H. P. Freund T. M. Antonsen, Jr. Principles of Free Electron Lasers Third Edition Principles of Free Electron Lasers (cid:129) H. P. Freund T. M. Antonsen, Jr. Principles of Free Electron Lasers Third Edition H.P.Freund T.M.Antonsen,Jr. UniversityofMaryland UniversityofMaryland UniversityofNewMexico Potomac,MD,USA Vienna,VA,USA ISBN978-3-319-75105-4 ISBN978-3-319-75106-1 (eBook) https://doi.org/10.1007/978-3-319-75106-1 LibraryofCongressControlNumber:2018932336 ©SpringerInternationalPublishingAG,partofSpringerNature1992,1996,2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To Lena Marion, Anna Jane, Thea, Kal, Annika, Tracy, Thomas Alexander, Margaret Elise, and Christine Marie Preface It has been more than two decades since the publication of the second edition of Principles of Free-Electron Lasers, and it has become increasingly clear that both experimental and theoretical developments in the field have progressed far beyond thecontentofthatprioredition.Asaresult,wejudgedittobeimportanttopreparea third edition to bring the material up to date. It is our intention in this regard to provideacomprehensivedescriptionofthepresentunderstandingoftheprinciples, theory,andsimulationtechniquesofthefree-electronlaserthatcanbeusedbothasa referenceworkandahandbook.Tothatend,extensivederivationsaregivenforthe spontaneous emission, the single-particle orbits, and both the linear and nonlinear formulations of the interaction as a resource for the student or the experienced researcher in the field. However, we also provide useful formulae that can be used as a starting point in the design and analysis of specific free-electron laser configurations. Tothatend,theworkbuildsuponthepresentationofthesecondedition.Atthat time, free-electron laser research and development encompassed both long- wavelength free-electron masers using pulse line accelerators, modulators, and induction linacs and short-wavelength infrared through ultraviolet free-electron lasers based upon radio-frequency (rf) linacs and storage rings. Since that time, however, the research into long-wavelength free-electron lasers has withered, although it has not completely disappeared, while the development of short- wavelength free-electron lasers has flowered. While we retain the description(s) relevant to the long-wavelength free-electron lasers in the book, the bulk of the new material in this edition is devoted to the analysis and simulation of short- wavelengthfree-electronlasers. The flowering of short-wavelength free-electron lasers has its genesis in the development of laser-driven photocathodes [1–3] and in the application of photo- cathodestotheelectrongunsintheinjectorsofrflinacs[4],whichhasenabledthe production of high-quality electron beams with low emittances. There are two principalthrustsofthisdevelopment.Oneisthequestforhighaveragepower,and this is exemplified in the application of an energy recovery rf linac for use in the vii viii Preface high-average-powerinfraredoscillatorattheThomasJeffersonNationalAccelerator Facility which produced an average power of 14 kW at a wavelength of 1.6 μm [5,6].Thesecondthrustistowardevershorterwavelengthswithhighpeakpowers, and this isepitomized by the Linac Coherent Light Source (LCLS) atthe Stanford LinearAcceleratorCenter[7].TheLCLSisthefirstofitskindoffourth-generation X-raylightsourceuserfacilitythatcameonlinein2009andproducesintense,short pulsesofX-raysatwavelengthsasshortas1.5Å.Atthepresenttime,thereisagreat dealofactivityworldwideinthedesignandconstructionoffourth-generationfree- electronlasers. The LCLS and many of the other fourth-generation light sources rely on the amplification of shot noise on the electron beam to high peak power levels on a singlepassthroughalongwiggler.Becauseofthis,therearerelativelylargeshot-to- shotfluctuationsintheoutputspectraandpowerlevels.Sincethisisundesirablefor many applications, research into techniques to produce coherent short-wavelength free-electron lasers is ongoing. One possible approach is through what is termed high-gainharmonicgeneration(HGHG).InHGHG,atwo-segmentwigglerisused inwhichamagneticdispersiveelementisplacedinthegapbetweenthewigglers.In this configuration, the electrons are injected into the first wiggler (termed the modulator) in synchronism with a high-power seed pulse which acts to impose a modulationonthelongitudinalvelocityanddensityprofilesoftheelectrons.Inmost cases, the dispersive element is a chicane composed of dipole magnets in which higher energy electrons in the tail of the electron bunch overtake lower energy electrons in the head of the bunch. As a result, the modulation imposed on the electronsinthemodulatorisenhancedbythechicane,andthisactstoprecondition the electrons for rapid radiation in the second wiggler (called the radiator). In the HGHGconfiguration,theradiatoristunedtoaharmonicoftheresonantwavelength inthemodulatorsothatcoherentradiationatwavelengthsshorterthantheseedlaser usedforthemodulatorcanbeproduced.ThefirstHGHGuser facility operatingat extremeultravioletwavelengthsispresentlyinexistenceatFermi-ElettrainTrieste, Italy[8]. In order to provide an analysis of many of these new developments in short- wavelength free-electron lasers, one of the principal additions included in this edition is a derivation and justification of the application of the slowly varying envelope approximation to the time-dependent simulation of short-pulse free-elec- tron lasers. This is one of the most important developments over the last two decades. In so doing, we have made an effort in this book to compare theory and simulationswithasmanyactualexperimentsaspossibleinordertodemonstratethe validityofourpresentsimulationcapabilities. Althoughtheprincipalfocusofthebookisonthefree-electronlaserinteractionin the wiggler, the current thrust toward ultrashort-wavelength light sources utilizing very long multi-segment wigglers with strong focusing systems and phase shifters necessitates some discussion of the elements of electron beam optics needed to understandthesesystemsforreadersthatmaynotbefamiliarwiththeseconcepts.As a result, we have included an appendix to explain the basic elements needed to understand the complex transport and focusing of electron beams, and we provide Preface ix referencestomanyofthefundamentalworksinthefield.Thenumberofreference works dealing solely with electron optics is extensive and complete, and we hope that the student of the field will use this appendix not only as a description of the relevantelectronopticsasusedinfree-electronlasersbutalsoasagatewaytomore completetreatises. Vienna,VA,USA HenryP.Freund Potomac,MD,USA T.M.Antonsen,Jr. References 1. E.Garwin,F.Meier,T.Pierce,K.Sattler,H.-C.Siegmann,Apulsedsourceofspin-polarized electronsbyphotoemissionfromEuO.Nucl.Instrum.Meth.120,483(1974) 2. D.T.Pierce,F.Meier,Photoemissionofspin-polarizedelectronsfromGaS.Phys.Rev.B13, 5484(1976) 3. C.K. Sinclair, R.H. Miller, A high current, short pulse, rf synchronized electron gun for the Stanfordlinearaccelerator.IEEETrans.NuclearSci.NS-28,2649(1981) 4. R.L.Sheffield,E.R.Gray,J.S.Fraser,TheLosAlamosphotoinjectorprogram.Nucl.Instrum. Meth.A272,222(1988) 5. G.R.Neil,C.Behre,S.V.Benson,M.Bevins,G.Biallas,J.Boyce,J.Coleman,L.A.Dillon- Townes,D.Douglas,H.F.Dylla,R.Evans,A.Grippo, D.Gruber,J.Gubeli,D.Hardy,C.- Hernandez-Garcia, K. Jordan, M.J. Kelley, L.Merminga, J. Mammosser, W. Moore, N. Nishimori, E. Pozdeyev, J. Preble, R. Rimmer, M. Shinn, T. Siggins, C. Tennant, R.Walker,G.P.Williams,S.Zhang,TheJLabhighpowerERLlightsource.Nucl.Instrum. MethodsPhys.Res.A557,9(2006) 6. P.J.M.vanderSlot,H.P.Freund,W.H.Miner,Jr.,S.V.Benson,M.Shinn,K.-J.Boller,Time- dependent,three-dimensionalsimulationoffree-electronlaseroscillators.Phys.Rev.Lett.102, 244802(2009) 7. P.Emmaetal.,FirstlasingandoperationofanÅngstrom-wavelengthfree-electronlaser.Nat. Phot.4,641(2009) 8. E.Allariaetal.,HighlycoherentandstablepulsesfromtheFERMIseededfree-electronlaserin theextremeultraviolet.Nat.Phot.6,699(2012) Preface to the Second Edition Theprimaryconsiderationinvolvedincontemplatingtheutilityofasecondedition ofanybookiswhetherornottheweightofnewdevelopmentsinthefieldwarrants the effort. In the case of free-electron lasers, the field has been growing so rapidly thatwejudgedthistobethecase.Thisrapidgrowthhasoccurredbothinthenumber of active free-electron laser experiments and user facilities worldwide and in the theoreticalunderstandingofthevariousoperatingregimes.Assuch,wefeltthatthe firsteditionwasbecomingoutdated,andthatasecondeditionwasnecessarytogive readers a complete description of the current state of the theory of free-electron lasers. Inorganizingthematerialtobeincludedinthesecondedition,wedidnotfeelit practicabletorewritetheentirevolume.Ifwe were tostart with a clean slate, then muchofthenewmaterialwouldbeincorporateddirectlyintotheexistingchapters. However,inordertominimizethecompositioncostsofthesecondedition,wechose inmostcasestoaddnewchaptersratherthanrewritetheexistingmaterial. Therewere,however,compellingreasonsformodifyingseveralchapters.Firstly, while our purpose is not that of a review in which a history of the experimental developmentoffree-electronlasersisimportant,wedoprovide(1)abriefdescrip- tionofselectedexperimentsinordertoillustrateandvalidatethetheoryand(2)an overview of the primary applications of free-electron lasers. This has necessitated somerevisioninChap.1aswellasasubstantialupdatingofthereferencescontained therein. Secondly, the material dealing with spontaneous undulator radiation in Chap. 3 deals exclusively with an infinite and uniform transverse configuration. This is insufficient in the treatment of superradiance in Chap. 15 (new to this edition); hence, we have added some description of the spontaneous radiation in a waveguide in the new chapter. Finally, we have corrected an omission in Chap. 5 dealing with the nonlinear formulation of free-electron laser amplifiers. The first edition was written largely with separate discussions of planar and helical wiggler geometries, and Chap. 5 included discussions of the nonlinear analysis of helical wigglersinbothoneandthreedimensionsbutdiscussedonlythethree-dimensional xi xii PrefacetotheSecondEdition analysis of planar wigglers. The lack of a one-dimensional analysis of planar wigglers is not a serious omission, but one which we felt it important to correct. As a result, a new section dealing with this subject has been incorporated into Chap.5. Withtheseexceptions,allnewmaterialhasbeenorganizedintofournewchapters dealingwith(1)wigglerimperfections,(2)thereversed-fieldconfiguration,(3)col- lective effects, and (4) amplification of spontaneous emission and superradiance. Theseare,inourview,theprimaryfieldsinwhichadvanceshavebeenmadesince thepublicationofthefirstedition. The issue of the effects of wiggler imperfections has important practical impli- cationsinthedesignoffree-electronlasers.Agreatdealofefforthasbeenexpended in the design of wigglers which minimize field imperfections, as well as in the incorporationofexternalsteeringmagnetstocorrectforknownimperfections.Asa result,wefeltthattheinclusionofachapterontheeffectsandimportanceofwiggler imperfectionswouldbeanimportantaddition. Thereversed-fieldconfigurationrefers toarecentexperiment inwhichahelical wigglerwasusedinconjunctionwithanaxialsolenoidalfielddirectedantiparallelto thewiggler.Thisconfigurationhadnotbeenstudiedpreviouslysincethecombined effects of the two fields in this orientation would result in a reduction in the transverse wiggler-induced electron velocity and, in turn, a reduction in the gain. Indeed,thishasproventobethecase;however,thereductioningainoccurredalong witharelativelyhighefficiency.Themaximum efficiencyfoundintheexperiment (which used a uniform helical wiggler) was in the neighborhood of 27% at a frequency of 35 GHz, which compared favorably with the previous record high efficiency of 35% at the same frequency using a tapered wiggler. As a result, no second edition would be complete without the inclusion of a description of this importantexperiment. The treatment of collective effects in free-electron lasers has been addressed in thefirstedition.Itbecameclearinthe3yearssincetheinitialpublication,however, thattherewerestillmisunderstoodaspectsofboththeimportanceofandsubtletiesin thetheoreticalanalysisofcollectiveeffects.Hence,achapterdiscussingthesepoints was felt to be important. This includes both a discussion of the Raman regime in which thebeamspace-charge wave isimportantandof theanalysisof self-electric and self-magnetic fields due to the DC charge and current densities of the beam. Bothcasesinvolveananalysisofseveralexperimentsinordertoillustratecriteriafor evaluationoftheimportanceofcollectiveeffects. The last new chapter deals with superradiance in free-electron lasers. There is some ambiguityinwhatthis termmeans.Inearly workon free-electronlasers, the term superradiant amplifier was used to denote an experiment in which no drive signalwas imposed and the radiation grew from noise in a single passthrough the wiggler. However, this type of radiation is now referred to as self-amplified spon- taneousemission(SASE),andthetermsuperradianceisalsousedtorefertocasesin which the radiation pulse breaks up into large-amplitude spikes. The nature of this process was still controversial at the time the first edition was published, and we