The Flight of a Relativistic Charge in Matter: Insights, Calculations and Practical Applications of Classical Electromagnetism PDF
Preview The Flight of a Relativistic Charge in Matter: Insights, Calculations and Practical Applications of Classical Electromagnetism
Lecture Notes in Physics Wade Allison The Flight of a Relativistic Charge in Matter Insights, Calculations and Practical Applications of Classical Electromagnetism Lecture Notes in Physics FoundingEditors WolfBeiglböck JürgenEhlers KlausHepp Hans-ArwedWeidenmüller Volume 1014 SeriesEditors RobertaCitro,Salerno,Italy PeterHänggi,Augsburg,Germany MortenHjorth-Jensen,Oslo,Norway MaciejLewenstein,Barcelona,Spain LucianoRezzolla,FrankfurtamMain,Germany AngelRubio,Hamburg,Germany WolfgangSchleich,Ulm,Germany StefanTheisen,Potsdam,Germany JamesD.Wells,AnnArbor,MI,USA GaryP.Zank,Huntsville,AL,USA TheseriesLectureNotesinPhysics(LNP),foundedin1969,reportsnewdevelop- ments in physics research and teaching - quickly and informally, but with a high qualityand the explicitaim to summarizeand communicatecurrentknowledgein anaccessibleway.Bookspublishedinthisseriesareconceivedasbridgingmaterial between advanced graduate textbooks and the forefront of research and to serve threepurposes: (cid:129) to be a compact and modern up-to-date source of reference on a well-defined topic; (cid:129) to serve as an accessible introduction to the field to postgraduate students and non-specialistresearchersfromrelatedareas; (cid:129) to be a source of advanced teaching material for specialized seminars, courses andschools. 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Proposals should be sent to a member of the Editorial Board, or directly to the responsibleeditoratSpringer: DrLisaScalone [email protected] Wade Allison The Flight of a Relativistic Charge in Matter Insights, Calculations and Practical Applications of Classical Electromagnetism WadeAllison DepartmentofPhysicsandKebleCollege UniversityofOxford Oxford,UK ISSN0075-8450 ISSN1616-6361 (electronic) LectureNotesinPhysics ISBN978-3-031-23445-3 ISBN978-3-031-23446-0 (eBook) https://doi.org/10.1007/978-3-031-23446-0 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewhole orpart ofthematerial isconcerned, specifically therights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To Kate Preface Thisbookisabouttheenergylossandthecoherentradiationemittedbyarelativistic chargeinmatter.Thesephenomena—locallydepositedenergy,Cherenkovradiation and transition radiation—are the basis of any charged particle detector able to discriminatechargesby their velocity.The absorptiveanddispersive propertiesof materialshaveafirst-orderroleintheclassicalelectrodynamicsthatdeterminesthe signals,theirsizeandfluctuations,yieldedbyeachparticleinanexperiment.Asa result,theseapparentlydisparatephenomenaarecloselyrelated. Thecross-sectionsforthesephenomenaderivedfromelectrodynamicsareused to generate distributions in thin absorbers, first for energy loss and then for scattering, including correlations between the two. Two specific applications are thenfollowed:thefirstshowstheenergylossresolutionandparticleidentification achievedinpracticewithamulti-particledetectorinthecourseofanexperimentat CERN; the second shows how, by including scattering as well as energyloss, the techniqueofionisationcoolingofacceleratorbeamsmaybereliablysimulated. The treatment assumes some knowledge of mathematical physics at an under- graduate level, specifically Maxwell’s Equations and classical optics. It is based on a series of lectures given at the University of Oxford to graduate students in experimentalparticlephysics.Bothasastudentmyselfandlaterinmycareertoo, I always found the omission of steps in the derivation of a result most unhelpful in my search for real understanding. So, in this book, instead of appealing to an authoritative reference or leaving a derivation as an “exercise for the student”, mathematical details are worked explicitly for the student to follow and establish hisownsatisfaction. For sound historical and theoretical reasons, the standard works on the subject arebasedontheprinciplesofspecialrelativity.ThepagesofbooksbyJDJackson, Landau and Lifshitz, and others are well studied by students today, as they were by their parents and grandparents before them. These start from a picture of the fields of an electric charge in vacuum, which is then modified for the effects of dispersionandabsorptionin realmaterialmedia.However,in doingso, theyomit theintuitiveunderstandingthatcomesfromconsideringdispersionandabsorption as first-order effects. For instance, at speeds of a charge close to that of light, dispersioncausesmajorchangestotheformoftheelectromagneticfield.Andthen, frequency-dependentvariations give a picture and results that are not obvious as simpleextensionsofspecialrelativity. vii viii Preface Whilefundamentaltheoreticalphysicsconcernsitselffirstwithbehaviouratthe hardendofthespectrum,themostrelevantresponseforradiationdetectorsisatthe softendofthespectrum.Forthesethereisapreferredframeofreference—thatof themedium—thatundercutstheaxiomaticrelevanceofspecialrelativity. For signals detected by instrumentsin a high-energyexperiment,absorption is a first-order effect. Since the charge of each particle is very small, 1.6 × 10−19 Coulombs, signals are also small, so that signal-to-noise ratios and detection efficienciesarealwayscritical.Inaninteraction,theneedistomeasurethevelocities of many such charges simultaneously, each within a thousandth of the speed of lightinvacuum.Thecalculationofthesesignalsandtheirfluctuationsiscentralto understanding,analysinganddesigningexperiments. PartIofthebookintroducessomesimpleideasthatarerelevanttotheinfluence of a source moving at constant velocity. These are applied to the electromagnetic fieldandusedtodescribetherelationshipbetweendifferentphenomena. Part II builds up a precise descriptionof the electromagneticfields of a charge in steady motion in terms of the properties of the medium. The energy loss and scattering cross-sections are deduced from these and used to predict distributions in finite thicknesses. The analysis is validated by comparing with experimental measurements. Two practicalapplicationsarediscussedin PartIII.First,theISISdetectorwas designed to identify the decay products of charmed particles by energy loss and usedsuccessfullyinexperimentsatCERN. Second,thecoolingofbeamsofhigh- energymuonsinliquidhydrogenwassimulatedusingthemethodofPartII.Inboth cases, the improvement in simulation compared with simple traditional formulae wascrucial. Oxford,UK WadeAllison December2022 Acknowledgements This study grew out of a discussion with Lou Voyvodic when we were both at Argonne National Laboratory in 1970, namely how might relativistic charged particlesofknownmomentumbedistinguishedexperimentally.Overthefollowing decade,thetheoreticalunderstandingthatgrewwasacollaborationwithJohnCobb. Manyofhisideasprovedessentialtothiswork. The experimental work benefited from the encouragement of John Mulvey at Oxfordandinvolvedmanypeople,atOxford,theRutherfordAppletonLaboratory, CERN and in the United States. Nothing can be done withoutmutualconfidence, andI acknowledgethetrustthatothersin theinternationalcollaborationthatbuilt theEuropeanHybridSpectrometershowedintheISISProject,anapparentlyspec- ulativeinstrumentbuiltontheoreticalcalculationsthatlackedinitialverification. In addition to John Cobb, there are several people in the Oxford group that I should thank for sharing their skills, judgement and mutual confidence: Barney Brooks for his broad knowledge of electronics and readiness to engage new and unfamiliar hardware problems; Peter Shield for the crucial design of the ISIS electronics; Nick West for the developmentof the ISIS software; also the staff of the mechanical and electronic workshops in the Oxford Physics Department who builttheISISchamber. IacknowledgewiththankstheessentialcontributionsofSimonHolmesandJohn CobbtotheworkonIonisationCoolingdescribedinChap.9. Recently, following a stimulating discussion in Vienna with Martin Tazreiter, I resolved to write up the whole story, a work that would not have been concluded withoutthesupportofmywifeandfamily. IamgratefultoGeorgViehhauserforhisinterestandcarefulworkingthroughthe mathematics,and also to my editor,Lisa Scalone of SpringerNatureSwitzerland, forguidingmethroughthelabyrinthofpublication. ix Contents PartI BuildingonSimpleIdeas 1 Wavesandsources........................................................... 3 1.1 EnergyLoss,Cherenkov,andTransitionRadiation................... 3 1.2 ConsideringaTwo-DimensionalScalarField......................... 4 1.2.1 RealTransverseWaveVector .................................. 6 1.2.2 ImaginaryTransverseWaveVector............................ 6 1.2.3 TheFieldofaChargeinVacuumbyAnalogy ................ 6 1.2.4 TheFieldofaChargeinMatterbyAnalogy.................. 8 1.2.5 ConclusionsfromtheTwo-DimensionalFieldStudy......... 9 1.3 ConsideringaPhotonwithEffectiveMass ............................ 10 1.3.1 AFieldMediatedbyMassivePhotonExchange.............. 11 1.4 ConsideringFreePhotonEmission .................................... 12 1.4.1 KinematicConditions .......................................... 12 1.4.2 EmissionwithRecoilinaPeriodicMedium.................. 13 1.5 ConsideringDiffractedCherenkovRadiation ......................... 14 1.5.1 RadiationEmittedPassingThroughaSlab.................... 14 1.5.2 TransitionRadiationintheX-RayRange ..................... 17 1.5.3 X-RayTransitionRadiationDependenceonEnergy andAngle ....................................................... 18 1.5.4 X-RayTransitionRadiationLimitforThinSlabs............. 20 1.5.5 SummaryofConditionsforX-RayTransition Radiation........................................................ 20 References..................................................................... 21 PartII CalculationsinClassicalElectromagnetism 2 TheInfluenceofaPassingCharge......................................... 25 2.1 ElectricandMagneticFieldsinVacuum............................... 25 2.1.1 TheForceonaCharge.......................................... 25 2.1.2 Maxwell’sFieldEquations..................................... 26 2.1.3 AShortFieldPulsefromaMovingCharge................... 27 2.2 EquationsModifiedforMedia.......................................... 28 2.2.1 PhysicalInterpretationofResonantDispersion............... 29 xi
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