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6.2 Transition Radiation

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6.2 Transition Radiation Contents I General introduction 9 1Preamble 11 2 Relevant publications 15 3 A first look at the formation length 21 4 Formation length 23 4.1Classicalformationlength..................... 24 4.1.1 A reduced wavelength distance from the electron to the photon ........................... 25 4.1.2 Ignorance of the exact location of emission . ....... 25 4.1.3 ‘Semi-bare’ electron . ................... 26 4.1.4 Field line picture of radiation . ............... 26 4.2Quantumformationlength..................... 28 II Interactions in amorphous targets 31 5 Bremsstrahlung 33 5.1Incoherentbremsstrahlung..................... 33 5.2Genericexperimentalsetup..................... 35 5.2.1 Detectors employed . ................... 35 5.3Expandedexperimentalsetup.................... 39 6 Landau-Pomeranchuk-Migdal (LPM) effect 47 6.1 Formation length and LPM effect.................. 48 6.2 Transition radiation . ....................... 52 6.3 Dielectric suppression - the Ter-Mikaelian effect.......... 54 6.4CERNLPMExperiment...................... 55 6.5Resultsanddiscussion....................... 55 3 4 CONTENTS 6.5.1 Determination of ELPM ................... 56 6.5.2 Suppression and possible compensation . ........ 59 7 Very thin targets 61 7.1Theory................................ 62 7.1.1 Multiple scattering dominated transition radiation . .... 62 7.2MSDTRExperiment........................ 63 7.3Results................................ 64 8 Ternovskii-Shul’ga-Fomin (TSF) effect 67 8.1Theory................................ 67 8.1.1 Logarithmic thickness dependence . ............ 68 8.2Results................................ 71 9 King-Perkins-Chudakov (KPC) effect 75 9.1 Introduction to the KPC effect................... 75 9.2KPCExperiment.......................... 81 9.3Results................................ 84 10 Ultrarelativistic ionization energy loss 87 10.1 Introduction . ............................ 87 10.1.1 Loss of density effect.................... 87 10.1.2 Coherence length effect................... 88 10.2 ’Ogle’ Experiment . ........................ 89 10.2.1 Background from synchrotron and transition radiation . 90 10.3 Results ................................ 91 11 Ultrarelativistic heavy ions 95 11.1 Fragmentation experiment . .................... 96 11.2 Results and discussion . .................... 98 11.3 Ionization energy loss for ions . ................100 11.3.1 Nuclear size effect.....................100 11.3.2 Free-free pair production and bremsstrahlung . 101 11.3.3 Bound-free pair production . ................101 III Interactions in crystalline targets 103 12 Strong crystalline fields 105 12.1 The critical field . ........................105 12.2 Strong fields in crystals . ....................109 12.3 Crystal parameters . ........................110 CONTENTS 5 12.3.1 Crystal lattice . .......................110 13 Channeling 113 13.1 Critical angles . ...........................115 13.2 Positively and negatively charged particles . ...........116 13.3 High energy channeling radiation . ...............118 13.4 Coherent bremsstrahlung . ...................120 14 Quantum or classical description? 125 14.1 Particle motion ...........................125 14.2 Emission of radiation . .......................126 14.3 Classical recoil ...........................128 15 Radiation emission in strong fields 129 15.1 Threshold for strong field effects..................130 15.2 The classical limit of synchrotron radiation . ...........131 15.3 The Constant Field Approximation (CFA) . ...........131 15.4 Virtual photon density . .......................137 15.5 Spin processes . ...........................138 15.6 Doughnut scattering suppression . ...............140 16 Radiation emission experiments 141 16.1 Side-slip ...............................143 16.2 Coherent resonances in radiation emission . ...........145 16.3 Quantum suppression . .......................146 16.4 Spin-flip in a strong field . ...................147 16.5 Generation of polarized GeV photons ...............147 16.6 Search for short-lived photo-produced particles . 150 17 Ultra-low emittance beams from crystals 153 17.1 Radiation cooling . .......................153 17.2 Radiation cooling in a ‘continuous focusing environment’ . 157 17.3 Excitation-free radiation emission . ...............158 17.4 Results . ...............................160 18 Photons in strong fields 163 18.1 Pair production ...........................163 18.1.1 Total and differentialrates.................164 18.1.2 Enhancements in crystals . ...............165 18.1.3 Suppression of incoherent contribution . .......166 18.1.4 Coherent resonance for pair production . .......167 18.2 Corrections to the CFA .......................167 6 CONTENTS 18.3 Photon splitting . ........................168 18.4 Delbruckscattering.........................170¨ 19 Trident production 171 19.1 Trident experiment . ........................172 19.2 Results and discussion . ....................174 20 Beam-beam interactions - beamstrahlung 179 20.1 Quantum treatment of beamstrahlung . ............180 20.2 ’Coherent pairs’ . ........................183 20.3 ’Landau-Lifshitz’ pairs and tridents ................185 21 Non-crystalline strong fields 189 21.1 Strong fields from plasma wakefields ................189 21.2 Astrophysical strong fields . ....................190 21.3 Strong fields in nuclear collisions . ................190 21.4 Strong laser fields . ........................191 21.5 Hawking radiation and Unruh effect................193 21.6 The geomagnetic field as a strong field . ............194 22 Channeling in bent crystals 197 22.1 Introduction . ............................197 22.2 Deflection of charged particles in bent crystals . ....198 22.2.1 Critical curvature . ....................198 22.2.2 Strong fields ........................198 22.2.3 Dechanneling ........................199 22.2.4 Model for deflection efficiency...............201 22.2.5 Comparison - model vs. experiment ............202 22.2.6 Volume capture and reflection . ............203 22.2.7 Axial deflection . ....................206 22.3 Radiation damage . ........................206 22.3.1 Imperfections and radiation damage ............207 22.4 Momentum and charge dependence ................207 22.4.1 High-Z crystals.......................208 22.4.2 Momentum dependence . ................208 22.4.3 Low energy, 1GeV...................208 22.4.4 Highly charged ions ....................208 22.4.5 Pion deflection, positive and negative charges . 209 22.5 Extraction . ............................209 22.6 Crystalline Undulator ........................211 22.6.1 Radiation from bent crystals ................211 CONTENTS 7 22.6.2 Crystalline undulator . ...................212 22.7 Applications related to bent crystals . ...............213 23 Ultrarelativistic heavy ions in crystals 215 23.1 Ionization energy loss . .......................215 23.1.1 Restricted energy loss ...................215 23.1.2 Ionization energy loss for channeled ions . .......216 23.2 Proton loss and capture in bent crystals ...............216 23.3 Results . ...............................218 IV Future projects 221 24 LPM effect in low-Z targets 223 25 Magnetic suppression 227 26 Bremsstrahlung emission from γ = 170 Pb82+ 233 27 Efficient positron production in diamonds 239 V Conclusion and acknowledgments 241 28 Conclusion 243 29 Acknowledgments 245 VI Appendices 247 A The quasiclassical approximation in QED 249 A.1Classicalradiationtheory......................250 A.1.1 Potentials and fields . ...................250 A.1.2 Radiation intensity . ...................252 A.1.3 Radiation from ultrarelativistic particles . .......256 A.1.4 Qualitative treatment of radiation . ...........258 A.1.5 Properties of radiation in magnetic bremsstrahlung limit . 261 A.2Quasiclassicalmethodinhigh-energyQED............265 A.2.1 The Probability of Radiation in a Stationary External Field 265 A.2.2 Disentanglement . ...................269 A.2.3 Radiation intensities in the quantum case . .......272 8 CONTENTS B List of symbols 275 C Danish summary 281 Part I General introduction 9 Chapter 1 Preamble The aim of the present dissertation is to summarize the results from the publica- tions shown in chapter 2, to extract what they have in common and where they supplement each other, and to put the results into a broader perspective. This means that there is unavoidably some overlap with results that have already been published, in particular between the part on interactions in crystals and the review paper, [Ugg05]. However, I have attempted to write here a coherent summary of the results obtained at CERN - in my case since 1992 - on penetration of ultrarel- ativistic particles. In the first main part of the dissertation, the penetration of ultrarelativistic particles in amorphous matter is discussed. The focus is on the existence of a formation time for the generation of radiation, which results in a variety of phe- nomena in radiation emission, e.g. by variation of the thickness of the target. In a sense, the question being addressed is the origin of light, although evidently from a rather limited perspective, since an answer to such a broad question must be sought in many other connections as well. It turns out, however, that by the use of ultrarelativistic particles - generally defined as particles with a Lorentz fac- tor significantly above unity - time dilation enables the investigation of the light emission process, ’while it takes place’. In the second part, the focus is on strong field phenomena, investigated by means of
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