≈ γ M e 2πc 2π ⎞ x cos ⎛ ct ⎝ d ⎠ d o (7-46) Setting the change in momentum equal to the force gives ⎛ 2π ct ⎞ = dp⊥ ≈ γ M ⎛ 2πc ⎞ x sin ⎛ 2π ct ⎞ F ≈ q e Boc sin e ⎝ d ⎠ o ⎝ d ⎠ ⎝ d ⎠ dt (7-47) Solving for the maximum deflection of the electron gives xo = q e Boc ⎛ d ⎞ q B d2 d K insert = e2 o = , γ M e ⎝ 2πc ⎠ 4π γ M ec π γ (7-48) Synchrotron Radiation ■ where the deflection parameter for the insertion device, Kinsert, is defined as K insert = q e Bod 2πM ec (7-49) The maximum deflection angle of the electron path from the z axis is θ≈ v ⊥ max K insert = γ v (7-50) This value is also the angular width in the deflection plane for radiation from the wiggler In general, the emission from successive periods of the wiggler is incoherent, since the fields not overlap For that reason the power from the wiggler is proportional to the number of magnets Nmag To evaluate the power from a single wiggler magnet from equation 7-29 it is necessary to estimate the bending radius Using the acceleration from equation 7-47, and comparing that value with a = v 2/R from equation 7-2, yields d2 d ⎛ 2π γ ⎞ d γ 2π ⎞ c = a = xo ⎛ c = ⇒ Ru ≈ = ⎜ ⎝ d ⎠ Ru 4π x o 4π ⎝ d K insert ⎟⎠ 2π K insert (7-51) Applying that result to the power per arc from a single magnet with an electron current J yields Pχ ,1 ≈ qe q ⎛ 2π K insert ⎞ q e K insert γ 4J = e ⎜ γ J= γ J γ ⎟⎠ 6πε 3ε ο d 6πε ο R ο ⎝ d (7-52) The total power for each turn around a magnet then depends on integrating over the angle which contributes to the beam The angle is proportional to the deflection angle, Δθ ≈ K insert γ The angular integral, and a more exact calculation of the radius of deflection, which varies as the electron oscillates, yields an additional factor of π/2 There are then 2N arcs (for a wiggler with N periods), so that the power in the beam for the wiggler P≈ πq e JN 2 γ K insert 3εo d For wigglers (7-53) The spectrum is similar to that for an individual magnet Wigglers with small deflection parameters, K