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www.lunex5.com Historical survey of Free Electron Lasers M. E. Couprie Synchrotron SOLEIL M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Introduction www.lunex5.com Free Electron Laser Free Electron Laser: «simple and elegant gain medium» : an electron beam in a magnetic field - broad wavelength tunability (vibration frequency can be adjusted by changing the magnetic field or the speed of the electrons) - excellent optical beam quality - high power free electrons bound electrons in atoms and molecules : vibrate at specific frequencies Synchrotron radiation Vacuum tubes Lasers Free Electron Laser M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 I. The origins of the Free Electron Laser (LQVWHLQ www.lunex5.com /µDEVRUSWLRQ 1.1 :The photon-matter /µDEVRUSWLRQ interaction processes 6LOHSKRWRQDODERQQH ORQJXHXUG¶RQGHLOHVW DEVRUEp SDUO¶DWRPHHW O¶DWRPHHVWH[FLWp 6LOHSKRWRQDODERQQH ORQJXHXUG¶RQGHLOHVW DEVRUEp SDUO¶DWRPHHW O¶DWRPHHVWH[FLWp Absorption E E to an excited state a photon is absorbed and drives an atom (Q$OEHUW(LQVWHLQ Excited Non excited $EVRUSWLRQ atom SUpGLWO¶pPLVVLRQVWLPXOpH atom E E $EVRUSWLRQ E /µDEVRUSWLRQ /µpPLVVLRQVSRQWDQpH E E + photon 6LOHSKRWRQDODERQQH ORQJXHXUG¶RQGHLOHVW $WRPHQRQH[FLWp DEVRUEp SDUO¶DWRPHHW SKRWRQ O¶DWRPHHVWH[FLWp 8QDWRPHH[FLWp HVWLQVWDEOH LOpPHWXQSKRWRQVSRQWDQp DXERXWG¶XQWHPSVDOpDWRLUH SDUODGXUpHGHYLHGX spontaneousGRQQp photon after a $WRPHH[FLWp QLYHDX Spontaneous Emission $WRPHQRQH[FLWp $WRPHH[FLWp The excited atom being unstable, it emits a ,OIDLWODV\QWKqVHGHVWUDYDX[GH duration depending on theSKRWRQ lifetime of the excited level. E $EVRUSWLRQ E 1917: black-body analysis $WRPHQRQH[FLWp prediction of the stimulated emission SKRWRQ E E 3ODQFNTXDQWLILFDWLRQGHVQLYHDX[G¶pQHUJLH E %ROW]PDQQPpFDQLTXHVWDWLVWLTXH Excited atom %RKUTXDQWLILFDWLRQGHODPDWLqUH E ePLVVLRQ VSRQWDQpH /µpPLVVLRQVWLPXOpH E /µpPLVVLRQVWLPXOpH E 3RXUUpVRXGUHOHVpTXDWLRQVGXFRUSVQRLULOHVW E REOLJp GHUDMRXWHUO¶pPLVVLRQVWLPXOpHDX[ EEmission Stimulated LQWHUDFWLRQVPDWLqUHUD\RQQHPHQWFRQQXHV $WRPHH[FLWp E E NonePLVVLRQ excited atom $WRPHH[FLWp O¶DEVRUSWLRQHWO¶pPLVVLRQVSRQWDQpH ePLVVLRQ Excited atom + E VWLPXOpH + VWLPXOpH Photon E $WRPHQRQH[FLWp SKRWRQ E 2 identical photons (wavelength, direction, phase, Epolarisation) E A photon is absorbed by an excited$WRPHH[FLWp atom, which results in the emission of two photons with identical $WRPHQRQH[FLWp $WRPHH[FLWp $WRPHQRQH[FLWp wavelength, direction, phase, polarisation, whilethe atom returns to its fundamental state. SKRWRQ SKRWRQVLGHQWLTXHV Stimulated emission was seen as SKRWRQ addition of photons to already existing photons, and notSKRWRQVLGHQWLTXHV as the amplification même longueur d’onde même longueur d’onde of a monochromatic wave with conservation of its phase. The notion of light coherence, related to its même direction même direction même phase undulatory properties, was not considered at that time. même phase même polarisation même polarisation M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 I. The origins of the Free Electron Laser www.lunex5.com 1.3 The early times of synchrotron radiation Josepf Larmor (1857-1942) Alfred-Marie Liénard (1869-1958) J. Larmor, On the Theory of the Magnetic Influence on Spectra ; And On the Radiation from Moving Ions, Phil. Mag. 44, 503-512 (1897) First correct calculation of the emitted power by an accelerated charged particule first specific prediction of time dilation : "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio (1 – v2/c2)1/2". (E/mc2)4/R2 A. Liénard, L ‘ Eclairage électrique, 16, 5 (1898) George Adolphus Schott(1868-1937) Dmitri Ivanenko (!"#$%&#' !"#$%&#()#* +),-($-./) (1904-1994) Isaak Yakovlevich Pomeranchuk (+0,,$. G. A. Schott, Ann. Phys. 1$./)2()#* 3/"(&,-*4$. 24, 635 (1907), G. A. S c h o t t , (1913-1966) Electromagnetic Radiation, : And the mechanical reactions arising from it, Cambridge University Press (1912) angular and spectral distribution and polarization properties Julian Seymour Schwinger (1918 –1994) Physics, 1965 J . S c h w i n ge r, Phys. Rev. 70, 798 (1946) peaked spectrum Edwin Mattison McMillan (1907-1991) Chemistry, 1951 E. M. McMillan, PRL 68, 1434 (1945) Synchronism and phase stability Vladimir Iossifovitch Veksler (52,6#"#& +/0#7/)#* 5(.02(&) (1907-1966) D. Ivanenko and I. Pomeranchuk, Phys. Rev. 65, 343 (1944) energy losses due to radiating electrons would set a limit on the energy obtainable in a betatron (around 0.5 GeV). V. Veksler J. Phys. USSR 9, 153 (1946) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 peaked spectrum [Phys. Rev. 'Fl, 563 (1947)) I. The origins of the Free Electron Laser D. K. C. MACDONALD AND K. FIG. 1. Normal cadmium (above) and isotopes altered by neutron absorption (below). MENDELSSOHN Clarendon Laboratory, Oxford, L'ngland AND www.lunex5.com A. J. BIRCH Dyson Perrins Laboratory, Oxford, England &HE Editor regrets that Fig. 2 of the first of the above papers has been interchanged with Fig. 1 of the second paper. The captions, however, are right, as they stand. to 1.6+0.2 percent, about one-eighth of its normal abundance, and that the isotope at mass 114 was increased to 39.5+1.5 percent. Within the limits of the accuracy attained, the increase in 114 is equal to the decrease in 113. Any changes in the abundances of the isotopes at masses 110, 111, 112, and 116 were less than five percent. It was noticed, however, that in both samples the isotopes at 110 and 111 had a greater difference in abundance than is indicated by Nier's measurements (12.8 and 13.0 percent). We may conclude that the other main isotopes have absorbing cross sections less than one-fortieth. of that of Cd", and that if any (n, 2n) or other reactions occur, they are comparatively rare. 1.3 The early times of synchrotron radiation Erratum: The Quadrupole Moments and Spins of Br, Cl, and N Nuclei 1946 : first energy loss measurement [Phys. Rev. Vl, 644 (1947)] J.C.P.H.Blewett,A. Phys. Rev. 69, 87 (1946) N. F. R. MERRITT J. Bell Telephone et Laboratories, Murray Hill, !mJersey F. K. Gloward al., Nature 158, 413 (1946)I TOWNES, HOLDEN, BARDEEN, AND ~HE Editor regrets that Figs. 1 and 2 of the above paper have been interchanged. The captions for the figures, however, are correct as they stand. B. J. Moyer, B. Peters, 1947 : first observation of synchrotron radiation Isotopic Changes in Cadmium by Neutron Absorption A. Argonne Nationa/ Laboratory, Chicago, Ilbnois N a recent letter B. J. Moyer, B. Peters, and F. H. Schmidt' report that the absorption of thermal neutrons in cadmium that had been enriched in the isotope at mass 113 was six times normal, and conclude that this isotope is mainly responsible for the large absorption in this element. The mass spectra reproduced in Fig. 1 illustrate another phenomenon that also indicates the absorbing isotope, namely, the gradual alteration of the isotopic constitution of an element by long exposure to neutrons. The upper mass spectrum shows the normal isotopes at masses 110, 111, 112, 11.3, and 114, with Cd"3=12.3, and Cd"4=28 percent. The faint isotopes at 106 and 108 do not show on the prints. The lower spectrum shows the changed isotopic abundance in a sample scraped from the surface of a piece of metal that had been used to absorb intense neutrons from a pile over a long period of time. These neutrons include a considerable number with energies above the thermal range. Photometric measurements, made by using Nier's measurements of the normal cadmium abundances as standards, showed that the isotope at mass 113 was reduced - ELDER, A. M. AND GUREWITSCH, R. POLLOCK V. LANGMUIR, H. C. '" 'IGH May 7, 1947 energy electrons which are subjected to large accelerations normal to their velocity should radiate electromagnetic energy. ' 4 The radiation from electrons in a betatron or synchrotron should be emitted in a narrow cone tangent to the electron orbit, and its spectrum should extend into the visible region. This radiation has now been observed visually in the General Electric 70-Mev synchrotron. ' This machine has an electron orbit radius of 29.3 cm and a peak magnetic field of 8100 gausses. The radiation is seen as a sma11 spot of brilliant white light by an observer looking into the vacuum tube tangent to the orbit and toward the approaching electrons. The light is quite bright when the x-ray output of the machine at 70 Mev is 50 roentgens per minute at one meter from the target and can still be observed in daylight at outputs as low as 0.1 roentgen. The synchrotron x-ray beam is obtained by turning off the r-f accelerating resonator and permitting subsequent changes in the field of the magnet to change the electron orbit radius so as to contract or expand the beam to suitable targets. If the electrons are contracted to a target at successively higher energies, the intensity of the light radiation is observed to increase rapidly with electron energy. I f, however, the electrons are kept in the beam past the ~ - ~ ~ F. R. Elder et al., Physical Review, 71, 11, (1947), 829-830 J. P. Blewett, 50 years of synchrotron radiation, J. Synchrotron Rad. , 5, 135-139 (1998) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Schmidt, Phys. Rev. 69, 666 Research Laboratory, General Blectric Company, Schenectady, %no Fork J. DEMPSTER May 1, 1947 General Electric 100 MeV (1947) F. H. Radiation from Electrons in a Synchrotron F. R. ~ and (1946). www.lunex5.com easily obtained from electrons with speeds ranging from a megavolt, say, to 1000 Mev. Several applications suggest themselves. We shall discuss them under the following headings: (1) production of energy in rather inaccessible spectral bands, viz., millimeter to infrared radiation j* (2) speed monitoring for electron beams produced by linear or other accelerating devices; (3) speed measurement for fast individual electrons or other particles (mesons, protons). We shall also briefly consider the radiation emitted by an electron moving through an electromagnetic wave traveling in the opposite direction. This occurs, e.g., in a linear accelerator in which a wave is reflected fields. Hence, we shall be mainly interested in the case of transverse fields, as shown in Fig. 1. The spatial field distribution may be fourier analyzed. Let the fundamental wavelength be 10• It will be shown that the frequency of the emitted radiation varies with the angle of observation. The fundamental component of the radiation emitted under the angle (j (see Fig. 1) has a frequency I. The origins of the Free Electron Laser 1.3 The early times of synchrotron radiation w=\l,e=21T/3c/lo(1-f3 cos8). The undulator • Calculation of the field created by a relativistic particle in the magnetic sinusoidal field (i.e. such as produced by undulators) * Notes added in proof: According to reports of the Electronics (1) Beam M.I.T., P. D. Coleman working Research Motz H. : Applications of the radiation from fastLaboratory electronatbeams, Journ. Appl.isPhys. 22,on such a scheme. Prior reference to the problem treated in this paper by V. L. Ginsburg, Radiation paper has also been 527--535 (1951) of microwaves and their absorption in air, Bull. Acad. Sci. U.R.S.S. Ser. Phys. 9 (1947), No.2, 165 (in Russian). FIG. 1. Schematic arrangement of undulator magnets. 527 830 • Influence of the bunching of the electrons on ÉLECTRONIQUE. –toProduction d'ondes millimétriques par un ondulateur [This article is copyrighted as indicated in the article. Reuse of AIP content is subject the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 195.221.0.34 On: Sat, Note 01 Aug 2015 the coherence of the produced radiation magnétique. de 20:55:40 M. RENÉ COMBE et Mme Thérèse FRELOT, • observation of the polarized visible radiation présentée par M. Louis de Broglie. from an undulator installed on the 100 MeV Après avoir décrit un dispositif destiné à produire, par application de l'effet Doppler relativiste, un rayonnement de courte longueur d'onde, on donne les résultats concerStanford accelerator. nant la puissance et le spectre de fréquences. A buncher set-up after a 3.5 MeV accelerator Nous avons construit un ondulateur (*), composé d'un aimant, d'un guid banc de mesures, et d'un correcteur de champ, et qu enables to achieve 1 W peak power at 1,9 mm d'ondes spécial, d'un 13< fait suite à un accélérateur linéaire d'électrons fonctionnant en régime pulsé thanks the the bunching of the electrons. (5o impulsions de fxs/s). Le des électrons s'étend de i,5 à 3,oMeV 1\1 0 T Z, THO 1'\, ,\ 1'\ /) '" HIT E H \' R S T R.F. LOAD DEfLECTED IRON PLATE BEAM 0,5 COUPLER FIG, 6. Equipment outline for buncher tests. spectre i corresponding to light passing through the two polaroid inches. The filling time is 0.2 microseconds. An input Motz H.,Thon W. ,Whitehurst R. N. : Experiments on Radiation by Fast maximum MeV. polarization. power up to 8 M w is required and was obtained from a avecwindows un was 2: 1 in favorà of2,3 perpendicular Electron Beams , Journ. Appl. Phys. 24, 826--833 (1953) Subtracting the background makes the evidence for Stanford high power klystron operating at 2856 Me/sec. L'aimant, produit sinusoïdal, B obtained 960 from permanent, un champ e gauss, polarization even stronger. A quantitative determinaElectron pulses drawn atavec 80 kv are = a was not /= 16tioncm. Leattempted. tungsten filament gun and injected into the guide d'ondes, rectangulaire (dimensions intérieures 4oaccelerator. X 25mm) The gun pulse lasts 1 microsecond and is applied 0.2 microseconds after the klystron pulse. Tests of this buncher revealed an energy spectrum A qualitative experiment was also carried out of 0.2-Mev half-width at 5 Mev. The accelerator concerning the color distribution of the light. An interference filter passing a band 100A wide centered collects electrons during the full period of the traveling on 4400A was used. Theoretically, the color of the light in the accelerator and bunches them to within 30°; should range from green (5500A) to blue (3400A) in and it may have been better than indicated by the the energy range from 95 Mev to 120 Mev. The light foregoing numbers. Figure 6 shows a block diagram of fell on a photomultiplier 1P21, which has a sensitivity the set-up used for testing the buncher. The buncher curve starting at 3000A, rising sharply to a peak at is followed by a standard (2-ft) accelerator section, 4OOOA, and falling to almost zero at 7500A. We got i.e., by a uniformly disk-loaded section which obtains maximum transmission at 90-95 Mev andONDULATEUR almost no power coupled out of the end of the buncher through transmission at 120 Mev. We consider this as a very a phase shifter which allows variation of the relative rough indication of agreement with theoretical pre- phases of buncher and standard section ranging over 360°. For energy measurement purposes the beam can dictions. be magnetically deflected into a channel leading to a V. and MILLIMETER WAVE GENERATION Electron!Lasers!and!Energy!Recovery!Linacs !(FELs !ERLs), Hamburg, Germany, 31 !May –10monitor. !June, 2016 It was necessary to insert colliradiation plan IIG-inch clearing holes in order to obtain mators with 1. The Electron Buncher good energy resolution. à à • Emission of the radiation spectrum (6 mm) produced from an undulator installed on a 2.3 MeV accelerator 3. Color Combes R., Frelot T. , présenté par L. de Broglie, Production d'ondes millimétriques par un ondulateur magnétique. Comptes-Rendus Hebd. Scéance Acad. Sci. Paris, 241, 1559 (1955) M. E. Couprie, CAS School Free jeudi 2 juin 2016 est étanche et permet le passage du faisceau, compte tenu de la vibration dans le vertical(la trajectoire est sensiblement une sinusoïde d'amplitudemm) Ce guide doit aussi satisfaire certaines conditions relatives l'existence des Marie-Emmanuelle COUPRIE and Mathieu VALLEAUvelocity is 2> and the interval as: Let’s consider theinlongitudinal velocity : 1 < cal, um difference between average longitudinal velocity electron longitudinal relativistic electron ofKvenergy and velocity v with respect to R are introduced along the β s direction. Its relativ e s the = oordinate system given Fig.A˙1.1 with 1 u 2 Ee 2 β ≈ 1 − − sin (k s) (55) � � Marie-Emmanuelle and electrons Mathieu VALLÉAU cos (k→ s)2 = − B�uon relativistic βCOUPRIE β =position s Bu β4.1 u c 1−β2 xby u2γ s cos (ku s)dt = 2:Considerations 2π given −→ s factor γ is 2 → − − p. z) the horizontal (resp. vertical) is 2γ ver eo γ 2 s e z = Buz cos(ku s) z (48) Buz = Buz cos 2 mcurrent ent in the undulator s introduce in the area of the free of an undulator creating a periodic permanent magnetic ˙sm=oλγlaboratory γ u B β cos (k s) = − B β cos (k s)dt β u x u s u u has One : www.lunex5.com 2 2 2 2 mo γ The electron movement the KuBcin Ku c 1L L m Ku cwith N the number of periods λ . Let’s first consider oγ ting withhas: the undulator wavenumber ku˙given 2by:undulator 1 verage, one ˙ of peak amplitude , period λ , length = N λ (2 − 1)| = | (sin (2k s)| = (57) |v− < vs>≈|max umax u u u u 2region, u so : 1 component first order, cβ=st,| 4γ so2 uz βssin ∝ (kγ 2u s)whereas β ∝ . In consequence, the longitudinal of theuelectron u max 2 γ1 Let’sx4γ consider a laboratory without current, with a laboratory referential (0, x, z, s) with th 4γ 1 2π creating � ˙ ˙ γ = the laboratory free of current an undulator a periodic permanent magnetic 2 At first order, s ≈ cβ t, so β ∝ whereas β ∝ . In consequence, the longitudinal component of the electron = (49) k 1 u s s x 2 1 and < v >ofvery movement of anot relativistic electron ofrelativistic velocity vremains introduced atE the origin of the undulator coordinate along 2 with γKu electron 2 the 1 the γ undulator λu A 1 − β energy and velocity v respect to R are introduced s dir 21 −along close to 1. One gets β ≈ 1 and s ≈ ct. ity is practically modified by the β 2 = β s s eriod λ , length L L = N λ with N the number of periods λ . Let’s first consider < β >≈ 1 − − = (56) introduce in the area of the laboratory free of current an undulator creating a periodic permanent magnetic K c u u u u u u u s Marie-Emmanuelle COUPRIE and Mathieu VALL ÉAU β = 1 − u2 and β 2 The undulator scheme is shown in Fig. 18. remains very close to 1. One gets β ≈ 1 and s ≈ ct. velocity is practically not modified by the undulator 2 In4γ thes LUNEX5 case (in 400the MeV, γhelical = 783),s undulator. The field γcan be created2 by e maximum coordinate difference of the is2γ c: the 2γ. is electron movement undulator ]) in the two cases planar and s (longitudinal su∈ [0, Luvelovity factor given byof 4γ γ en, ofitudinal peak amplitude B , period λ , length L L = N λ with N the number of periods λ . Let’s first consider electron of velocity v introduced at the origin of the undulator coordinate along the uz u u u u u u Then, with β the normalised velocity of the electron: = velocity 1.65T and period λu =at1.5cm, i.e. = created 2.3, thisby difference is along the nic planar undulator of peak uthe 2 field Buof sovof :> ovement of a relativistic electron v introduced the origin ofKand undulator coordinate the two1cases and helical undulator. The field can be [0, Lu ]) inpoles. nated Kof u the2 planar maximum difference between the average longitudinal velocity < the electron longitudinal velocity is t is indeed very small. β ≈ 1 − − sin (k s) (55) s u 1 eB eB 1 eB eB 2 Lu ]) in the two cases of uthe and helical undulator. The field canv1beand created by udinal coordinate2γs 2( s ∈2γ[0, u planar u u 1, then E << the reduced velocity If γ >> Kuradiation, ˙ ˙ 2 can be1approxima −3 y : Synchrotron polarization, devices new sources β cos(k β = − cos (k s) ≈ − s) � γ = β cos(k β = − cos (k s) ≈ − s) . Numerically, it gives . e, the maximum value of the transverse velocity γ10β = x is givens by s γe. u 2.934 beam β = 1− 2 x u u ated poles. 2 m γ m γ 2 o o m γ m γ Synchrotron radiation and Free Electron Laser 1 − β c γ o o mo c ation, one has: 2 2 2 so : Ku chas : 2 Ku c Ku c 1 One : 2 = | (2 sin (k s) − 1)| = | (sin (2k s)| = (57) |v− < v > | u of max 1 sPlanar undulator case βbe≈approximated 1 − be2consa 1 Kumax < v > 2K�u sinThe ultra-relativistic beams (1�γ �� 1)cancan also withHelical β max the normalised velocity of1the Approximation ultra-relativistic beams 2 γ of 2electron: (ku4.2.2 s)uapproximation : longitudinal coordinate undulator case �� 4γ 4γ 4γ << 1 and the reduced velocity If >> 1, then < β >≈ 1 − − = (56) γ s � � � 2γ � eBu eBu � eBu γλu 2 2→ − � Planar undulator case 2 2 2γ 4γ c � � 1 x : horizontal direction ββx eB 0 u s)dt = βx �βz =− − eBu Kcos(k s) 2 2 u s)ds = − u2 λ1u (58) 1eB 1 2c u mdγE cos(k u sin(k v = − β m γc m γc 2π 2 u . comes : β � β � β � 1 � � �β � β � � β � β � 1 � � o cos(k o is o 2 case by a: vertical planar undulator Kcreated sin(k βdifference =creating − by −of permanent s)ds = − s) 2of the x x z . Ininuzthe LUNEX5 ( 400 MeV, γ β=is 783), relative maximum of the velovity 1 longitudinal Fig. 18 Planar undulator scheme, a periodic magnetic field by2two= arrays magnetscos(k arranged the Halbach 2 1 z direction = u s)dt x u u f normalized energy γ given γ = (with x z The total energy electrons given by : 2 dv 2 γ 2 γ 2γ 1 − − sin (k s) ical undulator field created by a planar undulator 4γ nalthe average longitudinal < vm > electron longitudinal velocity is c and u undulator field 2 Helical o2in configuration [55] created Vertical field invelocity green,am electron trajectory blue.2γ the m m γc 2π undulator field by planar undulator 2γ o γassociated o γc K as β ≈ 1− 2 o d Let’s define the undulator deflection parameter : 1.5cm, i.e. ofoKu = 2.3, this differencecis u mass, e the particle charge and c the speed of = 1.65T and period λ = cryogenic planar undulator of peak field B dτ u u 2γvalues of a planar undulator, creating a field the vertical direction expressed in(or the [0, Lu ] so along : In the small angle paraxial) approximation with small age over one undulator period One has : −6 consider first the case of a planar undulator, creating a field along the vertical direction expressed in the [0, L ] Case of its asmall. planar of Nparameter Case aa1helical undulator of� Nhorizontal define associated consider aKhelical creating magnetic both and[0,vertical offirst aundulator dipole, movement isdeflection givenLet’s etic field u periods u periods u field inexpressed 2 Lu ] 10 . ItBisdthe indeed very st’s consider the case of aundulator planar undulator, creating field along theofvertical direction inMarie-Emmanue the u as :a undulator � 2 E = γm c 24 2 2 2 o dv eBu λuThe total energy the electrons is−3given by : n is then given by βofit= 1− gle of observation ,Numerically, the direction of observation al as:K=u cev K K c is ×B thevalue particle time τ� , its . (57) gives 2.934 10 . ansverse, the ofcase the transverse velocity given by Kγuθ uc uK 2maximum o dτ d , with 2 Electron velocity in the planar undulator = (51) rval � � � 0 u γ = | as: (2 sin (k s) − 1)| = | (sin (2k s)| = 1 −→ 2 2 u u max � ofmax � 2 2 2πm − −−of−4γ − →2dynamics oλc 4γ 2−→ 4γ position R(τ) .the Infundamental case an�uniform magnetic θ �θ = 1 − β Let’s applyone equation the to the � case of this planar undualtor : ecapitulation, has:2π → − → − 2π eB � x z 0 with γ the relativistic factor, m the rest particle mass (m = 9 10 2 2 u u 2 → − → − o o (59) < β > B = B sin( s) x = B sin(k s) x γ �. λu � θ −�<< ��θthe � θz velocity � θz � 1approximated � � θ(48) ux ux uE u c2 = Buz cos z−→ B s)2π z�→ Buz whose Ku 11=and (51) x→ xcan → −puz cos(k uθ c of circle, radius ρsis given x → − = γm 2= dby Ku21z→ → − 1 2 → − − � o − K c reduced be as : If γ >> 1, then It is given in practical units as : = B cos s z = B cos(k s) z (48) B λ u Ku → f =LUNEX5 e(2E(1 ++ v x BK)γ ) uz uz 2πm uo cγ = energy − u − → and the kinetic energy particle is the sum of the rest energy E case ( 400 MeV, 783), of the longitudinal velovity is 4γuz2 . dtIn 1=the → − o − u 2π 2 2γ − sin (k s) so : λ 2π → sin (k s) u u u = B cos s cos(k s) z B z = B → −z = B cos(ks)uz → −z u u γ → − −31 kg → −p , being → −p = γm→ λu γ particle umass (m = B cos s (48) − with the= electron momentum c β . Buz m γβ c o1.5cm, with γ the relativistic factor, m the rest = 9 10 1.65T and period λ = i.e. of K = 2.3, this difference is peak field B uz uz u o → − 1 o o u u u K o 1 mber k given by: u − → 2 u in In absence of electric field and inas =undulator (1.1)expression, Ku =it0becomes: 0.934Bu (Tλ)λ (52) 24 Marie-Emmanuelle βmomentum is given practical units : the u (cm) cos (kthe s)kinetic − ββenergy =1(58) − hρthe wavenumber kusubstituting given by: u u β ≈ 1 − = 0 B .ctory γ 2 2 eB us and energy Ek as particle energy is the sum of the rest E 2 in the dplanar undulator case Ku γ o 2 1 2γ Ku 2 −3 1 − − sin (k s) u velocity 2 Ku 2π the it2γtransverse gives 2.934 10 . βx = 0, one can take the integration constant e of the transverse velocityentering is given bydundulator With an electron without 1 2γ 2 2π γ . Numerically, 1 − − = (49) k u of city inequal the vertical is: zero, the movement takes place in the horizontal plane 2 with the undulator wavenumber k1γubegiven by: The total energy of the electrons given by the :(x, s). = 0.934B )λ mitted radiation indirection a cone solid angle 2γ 2 2γ(52) 1 isu (cm) (49) kK to zero, one gets u (T u u= λ u << 1 and reduced velocity can be approximated as : If γ >> 1, then inutaverage over one undulator periodleads to : Ku λu γ ω with ω = k c, a further integration u u (ku s) mation of the angles from the particle frame toElectron velocity in the helical undulator case γ sin Ku 1 own in Fig. 18. Since the velocity in the vertical direction is zero, the movement takes place in th ith an electron entering the undulator without transverse velocity β = 0, one can take the integration constant 2 (ku s)isinvery e undulator schemeradiation shown Fig. collimated, 18. 2 x Ku → − 2π 1.2). Synchrotron K γ issin E = γm c 1 u o 0 → − 1 Ku sin (k βx = (53) (ku s) cos −− γleads γfurther integration u s) β = (49) k β ≈ 1 0 ṡ = zero, one gets : the u c[1 − − (1 − cos (2ω t))] With k s = ω t with ω = k c, a to 2: of the undulator, β (58) γ mtoenergy, the smaller collimation angle. − − − − → Considering an electron arriving on axis without angle at the one u 2entrance u 0 u u u 2 2 −31 8 m/s). 2γ λ 2 2γ 4γ u with γ the relativistic factor, m the rest particle mass (m = 9 10 kg), c the speed of light (c= 3 10 (59) < β > K o o 1 theKunumber of photons The approach is to enter define the brilliance as 2 1 − 2γ12 − 2γu2 sin2 (ku s) : common 1 − Considering the electron at the origin position, one Kthat 1 2 − 2takes integration con u ˙ 2γ 2γ and the kinetic energy E as follows : particle energy is the sum of the rest energy E (1 + ) 1 − g that the electron enter at the origin position, one takes integration constants equal to zero, and one gets The total energy of the electrons is given by : With an electron entering the undulator without transverse velocity β = 0 and using β = 0 one can take the o k z z 2 The undulator scheme is shown in:ond Fig. and 18.2γ 2perKuunit of phase space (or the density distribution r period sin (ku s) βx = (53)in phase space integration constant equal to zero, one gets : → − Since the velocity in the vertical direction is zero, movement takes place in the h γ − → d= β the − to 2e → � E γm c corresponds to the geometrical optics frame. It enables describe some o Ku c Ku c � β x B = 0 sin (ω t)dt = cos (ω t) x = K c K c n trajectory in the planar undulator case With k s = ω t with ω = k c, a further integration leads to : u u u u u u u βz =u 0 γ γωu dtsin (ωmu(54) γ −31 x = = − cosgeneral (ωut) ex ot)dt −−−−→ ˙ γ γω 0 propagation properties of the rays through optical elements. The u ith an electron entering the undulator without transverse velocity β = 0 and using β = 0 one can take the y = 0 with γ the relativistic factor, m the rest particle mass (m = 9 10 kg), c the speed of light (59) z enter < β > z c position, � is zero, the (60) o o one takes � � Considering that the electron at the origin integration consta 2 K K c he velocity in the vertical direction movement takes place in the horizontal plane (x, s). 2 2 2 u u K The expression the longitudinal electron velocity is then by :of the rest energy u K+ Ku is λu given (2ω s = 2π Eyo = cos (ω sin (ω uzero, u λu gets (1 ) Kone 1equal − 12γ212of and the kinetic energy E= follows :isu t) particle energy the sum u t)dt ation constant to : c(1 − − )t + sin (2ω t) =< v > ct + sin t) k asγω γ sin s = B sin(k s) B u u 2 of the brilliance B (or spectral brightness in a narrow bandwidth) given b 2 2 2 u u u u : � leads to : 16πγ 16πγ integration h ku s = ωut with ωu2γ= ku4γ c, a further β λ x u � 2 � � → − → − 1 Ku 2 Ku λof 2π u β s = c(1 − )t =< v > ct one : mechanics Using β and B the Wigner distribution [136, 46] as defined in quantum as 1 1 K z 2 − 2gets gives, the1 numerical LUNEX5, um amplitude of the transverse motion isβ γ =2π , which uexample cos s a= B 2 Buof 2 β 2 for u� cos(ku s) 2γ 4γ K c K c 1 − − = − − sin (k s) λ K 1 β = 0 (54) u u s u u dulator u x z xsystem = γ in sinphase (ωut)dtspace. = − γωuThe cos (ω β γ 2twice γu2t))] γ 2 aa maximum µm. In case the longitudinal direction occurs at the frequency, with amplitude u t) − (1 − cos (2ω ṡ = oscillations c[1 − s probability density of quantum Wigner dis 2 2 0 � 2γ 4γ K c K c The electron trajectory is helical. There is no oscillatory movement in the longi u E. Couprie, Free horizontal Electron!Lasers!and!Energy!Recovery!Linacs 31 !May –10 !June, 2016 ction is so zero, movement takes place in the plane (x, s).given by : !(FELs and !ERLs), Hamburg, = uGermany, .56 nm, 2720 times smaller thanCAS theSchool maximum transverse amplitude. cos (ω t)dt = sin also (ωut)been ad : theof y ojece expression theM. longitudinal electron velocity is then u eB u ˙ γ γω [47], first developed in the statistical quantum mechanics, has u − mo γ β2s cos (ku s) sidering that the electron at the origin position, onebytakes integration constants andβone further leadscreating to :enter x = gets jeudi 2aintegration juin 2016 quency. to zero, Planar undulator scheme, a periodic magnetic field created two arrays of permanent magnetsequal arranged in the Halbach eating periodic magnetic field created by two arrays of permanent magnets arranged in the Halbach I. The origins of the Free Electron Laser 1.3 The early times of synchrotron radiation c particle of normalized energy γ given by γ = (with particle mass, e the particle charge and c the speed of o the magnetic field B of a dipole, its movement is given = ev × B , with the particle time τ , its tion, as γm )c , and its position R(τ) . In case of an uniform magnetic lows an arc of circle, whose radius ρ is given by m γβ c ρ= eB (1.1) 3.4 Brilliance and mutual coherence eives the emitted radiation in a cone of solid angle betic transformation of the angles from the particle frame to (see Fig. 1.2). Synchrotron radiation is very collimated, ectron beam energy, the smaller the collimation angle. www.lunex5.com � �� Bus � 0 Bus � 0 I. The origins of the Free Electron Laser Velocity � Velocity � nsidering that 1γ � = 1 − βx2 − βz2 − βs2 with the deflection parameKux 2π !"#$%&'()*)&#+&'+("* � � β � � cos� s � ϕ� β � 0 eB λ z z eB λ eB λ � � uz u u u ux u γ λ u � , Kuz = 2πmo c ). In the wiggler z given by Ku =�2πmo c (K ux = 2πm c o K K 2π 2π u uz Recall βKon Undulator radiation : condition of interference � sin� s� β � cos� 1 x u γ λu respect to . For Kux = Kuz = Ku x γ λu s� gle of the velocity is large with � γ γ � � 2 2 2 2 � � Kuz K Kux Kux 2 1 2π 1 2 u � � Ku 1� s�� the trajectory.βs � 1 � γ 2 �electron 2 � integration 2 sin � λu gives 2 �frame 2 � 4γ 2 e has βs = 1 − γ12 β−s � . A second γ γ 4γ 4γ 2 2γ 1.3 The early times of synchrotron radiation c ase, the electronsTrajectory execute smooth sinusoı̈dal oscillations in the horiθ Trajectory λ o that the radiation � is kept in the same uemitted cone. In addition, the � Kux λu 2π !"#$%&'()*)&#+&'+("* � � z � � sin� s � ϕ� z � 0 at twice the pulsation in the longitudinal direction. The interference � � 2πγ λ u � Resonance� condition : K u λu the wavelengths which nλ =τ� c(1 − βs )t,interfers with n constructively an integer, βsx � Kuz λu sin� 2π s� nx for n2π �which cos� wavelengthsλfor one electron radiation 2πγ λu 2πγ λu l reduced velocity of the electrons. The fundamental resonant wave� � 2 2λ 2 2 � � K cK K K 1 4π u u u 1 observer frame uz � � ux s� �βγsrays �n 16πγ between : nλ 2 two 2).�cτ 2 sin� λu c τ�of βs , its � �1 � 2γ 2 � γ 2 � γ 2 �cτ � − Using the expression ed for Path n = difference 1, i.e. for λ1�1=�λuthe 2γ(1 = nits λnharmonics => n λin λu (1planar - βscosθ)/ u/vs - λucosθ/c r = the esonantcλwavelength and caseβ:s 2/2 2 Synchrotron radiation emitted ahead (small angle) => cosθ≈1 -θ λ2u 2 K2u nλ1n-= βs≈ <βs> = 1/2γ 2-(1 Ku+/2γ ) � (2) 2γ 1, considering 2 in Table that 1 γ � λ=λ’ ϒ(1-βcosθ) 2= λu (1-βcosθ) 1 � βx2 � βz2 � βs with the defl cosθ=1eBuz2λu eBu λu eBuxθλ22u/2 2 2 2 by Ku � 2πmo c (K , K 1/2ϒ -K /4ϒ =1- � 1/2ϒ (1+K /2) ) uz (3)ux �βz=12πm c 2πm c !"#$%&'()*+&,--.##+&/&0(123&456&7#8$2"2892&,:;:1-&<=><?@&<ABC& 1-βzcosθ=o 1/2ϒ2 (1+K2/2+ϒ2 θ2) o Ku regime, the angle of the velocity γ is large with respect to 1γ . For of the ngth λn of the emitted radiation can be varied by a modification θ =0 λ=λ’ ϒ(1-β) !"#$%&'()*+&,--.##+&/&0(123&456&7#8$2"2892&,:;:1-&<=><?@&<ABC& 2 θ =π λ=λ’ ϒ(1+β) Kudeπgap for permanent magnet insertion 1 netic field (by changing the and ϕ � 2 , one has βs � 1 � γ 2 � 2γ 2 . A second integration give wer supply current for electromagnetic insertion devices). In the time 2 λ K u nλnter +uzγ 2 given = Ku2,(1K+ux ,u K θ 2) 2γ 2 Wavelength tuneability by change of magnetic field or electron beam energy theofplanar case,periods the electrons execute smooth sinusoı̈dal oscillat server receivesM.In aE. Couprie, train N magnetic which can be considu CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 ontinuous of radiation respect the bendingismagnet zontal plane, with so that thetoradiation kept in the same emitted cone. jeudi 2 juin 2016 emission changing the gap for permanent magnet insertion deI. The origins of the Free Electron Laser rent for electromagnetic insertion devices). In the time www.lunex5.com s a train of Nu magnetic periods which can be consid1.3 The early times of magnet synchrotron radiation ssionradiation, of radiation with respect to new the bending otron polarization, devices and sources 5 trum, square of the FourierRecall transform this train, is of of undulator radiation : linewidth omposed of acardinal, series of square sinus cardinal, centeredThe on odd harmonics. The square sinus centered on odd harmonics. • Homogeneous linewidth ogeneous” linewidth ofgiven the: harmonics is thus given by : interference from trains idth of therelative harmonics isNthen by : u periods ∆λ 1 = λn nNu 1 ∆λ = α Nu2 Intensity λn nNu U20 case, 0.97 T, 2.75 GeV filament electron beam (16) (4) 3.9 nm.mrad et 39 pm.mrad 2 2 us linewidth”Nu= refers case of a single electron. 300 =>to 0.3 the % on∆H1, 0.07 % on H5 λ γ θ Nu = 100 => 1 % on H1, 0.2= % on H5, 0.07 % on H15 (5) 2 w-band in the frequency domain. In other words, the Ku λn and Synchrotron radiation, polarization, devices sources Synchrotron radiation, polarization, devices andnew new sources 5 5 1 + • Inhomogeneous linewidth 2 en different points of the trajectory, leading to sharp composed a series squaresinus sinus cardinal, cardinal, centered harmonics. The then then composed of aofseries ofofsquare centeredononodd odd harmonics. The 0.1% energy spread 2σ ∆ λ γ - energy spread : ”homogeneous” relative linewidthofofthe the harmonics byby : : ”homogeneous” relative linewidth thusgiven given =harmonics isisthus (6) E donner la :longueur d’ondeλ∆ncritique γ et la puissance Storage ring SOLEIL = 0.1% 1 λ ∆ λh = 1 Conventional linac : 0.01 % (4) xxxxxxxx = (4) electron. λ nN n u e so-called ”homogeneous linewidth” refers to the case of a single λn nNu 0.1% energy spread - divergence and size nm.mrad et 39 pm.mrad θ 22 mission is then a narrow-band ∆inλ =theγ 22frequency domain. In 3.9 other words, the (emittance) (5) 100interferes µrad SOLEIL U20: 10% field between 100 µrad LUNEX5, U15, 0.01% ∆ λλi γ θKu2 n = 1points + K2 2 different λn 1+ u (5) to sharp d of the trajectory, leading al peak emission. The ”inhomogeneous” 2σγ 2 broadening of the undulator line re∆λ cteristics -observation angle = refers to the case of a single electron. (6) The so-called ”homogeneous linewidth” λ γ n rom the electron beam energy spread, size and divergence. The emission is then a narrow-band in the frequency domain. In other words, the 2K2 σ 2γ =>leading When toinhomogenous bandwidth 2πpoints ∆λ u emitted field interferes between different of the trajectory, sharp = (7) 2 λ2 becomes dominant, λ 1 + K beam size n u broadening u spectral peak emission. The ”inhomogeneous” of the undulator line re- then Intensity α Nu sults from electron beam energylinewidth” spread, size and Thethe so-called ”homogeneous refers to divergence. the case of a single electron. ics of synchrotron radiation emissioncharacteristics is then a narrow-band in the frequency domain. In other words, the ectronThebeam M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 emitted field interferes between different points of the trajectory, leading to sharp Wiechert potentials spectral peak emission. The ”inhomogeneous” broadening of the undulator line rejeudi 2 juin 2016 otron radiation, polarization, devices and new sources 25 I. The origins of the Free Electron Laser Synchrotron radiation, polarization, devices and new sources www.lunex5.com 1.3 The early times of synchrotron radiation n(s) = Ne S(s) Synchrotron radiation, polarization, devices and new sourcesemission Coherent n(s) = Ne S(s) (30) 25 Synchrotron radiation, polarization, devices and new sources n, devices and new sources E(ω) = Eo (ω)Ne f (ω) n(s) = Ne S(s) 25 (31) E(ω) = Eo (ω)Ne f (ω) (30) n(s) = Ne S(s) � ∞ � ∞ ωs) ωs)e f (ω) E(ω) = Eo (ω)N f (ω) = ds (32) S(s)exp(i n(s) = Ne S(s) E(ω) = Eo (ω)Ne f (ω) (31) ds f (ω) (30) = S(s)exp(i −∞ � ∞ c −∞ f (ω) = � ∞ c S(s)exp(i ωs) ds c ωs)2 + N ] −∞ 2 2 I(ω) = I (ω)[N (N − 1) f (ω) (33) e e ds (32) −= e S(s)exp(i Kux Kuzf o(ω)→ → − −∞ 2 + )| hn (0, 0) u |2 c Incoherent(31) I(ω) = I (ω)[N (N − 1) f (ω) + Ne ] o e e Coherent απN = (1 + 2 enγ 2 2 Short bunch case of short electron bunch Gaussian expression order of magni case of bunched beam Bunched beam S(s) = Ex : Gaussian beam 10 orders of magnitude for λ>>σl 8 for λ=2σl 5 for λ=σl M ∑ S(s − mλr ) m=1 Coherent emission for λ=λr/n with the form factor, corresponding the bunching efficency (equivalent to the form factor in Bragg diffraction) Fig. 17 FEL configurations : a) oscillator case with an optical cavity enabling t M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Synchrotron radiation and Free Electron Laser → − → − 0 βthe tube), as shown in Fig. 19a. . In the first one, an electric field oscillates on a length ∆ s at a frequency ν → − √ I. The origins of the Free Electron Laser 1 ranging between 1 and 10 GHz (i.e. with corresponding wavelengths of 30-3 cm). The electrons, generated → − d velocity of the electrons, with γ = dγ eβ .E 2 XX revoir equation XXX cathode, enter in the first cavity where the dγ e β . Einput RF signal is applied. They can gain energy according to : 1−β = (69) www.lunex5.com = (6 dt power mcvacuum gh tubeonwhere electron bunches passing through openinside cavities waves gn of ∆W the moment t when the electron arrives theexcite cavity. modulated in time ∆s → 1 depends 1� is dt RF∆W mc − ∆s → − ∆W1 = It β . E dtαE.β cos ωt. = E.∆ s. cos ωt 1 n with the magnetic field, the frequency being determined by the geometry of the cavity. period electrons, ∆W1 = 0 since oral → − λ β . In average over β 01 the electrons have with γperiod = √ 1T 2= 2πω or spatialwith √ β the velocity the electrons, with γ =This 1−β tor for the generation of microwave signal from direct supplied to the tube. The XXX revoirenabling equation XXX phases. Then, the electrons enter into thenormalised drift the space (seecurrent in of Fig. 19b), the electrons to accumulate 1−β 2 eeelectron bunches passing through open cavities excite RF waves Begining of the twentieth century : rapid and spectacular development of electron beams inthrough vacuum tubes The sign of ∆W1where dependselectron on the moment t whenpassing the electron arrives inside the cavity. ∆W 1 is modulated RF signal. It is now usedisfor microwave ovens. The magnetron isan a high power vacuum tube bunches open cavities excite RF wa s. The drift space length adjusted to enable optimal electron bunching. 1 he frequency being determined by the geometry of the cavity. It or spatial period λ β . In average over the electrons, ∆W = 0 since the electro at a temporal period T = 1 2πω radiodiffusion, radar for iceberg or military use (high frequency oscillations d by Applications the Russel and: Sigurd Varian brothers [207] consists of twomagnetic cavities (metal boxes along oscillations by detection interaction with the field, the frequency being determined by needed). the geometry of the cavity I.4 :The development of vacuum tubes crowave signal from the direct current supplied to the tube. Thisdifferent phases. Then, the electrons enter into the drift space (see in Fig. 19b), enabling the electrons to accu g. 19a. . In the first one, an can electric fieldasoscillates on afor length ∆ s atThe a frequency ν= 2π f tofrom in bunches. drift length is adjusted enable the an optimal bunching. act only an oscillator the generation ofspace microwave signal directelectron current supplied to the tube. T for microwave ovens. Example : the klystron 10 GHz (i.e. with corresponding wavelengths of 30-3 cm).signal. The electrons, generated at the ovens. can not (metal amplify the RF It is now used for microwave Varian brothers [207] consists device of two cavities boxes along where input RF is∆klystron, applied. They can gain to :Varian brothers [207] consists of two cavities (metal boxes alo The invented the and Sigurd Cavity 1energy ncavity electric field the oscillates on asignal length s at a frequency ν by = 2π f Russelaccording theThe tube), as shown in Fig. 19a. theoscillates first one,onana length electric∆sfield length ∆ sGHz, at a frequency an electric field at a oscillates frequency on ν=2a π f (1-10 i.e. 30-3 ν = 2 � ∆of nding wavelengths cm). electrons, generated at the. In s→ −30-3 ∆ s → − ranging between 1 and cm). The at the cathode, enterofin 30-3 the first the input (i.e. withgenerated corresponding wavelengths cm).cavity The where electrons, generated at ignal is ∆W applied. energy : s.10 . E gain dtαE.β cosaccording ωt. =toE.∆ cosGHz ωt electrons, (70) 1 = Theyβcan Synchrotron radiation and Free Electron Laser signalwhere is applied. 0 cathode, enterβin the firstRFcavity the input RF signal is applied. They can gain energy according to : ∆s → − → − ion XXX energy � ∆s αE.β cos ωt. = E.∆ s. cos ωt (70)gain dγ e β . E → − → − β = ends on the moment t when the electron arrives inside the cavity. ∆W is modulated in time ∆ s ∆W1 = 1 β . E dtαE.β cos ωt. = E.∆ s. cos ωt (7 dt mc β 0 or spatial period λ β . In average over the electrons, ∆W1 = 0 since the electrons have → − electron enter arrivesinto inside ∆W inenabling time hetheelectrons the the driftcavity. spaceXXX (see inmodulated Fig.equation 19b),The the to 1 is sign ofwith ∆Welectrons depends on accumulate the moment t when the electron arrives the1 cavity. The revoir XXX β the normalised velocity of the electrons, withinside γ=√ 1−β 2 In length averageisover the electrons, =sign 0 since the 1electrons have 1 optimal ce adjusted to enable∆W an bunching. ∆W is modulated at the a temporal T= 2π/ωthe orcavity. spatial ∆W period λβ. The ofelectron ∆W depends on the momentin ttime when electronperiod arrives inside is modulated in ti 1 The magnetron is a high power vacuum tube where electron bunches passi 1average over the electrons, ∆W =0 since the electrons have different phases. rift space (see in Fig. 19b), enabling the electrons at a temporal periodtoTaccumulate = In 2πω or spatial period λ β . In average over the electrons, ∆W1 = 0 since the electrons ha oscillations magnetic field, the being dete ble an optimal electron bunching. different phases. Then, the electrons enter intobytheinteraction drift spacewith (see the in Fig. 19b), enabling thefrequency electrons to accumul act only an oscillator for thebunching generation of microwave Fig. klystron principle : a) klystron b) electron by energy modulation in the klystronsignal drift space,from electronsthe ac in bunches. The drift space lengthcan is19adjusted toasenable anscheme, optimal electron bunching. in bunches, c) Phased electron in the second klystron cavity, electric field in red Cavity 2the RF signal. It is now used for microwave ovens. device can not amplify electrons haveRussel the same with respect to the[207] co The klystron, the invented by the andphase Sigurd Varian brothers Drift section electromagnetic wave in cavity, they arefield bunched. theIn tube), ascavity, shown in Fig. 19a. . Inphase thethe first one,tosince an electric oscillates the second the electrons have the same with respect the electromagnetic wave in the cavit Second energy exchange : they have beeninbunched (see in Fig. The electrons second energy exchange is given by : stron principle : a) klystron scheme, b) electron bunching by energy modulation the klystron drift19c). space, accumulate Then, the electrons enter 1 2πω ranging between 1 and 10 GHz (i.e. with corresponding wavelengths of 3 � l2 c) Phased electron in the second klystron into thecavity, drift electric space),field in redcathode, enter in the first cavity where → − → −input RF signal is applied. They c the β . E dt = Ne EL2 cos ωt ∆W2 = ∑ The electrons electrons 0 � ∆s accumulate in bunches. − ∆ sfield. The p → − L2 cavity, with Ne the number ofwith electrons, interaction of region in→ the second E the electric NeLthe electrons, the interaction 2 the number β . E dtαE.β ωt.field can = E.∆ 1= the electrons in the second cavity is ruled by ∆W the electrons themselves. The gain incos electric be ve The drift space length is region in the second cavity, E the electric field. The phase β 0 3 6 econd cavity, the electrons have the same phase with respect to the electromagnetic wave in the cavity, since (practically, 10 − 10 ) . adjusted to enable an of the electrons in the second cavity is ruled by the been bunched (see in Fig. 19c). The second energy exchange is given by : The XXX revoir equation XXX optimal electron electrons themselves. The sign on the moment t when the electron ins 3-106)arrives bunching. electric field of ∆W � l2 1 depends . The gain in electric field can be very high (10 → − → − 1 spatial period λ(1939) β . In average over the elec at a temporal period T = β . ER. H. dtVarian, =N ∆W2 = ∑ EL cos ωt (71) S. eF.Varian2 : A high frequency oscillator and amplifier. Appl. Phys. 10(5), 321--327 2πω J.or different phases. Then, the electrons enter into the drift space (see in Fig. 19 electrons 0 in bunches. The space lengthGermany, is adjusted an optimal electron b M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELsdrift and !ERLs), Hamburg, 31 !May to –10enable !June, 2016 e the number of electrons, L2 the interaction region in the second cavity, E the electric field. The phase of jeudi 2016 klystron scheme, b) electron by energy the klystron drift space, electrons accumulate ons in2 juin the second cavitybunching is ruled by themodulation electronsin themselves. The gain in electric field can be very high I. The origins of the Free Electron Laser www.lunex5.com I.4 :The development of vacuum tubes Block diagram of the klystron High Gain amplifier Bunching (velocity modulation) Coherent interaction with the EM field Oscillator Bunching (velocity modulation) - a block for the bunching, - a block for the phased interaction with the field : a high intensity electron beam excites the RF wave in the second cavity. The klystron can be operated in the oscillator mode with a feedback loop on the radiation. Coherent interaction with the EM field In a klystron, the cavity and the waveguides should be of the order of the wavelength. While looking for larger values of the frequency or for short wavelengths, the cavities and waveguides manufacturing thus limit the operation of the klystron to the microwave region. => Another system should be realised for the micrometer and submicrometer spectral ranges. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com I. The origins of the Free Electron Laser I.4 :The development of vacuum tubes Example : the accelerator More generally, an electron bunch can be accelerated or decelerated by an wave which period is longer than the electron bunch’s one => principle of the linear accelerator The electrons are produced in an electron gun : a thermo-ionic gun or with a photo-injector where the electrons are then generated in trains. With the conventional thermo-ionic gun, the electrons travel into the so-called buncher (a subharmonic or harmonic cavity) where the electrons travel on the edge of the RF wave, for acquiring energy spread and being bunched by the velocity modulation, as in the klystron case. Then, the electron beam is accelerated by an intense RF wave produced by a klystron and sent in the cavities of the accelerating sections. The accelerating section can be considered as a series of coupled cavities or as a waveguide where irises slow down the phase of the RF wave so that it becomes equal to that of the electrons. In the accelerating sections, the electrons should have the same phase with respect to the RF wave. For being so, they are bunched in small bunches. For example, for a RF frequency of 1.3GHz, the period is of 0.77 ns, 1 phase corresponds to 2.1ps. electron gun sub-harmonic buncher accelerating sections RF wave M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com I. The origins of the Free Electron Laser I.4 :The development of vacuum tubes Vacuum tubes such as klystrons and magnetrons and more generally electronics, discovered at the end of the thirties, knew a wide development during the second world war with applications such as radiodiffusion, radar detection, where oscillators with high frequencies are needed. The sources generally use electron beams submitted to electric or magnetic fields, where the ”bunching” is the key concept for the wave amplification. The use of resonant cavities at the frequency of the emitted wavelength can efficiently insure the retroaction needed for the production of a coherent wavelength. => This field of electronics enables to understand that in setting a loop on a wide band amplifier (in connecting one part of its output to its entry), on can transform it into a very monochromatic oscillator. => This concept will be used later for the maser and laser inventions. K. Landecker, Possibility of frequency multiplication and wave amplification by means of some relaticistic effects, Phys. Rev. 36 (6) (1952) 852-855J. Schneider, Stimulated emission of radiation by relativistic electrons in a magnetic field, Phys. Rev. Lett. 2(12) (1959) 504-505 R. H. Pantell, G. Soncini, H. E. Puthoff, Stimulated Photon-Electron Scattering, IEEE Jounral of Quantum Electronics 4 (11) 906-908 (1968) R. B. Palmer, Interaction of relativistic particles and Free Electromagnetic waves in the presence of a static helical magnet, J. Appl. Phys. 43(7) (1972) 3014-3023 K.W. Robinson , Nucl. Instr. Meth. A239 (1985) Csonka (1976) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Robe r t M. PH I LL I PS www.lunex5.com Research and Deve l opment , STAR M i crowave , 546 D i v i s i on St reet , Camp I. The origins of the Free Electron Laser 1.5 The ubitron : Undulating The Beam h i story of theInteraction ub i t ron, the or igina l FEL , is t raced f rom i ts i genera t i on in 1964 of mi l l imeter wave power at a level wh i ch rema i ns 1960 : Combining Travelling Wave Tubes and undulators The Ubitron : high-power traveling-wave tube which makes use of the interaction between a magnetically undulated periodic electron beam and the TE01mode in unloaded waveguide. 1. Int roduc t i on The ub i t ron ( ac ronym for undu l a t i ng beam i nteract i on) is an FEL wh i ch was se t t i ng records for r f powe r R M. Ph i l l i ps / H i s tory of the ub i t ron genera t i on 3 15 years be fore the t erm " f ree e l ec t ron l aser " was co i ned . As is so of t en the case , the i nvent i on of the I NPUT OUTPUT W I NDOW W I NDOW ub i t ron was acc i dent a l . The year was 1957 and I was search i ng , at the GE M i c rowave Lab , for an i nt erac t i on wh i ch wou l d exp l a i n why an X-band per i od i ca l l y focussed coup l ed cav i ty TWT osc i l l ated when a so l eno i d I NPUT OUTPUT WAVEGU I DE WAVEGU I DE focused vers i on d i d no t. The mos t apparent d i f f erence BEAM be t ween the t wo was the behav i or of the e l ec t ron beam ; ELECTRON GUN COLLECTOR one w i gg l ed wh i l e the other s i mp l y sp i ra l ed . Ou t of a pape r s tudy of ways of coup l i ng an r f wave to an undu l a t i ng ax i a l l y symme t r i c e l ec t ron beam came the I NTERACT I ON 45° MATCH I NG 45° MATCH I NG RAMP REG I ON RAMP i dea of coup l i ng to the TE O, mode by a l l ow i ng the wave F i g. 3 Schema t i c of f i rst four exper i menta l ub i t rons . These used FEL- l i ke w i gg l ed penc i l beam conf i gurat i on . to s l ip through the beam such tha t the e l ect r i c f i e ld The second par t of the ini t i a l i nvest i ga t i on cons i s t ed be l ow 50 kV was as h i gh as 50% but wou dropped i th l d wreverse d i rec t i on at the same i nst ant the e l ec t ron bu i l d i ng an X-band to observe beam / wave i ncreas i ng reach i ng a l ow 5% . The l ow f tube vo l tage , of t ransveedl octo i ity ehav i or . The i nt erac t i on reg i on of thi s and three subsem i ss i on was unexpec t ed bu t was a t t r i but nade-reversed . uen t S-band tubes , i l l ust rated schema t i ca l l y i n f i g . 3, qua t e magne t i c f i e l d amp l i tude and i nsuf f i c i ent ad j ustcoup aThe l ed cav i ty osc i l l at i on turned ou t to be a s lot had the appearance of the c l ass i ca l FEL. The exper i b i l i ty . Int erac t i on was observed i n the f orm of r f abmode wh i ch depends , not on the beam w i gg l e , bu t on ment a l tube p i c tured i n f i g. 4 used a 0 .3 i nch d i ame t er sorpt i on be l ow synchronous vo l t age and ga i n , above R. M. Phillips, The Ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide, IRE Transactions beam w i th a m i croperveance of 0 .7 . I ndox pe rmanen t synchron i sm . The omega -be t a d i agram der i ved f rom average beam d i ame t er . By the t i me thi s was recogn i zed , oni sted Electron Issue: 4these ), 231 - 241 (1960) magne t s , ass by t r i m Devices coi l s, we re!(Volume:7 used to w i gg l e ,!and da t a was a good ma t ch to the theore t i ca l hyper bo l a for ocus the R. beam i ng perpend i cu l of ar to p l ane of Nuclear the wavegu i deand . TheMethods 2 dB max iin ga i nofwas Imum was fResearch exp l or i A272 ng my(1988) new found M.. Focus Phillips, History thetheubitron, Instruments Physics 1-9 fast wave i nterac t i on , he w i gg l e occurs automa t i ca l l y as descr i bed i n a pape r the same for an r f dr i ve of 1 W and 1 kW , i nd i ca t i ng i neer i ng adventure wh i ch was to l ast for seven by Stur rock of St anford [1] , the conf i n i ng force be i ng the tha t the e f fect was mor e than j ust sma l l an s i gna l eng . produc t of w i gg l e ve l oc i ty and ax i a l magne t i c f i e ld . I present ed these concept s and ini t i a years l resu l ts, a tspan the the f requency range f rom 3 toGE 60 Microwave GHz andLab However , i f no ba l anc i ng force prov i ded , theSchool beam Free Electron!Lasers!and!Energy!Recovery!Linacs 17th E l ec t ron Tube Research Con f erence !(FELs i n Mexand i co !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 M. were E. Couprie, CAS set new wou l d spread un i mpeded i n the p l ane of the w i gg l e . C i t y i n 1959 [2] . The resu l ts caused qu i t e a st i r amongpowe r genera t i on records wh i ch wou l d s t and 2 ljuin 2016 Th jeudi i s prob em was so l ved by t aper i ng the magne t i c f i e ld those who apprec i a t ed the i r s i gn i f i cance . One of those i t t b m T a p p c t m w p o a compa rab l e i n e f f i c i ency w i th tha t of a s l ow wave t rave l i ng wave tube , and tha t the r f energy came ul t i www.lunex5.com ma t e l y f rom the ax i a l ve l oc i ty , not the much sma l l er w i gg l e ve l oc i ty . I t is i nterest i ng to not e tha t the resu l ts p i c tured i n f i g . 2 are qua l i ta t i ve l y s i mi l ar to those obt a i ned exper i ment a l l ytoat the s i xallowing LosTE01 A l amos abou tby years Idea :coupling mode ago w i th an FEL. I. The origins of the Free Electron Laser 1.5 The ubitron : Undulating Beam Interaction the wave to slip through the beam such that the electric field would reverse direction at the same instant the electron velocity reversed. 2 R . M Ph i l l i ps / H i story of the ub i t ron ELECTR IC F IELD FORCE Y DECELERATI NG U a =12 max = 1/2 D -S Z avq ACCELERATI NG E (a) 1 .2 PLANAR s s e 1 2 a + s Z =O - ;r (b) s - 0 r COAX I AL N (C) () PHASE POSITION ( Z-T) S N S C I RCULAR F i g. 1.Examples Examp l es of of beam-guide beam-gu i de ub i t ron conf i gurat i ons wh i which ch ubitron configurations prov i de 100times t i mes the the interact ion area of aof TWT. provide100 interaction area a TWT. The electron-wave interactionI .exhibits the same I NTRODUCT I ON type of first-order axial beam bunching characteristic of the conventional slow-wave traveling-wave tube => it can be used in extended interaction klystrons and electron accelerators, as well as traveling-wave tubes. F i g. 2. Ana l og compu t e r ana l ys i s o f ax i a l beam bunch i ng ver i f i ed TWT- l i ke pe r f ormance. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 X-band tube ( rec t angu l ar gu i de and penc i l beam) down to S-band , whe re co i l s cou l d be used to produce a mor e f l ex ib l e w i gg l er f i e ld . As was the case w i th the X-band tube , the b d i mens i on of the gu i de was i ncreased to www.lunex5.com about 12 t i mes tha t of s t andard wavegu i de in order to prov i de amp l e room for the penc i l beam to w i gg l e . Th i s gu i de mod i f i ca t i on , i t wou l d turn out , was respons i b l e for the poor beam t ransm i ss i on . The photograph of f ig . 5 is the th i rd of three S-band tubes wh i ch were f abr i ca t ed and tested . The peak beam t ransm i ss i on of the f i rst tube was about 60% at vo l t ages be l ow 50 kV , bu t aga i n dropped w i th i ncreas i ng vo l tage , componen t of the acce l era t i ng f i e l d as is passes near e i ther wa l l , resu l t i ng i n a ne t ax i a l dece l era t i ng force . The f undamen t a l per i od for thi s per i od i c d i sp l acement i nt erac t i on is one ha l f tha t of the TE oi per i od i c i nteract ion, so i t occurs at a l ower vo l tage , even though i t is a h i gher order mode . W i t h the d i scovery of thus compe t i ng fast wave i nteract i on, mode i nter f erence prob l ems and mode suppress i on t echn i ques were to become a pr i ma ry concern for the dura t i on of the seven year ub i t ron deve l opmen t e f for t . The second S-band tube d i f fered f rom the f i rst on l y . M. of Ph i l l i ps / H i story of the ub i t ron i n the add i t i on of a mode suppressor wh i ch made Ruse the fact that the TM modes have st rong l ong i tud i na l cur rent s i n the s i de wa l l s wh i l e the TE oi mode has on l y t ransverse cur rents . A mode suppressor cons i st i ng of ver t i ca l s l ots m the wa l l s backed by th i n s l abs of l ossy ceram i c was added to the next tube . The measured l oss to the TM , , mode ranged f rom 30 dB near cutof f to 10 dB at the h i ghest t rapped f requency , wh i l e the l oss to the TE oI mode was l ess than 0 .5 dB at a l l measured f requenc i es . The mode suppressor so l ved the prob l em. Beam t ransm i ss i on was at l east 80% at a l l vo l t ages through 150 kV . The max i mum ne t gam of thi s tube was a d i sappo i nt i ng 7 dB but the bandw i d t h was an encouragi ng 30%. Us i ng f eedback to obt a i n sa tura t i on , we mea sured a best e f f i c i ency of 10%. The th i rd tube , tha t shown i n f i g. 5, was mod i f i ed to obt a i n h i gher ga i n . I t d i f f ered f rom the second i n three respec ts : (1) Gun m i croperveance was i ncreased f rom 1 .0 to 1 .45 . (2) The c i rcu i t l ength was i ncreased by 50% . (3) Int ent i ona l TEoI mode l oss was i nt roduced to i nsure aga i ns t re f l ec t i on t ype instab i l i t i es . Th i s was done by ang l i ng the mode suppressor s l ots by 30 ° to the Y ax i s . Inser t i on l oss to the TE oI mode ranged f rom 19 dB at 2 .55 GHz to 3 dB at 4 GHz. 2 .5 2 .6 2 .7 2 2 9 0 3 .1 3 .2 3 .3 3 .4 3 .5 Beam t ransm i ss i on of at l east 80%.8 was aga i n ob DR3I VE FREQUENCY (kmc) t a i ned at a l l vo l t ages. Sma l l s i gna l ga i n at t wo va l ues of Measured sma l l i sditgna l ga i n of the ub i t ron of f ig. 5, at t wo va l ues of beam vo l t age . beam vo l t age is shown i n fFi igg.. 6.6 . The 3B bandw h was about 30% at 125 kV . The peak sma l l s i gna l ga i n , I. The origins of the Free Electron Laser 1.5 The ubitron : Undulating Beam Interaction F i g . 5. Photograph of S-band ub i t ron wh i ch produced 1 .2 MW of power . Cod cur rents were rheostat cont rol l ed . Ca thode is h i dden in the oi l t ank . Experiments : an undulated pencil beam in a rectangular waveguide. ob t a i ned a t 135 kV , was 13 dB . Max i mum sa tura t i on powe r was 1 .2 MW and t he ne t e f f i c i ency (a f t er subt rac t i ng dr i ve powe r ) was 10% . These ear l y resu l ts we r e a l l repor t ed i n a pape r pub l i shed i n Oc t obe r 1960 [3] . I n tha t paper , I s t a t ed tha t an e f f i c i ency enhanc i ng t ape red w i gg l e r expe r i men t was p l anned . The expe r i men t requ i red the w i nd i ng of spec i a l th i nner co i l s t o a l l ow t he magne t pe r i od to be dec reased . A t t he t i me of pub l i ca t i on , the expe r i men t had been comp l e t ed bu t i t was t oo l a te for i nc l us i on i n the pape r . A 10% t aper i n t he w i gg l er pe r i od i n t he f i na l 1 / 3 of the t ube i nc reased t he max i mum e f f i c i ency f rom 10% to 13% . Th i s i mprovemen t was in pa r t due to the conserva t i ve me t hod o f compu t i ng e f f i c i ency . Sa tura t i on ga i n as we l l as ou t pu t powe r i ncreased , l eav i ng l ess dr i ve powe r to be sub t rac t ed f rom the ou t pu t powe r i n compu t i ng e f f i c i ency . 5 3 .6 3 .7 300 GHz . One o f the 16 GHz t ubes i s shown in the pho t ogr aph o f f ig . 7 . The r f c i rcu i t cons i s t ed bas i ca l l y o f a 1 i nch d i ame t e r p i pe made of i ron and coppe r r i ngs , w i t h the i ron r i ngs serv i ng as po l e p i eces for rad i a l A l n i co V pe rmanen t magne t s. These prov i ded bo t h the undu l a t i on for t he i nt erac t i on and the beam f ocus i ng . To gua rd aga i ns t mod i ng prob l ems , each o f the spacers , wh i ch sepa ra t ed t he s l i ght l y re -ent rant magne t po l e p i eces , had embedded to t hem t wo l ossy ce ram i c r i ngs . The mode suppressor produced no measur ab l e l oss to t he TE ot c i rcu l ar wavegu i de mode bu t prov i ded 10 ' s of dB o f l oss t o TM modes o f conce rn. The conve rgen t so l i d beam gun used on th i s t ube was f rom a GE 20 MW S-band k l ys t ron . Two of these t ubes we r e bu i l t . The f i rst , des i gned for 170 kV opera t i on , prov i ded l ow ga i n and re l a t i ve l y poor beam t ransm i ss i on due to i nsuf f i c i ent magne t i c f i e l d . The second t ube was des i gned to ope ra t e nea re r the 250 !ERLs), Hamburg, Germany, !May !June, kV uppe r31l i mi t o f –10 the modu l a t2016 or whe r e t he magne t pe r i od was l onger and the f i e l d h i gher . Beam cur ren t was approx i ma t e l y 125 A . unique features : - very broad interaction bandwidth which results from the absence of a dispersive slow-wave circuit, - variable interaction phase velocity--hence, variable saturation power level. Among the physical embodiments of the Ubitron are a number of higher-order mode waveguide and beam configurations. =>interesting prospect for high-power millimeter wave amplification. R. M. Phillips,The Ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide, IRE Transactions on Electron Devices !(Volume:7 ,! Issue: 4 ), 231 - 241 (1960) R. M. Phillips, History of the ubitron, Nuclear Instruments and Methods in Physics Research A272 (1988) 1-9 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and jeudi 2 juin 2016 3. US A i r For ce t akes ove r www.lunex5.com I. The origins of the Free Electron Laser 1.6 The maser discovery Goal : create a «quantum» microwave sources in replacing the amplification by an electron beam by stimulated emission in molecules. In order to do a "quantum" microwave oscillator, an excited molecules is introduced in a microwave cavity which is resonant for the frequency of the molecule transition. Population inversion: - Townes, Basov et Prokhorov : spatial separation of excited molecules (SternGerlach type), efficient but not very practical. Charles - proper exciting radiation of the atoms and molecules. Townes 1949 : "optical pumping", with circularly polarised light for selectively filling some (1905-2015) Zeeman sub-levels of atoms (Alfred Kastler (1902-1984, Nobel 1966) and Jean Nobel 1964) Brossel). -1951, population inversion by RF radiation enabling to create samples of temperature", (E. Purcell and R. Pound, working on Nuclear Magnetic LE"negative MASER A AMMONIAC Resonance) Nicolay Gennadiyevi 1954 : first MASER in the micro-waves LE MASER A AMMONIAC ch Basov (NH3 molecule). (1922-2001) Nobel 1964 Charles Townes, 1954 Aleksandr Mikhailovich (+Basov, Prokhorov (1916-2002) Prokhorov : Nobel 1964 Nobel 1964) Jet moléculaire Focalisation Inversion de population Cavité micro-onde Emission stimulée Columbia University Oscillation ! (1954) 282. J.P. Gordon, H. -> J. Zeiger and C.H.auto-entretenue Townes, Phys. Rev., 95 J. 1954 P. Gordon, Zeiger and C. H.PTownes, 99GHz (1955) 1264. 14 J.molécules/sec, : 10H. = 10-9Phys. W, fRev., = 24 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 A. Kastler (1902-1984, Nobel 1966) www.lunex5.com I. The origins of the Free Electron Laser 1.7 The laser discovery 1958 : principle of realisation of the laser by Charles Townes and Arthur Schawlow (1921-1999, Nobel 1981) Bell Tel. I.aboratories, Charles Townes (1905-2015 Nobel 1964) Arthur Leonard Schawlow (1905-1999 Nobel 1981) «The extension of maser techniques to the infrared and optical region is considered. It is shown that by using a resonant cavity of centimeter dimensions, having many resonant modes, maser oscillation at these wavelengths can be achieved by pumping with reasonable amounts of incoherent light. For wavelengths much shorter than those of the ultraviolet region, maser-type amplification appears to be quite impractical. Although use of a multimode cavity is suggested, a single mode may be selected by making only the end walls highly reflecting, and defining a suitably small angular aperture. Then extremely monochromatic and coherent light is produced. The design principles are illustrated by reference to a system using potassium vapor.» A. L. Schawlow C. H.Townes, Infra-red and optical masers, Phys. Rev. Lett. 1940-1948 (1958) Patent, Optical Masers and Communication, by Bell Labs. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 mode would extremely small ( of the order of 1 micrometer) and becomes λ become 2Lc lasers). C.are Townes and A.using Schawlow not doable at that time. Nowadays, these cavities manufactured nanotech-at Bell Labs, G n practice, in order to focus the light transversally and to avoid diffraction losses, www.lunex5.com Prokhorov at Lebedev propose to feedback nologies (for VCSEL (Vertical Cavity Surface Emitting Laser)institute semi-conductors of the mirrors should be concave.The light circulating in the optical resonator is lasers). C. Townes and A. Schawlow(Fabry-Perot at Bell Labs, G. Gould at Columbia and A. a plane wave, and the radius of the light changes along its propagation. In case of type used in spectroscopy). In a Fabry-P 1.7institute The propose laser Prokhorov at Lebedev todiscovery feedback withradiation, antrips openpolarization, resonant devices cavity light makes round between the two Synchrotron and mirrors new sourceson vity with two concentric mirrors, the light radius is minimum at the waist w and 0 (Fabry-Perot type used inuse spectroscopy). In a Fabry-Perot cavity of length Lc , the To shorten the wavelength, a Fabrylight Perot type: optical resonator rges according to XXXXXXXXREF Khogelnik, YarivXXXXXXXXXXXXX to interact at each pass with the amplifier cmedium c light makes round trips between the two mirrors on which it is reflected. For the ν= = � be in phase with the one from the previous pass. In oth In order to achieve an optical cavity resonant on its fundamental mode would become extremely λ 2L c light tomaser, interactthe at maser each pass with the amplifier medium, and to get larger, it should s2becomes not doable small ( of the order of 1be micrometer) and that time. oneatround should be topath an integer number pan in = phase pass. In other terms, theequal optical 1 +the2 one from the previous (41) w(s) w0 with Intrip practice, in order to focus thefor light transversally ZR be equal to an integer number p of wavelength λ , i.e.: one round trip should one of the mirrors should be concave.The light circulat Conditidion for the light to interact at each pass with the amplifier medium: apolarization, plane wave,devices and theand radius of2L theclight changes alo = p.λ with ZR the Rayleigh length, i.e. the distance from the waist for whichradiation, the not radius √ Synchrotron new sources the light should be in phase with the one from the previous2Lpass : (38)the light radius is c = p.λa cavity with two concentric mirrors, he light beam is increased by a factor of 2. It is given by : the optical path for one round trip should be equal to an integer number p of wavelength λ c c diverges according to XXXXXXXXREF Khogelnik, Y = ν = p.λ πw20 λ 2L p.λ cLc = � (42) = Z R (39) = L For a fixed cavity length Lc, only the λwavelengths verifying can be present in the ”optical maser” light. Thes2 c 2 2 Synchrotron radiation, polarization, devices and new sources In practice, in orderare to focus transversally to d longitudinal modes associated to different values of p verifying this equation called the thelight longitudinal modes 1 +avoid w(s) = wand 0of the 2 corresponds to the diffraction an aperture of diameter 2wa0 .fixed The ZR opv only the For cavity length Lc , light , only verifying this equation cancirculating be wavelengths Forofa light fixed by cavity length Lcone of the the wavelengths mirrors should be concave.The in the cavity. c associated cthe ationThe at the and at the exit ofin the cavity have thebysame characteristics. itthe present themodes ”optical maser” light. The longitudinal modes tolight. different present in ”optical maser” longitudinal shiftentry in frequency between two is given : a plane not wave, and radius of the light changes its propag = ν = with ZR the Rayleigh length, i.e.The thealong distance from(4 t √ be adapted to the user needvalues with the help of mirrors and lenses. The divergence of p verifying this equation arevalues called the modes of light the by cavlty. 2Lbeam a cavity with two concentric mirrors, the radius is of minimum of plongitudinal verifying this equation called the csources Synchrotron radiation, polarization, devices and new 35 2. Itlong isat g ofλ the light is increased aare factor as : he light beam θr can be expressed The shift in frequency between two modes is given : diverges according toby XXXXXXXXREF Khogelnik, YarivXXXXX The shift in frequency between two modes is given by c c and to avoid diffraction loss Rc In practice, in order to focus the light νtransversally 2 = = (40) πw0 � λ λ 2Lc ZR = 1/4 one ofθrthe should be : concave.The light circulating in the optical 1/2 = mirrors (43) divergence of the light beam 2 )] resonator λ -2R w = ( λ /2π) [L (L s 0 c c losses, cdiffraction πw0 In practice, in order to focus the light transversally and to avoid 1 + of w(s) = diffraction w 0 propagation. Rc not a plane wave, and the radius of the light changes along its Inan case 2 2 light by it corresponds to the ap one of the mirrors should be concave.The light circulating in the optical resonator is Z 2 w R 2 n the case of a HeNe laser at 633nm with a waist of 600 m, the Rayleigh length 0 2 radiation thewentry and at thez0exit ofIn / waist λ cavity =at πw λ its propagation. notzconcentric a0plane wave, and the radiusthe of the lightat changes along case of whav a cavity with two mirrors, light radius isαminimum the 0 the o 0a the order of 2m. Over 2m propagation length, the light beam diameter remains with ZRsthe Rayleigh length, i.e. the distance the waist for a cavity with two concentric mirrors, theadapted light radius is minimum at thefrom waist w0 and can be to the user need with the help of mirror √ diverges according toaccording XXXXXXXXREF Khogelnik, YarivXXXXXXXXXXXXX tically constant. The beam is very directional. w0 diverges to light XXXXXXXXREF Khogelnik, : : 2. It isasgiven by of the beam byθarYarivXXXXXXXXXXXXX factor can be of expressed : of is theincreased light beam XXX je n’arrive pas faire micronXXXXXX �� 2 XXX cas de la longueur de Rayleigh et duLwaist, λ 2s2 c LEL SACOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX πw s 0 θr = (41) According to the user need, it can be focused or expanded (4 w(s) =w(s) w0= w01 +1 + Z2R2 ZR = λ πw0 METTRE fig cavite optique, ZR In the case of a2m HeNe laser 633nm with of with ZRRayleigh the trs Rayleigh length, i.e. theof distance from the waist foratby which radius itdirectif corresponds the diffraction of light an the aperture of dia of peut a HeNe at 633nm, waist of 600 µm, length ofetthe 2m. propagation length, the lighta waist √Over Toutefois,Case on ne paslaser obtenir simultanment un faisceau de order trs to peIt is given : cavity of the is byisentry a of factor of theand order of 2m. Over 2m propagation thec practically =>light The beam beam is increased very directional. radiation atfaible the at2. the exit ofby the have length, thethe same ZR constant. thedes Rayleigh length, i.e. the distance from the waist for which rad ayon. Enbeam effet,diameter plus on remains focalisewith (en utilisant miroirs concaves de rayon √ constant. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs andpractically !ERLs), Hamburg, Germany, 31The !May beam –10 !June, 2016 isof very directional. can be adapted to the user need with the help mirrors and lenses 2 ourbure), plus w0 est petit, mais plus le faisceau diverge ensuite (la longueur de πw 2. It is given by : of the light beam is increased by a factor of 0 jeudi 2 juin 2016 XXX (42) Z = je n’arrive pas faire micronXXXXXX I. The origins of the Free Electron Laser www.lunex5.com I. The origins of the Free Electron Laser 1.7 The laser discovery 1960 : First Ruby laser (Ion CR3+ in ruby) Hughes Research Laboratories T.H. Maiman, Nature, 187 (1960) 493T. Maiman, Stimulated Optical radiation in Ruby, Nature 187, 493-494 (1960). T. H. Maiman, Hoskins, D’Haenens, Asawa and Evtuhov, Phys. Rev., 123 (1961) 1151. In 1954, N. Bloembergen, Basov and Prokhorov propose the 3-level MASER concept : with a proper illumination of a solid such as a Ruby crystal, population inversion takes place. first working laser by generating pulses of coherent light from a fingertip-sized lump of ruby illuminated by a flash lamp Easier to operate than the equivalent gas based maser. It has been used in particular as a very low noise amplifier. Theodore Harold Maiman (1927-2007) !"#$%$&'$( M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com I. The origins of the Free Electron Laser editorial Remembering the laser diode 1.7 The laser discovery Fifty years ago, researchers at a handful of laboratories around the world were reporting lasing from the first semiconductor lasers. Our IT infrastructure today relies on their diligence and success. GENERAL ELECTRIC RESEARCH AND DEVELOPMENT CENTER, COURTESY AIP EMILIO SEGRE VISUAL ARCHIVES Applied Physics Letters by Marshall Nathan’s In 2010, the 50th anniversary of group at IBM’s Watson Research Labs2 and Ted Maiman’s experimental demonstration of the first ruby laser quite rightly gave Ted Quist’s group from the Massachusetts rise to substantial publicity, including Institute of Technology Lincoln Labs3. celebratory events such as the LaserFest series A flurry of results then followed from (www.laserfest.org) and much coverage in a around the world, including the first visible wide variety of newspapers and magazines. semiconductor laser by Nick Holonyak’s 74 1964 CHARLES H. TOWNES However, in many ways it was actually group at General Electric’s lab in Syracuse the successful development of the GaAs (who became famous for inventing the semiconductor laser diode in 1962 that really light-emitting diode that same year) as well ignited the laser revolution. The fabrication as demonstrations by Cyril Hilsum and of a semiconductor laser kick-started the colleagues at the UK’s Services Electronics important field of optoelectronics and showed Research Laboratory and a Russian group of that lasers could, in principle, be fabricated scientists led by Nikolay Basov. in a miniature, cost-effective format that Speaking at the event, Marshall Nathan showed great promise for mass-production in says that in early 1962 he was at IBM a form similar to electronic devices. Shortly studying the photoluminescence from GaAs afterwards, the demonstration of electrically when the department director Rolf Landauer pumped devices capable of operating at announced that he wanted IBM to be the room-temperature with high output powers first group to make a GaAs laser and threw a further added to the practicality and appeal of team of people onto the project. In February, semiconductor lasers. Nathan and his co-workers tried using a FLASH TUBE In contrast, if lasers had remained limited flash lamp to pump a sample of GaAs but to getting their gain from doped glass crystals were unsuccessful in achieving lasing. Then, Fig. 3. Schematic diagram of a ruby (optically excited solid-state) laser. When the such gas as ruby or Ti:sapphire, or gas mixtures following further research in September as HeNe 1962, they observed “spectacular line flash tube is activated, electromagnetic oscillations occur within the ruby rod,such and someor CO2, their technological narrowing”, which suggested that lasing was impact would have been considerably less of these light waves are emitted in a beam through one partially reflecting endand of the theworld rod.of photonics would look very the USA, Yuri Popov from Russia, Maurice taking place. Bernard from France, Jim Coleman from the “We sent the results to Applied Physics different. Although the use of high-power USA and Cyril Hilsum, Robin Thompson and Letters, hand-delivered,” said Nathan. “We lasers for materials processing applications John Orton from the UK. then started to get lots of results very quickly, and welding might still have Not very long after the ruby laser was developed, Javan, Bennett such andastocutting HerThe competition between various such as continuous-wave lasing at 4.2 K, come fruition, many other tasks that we scientists (such as Gordon Gould, room-temperature lasing and measurement take for granted of today would probably not riott35 obtained maser oscillations from neon atoms excited by collisions Charles Townes, Art Schawlow and of far-field emission patterns,” said Nathan. have been feasible. Take, for example, optical Ted Maiman, among others) to achieve the “The first real semiconductor laser at IBM storage and communication networks, the second kind with metastable helium, in accordance with an ideadata previousfirst experimental demonstration of a laser was made in October 1962, and we got the which today represent two of largest and 36 only amarkets for laser technology. in 1960 is well documented (see the excellent patent out in just five days.” ly put forward by Javan . This system, illustrated in Fig. 4, requires most important account in Jeff Hecht’s book “Beam: The Astonishingly, Nathan says at the time is unlikely that fibre-based data networks, gaseous discharge through a tube containing a mixture of helium ItCDs, and neon Race to Make the Laser”). However, the that the researchers at IBM didn’t know that DVDs and BluRay players would have quest to develop a semiconductor laser two they had serious competition from General been seriously at low pressure, and two reflectors at the ends of the tube. It oscillates at thepursued or even considered Electric and were shocked to learn Hall’s APL practical without the realization of an efficient years later was arguably just as exciting, fastpaced and competitive, with a handful of paper had been submitted 11 days before and low-cost laser diode. research groups all reported working lasers their own, effectively scooping them. “We had Given this context, it is pleasing to see based on GaAs p–n junctions within a short no idea that General Electric was working on that the 50th birthday of the laser diode has 1 9 6 4 C H A R L E S H . T O W N E S 76 period in the autumn of 1962. this,” commented Nathan. This story is not not been overlooked. The Institute of Physics Ultimately, Robert Hall (pictured) and his only an interesting history lesson, but also a in the UK organized a two-day celebratory group at General Electric’s research labs in valuable reminder of just how exciting and seminar entitled “50th Anniversary of the Schenectady is credited as getting there first. fast-paced research can be. ❒ Laser Diode” at the University of Warwick Their report of coherent infrared (850 nm) on 20–21 September 2012, during which SILVER RIBBON emission from a GaAs laser appeared in several of the founding fathers of the References 1. Hall, R N, Fenner, G. E, Kingsley, J. D, Soltys, T. J and Carlson R. O. the 1 November 1962 issue of Physical technology reminisced about the early days Phys. Rev. Lett. 9, 366–369 (1962). 1 Review Letters . This was simultaneously of its development and the race to make 2. Nathan M,I, Dumke W.P, Burns G, Dill F, H, Jr and Lasher G the first laser diode. Speakers included accompanied by reports of lasing from SILVER-GOLD Appl. Phys. Lett. 1, 62 (1962). 3. Quist T.M et al Appl. Phys. Lett. 1, 91 (1962). Marshall Nathan, formerly of IBM Labs in GaAs devices appearing in the journal EVAPORATED STRIPE 1966: Mirek Stevenson and Peter Sorokin at General Electric first dye laser tuneable yellow to red .... 1962 : R. Hall first semi-conductor AsGa laser (diode laser) 1960: Ali Javan first gas laser (He-Ne) Gaseous discharge CW source of infra red, 1 mW p-n junction of the semiconductor gallium arsenide through which a current is passed can emit near-infrared light from recombination processes with very high efficiency. (MICROALLOYED) NATURE PHOTONICS | VOL 6 | DECEMBER 2012 | www.nature.com/naturephotonics Fig.4. Schematic diagram of a helium-neon (gas discharge) laser. Electrical excitation Javan, Bennett and Herriott, Phys. Rev. Letters, 6 (1961) 106. can initiate a steady maser oscillation, resulting in an emitted light beam from either end of the gas discharge, where there are reflecting mirrors. Fig. 5. Schematic diagram of a gallium arsenide (injection, or semiconductor) laser. A small between the silver the molybdenum disc can produce50 R. J. voltage Keyes applied and T.M. Quist, Proc.ribbon IEEEand (Inst. Electron. Elec. Engrs.), maser oscillations with resulting emission of coherent infrared radiation. 795 1971: Concept of the Free Electron Laser 1977 : First FEL in the IR (Stanford, USA) 1983 : First FEL in the visible (Orsay, France) (1962) 1822. Hall, Fenner, Kingsley, Soltys and Carlson, Phys. Rev. Letters, 9 (1962) 366. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 One might consider the population of the virtual level in a Raman maser (see Fig. 6) to be greater than that of the first excited state, so that there is no www.lunex5.com I. The origins of the Free Electron Laser 1.7 The laser discovery The limitations of the «optical maser» «As one attempts to extend maser operation towards very short wavelengths, a number of new aspects and problems arise, which require a quantitative reorientation of theoretical discussions and considerable modification of the experimental techniques used.» ... «These figures show that maser systems can be expected to operate successfully in the infrared, optical, and perhaps in the ultraviolet regions, but that, unless some radically new approach is found, they cannot be pushed to wavelengths much shorter than those in the ultraviolet region.» A. L. Schawlow and C.Townes, Infra-red and Optical masers», Phys. Rev. 112 1940 (1958) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 e original paper from A. Schawlow and C. Townes � [207], it was written that :”As one attempts to extend maser in Table 1, wavelengths, considering that 1γof=new aspects 1 − βx2and − problems βz2 − βs2arise, withwhich the require deflection paramen towards very short a number a quantitative www.lunex5.com ation of theoretical discussions and considerable ofeBthe experimentaleBtechniques used. ” and eBmodification uz λu u λu ux λu Kuthat , Kmaser Ku = 2πm (Kuxsuccessfully = 2πmo c in , Kthe = 2πmooptical, theperhaps wiggler ux , Ksystems uz given uz infrared, figurester show canby be expected to operate and c ). In oc II.1 The FEL concept emergence : Motivations for an exotic laser K 1 traviolet regions, the but that, unless radically newu approach iswith found,respect they cannot be. pushed to wavelengths regime, angle of some the velocity is large to For K ux = Kuz = Ku γ γ J. Madey orterJ. M. than those in the ultraviolet region.” 2 K «Schawlow and Townes’ descriptions of masers and lasers coupled with π 1 u J. Madey, Univ., thought that ”Schawlow and Townes descriptions of masers and lasers couandfrom ϕ =Stanford, , one has β = 1 − − . A second integration gives the trajectory. s 2 2 γ2 2γ new eigenmodes understanding theoffered Gaussian free space offered h the new understanding of thethe Gaussian of free of space a new eigenmodes approach to highoffrequency In the planar case, the electrons execute smooth sinusoı̈dal oscillations theconstrained horin that was not constrained by the limits totothehigh capabilities of electron tubes [144] hein wondered a established new approach frequency operation thatand was not by plane, so that theestablished radiation islimits kept in the the same cone. addition, there zontal was ”a Free Electron Radiation Mechanism that Could Fulfill theseemitted Conditions” andIn considered thethe the to capabilities of electron tubes» t possible radiation processes. He firstthe examined, Compton which direction. appeared as the promisbeam oscillates at twice pulsation in theScattering longitudinal Themost interference didate. Indeed, Stimulated Compton Backscattering has been analysed by Dreicer in the cosmic blackbody takes place for the wavelengths for Electron which nλRadiation βs )t, with nthat an integer, βs these n = c(1 −Mechanism - Was there aλnFree Could Fulfill n. XXXX chercher la REFXXXXX. theBack longitudinal reduced velocity the pulse electrons. Theoffundamental resonant waveConditions? Compton Scattering (CBS) process between of a laser and a bunch relativistic particles (electrons, (1 −theβshead-on ). Using the expression of βs , it is obtained forhigh-energy n = 1, i.e. for λcoming s, etc.)length leads to the production of radiation collision between the photons 1 = λufrom particles. In order reduce the Compton divergence ofScattering the scattered radiation, itas is the better toplanar usePromising a relativistic electron comes fortothe resonant wavelength and its harmonics in the case : Candidate Appeared Most hich radiation cone is reduced to 1/γ. For relativistic particles (i.e. γ >> 1), he energy of the produced photons Benefit given by : of using relativistic electrons beams: 2 II. The invention of the Free Electron Laser concept λu Ku nλn =2 2 (1 + ) 4γ E2γ ph 2 = (2) => Strong periodic field (78) ECBS 2 1 + (γθ ) Undulator Ku2 the 2CBS E ph- tuneability the energy of the initial photon beam, θ the λ angle between u 2 photons and the electron beam nλ + γ = (1 + θ ) radiation could be tuneable.(3) n easily 2be changed, so the CBS y. The energy of the relativistic electrons can 2γ 2 alysis of the stimulated Compton Backcattering ware carried out [126]. J. M. J. Madey had the idea to make Needmore of high peakbycurrent = magnetic > emitted nomenon efficient using field radiation of an undulator He considered that ”Relativistic of the can [123]. be varied by a modification of the The wavelength λnthe electron sources s can also notbeam tell the differencefield between and virtual photons, permitting the substitution of adeundulator magnetic (byreal changing theincident gap for permanent magnet insertion periodic transverse magnetic field for the usual counter-propagating real photon beam”[144] . He was aware of vices orexperimental the power[24] supply electromagnetic insertion devices). In theThe time retical workcurrent of Motz, for where radiation from bunch beams has been observed. => [23] FEL and concept J. M. J. Madey, Nobel Symposium, June 2015 domain, the observer receives a train of Nu magnetic periods whichSigtuna, can Sweden, be considn be the one generated by an undulator. J. M. J. Madey,Wilson Prize article: From vacuum tubes to lasers ered as quasi-continuous emission of radiation with to ST the bending magnet Can gain be achieved with such a system? and backrespect again, Phys. Rev. Accel. Beams 17, 074901 (2014) radiation. The radiation spectrum, square of the Fourier transform of this train, is E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 he FEL quantumM.approach jeudi 2 juin 2016 II. The invention of the Free Electron Laser concept frequencies due to the scattering of an electron beam by Ation least twoin authors haveionized considered in concluding detail the the cores neutral and matter www.lunex5.com process of induced gain bremsstrahlung at radio optical that appreciable was available underand favorable frequencies dueThis to theanalysis scattering of an electron beam by conditions.1-3 deals with the radiation JOURNAL OF APPLIED PHYSICS VOLUME 42,cores NUMBER 5 the ion neutral and ionized matter concluding APRIL 1971 emitted by a in relativistic electron beam moving through JOURNAL OF APPLIED PHYSICS VOLUME 42, NUMBER 5 APRIL 1971 that appreciable gaindcwas available a periodic transverse magnetic field. under We willfavorable consider Stimulated Emission of Bremsstrahlung in a Periodic Magnetic Fieldwith analysis the radiation the as This the scattering ofdeals virtual photons using the Stimulated Emission of Bremsstrahlungconditions.1-3 in aprocess Periodic Magnetic Field emitted by a relativistic electrontobeam through Weizsacker-Williams method' relatemoving the transition JOHN M. J. MADEY JOHN M. J. MADEY to the more easily calculable rates arates periodic transverse dc magnetic field. Wefor willCompton consider Physics Department, Stanford Stanford, California 94305 J. M. J. Madey.: Stimulated emission of Bremmstrahlung in aStanford, periodic magnetic field; J. Appl. Phys., 42, 1906--1913 (1971) Physics Department, Stanford University, University, California 94305 Asthe shall be seen, finite gain photons is available under scattering. the process as scattering of virtual using the (Received 2020February in final finalform form21 21 August 1970) (Received February 1970; 1970; in August 1970) Stimulated emission of Bremmstrahlung : transition the appropriate conditions from therelate far-infrared through Weizsacker-Williams method' to the of laser-type the visible region raising the possibility rates toto the more easily rates for Compton The Weizsacker-Williams methodis isused used to to calculate calculate the gain due thethe induced emission ofcalculable radiation The Weizsacker-Williams method the gain due to induced emission of radiation S TIM U L ATE D EM ISS ION 0 F MAG NET I C B REM SST R A H L U N G 1913 electron through periodic transa single electromagnetic mode paralleltoto the the motion motion ofofascattering. amplifiers and oscillators thesegain frequencies with the As shall bea seen, finite is available under arelativistic relativistic electron through a at periodic transinto a into single electromagnetic mode parallel through the visible region raising verse dc magnetic field. Finite gain is available from the far-infrared further possibility of partially coherent radiationthrough sources is available from the the far-infrared through the visible region raising verse dc magnetic field. Finite gain appropriate from far-infrared at these frequencies further the possibility of continuously tunable amplifiers and oscillators We have omitted from this analysis the consequences that conditions usefulwith gainthe would bethe available to beyond at these frequencies with the further the possibility of continuously tunable amplifiersinand oscillators and x-ray to beyond 10 keV. in the ultraviolet of partially coherent radiation the ultraviolet and regions to beyond 10regions keY. possibility of laser-type the visible region raising the possibility of the absorption occurring in thesources nuclei lying just 100 A.x-ray possibility of partially coherent radiation sources in the ultraviolet and x-ray regions to beyond 10 keY. numerical examples considered. ON 0 F MAG NET I Several C B REM SST R A Hthe Lare Uabsorbers. N G 1913effect of this In geometry, the devices suggested herein with resemble the examples surface ofare The amplifiers and oscillators at these frequencies the ACKNOWLEDGMENTS Several inside numerical considered. 5 process is to reduce the reflection coefficient within further the by Motz in 1950 the undulator structures proposed possibility of partially coherent radiation sources I wish to thank Professor W. M. Fairbank for his At leastthat two authors have considered thean where onsequences useful gainline would beR= available beyond Mossbauer from 1 to in todetail for angle of 6 and subsequently developed by him as sources to beyond 10 keV.of in theencouragement ultraviolet{j=vz/e ofand this x-ray analysisregions and to acknowledge my process of induced bremsstrahlung radio and optical where At least two authors have considered in the detail the coefficient incidence of 0.47° while at leaving reflection lying just 100 A. millimeter wave and infrared radiation. However, withthe Professor H. A. Schwettman who has In discussions geometry, devices suggested herein resemble and due to thethe scattering of an electron by this outside line essentially unchanged. While would fect of this frequencies process of induced bremsstrahlung at radio andbeam optical {j=vz/e ACKNOWLEDGMENTS had a concurrent and independent interest in the '1'=structures 1/ (1substantially reduce theelectron numberconcluding of reflected photons, Motz' proposal was{j2)1/2. entirely classical requiring a5 cores in neutral and ionized matter t within the the ion by Motz in 1950 the undulator proposed and frequencies due to the scattering of an beam by of a free-electron laser. In this 6application to the thank Professor W.still M.appears Fairbank for his enough bunched estimated be large to an angle of thatI wish appreciable gain was flux available under tofavorable beam harmonically related toasunique the magnet 1/recognized (1{j2)1/2.the and subsequently developed him sources of the ion cores in neutral and ionized matter concluding In the limit these fields approach inby detail those he potentially encouragement of analysisdeals and to acknowledge my the angular partlcularly, '1'= beThis of this experimental interest provided that n coefficient conditions.1-3 analysis with the radiation not apply toin the process of period. do of real photons moving associated withThese a wave packet millimeter wave infrared radiation. gain was available under favorable properties forrestrictions the and construction of such a device of However, the discussions Professor H. A. beam Schwettman who has spread in theelectron reflected beam due to imperfections in the e this that would appreciable emitted by awith relativistic moving through In direction the limit these fields in detail those the -proposal z'. Assuming that theapproach matrix element for stimulated emission. electron beam in was the superconducting linear accelerator a concurrent and independent in the conditions.1-3 This analysis deals thewillradiation mirrors could be keptwith at a interest minimum. Motz' entirely classical requiring a ed photons, ahad periodic transverse dc magnetic field. We consider ofis real photons moving in this associated with a resemblance wave packet built at Stanford. Itchanging is also my pleasure to iscloser a continuous and slowly of the aNote free-electron Inmoving this application to be function found between Added in Proof. The classical result scattering for bunched the Abeing e enough to the emitted byprocess a relativistic electron beam through as scattering oflaser. virtual photons using the beam harmonically related to the magnet acknowledge the contributions of R. H. Pantell, the Assuming that the matrix element for of thedirection initial photon mass, in the limit that the photon partlcularly, radiated he recognized the potentially unique energy calculated using the synchrotron radiathe angular paper and that of Pantell, and the PuthofF who Weizsacker-Williams method' field. to relate the transition a periodic transverse dc magnetic We will consider not apply of period. These restrictions do Soncini, S. isA. Johnson, Levinson, W. A. Little,toand L.process V. energy in the electron restM. frame is slowly large in changing comparison properties fortion the formula construction of(38)] such is a device of the a continuous and function scattering [Eq. also proportional to the ctions the in the rates as to the scattering more easilyofcalculable rates for using Compton proposed the use University, of mass stimulated Compton process virtual photons the with Knight of Stanford andexpressions of A.inverse Yariv of the stimulated emission. electronthe beamsquare in theofsuperconducting linear accelerator the photon mass excess, the zero the magnetic field strength provided that an initial of the photon mass, in the limit that the photon be seen, finite gain is the available under scattering. As shallmethod' but werecan restricted inbeobtain gain tothe the infraredthis by scattering California Institute of Technology. Weizsacker-Williams relate transition being built account at Stanford. Ittoisof also to is taken the my shiftpleasure in wavelength of the (for Compton scattering) be is used to A closer resemblance to found between sult for the the energy in the electron rest frame is large in comparison appropriatethe conditions from theoffar-infrared through the low microwave photon densities obtainable at acknowledge contributions Pantell, the more emitted easily calculable rates forH.(38) Compton radiation. If WlO inR. Eq. is understood topaper be desired transition rates. otron rates radia- to andMarcuse, that ofexcess, Pantell, Soncini, and PuthofF who the visible region raising the possibility of laser-type with the photon mass the mass zero expressions 'D. Bell System Tech. J. 41,1557 (1962). the frequency of the beam S. A.AsJohnson, M. Levinson, W. backscattered A.isLittle, andphotons L. V. at a The virtualD.photon mass excess can be computed in shall be seen, finite gain available under scattering. present as compared to stimulated the number of virtual photons onal to the amplifiers Marcuse, Bell System Tech. J. 42, 415 (963). proposed the use of inverse Compton and oscillators at these frequencies with the 2 (for Compton scattering) can be used to obtain the 'Yomc in the weak field limit and if the actual energy of Knight of Stanford University, and of A. Yariv of the M. V. Fedorov, Sov. Phys. JETP 24, 529 (1967). the laboratory frame since it is a scalar invariant: ded that the an appropriate conditions from the far-infrared through in atransition strong dcrates. magnetic orTheory electric field. further possibility ofenergy partially coherent radiation sources 4 W. Heitler, The Quantum Radiation (Clarendon but were restricted inof gain to the infrared by scattering beam is selected to compensate for the wavedesired California Institute of Technology. ngth of the 2 2 2 2 Oxford, England, 1960), p. 414. ' of laser-type the visible raising the possibility and x-ray regions to beyond 10 keV. in the region ultraviolet e = m c4=ELp (hw)L (qh)2e (2) . v and length shift due to the magnetic field [Eqs. (43)The thevirtual low microwave photon densities obtainable at photon mass excess be computed in rstood to be H. Motz, J. I.App!. Phys. 22, 527 can (1951). TRANSITION RATES amplifiers and oscillators at these frequencies with the In geometry, the devices suggested herein resemble 'D. Marcuse, Bell System Tech. J. 41,1557 (1962). (44)], then in the region of validity of Eq. (38) the Motz, J. App!. Phys. 826 (1953). invariant: s at a beam the present laboratory frame since it 24, is a H. scalar asH. compared to the number of virtual photons Since w= 0 in'H. the lab frame: 5 2 D. Marcuse, Bell System Tech. J. 42, 415 (963). R. Pantell, G. Soncini, and E. Puthoff, IEEE]. Quanby Motz in 1950 the undulator structures proposed further possibility of partially coherent radiation sources A vector potential is given by radiated energy per magnet semi-period if the actual M. V. Fedorov, Sov. Phys. JETP 24, 529 6(1967). tum Electron. 905 (1968). or electric field. in a strong dc magnetic and subsequently developed byoftohim as (Clarendon sources 2=qhe. e2 iQuantum i 4,mv 4 W. Heitler,and The x-ray Quantum Theory Radiation beyond 10 keV. the ultraviolet e2== (hw)L m vP.2c4=ELp (qh)2e 2(Benjamin (2) . (3) 8 R. Feynman, Electrodynamics New 2 regions 2 ofq r the in waveA(z) Re[(Bo/q)eiqz]y Oxford, England, 1960), p. 414. ' CB)2. York,1962),p.94. ' millimeter wave and infrared radiation. However, d E ('Yo4e )(X s. (43) In and geometry, the devices suggested 2 I. frame: TRANSITION 5 H. Motz, J. App!. dwdfJ Phys. 22, 527 (1951).herein resemble Weizsacker-Williams method would RATES then J. D. Jackson, Classical Electrodynamics (Wiley, be New York, c 4mc Motz' proposal was entirely classical requiring a5 The Since w = 0 in the lab Eq. (38) the 'H. Motz, J. App!. Phys. 24, 826 (1953). 1962), p. 481. in the frame yields a magnetic field by Motz in magnet 1950 expected the undulator structures proposed to!(FELs belab applicable inI. the limit: E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs and !ERLs), Hamburg, Germany,Dokl. 31 !May –10Nauk. !June, SSSR 2016 bunched beam harmonically related to the 7 R. H. M. Pantell, G. Soncini, and H. E. Puthoff, IEEE]. QuanL. Landau and Pomeranchuk, Akad. A vector potential given by This result remains valid for arbitrarily large magnetic 6 and subsequently developed by him as sources of e2 tum Electron. 4, 905 (1968). 92, 535 (1953). i Vmvi mve2i i =qhe. not to(Benjamin of period. Thesefields. restrictions do B= xA= -i) Boeiqz]i. Evidently the apply increase inthe theprocess scattering hv=an'Yhqe» qhe, (4) of (3) jeudi 2 juin 2016 8 R. P. Feynman, Quantum Electrodynamics New transition 11 For account of the=Re[( experimental features this II.2 The FEL quantum approach z'. 2 3 5 7 3 9 10 and where In the lim and associated the direct In the lim scattering associated of the init the direct energy in with the p scattering (fortheCom of ini desired tr energy in Thethe virp with the (forlabora Com desired tr The vir Since w= the labor The w We Since = expected The We which red expected transition electron frame red w which E= field transition period Aq electron set equal frame w of thisE an = field With period Aqa beam the set equal in this the ele of an With a beam the Since the in the ele with E the energy of the initial photon beam, θ the angle between the CBS photons and the electron beam II. The invention of the Free Electron Laser concept trajectory. The energy of the relativistic electrons can easily be changed, so the CBS radiation could be tuneable ph www.lunex5.com First analysis of the stimulated Compton Backcattering ware carried out [126]. J. M. J. Madey had the idea to mak the phenomenon more efficient by using the magnetic field of an undulator [123]. He considered that ”Relativisti electrons can also not tell the difference between real and virtual incident photons, permitting the substitution of strong, periodic transverse magnetic field for the usual counter-propagating real photon beam”[144] . He was aware o J. M. J. Madey.: Stimulatedtheemission of Bremmstrahlung in a periodic magnetic field; where J. Appl. radiation Phys., 42, from 1906--1913 (1971)has been observed. Th theoretical [23] and experimental [24] work of Motz, bunch beams J. M. J. Madey, H. A.beSchwettman, W. M. Fairbank, IEE Trans. Nucl. Sci. NS-20 (1973) 980 fields can the one generated by an undulator. II.2 The FEL quantum approach 4.4.2 FEL quantum Virtual photons : associated to theThe magnetic field approach Weisäcker-Williams approximation: According to the Weisācher-Williams approximation, the undulator field of period λu can be assumed to be a plana Undulator : similar to the fieldwave of a ofplanar wave of wavelength ; λu virtual photons. By Lorentz transformation, the wavelength λ � of planar wave in the moving frame of th electrons in the undulator, is given by : Fields in the moving frame of the electrons in the undulator Undulator wavelength in the electron ‘s frame : λu/Υs = λ’ λ� = λu γs (79 the electrons see the magneticPhoton field as a planar wave emission and absorption are forbidden by conservation of energy and momentum. For free electrons, on can then consider a two photon process, such as Compton scattering, as shown in Fig. 22. The emission is then again given by the Doppler according to : absorption forbidden dueeffect, to the conservation Photon emission / of energy and momentum => for free electrons : two photon process: Compton scattering emission : Doppler effect λ = λ’ / (1 + βs) Υs= λu/ 2 Υs2 = λu/ 2 Υ2 Stimulated Compton scattering gain : transition rate(diffusion) - transition rate (absorption) does not depend on Planck constant. E. Schrödinger, Annalen der Physik IV, Folge 82, 257 (1927) P. L. Kapitza, P. A. M.ab Dirac, Proc. Cambridge Phys. Soc. 29, 297 (1933) H. Dreicer, Phys. Fluids 7 (1964) 735 R. H. Pantell, G. Soncini, H. E. Puthoff, Stimulated Photon-Electron Scattering, IEEE Jounral of Quantum Electronics 4 (11) 906-908 (1968) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 The original calculation, performed in [123], is not reproduced here. One prefers nowadays to use� a classical approach, which is simpler and which can explain the FEL in the majority of cases. s In the Raman regime,ofthethe scattered wavenumber k is the sum / difference o II. The invention Free Electron Laser concept plasma wavenumber k�p , leading to the Stockes and anti-Stockes lines : www.lunex5.com 4.4.3 The FEL regimes Synchrotron andpulsation, Free Electron Laser e in the electron frame, with ω p radiation the plasma ωr the resonant pulsation, and ωs the Synchrotron radiationand andFree Free Electron LaserElectron II.3 The nchrotron radiation and Free LaserFEL regimes Synchrotron radiation Electron Laser � is � � The FEL can thus be described as a Stimulated Compton Scattering, as shown in Fig. 23. If the electronic density = k ± k k The Raman FEL regime s i p large enough, a plasma wave can develop. 31 31 The RamanFEL FELregime regime Synchrotron radiation and Free Electron Laser The Raman Synchrotron radiation and Free Electron Laser � is the sum / difference of the incident wavenumbe In the Raman regime, the scattered wavenumber k Raman regime k� and � Compton regime s In the Raman regime,In theThe scattered wavenumber k is the sum / difference of the incident wavenumber of the the laboratory frame, it comes: � s i k� and Raman FEL regime � In the Raman regime, the scattered wavenumber k is the sum / difference of the incident wavenumber of the s to the Stockes and anti-Stockes lines : i , leading plasma wavenumber k p , leading to the Stockes and anti-Stockes lines : plasma wavenumber k� �pThe Raman FEL regime to the Stockes lines : plasma wavenumber k p , leading In the Raman regime,and the anti-Stockes scattered wavenumber ks� is�scattered the sum / wavenumber difference of the incident wavenumber k the k s′ is the sum / � is� the� sum / difference of the incident waven �anti-Stockes � the�wavenumber Inplasma the Raman scattered k , leading Stockes and linesincident :s =ω wavenumber ± k ks�� = kto = ki ± kofp the k s s The scattered wavenumber ks′regime,k�pthe ω ± ω(83) difference wavenumber i� p� s i p (83)ki′ and = k ± k k � s i p � wavenumber to the Stockesofand anti-Stockes lines : kp, leading to the plasma k p , leading �the �: equals incident wavenumber k ′: the plasma wavenumber i avenumber equals the incident wavenumber k In the klaboratory frame, it comes: � � � s i In the itlaboratory frame, it comes: p = k ± k k In the laboratory frame, comes: s i p Stockes lines where the plasma pulsation ω is given byand : anti-Stockes he Raman FEL regime the Raman regime, the scattered wavenumber k is the sum / difference of the asma wavenumber k , leading to the Stockes and anti-Stockes lines : p ks� = ki� ± k�p ± ωs = ωi(82) � ω p �� In the laboratory frame,ωits comes: = ωi ± ω p (84) ωs = ωi ± ω p � � (84) In the it comes: where the plasma pulsation ω plaboratory is given by frame, : si ± ω p i n ep2 ω = ω J e s where theω plasma pulsation ω is given by : 23 Stimulated Compton Scattering scheme in the electron frame, with ω the plasma pulsation, ω the resonant pulsation, and ω where theFig.plasma pulsation is given by : e e p r s the p p � � scattered pulsation ωp � = = 2 3 3 � ne eω p is given � � Jby where the plasma pulsation : ωs = ωi ± ωε ee p o mo γ ε m cγ o o ωp = (85) 23 = 2 n e J e 3 � n e J e e e e e ε m γ ε m cγ � o o o o ωp = =is given (85) ω =cγ 3: = where the plasma pulsation ω 3 2 p 3 3 εo mo γ εopmoby Joecγ e εothe mno eγecurrent εo mdensity with n the electronic density and J Je = ne ec . ω = = with neThe theCompton electronic density and J the current density J = n ec . p e e e e e 3 3 � � FEL regime εo mo γ εo mo cγ done by the Practically, one considers that the FEL is in the plasma regime if the number of plasma oscillation with ne the electronic density and J the current density J = n ec . 2 e e e with ne the electronic density and Jthee that the current density ne eciplasma . nsein Je eNpp regime Practically, one considers the FEL if the num e e= the In the Compton regime, the scattered wavenumber ks� equals incident wavenumber ki� :isJ electron whileone it travels intowith the undulator is at least one. ω = = done by the Practically, considers that the FEL is in the plasma regime if the number of plasma oscillation N ne the electronicthat density and Jeisthe current density Je =3 nif . number pplasma e ecthe 3p of plasma oscillation N Practically, one considers the FEL in the regime ε m γ ε m cγ Practically, one considers that the FEL is in the plasma regime if the number of plasma oscillation o at o least one. o � � the undulator is electron while itoneistravels into electron while it travels into the undulator at least one. �in the plasma (82) kthat Practically, considers regime if theonumber of plasma oscillation N p s = kithe FEL is while itwhile travels into the undulator is at least one. by the electron it travels into the undulator is at least one. Np doneelectron p Nuthe λu ωundulator Je e one. Nu λu into p andNJu λuthe electron it=travels atcurrent least with newhile theNpelectronic density Je =� ne ec . = e is� =density � 3 λ 2πc 2πc ε m cγ N λ ω N λ λ J e N o oe u that u p the FEL u pu u u �if the number of plasma oscilla Practically, plasma regime = Nu λuis inNthe Np one = considers = λ ω N λ ee p Nu λu Je e ucγ u3λN pωupλu N u uλ u u Nu λJJueeω N λ N λ 2πc 2πc ε m u u u u p o o = N = = electron while it travels into the undulator atpleast one. = 2= p N p = is N Thus N p > 1 if =2πc 33 =e λp λp = 2πc 2πc εεoom e oocγ 2πc m cγ λp 2πc 2πc εo mo c � Thus No > 1 if 2 3 3 p 4π εo mo c γ 3 Nu λu 3 N λ ω λ J e N Thus N pThus > 1Nifo >if 1 if (86) Je < u u p u u e o o o o 2 λ 2N 2eN 3 3= = = u 4π ε 3 o mouc γp Thus No > 1 if Je < λp 2πc 2πc ε m cγ o o (86) 2 ε2 εm 3cγ3 γ3 3 periodic transverse 4π m M.manque Kroll, P. L. Morton, M. N.XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Rosenbluth, Stimulated emission from relativistic through a spatially o o AN CLIO 4π c eNu2 λu2 electrons passing o o J < e < J 2λ 2 magnetic field., Phys. Rev A 17 (1978) 300 e e e e e eN Thus N > 1 if 2 2 o u u eNu λu 2 3γ 3 manque AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 4π m c M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 ε !June, 2016 o o manque AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX J < 2 3 3 manque AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX jeudi4.4.4 2 juin 2016 The FEL classical approach 4π εo meo c γ 2 2 ks� = ki� k = k ±k In the laboratory frame, it comes: ω = ω ±ω where the plasma pulsation ω is given by : ω = � ne = ε m γ � Je ε m cγ with n the electronic density and J the current density J = n ec . Practically, one considers that the FEL is in the plasma regime if the number o I; (Ig II. The invention of the Free Electron Laser concept analysis of the small-signal regime a free-elecI((s) = 2c ~oh((s) of+((s)l the amplification is due to stimulated scattering www.lunex5.com and )'o is the classical radius of the electron. The term sin(pL/2)/(pL/2) appearing in the gain formu n distribution. la is a, consequence of the finite length of the cavity. As pointed out by Sukhatme and Wolff, this finit the momentum conservation ness implies a field of period a pure electromagnetic field law is relaxed, so that electrons with a momentum with ~, by that can scatter light from &; to w, Et is therefore natural to consider two cases, in this approximation cavity bandwidth re- Weizsäcker-Williams of wavelength : limits. In the large-cavity small-cavity limit, the electron momentum namely the large-cavity and Vuat)MF. MovRλu1Y PHYSICAL LETTER ireplaced by a pure electromagnetic REVIEW' field of wavelength for extreme relativistic = limit : the static undulator fieldh7,ofNt period broad the which distribution to bandwidth, can is compared cavity therefore be very approximated =(1+P)Z, 2~„ ~, by = small-cavity limit transverse to the opposite corresponds current case, where the initial electron mome λi = (1 + 6βfunction. J s) λu ≈ 2λThe u t =ch, ((o, =ch, is the frequency of the incident (scattered) field. hin tum distribution function and F(P,(d, ) can be taken as )a () function, andof phase approximation, and neglect the depletion of t ing amplitude Case erioda pure transverse (2 F(t.) =I{P.-Po) sumed to be electromagnetic very intense.field or => Usual classical problem, to scattering at a constant rate inside thedistribuelectrons be injected limit of a homogeneously lat Taking thethe broadened medium. We shall consider This corresponds to of thiscav only the e We the describe motion electron electron motion : collisionless relativistic complicatedofbythe the Stanford relativistic experiment. nature of to the condition ter since it corresponds case, adiation the collisionless relativistic t) P, by f(x, Boltzmann equation, with P the canonical h'"=n, F(t), the ), particles Maxwell With formula, becomes the gain (29), anaBoltzma, nnx equation' momentum, the position equations the electron and is the initial electron mom where is density, F(t), n, ) Relevant radiation : off, ~ ' = n (sing/)))'+ (sinn/))}'yo'[I +(Uo/c)'j (3 sf mh, h; af o'Uo', der I;correction «f = af +x] back scattered, with a Doppler shift h is to d'g cL -h; h, =0, +P]' (3) ' dt Bt Bx, BP& of the wavelength ewhere vo H~/OPO an '! — = h")(z, expl-ia(d(t c. , n, )j+c. z/U.noting p„f) reduced distribution in Maxwell eq. that that Development where ofP the is reduced the canonical momentum, x posithe and with and term obtain, Eq. (18) distribution in perturbations diaz n = p. L/2. is small-signal »k& for y»=>small and a: incident dot expresses tion, theory total derivative with 1, signal gain and scatteredthe modes are kept Thetime. the bracket secondThe termtotal inside is of the orA'" respect to number of electrons d n of der New hyp : fiI II.3 The FEL classical approach . 24- ' —— '„', — ' ' N(t) a. ' is - slowly varying amplitude and phase (sin))/r)) )(;/2)(L && 1. = J«3xf«'Pf(x, - depletion of the incident field neglected N(t) P, t). , (32) Thenetpoint η=0 : no gain g =0 corresponds to the condition for (4) rexact Therefore, except for g = 0, we can neglect this η<0 : v>v conservation of momentum, and, at this in Raman scattering o, gain, eq. of Stockes line mag- => electron The Boltzmann is coupled via the trans- η>0 : v>vo, absorption, eq. of anti- Stockes line equation density fluctuations (bunching) responsible the scattering verseforcurrent J~ to the Maxwell s +V A —e the coefbora- where A is equations We observe that h(') describes the electron density fluctuations 8 A/st = —poJr, scattering. The Gain is produced by a bunching of (5) the electronic density in presence of a field Introducing h into the Maxwell equation, and integrating the vector potential, and small-signal gain n, defined by F.Jr(x, A. Hopf, Scully,P-, W. H. Louisell, Classical theory of a(6Free Electron Laser, Opt. Comm. 18 (4) (1976) 413-416 ef«'PM.vrO.f(x, t)P.=Meystre, F. A. Hopf et al., Classical theory of a free-electron laser, Phys. Rev. Lett 57 (18) 1215-1218 (1976); t). the electron charge, and v~ the transHere, M.e E.is Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 ion verse component of the electron velocity. jeudi 2 juin 2016 (bunch over the len www.lunex5.com II. The invention of the Free Electron Laser concept II.3 The FEL classical approach Appropriate magnetic field description Studies on radiation from electrons traveling through a static transverse periodic magnetic field : classical, semiclassical, and quantum field theories. Stimulated emission rates and laser evolution equations describing exponential gain and saturation. One-body classical Lorentz force equation in the presence of periodic magnetic field and a plane electromagnetic wave. Phase space paths for electrons are related to those of a simple pendulum and describe laser gain, saturation, and coherent electron beam modulation. A single particle classical theory : amplification due to the single electron stimulated Thomson scattering. necessary tool for the description of the electron dynamics in a storage ring with a free electron laser device. Saturation : Jacobi elliptical functions W. B. Colson, Theory of a Free Electron Laser, Phys. Lett. 59A, 187 (1976) W. B. Colson, One body electron dynamics in a free electron laser, Phys. Lett. 64A (2), 190-192 (1977) W. H. Louisell, J. F. Lam, D. A. Copeland,W. B. Colson, "Exact" classical electron dynamic approach for a free-electron laser amplifier, Phys. Rev. A 19 (1) (1979) 288-300 W. B. Colson, C. Pellegrini, and A. Renieri, editors for the "Free Electron Laser Handbook", North-Holland Physics, Elsevier Science Publishing Co. Inc., The Netherlands (1990). A. Bambini, A. Renieri ,The free electron laser : A single particle classical model, Lett. Nuovo Cimento 21, 399-404 (1978) A. Bambini, A. Renieri , S. Stenholm, Classical theory of a free electron laser in a moving frame, Phys. Rev. A 19, 2013-2025 (1979) gain scheme electrons + Undulator + Electromagnetic wave Lorentz equations electron bunching Maxwell eq. coherent emission M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Marie The FEL6resonance Fig. 25 Intensity spectral distribution for different values of N , in red (resp. green), the undulator number of periods II. The invention of the Free Electron Laser concept u multiplied by 5) with respect to the blue case. In the classical [124], let’s consider plane waveoscillations traveling in the sameh Theapproach electrons execute smooth asinusoidal in the radiation, is stored in an optical cavity (see Fig. ??a), ena electricII.3 field in the trajectory plane. This wave can be the spontaneous emission FEL classical thatThe the radiation is kept inapproach the same emitted cone. In addition, t resonator), an external optical wave properly tuned. direction. optical wave on many passes. FEL oscillators cover aMarie-Em spe at or twice the pulsation in the longitudinal The interfere The FEL resonance 6 As shown in Fig. 26, the electron is resonant with the light wave of wavelength Themirrors resonance for the wavelengths when the n In the classical approach [124], let’sλconsider awhich plane wave:traveling in thethe same direction as the ele to the VUV, where are available. After theoreti by λ , the wave has travelled by λ + λ or more generally, with n being an integer u u r The electrons execute smooth sinusoidal oscillations the hor Consider a plane wave travelling in the same direction as the electron, with field in the trajectory plane. electric field in the trajectory plane. This wave its canelectric be the spontaneous emission (onein pass or stored The travel times the optical electrons resonator), anby external wave properly tuned.photon writes : The electron is resonant with the wave if :spent that theorradiation isIR kept inand thethe same cone. In addition, ther concept in 1971, the first FEL wasemitted achieved in 1977 www.lunex5.com shown in Fig. 26, the by electron with lightc(1 wave− of wavelength nλthe βs )t λr if, when the elect while the electron progresses by λu, theAswave has travelled λu+ isλ,resonant (λu+ nλ) n= to atλutwice the longitudinal The interferenc by , the wave has pulsation travelled by λuin + λthe generally, withdirection. n being an integer λu + nλr . r or more λ + nλ λ u r The travel times spent by the electrons and the photon uwrites =: (Stanford, USA)thein the oscillator configuration. ACO (Or λu for which : wavelengths when the λ n with n an integer, βs the longitudinal reduced velocity of the v c s λ λ + nλ the second worldwide FEL (first visible radiation) in 1983 = damental resonant wavelength is obtained bor n = 1, i.e. for λ1 = v c so : nλprogresses n = c(1 −byβsλ)t, the wave has travell Fig. 26 Undulatorsoresonance condition : when the electron : λ gets the expression of the the of βand monic generation [?] in the UV VUV [?], followed byre s , one longitudinalUsing velocity of the expression electrons 1λ ( β ) ele λλ u:11− − λβu )(1(1+ β−velocity ) βs )(11+ − of ββsthe 1 s theto − β βs λ (1reduced with n an λ integer, longitudinal uλaccording and its harmonics, ( = λ = − 1) = ) = λr [?]. = λiu = ( First −β 1) = )n = β (1(+ β ) n n β β (1 + β ) FEL (Orsay, France) FEL applications started damental resonant 1, + i.e.βsfor n βswavelength n is βobtained nbor n = βs (1 ) λ1 = λ s to + λ /2v u s 2 the expression of the reso Using [?, the expression of βs , one gets K λ UV-FELsLet’s inconsider biology ?] and surface science [?] in 1993 uβ ≈ 1, the udenominator of the first the case of a planar undulator. With s (1 + ) and its harmonics,Planar according nλ to :n = 2 K 2γ 2 the resonant wa 1 + in the numerator, 2 and built developing the expression of 1 nm − βs2 =[?]. were then down to 190 γ γ 2 u u r s u r u s s u s 2 s s 2 u 2 s s u 2 s s s Ku λu radiation can be The wavelength λn of the emitted nλn = 2 (1 + ) varied by a 2γ→ 2 − 2 to + λ /v undulator magnetic field (by changing λthe permanent m → − Kfor u gap u u s λr = radiation )be varied by a mo (1 +v δW = E dt the emitted can Thepower wavelength λn of 2 vices or the supply current for electromagnetic insertion d 2nγ 2 undulator magnetic field (by changing the gap for permanent mag domain, observer receives a train of Nu magnetic periods wh In the case of athe helical undulator, the resonant wavelength comes velocity : // E vices or the power supply current for electromagnetic insertion dev ered asdomain, quasi-continuous emission of radiation with periods respectwhic to t 2 the observer receives a train of N magnetic λu u K 2 λ λru = (1 +the Kuwith radiation. radiation spectrum, square of 2 transfo 2to the u )Fourier 2 ered The as quasi-continuous emission of radiation respect 2nγ Helical nλ (1 + θ ) + γ = n 2sinus then composed of aradiation series ofspectrum, square centered on o radiation. The squarecardinal, of the Fourier transform 2γ 2 Application numeriquexxxxxxxxx prendre les M. E. Couprie, CAS SchoolXXXX Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !Mayparametres –10 !June, 2016 de la manip d then composed of a series of square sinus cardinal, centered on odd ”homogenous” relative linewidth of the harmonics is then given FERMI, E XFELXXXXXXXXXXXXXX case : jeudi 2 juin 2016 u (see Fig. ??a), enabling interaction with the II. The invention of the Free Electron Laser concept www.lunex5.com cillators cover a spectral range from the THz The FEL e. After the theoreticalII.3 prediction ofclassical the FEL approach Energy exchange => bunching s achieved in 1977 on the MARK-III linac => amplification Light wave-electron interaction figuration. ACO (Orsay, France) [?] provided The amplitude of the interaction only depends on the The FEL oscillator : e radiation) in 1983 and first FEL based harlongitudinal position of the electron in the electron the historical configuration UVbunch [?], followed by results λr. on the SuperACO with the periodicity optical multi-pass, low gain regime The electronstarted tend to bunch given positions, pplications in thealong infrared and in the separated by λr. e science [?] in 1993.Various FEL oscillators Bunching (λr separation) takes place by velocity modulation (electrons set in phase). → −→ = E− v =0 dt for λ= λr, there is no average energy • (29) exchange at first order: half of the electron gain energy, half of them loose energy Ku2 2 2 (1 + + γ θ )to occur, λ should be slightly (30) For the interation 2 from λr : different one finds that for λ> λr amplification (gain and beam e ofdeceleration) mirrors, short wavelength FEL are usu(beam(SASE) acceleration) for λ< λr absorption mplified Spontaneous Emission (see GαLond2/Υ3 Optical feedback with an optical cavity pontaneous emission at the input of the FEL CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 saturation M.inE. Couprie, a single pass after a regime of jeudi 2 juin 2016 www.lunex5.com II. The invention of the Free Electron Laser concept Gain expression II.3 The FEL classical approach Gain expression mall signal gain is given by : Small signal gain : �2 ∂ Ku2 Lu 3 � 2πe2 2 ) sinc G=n ρ ( (ξ ) − J (ξ ) (πNu η) J n−1 n+1 e 2 2 2 εo mo c λu γ ∂γ e finds here on thethemain ofwave the isgain. Depending sign ofcharacteristics (λ − λr), the optical either absorbed to the benefit of a gain of kinetic energy of the electrons, or as is amplified to the of detriment of the energy ofThe the electrons. e gain varies the inverse the cube ofkinetic the energy. higher the energy, the lower the gain. But, ac onance condition, short wavelength operation requires the use of high electron beam energies. In con G varies as the inverse of the cube of the energy. The higher the energy, the lower the gain. But, according to the ame undulator length, gain is operation smaller requires at shortthewavelengths thanbeam at longer ones. resonance condition, shortthe wavelength use of high electron energies. In consequence, for a same undulator length, the gain is smaller at short wavelengths than at longer ones. The gain is proportional to the electronic density. The more electrons interact, the larger the gain. For short wavelength FELs where the gain is naturally small, one should employ beams with high electronic densities. The gain is proportional to the beam current. The gain is proportional to the third power of the undulator length, it seems that the longer the undulator, the higher the gain. As the undulator length, the gain width also decreases by 1/nNu, because of the interference nature of the interaction. Temporally, the light pulse should remain in the longitudinal bunch distribution, for the interaction to occur. Similarly, both the optical light and electron bunch should overlap properly all long the undulator propagation. To account for these effects, letʼs introduce some correction factors in the gain. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 wo 2 wo 2 1 + ( ) 1 + ( ∆ λ 1 perfect the laser transverse modes and the 2σx 2σz ) ven by : transverse overlap between ( )hom = ∆ λ (164) 1 λn mode nN and σz . Considering a laser of TEM00 of w the transverse u )hom A first reduction factor can from a non perfect transverse overlap between o , occur ( waist = (164) the www.lunex5.com Besides, the spontaneous emission broadening due to λntheofMadey’s 1 according u theorem, transverse dimensions thenN electron beam σxterms and σz(163) . Considering a laser of TEM00 s the inhomogeneous broadening from different contributions. The two first are related to the � Ff = � result II.3 FEL classical approach affect directly the gain. The homogeneous linewidth given : are related to the w wis o The o given 2 factor 2 from whereas the inhomogeneous result different contributions. Theistwo firstbyterms filling by : 1 + (broadening ) 1 + ( ) eam emittance. 2σx 2σz Gain correction terms electron beam emittance. 1 ∆λ 1 2θ 2 � � = (163) 1 ∆ λ γ • Transverse filling factor spontaneous : Non perfectemission transverse overlap due to ding the the Madey’s theorem, broadening energy spread and emittance ( ) = hom 2 2 � Ff =λn� wo 2 wo 2 ( (TEM00 )div =mode∆ofλ2 waist wo)γ θ (165) nN u the laser transverse modes 1 + homogeneous ( 2σ ) 1 + ( ) K gain. between The linewidth is given by : w wo 2 (165) λn o 2 ( u )div = 2σz x 1 + 1 + ( ) 1 + ( 2 Ku 2nx and σz. 2σx 2σz ) λ and the transverse dimensions of the electron beam σ 1+ 2 whereas the inhomogeneous broadening result from different contributions. The two ∆λ 1 2K2 σ 2 2π ∆ λ electron beam emittance. ( : According )hom Besides, =due (164) • «Inhomogeneous reduction» the the Madeyʼs theorem, spontaneous emission broadening due to energy spread du u ∆ λspread m, spontaneous emission broadening to energy and emittance according the the Madey’s theorem, spontaneous emission broadening 2σ ) = (166) ( γ λ nN σ n u and emittance affect directly the gain. (166) = homogeneous linewidth is given by : λ 1 + the Ku2( gain. λu2 )σγThe n ewidth is given by : affect directly λn The twoγ first terms are related nhomogeneous broadening result from different contributions. to the γ 2 θ 2 ∆ λ Inhomogeneous contributions Homogeneous linewidth on and Free comes Electron ( )div = r contribution fromLaser thecomes electron beam energy spread. mittance. Another contribution from the electron beam energy spread. Ku2 1 ∆ λ λ • Electron energy spread • Electron beam emittance n ∆λ 1 1 +=2 ( ) hom ( )hom = (164) 2σ λn nNu ∆ λ 2 2 γ 2 2 2 � � ∆λ θ γ λn nNu ∆ λ 2π K σ u −1 N λ ∆ λ (165) 2σγ (167) ( )div =( λ )σ2 γ = ( γ )σ = u u (167) Ku = nF whereas the inhomogeneous contributions are given by : 2 λ 2 λn ( = ) λ 1 + K 1 + σ γ n 1 + 2g u u are given by : λ γ n σ s into anItinhomogeneous reduction factor F expressed as : l inh 2θ 2 results into an inhomogeneous reduction factor Finh expressed as : ∆ λ γ 2σ ∆ λ γ spread. )div = ( Another (166) )σγ = contribution comes from the electron beam( energy ∆λ γ 2θ 2 Ku2 λ λ γ ∆ λ ∆ λ ∆ λ 2 n n 2 2 � �−1 �−1 � ∆ λ 2( � )σ ��(165) 1+ 2 nal(gain)div can : � ( ∆ λ )(2λn �)−1 = be expressed ( λn )σas −1 ( ∆ λ )2 �−1 � 2 div γ � ) ( −1 λ 2 2 2 K n u 1 + beam energy. spread. λn σγ λ+ λnλ σ ∆ 2π K σ n div n = 1 + . 1 (168) butionλcomes fromF the electron u 1inh + Synchrotron radiation Free Electron Laser = 1 + and . 1 + . 1 + (168) ∆F λinh ∆ λ ∆ λ 2 2 2 2 ( ) = σ ∆ λ ∆ λ ∆ λ 2σ 2 2 2 ∆ λ ( λn )hom ( ) ( ) γ 2 λ2 ( λn )hom ( λn )hom ( λnλ)nhom ( 1 )+ K= λn hom λn hom u u σ γ � � 2 K2 2 σ2 2 2 λ γ � ∆ λ 2π 2σγ n ∆λ K ∂ 2πe L u u � u 3 2 ( ) = (167) σresults −1 Itthe into inhomogeneous reduction factor Foptical expressed as : η) ngitudinal overlap between theFλelectron bunch ofan length σ(ξ the optical wave should beNbe main(G (166) )longitudinal inh l σand 2electron 2 RMS λ The overlap between the bunch of RMS length σ and the wave should be be mainσγn=overlap ) sinc ρ F F = ( ) − J (ξ ) (πN J • Longitudinal : between electron bunch of RMS length l n+1 n−1 l u u 1 + K λ e g u f inh n u u 2 2 2 λ γ 2 n optical Fgshort = 1+ 2 in 2 and e light wave in inε advance N λu maintained. with respect the respect electrons, andelectrons, for short electron bunch distributions, ∆ λ electron Ku σ distributions, 2π bunch c by ∂ γ and the wave be light wave in tained. The light in be inuadvance byλNuuThe λutoγwith to the for o mwave oshould ( )σ ∆=λ 2 σl 2 2 an inhomogeneous factor Finh expressed as:for : short electron � advance Nuλreduction respect to the electrons, and ∆λ 2 � u with factor ∆λ 2 � is introduced as cape. newby correction F � �u−1λu� g is introduced as : itAcould escape. A new correction factor F λ 1 + K ) ( g ) ( ( −1 n 2 2 2 σ div γ λn λn λn )σ − bunch could escape. ∆ λ distributions, 2π Kuit σ Fλinh2 = 1 + ∆ λ(167) . 1 + ∆λ 2 . 1 + ∆λ 2 ( )σ = � 2(The ∆λ 2 � ∆ λ ∆ 2 2 It results into an inhomogeneous reduction factor F expressed as : ( ) � � � � inh ) signal : )σ −1 ( λn )divgain ( λn expressed −1 −1 can be ( λas ) ( λn 1 + K λλn2)σγ small hom hom λ λn hom n n II. The invention of the Free Electron Laser concept Finh = 1 + u ∆ λu 2 . 1 + ∆λ 2 2( λn )hom 2 3 2 ( λn )hom . 1+ (168) � � ∆ λ2 2 ∂� ∆ λlength ∆ λopti 2 �−1 2 � � � π r λ N K factor Finh expressedoasu: u The the electron bunch of RMS σ and the ) ( ) ) ( ( −1 l u longitudinal 2 σ div � � γ λ λ λ 2) F− J=n+11 + n 2 n n 2σ G = n J sinc F F F ρ (ξ (ξ ) (πN η) n−1 . 1 + . 1 + K 2πe L gwave e σinand f RMS inh inhbywave u mainThe lightlength in advance Nu λshould with respect and for 3to the 3 tained. ∆λ u ∆electrons, λ u ∆ λshort 2be 2 2 nal overlap between the electron bunch of the optical be u l 2 2 γ ∂ γ ( ) ( ) ( ) ) ρ F F F G = n ( (ξ ) − J (ξ ) J n+1 n−1 e g f inh hom hom λ λ λ n n n hom 2 ∆λ ∆λ 2 ( ∆λλn )2hom overlap between 2 electrons, introduced it respect could( escape. Fg isbunch wave in in advance by)2Nu λ�u−1 with to )the and foroshort electron � �A new correction � � 2 2 εo m c factor λdistributions, ∂ ( −1 u γ as : σγ λn div λn σ −1 introduced as :The radius Aectronic new correction factor FgrisCAS . 1+ .School 1classical +Free Electron!Lasers!and!Energy!Recovery!Linacs (168) M. E. Couprie, !(FELs and !ERLs),the Hamburg, Germany,bunch 31 !May –10 !June, longitudinal overlap between electron of RMS σl and the density, the of the electron. The filling factor F2016length represents theo 2 jeudi 2 juin 2016 hom ∆λ 2 o ( λn )homor : f ∆λ 2 ( tained. λn )homThe light wave in in advance by Nu λu with respect to the electrons, and for sh m energy loss can occur. The electron energy is decreased due to the kinetic energy loss enabling ∆ γSR 1 can also be reduced by the accumulated effects of emission re γo Ku2 ku2 Lu emission along the = −spontaneous www.lunex5.com γo 3 II. The invention of the Free Electron Laser concept (9 II.3 radius ThereFEL e classical−15 = is 2, 8210 approach . In the example of LCLS, the tuneable X-ray FE with re the classical electron 2 4πεo mo c2 ∆ γSR 1 2 2 ∆ γSR (94) reλγo K=u k0.15nm, u Lu in Stanford, one hasγ:o Ku==−3.5, L = 110m, E = 14GeV , it comes u u 3 γo = 0.17%. Saturation In consequence, 2it can happen that the resonance condition is no more fulfilled. A solution is to adapt the magne −15 . In the example of LCLS, the tuneable X-ray FEL l electron radius = 4πε embeam is 2, 8210 field to thereelectron energy, with the so-called ”tapered undulator” for keeping the resonance condition. One c 2 o oc • Electron beam energy loss (unsatisfied resonant ∆ γSR condition) apply a linear change of the magnetic field along the longitudinal coordinate. Ku = 3.5, λ = 0.15nm, L = 110m, E = 14GeV , it comes = 0.17%. u u γo - energy exchange can happen that the resonance condition is no more fulfilled. A solution is to adapt the magnetic - (spontaneous emission) am energy, with of theenergy so-called ”tapered undulator” for keeping the resonance condition. One can Increase spread of the magnetic field along the longitudinal coordinate. Besides, the electron bunching and interaction via an energy exchange with the optical wave leads to an increase the energy spread of the beam, reducing in consequence the gain (intuitively, the gain bandwidth gets larger becau ead of the inhomogeneous contribution and the gain distribution flattens). Increase of energy bunching• and interaction via anspread energy exchange with the optical wave leads to an increase of intuitively, gain bandwidth gets larger because the inhomogeneous contribution and the Slippage he beam, reducing inthe consequence the gain (intuitively, the gainofbandwidth gets larger because gain distribution flattens flattens). contribution and the gain distribution The slippage can stop the interaction : the electrons travel slightly slower than the photons, and one at the exit the undulator, the time difference becomes typically Nucλ . For not the radiation to escape from an electron bunch • Slippage thatinteraction the radiation: the advance should travel remainslightly in the peak of thethan distribution : duration σl , one can - The slippage canconsider stop the electrons slower the photons, and one at the of thetravel undulator, theslower time than difference becomes uλ/c. the interaction : theexit electrons slightly and typically one at theNexit ofFor not the σl Nthe u λ photons, < Nu λ an electron bunch of duration one can consider radiation to typically escape from σl ,an e difference becomes . For not the radiation to escape electron bunch ofthat the radiation c 10from c advance shouldadvance remain should in the remain peak ofinthe : onsider that the distribution peak of the distribution : orthe radiation σl c σl Nu λ Nu < (9 < 10λ c 10 which gives 300 periods for 1 nm radiation, 10 fs electron bunch, 300 periods, or for 1 µm, 10 ps electron bunch Z. Huang, K. J. Kim, Review of the free-electron laser theory, Physical Review Special Topics-Accelerators and Beams, 10(3), 034801. σl c 10λ M. E. Couprie, CAS School –10 !June, 2016 NFree<Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May(95) u jeudi 2 juin 2016 www.lunex5.com III. The first Free Electron Laser experimental results Gain Measured The first FEL amplification in Amplifier Experiment Exactly Matches The 24 MeV beam, amplification of a CO2 laser at 10.6 µm Amplifier Experiment Setup Undulator period : 3.2 cm, length 5.2 m single pass gain : 7 % VOLUME 36, NUMBER 13 PHYSICAL REVIEW LETTERS 29 MwRcH 1976 acceleWinding the Superconducting Helix tor output with a signal derived from the rator master oscillator. The local oscillator phase was set to maximize the signal due to spontaneous radiation by the electron beam. The relative response of the detector to 1300-MHz mod- ulation was determined by observing the quantum Quctuations in the radiation from a 600 blackbody. A 1-m Czerny-Turner monochromator was used to analyze the spectral distribution of the spontaneous radiation propagating at angles of up to 1.3 mrad relative to the magnet axis. A heliumcooled germanium bolometer was used with the monochromator to detect the spontaneous radia- tion. Observation of the spontaneous radiation and the gain included measurement of (1) the spectral distribution and polarization of the spontaneous radiation, (2) the magnitude of the gain, and (3) the dependence of the gain on the electron energy, the polarization of the stimulating radiation fields, the electron current, the magnetic field, and the optical power density. L. Elias et al., ObservationAccording of the stimulated of radiationfor by emisto theory,emission the wavelengths relativistic electrons in a spatially transverse magnetic field, Phys. sion andperiodic are given absorption by SPON T. POWER I 24 MeV ELECTRON ENERGY GAlN ELECTRON ENERGY FIG. 2. (a) The spontaneous power at 10.6 p, m as a function of the electron energy. (b) The amplitude and phase of the modulation imposed on the 10.6-pm optical radiation from the CO& laser. Amplification corresponds to a positive. signal, The instantaneous peak gain attained a value of 7~/o per pass. The helix field amplitude was 2.4 kG and the instantaneous peak electron current was 70 mA. The electron energy was swept through a small range in the vicinity of 24 MeV. The full width in energy (half-width in wavelength) at the 1/e points in (a) is 0.4~/0. The power density of the 10.6-pm radiation in (b) was 1.4mlo' W/cm'. Rev. Lett. 36, 717-720 (1976) jeudi 2 juin 2016 1/e half-width of the spectrum is 0. 4%. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May(hv/v) –10 !June, 2016 The linewidth is close to the theoretical miniwhere r, is the classical electron radius (cm), mum. No harmonics were observed. The mag- x = 2πNu (1 − ω/ωr ) III. The first Free Electron Laser experimental results (157) he argument which appears in the spontaneous emission expression. ticewww.lunex5.com also that : 1 − cos x − 2x sin x d x Fig. 31 Spontaneous and small signal(158) free electron laser gain illustrating the Madey ’s theorem : the gain be = − emission (sinc )2 3 x dx 2 Madey’s theorems the spontaneous emission 2(1 − 1 cos x − 2x sin x) x d = −2 (sinc )2 (159) 3 x dx 2 an be expressed as the derivative of the undulator spontaneous emission expression as shown in Fig. 31 . able result which corresponds to the Madey’s theorem [131, 132]. g(x) = The gain can be expressed as the derivative of the undulator spontaneous emission expression. It is a remarkable result which corresponds to the Madeyʼs theorem. The Madey’s theorems are given by : 2αm2o c4 I < ∆ γ 2 > dΦ Synchrotron radiation and Free Electron Laser dΩ (θ = 0) = e2 λ 2 < El2 > Synchrotron radiation and Free Electron Laser 1 ∂ < ∆ γ2 > 2> < 1 ∂∆<γ2∆ γ>= 2 ∂γ < ∆ γ2 >= neous emission and small signal free electron laser gain illustrating the Madey ’s theorem : the gain being the derivative of s emission 2 ∂γ 45 (161) dΦ dΦ current, (θ = spectral 0) the angular spectral flux on-axis o with α the fine structure constant, I the beam flux on-axis of the undulator with α the fine structure constant, I the beam current, dΩ (θ = 0) thedΩangular emission. The first theorem relates the the energy spread < El2 > introduced by the optic emission. y’s theorems spontaneous are spontaneous given by : 2 > introduced by the optical wave to the spontaneous emission The first theorem relates the the energy spread < E spontaneous emission of the undulator. According to the second theorem, the second order energy exch l 2αm c I < ∆ γ > dΦ (θ = 0) = (160) ofis theproportional undulator. dΩ e λ <E > to the derivative of the spontaneous emission of the undulator. Due to the resonance relati According to the second theorem, the second order energy exchange < ∆ γ2 > is proportional to the derivative of the particles’ energy to the emission wavelength, the spectral ”gain” distribution is close to the wavelen the spontaneous emission of the undulator. of thetospontaneous versus λ . energy to the emission wavelength, the spectral ”gain” Due the resonance emission relationshipspectrum linking the particles’ CONFIRMATION th Madey experimentale distribution is close to the wavelength derivative of the spontaneous emission spectrum versus λ . 2 4 o 2 2 2 2 l CONFIRMATION th Madey experimentale Validity : Gain <0.2 J.M.J.Madey,H.A.Schwettman,W.F.Fairbank:,IEEETrans.Nucl.Sci.:20,980–980(1973) Gain expression J.5.3.4 M. J. Gain Madey: Relationship between mean radiated energy, mean squared radiated energy and spontaneous power spectrum in 5.3.4 expression apower series expansion of the equations of motion in a free-electron laser, Nuovo Cimento 50B, 64 (1979) The small signal is given by : The small signal gainCAS isgain given by : M. E. Couprie, School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 III. The first Free Electron Laser1. experimental results Our apparatus is shown schematically in Fig. width observed in the experiment is by no means A superconducting helix generates a periodic the limiting linewidth. As established by the ear43-MeV 4 2. A field of kG. transverse magnetic lier experiments, a homogeneously broadened electron beam from the superconducting acceleragain profile is attainable and the laser linewidth tor is fired along the axis of the helix. Radiation can be improved by means of intracavity disperhelix with the the electron beam through passing M. Madey, G. Ramian, H. A. Schwettman, and sive elements. Smith The efficiency of the present lasis limited by the fraction of the electrons' enamplified and a pair of mirrors at the ends of Physics Laboratory, Stanford is University, Stanford, California 94305 er the interaction region provide feedback. ergy which can be converted to radiation in a sin(Received 17 February 1977) The characteristics of the oscillator are listed gle pass through the interaction region. This limin Tables I and II. The wavelength was 3.417 p m itation would not apply to devices in which the Fac36 and the was 0. W. average output beam 892 was reaccelerated and recirculated power laser oscillator has beenD.operated above threshold at a wavelength A. G. Deacon et al, First Operation of a' FEL. PRLof38,electron 16, 1977, toring out the duty cycle of the machine, this through the interaction region as in an electron translates to a peak power of the order of V kW. storage ring, where efficiency above 20% should With a mirror transmission of 1.5% the intracavbe possible. ' The nanosecond electron bunch ity power was 500 kW. The total energy collected experiment in 0.01% of the electron has on the detector was Our beamfocused on the in- www.lunex5.com eacon, f L. R. Elias, High Energy A free-electron 4 p, m. ' First Operation of a Free-Electron Laser* J. The first FEL in 1977 J. J. T. I. 1977 : First Free Electron Laser by J. M. J. Madey in Stanford the first maser 1954, ve sought to develop a broadly tunf coherent radiation. Several ingens have been developed, of which the is the dye laser. Most of these deied upon an atomic or a molecular , and the wavelength and tuning refore been limited by the details electrons. ' ' research energy. between radiation and an electron teraction beam THRESHOLD The laser spectrum is shown in the upper half in transverse periodic spectrum magnetic field. a spatially 2 and the spontaneous in the lowof Fig. ABOVE the difference radiated er half. Of the Note schemes whichin the have beenpower: proposed, this best the generation infrared, the visible, also potential for yielding very high average power. We have pre1 raB cture. of a measurement viously 2 described C2 the results 4g2 First demo : on linear accelerator, MARK III, we report ' hors have realized that the constraints 6 pm.y~c2Inthethis 10.period, theX,gain of Letter is the at electron where magnet Stanford, infra-red electron classical radius, and B h atomic structure would not apply energy, r, theoperation the first of a free-electron laser oscilthe magnetic field strength. The wavelength varJ. M. J. Madey 3.4l 7p, ed on stimulated radiation by free lator. ies inversely as the square of the electron energy. Above threshold, the oscillator power increases suited to approach appears the by a factor of 10' over the spontaneous radiation. of radiation nm the oscillator linewidth Thecoherent (200 6Hz). was 8 in The the electron experiment was energy in the and the and ultraviolet, has chosen to satisfy the wavelength equation' A. 0.7m p. INSTRUMENT Wl DT H A. q The experiment demonstrates the capability of a free-electron laser to operate at high power at an arbitrary wavelength. We note that the lineHELICAL MAGNET (3.2 cm PERIOD) 43 MeV BUNCHED TH TABLE II. Electron beam characteristics. BEAM 43.5 MeV RESONATOR MIRROR I 1. Schematic 2.7m Energy (Ref. 8) Width (full width at half-maximum): 0.05% ~RESONATOR Average current MIRROR 130 pA Peak current (Ref. 7) 2.6 A Emittance (at 43.5 MeV): 0.06 mm mrad diagram of the free-electron laser oscillator. I 3.4lOp FIG. 2. Emission spectrum of the laser oscillator above threshold (top) and of the spontaneous radiation emitted by the electron beam {bottom). (For more details see Ref. 6.) 893 FEL oscillator at 3.4 µm, 43 MeV, 12.7 m long optical cavity M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 indicates the possibility of laser operation from er- the infrared to the ultraviolet. The instantaneous ll- www.lunex5.com peak current from the superconducting accelerator can be raised to the ampere level by reducing the duty cycle, and circulating peak currents in Hope as- excess of 10 A have beenSaturationobtained in electron storage rings. Use of a storage ring would be particularly attractive because the 42rf accelerating field for the h ring would have to supply only the energy actually transformed to radiation in the periodic field. The III. The first Free Electron Laser experimental results " 36, NUMBER in VOLUME storage ring13 FELs PHYSICAL RKVIKW overall efficiency of such a system thus would not be limited to the fraction of the electrons' energy Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU convertible to radiation in a single pass through the interaction region. The feasibility of the idea hinges on the form of the electrons' phase-space distribution after passage through the periodic 719 field, a subject currently under study. An electron current of the order of 1 A at 240 L. Elias et al., Observation of the stimulated emission of radiation by relativistic electrons in asufficient spatially periodic transverse magnetic field, for laser operation at MeV would be Phys. Rev. Lett. 36, 717-720 (1976) Fig. 28 Electron bunching due to the electron / optical wave interaction 1000 A for a 1-mm' electron-beam cross section. • Magnetic elements (dipoles, quadrupoles, sectupoles...) The measurements indicate that 0. @ of the elec• Emission of synchrotronConsidering radiationthis (dipoles, undulators) trons' can be converted to radiation in the energy electron bunching will enable to evaluate the second order energy exchange. • Compensation of the energy loss per turn with a radioperiodic field without evidence of saturation; the frequency cavity corresponding power output for a ].-A, ].0'-ey •5.3 Bunching Gain electron beam would exceed 10' W. Weis given of acknowledge gratefully bending Let’s consider now the optical wave. The FEL spontaneous emission by the synchrotron radiation emittedthe by contributions the Nu periods of the undulator. In the historical configuration, the the oscillator, the spontaneous emission ispersonnel stored in an magnets Hansen and others who Laboratory optical cavity, as shown in Fig. 29. It is the considered optical wave. synchrotron have assisted in this effort. radiation 6e undulator source = !" bank, W las c nume fer b 4H ~B J. Qu V 23S1 N Repo 8J. IEEE ~V S. P Tech P Bev. i~R % *) () % &' *-) $% -+ # +, ( + ~J. (197 of 15 ics L SPEA *Work supported in part by the U. S. Air Force Office of Scientific Research. iJ. M. Madey, Appl. Phys. 42, 1906 (1971). J. Th cess J. publi 6* Fig. 29 Free electron laser oscillator configuration FEL Renieri, A. (1979). Storage ring operation of the free-electron laser:The amplifier. Il Nuovo Cimento B Series 11, 53(1), 160-178. The first order energy averageofover electrons islaser: zero.the One should then calculate the second Dattoli, G., & Renieri, A. (1980). Storageexchange ring operation the the free-electron oscillator. Il Nuovo Cimento B Seriesorder 11, 59 energy exchange < ∆ γ2 > averaged over phases with the bunched electron distribution. (1), 1-39. M. E. Couprie, CASThe School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 change in electromagnetic power ∆ P is given by : jeudi 2 juin 2016 Detection of Brillouin Backscattering www.lunex5.com III. The first Free Electron Laser experimental results After the first FEL .... Unfortunately, none of the electron-beam sources available at that time had enough electron-beam current and satisfactory electron-beam quality to make lasing easy. Although gain was measured in several experiments, it was not until six years later, in 1983, that the second free-electron laser was operated in the optical part of the spectrum. The first was at Laboratoire pour l’Utilisation du Rayonnement Electromagnétique (LURE), in Orsay, France, where the electron beam in the storage ring ACO was used to acheive lasing in the visible. The second was at Stanford, a team from TRW used the superconducting accelerator previously used by Madey to acheive laseing in the near infra-red. The third was Los Alamos, where a newly constructed electron accelerator was used to acheive lasing in the mid-infrared. During the same period, development of ubitron-type devices began at several laboratories. Because the threshold electron-beam current at which space-charge wave can be excited increses as the third power of the electron energy, these devices were limited to low electron energy (no more than a few MeV), and long wavelength. Neverthess, Marshall and his co-workers acheived lasing at 400 µm with electron beam having an energy og 1.2 MeV and a peak current of 25 kA. sub-mm collective instabilities involved (space charge waves) C. Brau, Free Electron Lasers, Advanced in electronics and electron physics, edited by P.W. Hawkes, B. Kazan, supplement 22, Academic press (1990) M. Billardon et al., First operation of a storage ring free electron laser» Phys. Rev. Lett. 51, 1652,(1983) J. A. Edighoffer et al.,Variable-Wiggler Free-Electron-Laser Oscillation, Phys. Rev. Lett 52, 344 (1984) R.W.Warren et al, First operation of the Los Alamos Free Electron Laser», DOE_Report (1984) D. B. McDermott et al., High-Power Free-Electron Laser Based on Stimulated Raman Backscattering, Phys. Rev. Lett. 41, 1368 (1978) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com III. The first Free Electron Laser experimental results Optical Klystron Experiments The second Compton FEL : the first and first storage ringFIELD FEL away from the axis ofvisible the electron beam (Fig. 2). The VERTICAL MAGNETIC calculated trajectory is shown in Fig. 1 which shows a 209 AAAAAA/1~ Vinokurov et al, Prepint INP, large wiggle of about 2 mm amplitude for an electron D.A.G. Deacon, Optical klystron experiments for the ACO storage ring FEL, Appl. Phys. B34, energy of M. 240Billardon, MeV andP. Elleaume a gap of et 33 al, mm. 1984, 207-219 M. Billardon et al., Phys. Rev. Lett. 51, 1652,(1983) vvvvvvv lic vvvvvvv ' P. Elleaume, J. Phys. Colloq 44 C1-333 (1983) Vsible => 100 MeV 2. Spontaneous Emission HORIZONTAL ELECTRON TRAJECTORY sotorage ring superior in terms of electronic density, energy spread, emittance => higher optical gain 2.1. General Features of the Fundamental As was done for the undulator, the electron beam is initially aligned by optical means into the axis of the vacuum chamber within + 1 mm [-3]. The spontaneous emission pattern of the optical klystron looksisthe to thetoeye of an gain /pass lowsame ( 0.1% 10 as%)thatbecause :Fig. 1. Vertical magnetic field calculated for the Orsay optical klystron (gap: 33mm) and the corresponding calculated undulator [7, 6, 3], namely a series of concentric horizontal electron trajectory at an energy of 240 MeV • Relatively long bunch length ( several10 ps) coloured rings with a similar pattern produced by each harmonic at progressively largerisopening The meters • Straight section length limitedangles. to a few big difference appears in the spectrum. All storage ring FELs use a modified version of the Undulator The experimental set up used to measure the called “Optical Klystron” spontaneous emission spectrum has already been described [6]. It consists of a 1750mm focal length spherical mirror placed at about 6.5 m from the center Dispersive of the optical klystron. The light Undulator transmitted by a 75 ~tm Section pinhole placed at the Undulator focal distance from the mirror is sent through a lens into an M20 uv Jobin Yvon monochromator ( 4 ~ Fig. 2. Dispersive section permanent magnet configuration resolution with 0.1ram slits). The output of the optimizing the low field gain 209 monochromator is then sent into a Hamamatsu R 928 photomultiplier. Fig. 3 shows a spontaneous emission VERTICAL MAGNETIC spectrum of the fundamental at an FIELD energy of 240 MeV Magnetic Field Quality : Same requirement as other storage ring for a gap of 34.4 mm at low current in the ring. IDs in terms of multipole and shimming G We have compared the envelopecorrection of the oscillations with that of the emission spectrum of a perfect undulator having exactly N sinusoidal periods, the fields outside these periods being exactly zero. The I(t) emission spectrum dI/d2 of such an undulator is: Undulators for Storage Ring based FEL Oscillator – – Mirror reflectivity degradation observed at 240 MeV Optical Klystron Experiments away from the axis of the electron beam (Fig. 2). The calculated trajectory is shown in Fig. 1 which shows a large wiggle of about 2 mm amplitude for an electron energy of 240 MeV and a gap of 33 mm. 2. Spontaneous Emission 2.1. General Features of the Fundamental – AAAAAA/1~ vvvvvvv lic vvvvvvv ' V, 5/22 , P. Elleaume, CAS, Brunnen July 2-9, 2003. HORIZONTAL ELECTRON d~ - - TRAJECTORY (31 As was done for the undulator, the electron beam is with 6 = n~N (1 - 2a/2), initially aligned by optical means into the axis of the where 2R is the resonant wavelength and n is the vacuum chamber within + 1 mm [-3]. harmonic number. Fitting the envelope to curves given 6oooA sooo~ The spontaneous emission pattern of the optical by (3) gives N = 8.1 + 0.1 instead of 7. This discrepancy Fig. 3. Spontaneous emissionspectrum dI/d2dQ measured for an Fig.is 1.probably Vertical magnetic field calculatedsection for thefield Orsay optical electron energy of 238 MeV and a magnetic field parameter of klystron looks the same to the eye as that of an due to the dispersive which klystron (gap: 33mm) andwith the the corresponding calculated K = 2.09 at low current where the modulation is almost total. The undulator [7, 6, 3], namely a series of concentric could be partly resonant other 7 periods. It is horizontal electron trajectory at an energy of 240 MeV current decay I(t) is superimposed certainly not due to the fringe field of the half periods coloured rings with a similar pattern produced by each which slightly decreases the effective number of harmonicM.atE.progressively angles. The Couprie, CAS larger School opening Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 periods. The envelope of oscillations also presents a big difference appears in the spectrum. long, short wavelength tail with the secondary Plotting the Nd of each maximum as a function of 1/2, jeudi 2 juin 2016 The experimental set up used to measure the www.lunex5.com III. The first Free Electron Laser experimental results he rather general case of a periodic field is considered (period λu x and λu z) and The second Compton FEL : the first visible and first storage ring FEL hen analyzed in the case of the planar and elliptical undulator. The general expresion of the resonant wavelength is given by : Spontaneous Emission in the visible ACO 2 2 Kuz Kux λu + + γ 2 θx2 + γ 2 θz2 ) λn = 2 (1 + 2γ n 2 2 (30) eBu xλu eBu xλu Ku x = Ku x = 2πmo c 2πmo c (31) COMMENT METTRE DE L’ESPACE ENTRE LES DEUX FORMULES? RAOUTER FORMULE GNRALE K .1 Angular spectral flux dφ → − (θ , θ , ω, u) x z dΩ he angular spectral flux at the pulsation ω close the the one of he undulator harmonics can be expressed for a filament mono-energetic beam in he direction (θx , θz ) : M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 of the electron beam. Figure 4 presents two spectra: (a) is recorded without amplif ication (optical cavity completely www.lunex5.com detuned) and (b) is recorded at laser operation (cavity tuned). For case (b), the laser oscillates at three wavelengths, with the strongly dominant one being at A. =6476 A; each wavelength is locatat a maximum the Lett. versus wavelength gain51, M. ed Billardon et al., Phys.ofRev. 1652,(1983) ity was obtained between 640 and 655 nm by changing the magnetic gap [equivalent to a change of K in Eq. (1)]. The range of tunability is in fact limited for the moment by the mirror ref lectivity. A typical 75-&% average output power has been recorded at 50-mA current of 166-MeV electrons. This corresponds to a typical 60-mW output peak III. The first Free Electron Laser experimental results The second Compton FEL : the first visible and first storage ring FEL curve. ' Smaller gain/loss ratios would restrict the number of laser wavelengths to two or one. Typical laser lines are Gaussian if averaged over a long time scale of ~ 1 sec, with 2 to 4 A full width at half maximum. Figure 4 also shows an enlargement of the main laser-line spectrum recorded charge-coupled-deby using a one-dimensional closed to instead of the usual monovice to(CCD) detector threshold closed max Gain/ chromator exit slit. The aperture time is 3 ms. loss Each narrow square peak in this curve is recorded on only one CCD element and corresponds to a 0.3 A spectral width which is of the same order as the monochromator resolution. We conclude that there is a residual inhomogeneous contribution to the laser linewidth probably connected with the long-time-scale laser-pulse structure (see Fig. 4). The central wavelength of any line is always equal to the wavelength of maximum emission of spontaneous emission with the cavity completely detuned (no amplification) plus 0.15 'Max = 600 I Max A [=o4ogA Max =23800 =2350 =6476A =6538A 100 I 6400 0. 15& 6500 l 6600 AA 6700 FIG. 4. Spectra of the cavity output radiation under two conditions: cuive g, cavity detuned (no amp1ification) and curve b, cavity tuned (laser on). 1654 Transverse profile Temporal structure M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com III. The first Free Electron Laser experimental results The second Compton FEL : the first visible and first storage ring FEL Second FEL : on storage ring, ACO, Orsay, visible, 1983 M. Billardon et al., Phys. Rev. Lett. 51, 1652,(1983) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 R„~NIf„, onics. In e external where N is the number of periods of the radiator odulator) is the spontaneousand I the ring current. n. www.lunex5.com This emission modulation rate, resulting from the inulation in terference of the two undulators constituting the s either a This . interference is OK, at wavelength XL /n eld. Then driven by the strength of the dispersive section and harmonic the energy spread of the electrons and III. The first f„ Free Electron Laser experimental results First coherent harmonic generation results passing is ator) becomes of elecmirrors, as uv light. existing avelength g with a e, laser. multiplicafrom the rent outy and not ission by to the n fact in the elecbeen ob- f„~exp "n —242m. (N+ Nd) sk y ACO (Orsay, France), 166 MeV Nd-Yag at 1.06 µm, 20 Hz, 15 MW, 12 ns => CHG at 352 nm where Nd is the number of wavelength of the yttrium aluminum garnet (YAG) laser passing over an electron in the dispersive section and characterizes First undulator PHYSICAL REVIEW LETTERS VOLUME 53, NUMBER 25 R3 352 nm R3 = 3 Drift space or . Second undulator magnetic dispersive section L tILL114 I t1 I . '«sI'- «'stls'tssu%'Q'F I ~ emission I I t J i t l It I I I Focused pulsed laser 'Modulator" t lk1tll „[J&. I;„;;;. I t I electron traj ector y 352 nm R3 > 100 —— + — 0.3 "launcher" "Radiator" FIG. 1. Schematic principle of the experiment (see text). B. Girard,Y. Lapierre, J. M. Ortéga, C. Bazin, M. Billardon, P. Elleaume, M. R Praae res by e t aan l /optical Cohe r en t 70 Y. Petroff, Opitcal frequency multiplication Bergher, M.Velghe, The American Physical Society 2405 klystron, Phys. Rev. Lett. 53 (25) 2405-2408 (1984) 4. Exper i ment s k 0.2 100 ns ha rmon i c gene ra t i on in t he VUV r ange Linewidth FIG. 2. Time structure sharpening of the optical klystron emission Tab l e 1 measured on the third harmonic of the fundamental line at 3550 Thea lpulse to a passage of the ExperA.i ment resulcorresponding ts on ACO (1987) —O. i 0) electron through the OK in coincidence with the laser is In 1984, we had observed the th i rd ha rmon i c at 3547 shown a weak i camplification ratio (R3=3); 3(b) (a) for harmon Observed 5 ACO (Orsay, FIG. 3. Amplifica an ext erna l220 Nd -MeV YAG lNd-Yag aser [9] . Aatd i e l ect r i c m i r ror  of France), a strong for Cor amplification ratio 100). 3 respond i ng wave l ength(R[Â] 1773 incoherent 1064 emission separa t e the ha rmon i c f rom the f undamenwas used to 1.06 µm (36 MW) /2 = 532 nm, => CHG Integrated rat io Rnt 350 3-4of 0.2 mrad' angle ha rmon i c s i gna l was ana l ysed by a norma l wave . The 2 2 experiment) a bars, monochroma tor bandw i dth [?+] at 177 andta l106.4 nm We value is about 5 to 6 times more. ous3 emission meas i nc i dence gra t i ng monochroma t or . In order to ana l yse monochroma tor angu l ar aper tureexplained [mrad 2 1 this 1 .4 pulse-to-pulse fluctuations effect by considering the (curve c) the laser the coherent i ntens i ty in the proper " t i me w i ndow " of the 6000 Since 100the real spectr Spectcoherent ra l rat io emission R , (X, Sd) when recorded on a fast l aser Spectral pu l se , we used a cor respond i ngin tothe the i nc i dent Coherent Harmonic Generation Vacuum Ultra Violet less fluctuations are/puofl sethe order 1 of These scope. Numbe r of coherent photons .5 X 10 7 10than 5 0. 1 A, the (166 MeV) was Range on the Storage R. Prazeres, J.M.beam Ortéga,energy M. Billardon, " BoxRing -Ca rACO, " averager . The to obtain the re by 07 .07 severalm units spect raand l w do i dthnot[A]appear on Fig. 3 where the 0 .1 C. Bazin, M. Bergher, H. Fang, M. Velghe over averaged signal inis angu too M.E. l owCouprie, to ensure good stabY.i lPetroff i ty of , Nuclear the r i ng, and the l ar aper tureabout [mrad]50 laser pulses. They 02 0 .1 Inst.and Methods in Physics Reasearch A272 (1988), 68-72 electo time between a the correspond jitter might l aser powe r l i fet i me was on l y one hour . The i nc i dent tron and laser pulses of the order of a few (PL = 15 MW); th was 15 MW at 1 . 06 , um . Howeve r , the max i mum i n—102 (PL =100 nanoseconds considering the fact that the laser t egra t ed rat i o has been measured to be R3 t = 300, exhibits 2 to 3 !June, for a longitudinal pulse shape peaks 2016 section). (iii) We M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31tor !May –10 p l i ers . The bo t t om de t ec (CsTe ca thode) was devo cor respond i ng to a spec t ra l rat i o of R 1 (A , 0) = 3000 , "radiator" total duration of 12 nsec. We have also considered in thet ed jeudi 2 juin 2016 the 3rd harmon i c , and the top (CuBe ca thode) to — for a cur rent to the s torage r i ng of 1 mA . Th i s cor rethe toeffect of the lack of coherence of the laser 10 10 is lost whe s ) s s I www.lunex5.com III. The first Free Electron Laser experimental results Marie-Emmanuelle COUPRIE and Mathieu VA Efficiency simulations of the FEL evolution at saturation, physical considerations enable Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU COUPRIE and Mathieu VALLÉAU Small signal gain bandwidth : 1/2Nu . Using the∆resonance it comes ll50signal gain half width is of γ 1 ∆ condition, λ 1Marie-Emmanuelle 50 = =Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU 2 λ 4Nu ∆γ 1 ∆λ 1γ 1 ∆λ 1 = = ∆γ (181) Resonance condition => (181) γ λ ∆4N γ u 1=∆ λ 1= 1 of its kinetic ener n the electron travels on half the2 width of=γ the2gain curve, it can deliver up to λ 4N = (181) u 4N u γ it 2canλ deliver 4Nuup to 1 of its kinetic energy, the ectron travels: on half the width of the gain curve, y r comes 4Nu deliver up to 1 of its kinetic energy, the When the electron travels on half the width of the gain curve, it can diation andtheFree Electron Laser 3 mes :When electron travels on half the width of the gain curve, it can deliver up to 4N1 u of4Nitsu kinetic energy, the efficiency r comes : efficiency r comes : 1 1 r =at mple of the CLIO infra-red free with 48 undulat (182) r = electron laser 1 Lab. Chimie Physique (Orsay) 1 4Nu (182) r = 4Nu (182) r = fficiency is of the order of 0.5 %. 4Nu 4Nu 1 m efficiency is found in considering the total width of the gain curve, which would lead to r = . It would lead 2Nwhich maximum efficiency is found in considering the total width of the gain curve, to r = u 1 r = 1 provides can be overcome in using tapered undulator, as already introduced. The tapered undulator The maximum efficiency is found in considering the total width of the gain curve, which would lead to . It The maximum efficiency is found in considering the total width of the gain curve, which would lead to r = . It 2N realistic because energy spread effect can limit the process. u 2Nu er less realistic because energy spread effect can limit the process. isofhowever however less realistic because energy spread effect limit the process. less realistic energy spread effect can limit the butprocess. just changing the angle of the array on which a netic field along thebecause longitudinal direction Bcan z (s) leis the CLIO infra-red free electron laser at Lab. Chimie Physique (Orsay) with 48 undulator periods, In the the example of theCLIO CLIO free electron at at Lab. Chimie Physique (Orsay) with 48 undulator In example the infra-red electron laserlaser at Lab. Chimie Physique (Orsay) with undulator periods, example of CLIO infra-red free electron laser Lab. Chimie Physique with 48periods, undulator p of the order of the 0.5of%. ndulator magnets. There isinfra-red alsofree the possibility to vary the period, but it is48(Orsay) slight less convenient. the efficiency theorder order 0.5 the efficiency isis ofof the ofof 0.5A. %.%. N. 50 periods, r =The 0.1 %tapered undulator provides a n be overcome in using tapered undulator, as already introduced. ency is of the order of 0.5 %. anceThe condition becomes : inusing limit overcome in tapered undulator, as already introduced. The tapered undulator provides a The limitcan canbe be overcomedirection using tapered undulator, as already introduced. The tapered undulator provides a ic field along the longitudinal B (s) but just changing the angle of the array on which are z imit canmagnetic be overcome inthethe using tapered undulator, as already introduced. tapered undulator pro varying field along longitudinal direction Bz (s) but just changing the angle of the The array on which are varying magnetic field along longitudinal direction B (s) but just changing the angle of the array on which are z � � ulator magnets. There is also the possibility to vary the period, but it is slight less convenient. � � 2 located the magnets. is also possibility to vary theubut period, butchanging it but is slight less magnetic field along the There longitudinal direction Bztoz(s)λ (s) theconvenient. angle of the array on wh λthe 1 eB (s) located theundulator undulator There is also possibility vary the just period, it is slight less convenient. u the ce condition becomes : magnets. λ = 1 + (14 The resonance condition becomes : The resonance condition becomes : 2 2 he undulator magnets. There�is also the possibility toovary the period, but it is slight less convenient. 2γ 2 c � 2πm s � � � u (s) 1 eBλz (s)λ λu : � 1 �2eB�(s)λ (s) �2 � � � esonance condition becomes z eBlaser. u(s)λ uparameter 2 Generators of Coherent Radiation, (183)1, 89--112(183) 1 M. + Nλ:Variable λP.= 1 λ (s) Kroll, N. M., Morton, L., Rosenbluth, free-electron In Free-Electron (1980) z u u 2 2 1 + = maintain the resonance. 2γ Efficiency 1-2 % XXXXXX was reported [134] 2 λ of 2πm c o 2 2 (183) 1 + = s 2γs 2γ 2 �2 22πm2πm oc 2 � c o s � �2 jouter ref, Los Alamos, tapered und, aintain the resonance. Efficiency of 1-2 % XXXXXX was reported [130] 1 λ eB (s)λ (s) Storage Ring based FEL : z u u enables to maintain the resonance. Efficiency of 1-2 % XXXXXX was reported [130] enables to maintain the resonance. Efficiency 1-2 % XXXXXX was reported [130] 1+ 2λ = P of uter ref, Los Alamos, und, 2 α IE42 2 Renieri limit ref, : tapered <P> χ (∆σtapered agramme LEL XXXXRajouter Losα Alamos, γ/γ) Pund, sync 2γ , sync 2πm c o XXXXRajouter Los Alamos, tapered und,s amme LELdiagrammeref, schma LEL EL sur anneau de stockage Renieri, A. (1979). Storage ring operation of the free-electron laser:The amplifier. Il Nuovo Cimento B Series 11, 53(1), 160-178. schma diagramme LEL sur anneau de stockaga Cas du LEL sur anneau de&stockaga es to maintain theDattoli, resonance. 1-2of % XXXXXX was reported G., Renieri, A. Efficiency (1980). Storage ring of operation the free-electron laser: the oscillator. Il Nuovo Cimento[130] B Series 11, 59(1), 1-39. Cas du LEL sur anneau de stockaga E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 XRajouter ref,M.Los Alamos, tapered und, jeudi 2 juin 2016 conducting accel. erator is ssteered down the axis of the tapered wiggler. The eel.ectron beam c aracteristics are s bown own in Table I. The cavity www.lunex5.com tween the sides of each wigg er ' ' magnnets is increased the fie gap between the m ' ' axis falls, creating a m ag netic field taper. t of the electrons from e a taper~ thee deviations III. The first Free Electron Laser experimental results e -ll. :-:". -'. , "-b. .".-'-. ' con- tron thi th. t r fo, ac is on based on the Ha Hal. bach design, Th ewiiggler t' SlS lllg of a pair of linear arrays ra s oof SmCO, perSICAL NUMBER VOLUME manent52,magne t s. 5 The arrays arepHy t AL in constant — el. en th (X = 3 .6 cm ) but can be made to var vary Th th i o path leng decelerate through the wigg er, REVIEW ecf r equency LETTERS need not change. e. This al. l,ows gotheJANe vAR»&84 ' ' trons t o s t ay in resonance with the op tical ie l.d PNEUMATIC ADJUSTABLE tthe full l.eng th of the wiggl. er. An advantage - 1/ 4X ENTRANCE/EXIT ASSEMBLY -1 CAVITY MIRROR ACTUATED control 1ing th e spacing between the magnet p anes. SCREEN er is that the configuration and / g&, The wiggler consis h conamoun t of t ap er may be adjusted for study. en f OPTICAL DIAGNOSTICS ! i uration used taining f ifteen periods. The conf igur lerI one incorporate in o t ns large5 smal, l-signal gain comp REVIEW LETTERS PHYSICAL p NUMBER VOLUME 52, The Stanford experiment in the taper configuration I 1984 JANLJARY ELECTRON SPECTROMETER TV MONITOR SUPE RCONDUCT ING ACCELERATOR )0 i e BEAM sections ler s give arge characFEL oscillator AM TABLE ENTRANCE CONSTANT E ELECTRO SECTION II. Tapered-wiggler CONSTANT EXIT TAPERASLE W GGL E R 90K IN 6teristics. TAPER TAPER SECTIONS WIGGLER MAGNETIC At IhFTig h er optical klystron. Var jouss dijag nostics g ain as in an optical. 6-1/2X 6-1/2X f u I. in the operation 15K 320.04 cm 15K are help ' 34cm 53 34 cm 53. 58. 59 cm 28 58 cm 28. 58 cm fields the prebunc cher c er prrrovides momentum m oduinser of th' FEL. A total of fourteen (a) ' cm 542 t' g' erd p rescent screens,s nine inside the wiggler, ag 66lation MeV of the el.ectron beam; 'd' NUMBER 2.9 3.6 cm period, Halbach type, VOLUME 52, Power' 4Wb elecsion section (b y p rovi ing a momentum-dependen m nt iinformation on 5the kG f theREVIEW oruntapered positio PHYSICAL MWb 2 1. Peak power 1268 cm at op tical. waveo a set of horizontatal tron beam. For eac h scrreen path eng ) 460 MWb Peak cavity power FEL oscillator TABLE Tapered-wiggler II. " characthe alignlengths at the entrance o p ll GW/cms for Peak cavity intensity teristics. the tapered Wavelength 1.57 pm d t a FIG. ment of m the ing within t xc ofedthe multicomponent 1. Schema i electron ler FEL esystem. wigg h'ich defines the4 psc section and, therefore, higher extraction e beam ewlength ls. Focus ocus laserMicropuls optical axis. I DR rou p s.. ' gro eral. An op t'ica l. kl. ystron variant of a stant wiggl. er oscillated a TABLE I. Characteristics of the su p erconducting ac7 4 Macropulse length Repetition rate 5 ms 10 Hz ciency. ~ Power' Bandwidth LASING SPECTRUM LETTERS I I I I )0 (a) JANLJAR LASING SPECTR 1.3% FWHM 1.3% 4Wb power 2-0.1.2 MWb constant d th e 0. of the main wigEfficiency, When Peak wiggler magnets untapere, MWb 460 Peak1%cavity taper power ce a maximum 1.1% field of 2. 9 kG produ gl. er sections celerator in the experiment. 2 $ GW/cm " Peak Oio(Sic 1.ll cavity taperintensity 2P these sec ions e front an d re ar1.of on axis. i . 1. Wavelength 57 pm pp were measured over These quantities averaging Micropuls e length Emittance 0.15~from mm mrade 'at 66 MeV) 1. t by h h 4 tpsc l th A 66-MeV electron beam shots. many Macropulse length spreaderator is s Energy accel. 0.03$() tween the sides of each wigg 5erms steered down the axis 1% taper. conducting rate CONSTANT ' ' 10 Hz PREBUNCHERRepetition TAPERED DISPERSION Bunch length 4.3 ps SECTION MAGNETS Inferred under the the optical assumption pulse the~ magn m thatSECTION nets is increased the fie on between arThe el. ectron beam of the tapered e c wiggler. gap Bandwidth 1. 3% Current 0.5-2.5 A ' shape. ' measured electron pulse2-0. shape is the same as the constant axis Efficiency, 0. field wiggler creating t taper. are s bown ag netic acteristicsEnergy own in Table66I.MeV The cavity t swiggler elemen of a themmulticomponent 2.falls, Key deceleration. BasedFIG. on electron taper 1. 1% 1% of the electrons from e e a taper~ thee deviations system. I 1.3% FWHM 4%%u() SPONTANEOUS SPECTRUM I, -'. -ll.:-:"."-b. .".-'-. 4%%u() 1.2 $ 2P taper 1.4 1.5 1.7 , is controlled by four sets of quadrupole coils exth.measured Th tron r byalignment were ac design, conTh ewiiggler is based on the Hal. Ha bach path leng averagingth over i t o teriorThese to thequantities mirror Cavity wiggler. FIG. 3. {a) Lasing spectrum and (4) spontaneous outshots. decelerate use of the the reflection accomplished s oof SmCO, per- wasmany SlSt'lllg of a pair of linear arrays ra wigg of the by through the outcoupler. of the FEL as measuredof through put To compensate for the average energy loss of the electrons totaper. the optical. wave, the magnetic field is made aecfunction the wiggler 1% insertionbeam onto one of three HeNe alignment al. l, f need not This ows the change. e time-averaged peak lasing power is 95 kW while manent magne t The arrays are constant t in equency that the optical pulseThe Inferred under the assumption ' ' al. and position,el.compensating for average changes in the electron energy, y, so that X, in the resonant condition remains constant. The0.95 mW. the of the as ayertures cavity peaking Q spontaneous power is only peak ie = 3 6 cm ) but can be made to vary in measured resonance the shape. tical l.d o bysline t with pulse opthe en th (X — var seen is the tsame as the electron ay shapetrons laser (514 nm) of antoargon by the green reduction of the magnetic field decreases the path length traveled by the=l.eng el.ectrons compensate for their slowing down. This electron deceleration. Based on o the full th f the t wiggl. 99. at the third harmonic An advantage (mirror ref lectivity tapering allows to remain resonance they traverse the wiggler, even significant amounts of their energy.where N is of the fundamental). control 1ing electrons th e spacing between inthe one expects magnet as an efficiency of 1/(2N), that lose and er as is they the configuration p anes. 1.4 1.5 1.7 the effective en characteristics ofer the oscillator are listed number of wiggler periods (131 exsets of quadrupole coils is controlled The wiggler consis h con- The byf tfour be adjusted amoun t o for study. may ap J. A. Edighoffer et al.,Variable-Wiggler Free-Electron-Laser Phys. Rev. Lett 344 57 Table II. The wiggler. was and the (1984) wavelength 1.mirror periods with the dispersion section turned off) p, m52, toOscillation, the alignment Cavity uration used in terior taining f ifteen periods. The conf iigur in o lerFIG. one incorporate spectrum and spontaneous 3.to{a) macrothe linac average output during 0.Lasing 38% efficiency. power This (4)comuse of the reflection of thewhich amounts was accomplished bysmal, the outcouple put of the FEL l-signal large tayer. With gaincycle comp pares favorably p was t4 Wnswith the duty yulse with as the measured measured through efficiency of insertiononto one of three HeNe alignment beam M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 The time-averaged is lasing power peak 0.4/o. Benson etal. demonstrated about 0.2% 95 kW w of the machine factored out this translates to a al. ayertures and by peaking the Q of the cavity as the peak spontaneous power is only 0.95 mW. efficiency with a 160-period wiggler. peak power of 1.2 MW. With a mirror transmisFor the jeudi 2 juin 2016 i ler sections give arge s seen by the green line (514 nm) of an argon laser SPONTANEOUS S I ' s. . fo, thi r e. 9'%%uo . er, er. I . 1%%uo " ga i n w i t h t he p r ebunche r a l l ows t he a t t a i nmen t o f h i ghe r p l es of these ex t remes . (Recent ca l cu l a t i ons of powe Cav r i t y - Wave l eng th tun i ng , coppe r s t ance cav i t y powe r s f or t he same beam cur r en t and e f f i c i ent i a l beam qua l i ty . 0 . 52 M versus t i me i nd i ca te that , even w i th zero no i se in theRay l e i gh- d iSpa Ou t pu t coup l i ng 0 . 5% c i es 1 . 5-2 t i mes h i ghe r . Th i s enhancemen t i s expec t ed e l ec t ron beam energy , h i gh- f requency powe r f l uc tuar5.1 i ngdown / pass 3 - 3 . 5% Cav i t y f rom t heor y f or bo t h w i gg l e rs , bu t t he r e i s no t enough Sma l l -s i gna l ga i n t i ons of sma l l (5 to 10%) amp l i tude , s i mi l ar to that seen www.lunex5.com concen t r i c Nea r da t a f or t he 30% w i gg l e r w i t hou t p r ebunche r t o ve r i f y i n f ig . 6, wi l l st i l l be present . ) The SSG was rout i ne l y measured at the beg i nn i ng of t he enhancemen t f or th i s w i gg l e r. Opt i ca l output powe r was not the on l y parameet er -beam a f f ec t ed by the no i se in the e l ec t ron beam . Spec t raEne l rgy each l as i ng exper i ment by use of a l i qu i d-He coo l ded , 21 MeV 12 D . W Fe l dman e t a l . / H i gh ex t r ac t i on e f f i c i ency expe r i men t s Barbara Research Mode l measurement s , in par t i cu l ar , d i f f ered f rom shot to shotM. i c ropu lHg : Gergephotode t ec tor (Sant 1 . 5-5a nC se cha 3 . 2 . Compa r i son w i t h ca l cu l a t i ons The qua l i ta t i ve f ea tures of the spect ra , that is, waveEm 9145-2HS) . The SSG depended s tad rong l y on the peak - i t t ance 3 rr mm mr y l sew i det hl ecpt rron cur rent r, . and necav t =10 vail tues rang irng 15 ttoi ma 60% Tab l e 1l ength range , amoun t of deta i l , etc . , were re l at i ve l Pu ebunche The yps powe s farom r e es t ed f orThe pu lhse i ghes t e f f i c i enc i es ob t a i ned f rom each w i gg l e r cons t ant f rom macropu l se macropu l se , but the deta i l s were recorded for respec t i ve peak cur rents f rom 30 to m to Charac t er i s t i cs o f t he w i gg l ers and sys t em pa r ame t e rs used w i d t hs o f 10 ps . The ex t r ac t i on e f f i c i enc i es comb r epriesen na t iton we r e compa r ed w i t h co r r espond i ng ca l cuFWHM 50 unnorma l i zed var . Alamos In spec ral epresent i nexperiment sect .4, we l ec°)rt edwas A The cur rent requ i red to reach the l as i ng thresho l d Los oscillator wave. 5l eng t h se t ape t he expe r ii ed men t s . the The w i tgg r w i t h ed 12% ave r ages t aken ove r a numbe r o f mac ropu l sesl a tand re i ons amade us i ng t he e - beam code PARMELA t o was 5 A. A s l ight l y h i gher va l ue of 7 A was necessary to i st ii ous c examp arget s.numbe of l mea The rw i gg e r w-i t h used mcharacter our prev amp l lies f i erf rom expear i lmen = 20% be l ow t he h i ghes t s i ng l e pu l se ex t r ac t i on ob mode l t he acce l e r a t or and beam l i ne and t o gene r a t e an produce s i gn i f i cant output powe r measurab l e w i th our surement for r disi scuss i onon oft he the i ri gnquadl ii scussed tat i ve , i not n re f . 30% wave l eng t hs t ape based des irques se rpyroe ved . lene The t taec. ftor or . tFhe gg i s spa t he e l ec tl ron -beam When bo t h w ti echn i near ec t rgy r i cdade[7] i g. 30% 8 shows anl eexamp l e rofse . deta i l ed, features , Some proper t i es of the opt i ca l beam [4] . t he i r ag r eemen t was w i t h i n abou t tAhe l rl ,o fi a tl he sysstar t ems same gene r aal- t r end w i t h exponent r i se, t i ngshow f rom t he i ncoherent spont were qu i t e i nsens i t i ve to the no i se . Spa t i a l beam qua lwe i t yr e usedthet oge 15% . neous i on . Th osc i12% l l ogram is l ac was a pr i me examp l12% e , show i ng no ev i dence of dePre t er- i ora30% cav em i t yi sspowe r . i sThe w i gg e rtua , lwl iy t ah measure and w i t hou t pr e t i on f rom no i se , w i gg l e r of the SSG of the pu l se energy , ra ther than w i gg l e r bunche r bunche r , shows sa t ur a t i on . Th i s maypower be , caused t by ' 2`o VJ I GGLER - -because l i mi t ed bandw i d t h of the de t ec t i on sys2 . 5 . Pr ebunche r tofh the 0 g row m t he e -beam ' s em i t t ance when t he m i c ropu l se 30 ' , V , ' I GGLER . 66 W i gg l e 4.2 r 73 ( i n i t i a l ) 273 3 Fas t in i t i a l t rans2i ent t em ( - I GHz ) re l at i ve to the - 30-ps opt i ca l pu l ses . of e l ec t ron ene rgy chanumer rge iapp 3 nC . t empora The cur ves i n f i g . 1 a r e zi n- i 2 " - PREBUNCHER - Wave l eng t h ( cm) 2 44 ( f i na l ) 210 3 . 66 F rom ca l roaches anarl ystios of l tprof The use o f a p r ebunche i mpthe rove ex t r ac i on i leef -of the 4 O 30 ° - PREBUNCHER 0 196 B W i gg l e rA( i nsecond i t i a l ) (T) . 29 e l ec t ron t endedl se ,to wei lde l ust erm t ra tienedt r that ends and do no t purlepr prob l 029 em present ed by0 the beam se esen t any f i c i enc i es cur a t rent h i ghpu op t i ca l powe r was desc r ithe bedSSG i n r eatf . the [4] . 300 .0 l er Tapeoccur r (X)red at the star12 . 0 of osc i l l at i on peakt heor t up . When the0acce shouyl .d be 10% grea t er than measured because the The p r ebunche r i s a shor t (2 . 5 pe r i od) w i gg l e r p l aced i n pa rabo l i c powe r ga i n depends Fo rm oaftor t ape r = l i near on thedoes was turned on at the beg i nn i ng of each macropu l se , i ns tno ant aneous l ue of s the exh i b va i t pass any i gn o f sa t ur a f ron t o f t he p The r i ma r30% y w iw ggi gg l e r.l e rAs t he etl ec t rons U . i ts e l ect r i c f i e ld i ncreased i n a rough l y exponent i a l m i cropu l se cur rent A l so , the measured va l ues shou l d be . 4 zGW and t i on up t o a cav i t y powe r o f app rox i ma t e l y 8 t hrough t he pr ebunche r , t he i r ve l oc i t y i s modu l a t ed so Op t i ca l i ncreased by an add i t i ona l 20% to accoun t for the w_ 3 , f ash i on . Once the f i e ld was w i th i n a f ew percent of i ts e f f ri esonan c i enc i es i nc r eased may be capab l e o f st i lal round h i ghe rt he t . The U Las i ng wave l eng t h 10 . 88 - 11 . 4 l m as t o p roduce bunch i ng knowna non l i near i ty acoft i on the photode t ec tor . By app l i ca- I l f ina l va l ue and st i l l i ncreas i ng , three th i ngs happened : a l lrows a t t a, i nmen t o f h i ghe r gg l e r a rre cor ec t l yt he spaced coppe r n w i t h r tand he pwr iebunche pa r t i c l e . I f t ga he ibunche Cav i (1) t y the cur rent through the undu l a tor i ncreased form w l i ght i sbeam an i ncur t egra l t and e f f i c i enRay l ezero i gh dtoi s ti ts ance 0 . 52 M i t y t he powe r st rons f or and t he same r en s l i ppage be tcav ween e l ec f i na l va l ue , (2) the max i mum of the SSG z' t ween pr e Ou t pu t coup ng response to the energy 0 . 5% change , sh i f ted f rom numbe r o f wave t hs itni mes t he hdri ghe i f t space c i es l eng 1 . 5-2 r . Th i be s tenhancemen t i s 0expec t ed func t i on ,l im 2e l ec t rons / pass to i ts f ina l 3va- 3l ue. 5% r andf rom w i gg tl heor e r . The Cav i tl onger y r i ngdown wave l engths , and (3) becausebunche of y f orbunched bo t h w i gg l e rs , buatr et hei n-r e i s no U t enough Q concen tr ic l e r a t t he op tw ii mum f or tcap ur e nomsochronous 60° bends , the m i cropu l se sepj ec t ed i n t o t da he twai ggf or Nea rthe gg l e phase r w i t hou p rt ebunche r t o ve r i f y t he 30% ara t i on i nterva l measured at the undu l a tor sh i f ted f rom and dece l e r a t i on , p roduc i ng an i mp r ovemen t i n ga i n x w t he enhancemen t f or th i s w i gg l e r. e -beama s i gn i f i cant l y shor t t i me to i ts norma l 46 ns. A l l three and e f f i c i ency o f t he l ase r by a l mos t a f ac t or o f 2. Ene rgy of these processes occur red w21i thMeV i n the f i rst 10 I ts of cha rgewe observed rap 1i d. 5-5 nC of the opt i ca l M i c ropu l sewhen 3 . 2 . Compa r i son w i t h ca l cu l a t i ons l as i ng growth Em i t st iance 3 rr mm mr adgrowth and gna l . Norma l l y , al l three t ended to reduce 3. Expe r i men t a l r esu l t s =10 cont thatpswas not cons i st ent Pu l sew i drt ihbut ed to a measured SSG The h i ghes t e f f i c i enc i es ob t a i ned f rom each w i gg l e r w i th the measured sa tura t ed powe r or ext rac t i on ef r e opcompa r ed rw i t h co r r espond i ng ca l cut i onvewe 3 .1 . Ex t r ac t i comb on e f fi ina c i ency rsus t i ca l powe °) FWHM unnorma i zed f i c i ency and , ladd i t i ona l l y , var i ed er rat i ca l l y f rom day to l a t i ons made us i ng t he e - beam code PARMELA t o day re f l ect i ng m i nor changes i n the t i me dependence of e f - t o gene r a t e an F i g . 1 shows va lacce ues lob nedand f or beam ex t r ac i on and CAV I TY POWER ( GW ) mode tlhet he e rtaatior l itne the acce l ara tor f i e ld . III. The first Free Electron Laser experimental results The Los Alamos experiment i c i enc i es ve r sus es t i ma t ed i n t r acav i t y powe r whe r e bo t h t he e l ec t ron -beam ene rgy [7] . When bo t h t echn ifques t ape rt ed w i gg l e rs a r e ope r a t ed w i t h and w i t hou t t he Opt i ca l resu we r e 5. used t oge t he rl ts , t he i r ag r eemen t was w i t h i n abou Fig 1 40 % gain 15% . Ex t rac t i on e f f i c i enc i es versus cav i t y powe r for severa l w i gg l e r -prebunche r comb i na t i ons . A d i scuss i on of the opt i ca l resu l ts is d i v i ded i nto F i g. 8, Exponent i a l r ise of the l as ing mi cropu l se energy f rom seven top i cs tha t i nc l ude the fo l l ow i ng : t ss' 2`o VJ GGLERto saturat - at the star t of the spont emi en I route R.r W.,h Newnam, B. E.,Winston, J. G., Stein,W. E.,Young, L. M.,aneous & Brau, C. iA.on(1983). Results- of-ionthe Los Alamos free-electron laser experiment. Quantum Electronics, IEEE 2 . 5 . PrWarren, -ebunche The growt of opt i ca l powe r w i th t i me f rom spont a0 30 ' , V l, se. ' I GGLER e l ec t ron-beam macropu A net sma l l -s igna l energy ga in of Journal 19(3), neousof,em i ss i on391-401. to sa tura t i on , i nc l ud i ng measure 34% per cav izty round t r ip is represented . -The cor respond i ng i 2 " - PREBUNCHER B. E. W. Sheffield, Goldstein, Brau:powe Ther Los Alamos free electron-laser oscillator: Optical performance, Nuclear Instruments and Methods in men t so fofaoptp irR. ca l gaWarren, i n , r t oR. L. The useNewnam, ebunche i mp rove exJ. tC. r ac t i on e f - C. A.gross ga i n is 52%. 4 O 30 ° - PREBUNCHER - A: Accelerators, f i c i encPhysics i es a t Research h i gh op t iSection ca l powe r was desc rSpectrometers, i bed i n r e f . [4]Detectors . and Associated Equipment 237 (1), 187--198 (1985) The p r ebunche r i s aM. shor t (2 . 5 peCAS r i od) w i gg Free l e r pElectron!Lasers!and!Energy!Recovery!Linacs l aced i n E. Couprie, School f ron t of t he p r i ma r y w i gg l e r. jeudi 2 juin 2016 As t he e l ec t rons pass U z !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 www.lunex5.com III. The first Free Electron Laser experimental results Accelerators for FELs Storage ring RF linac ACO,VEPP 3, Super-ACO, DUKE, NIJI IV, UNSOR, DELTA, ELETTRA... Electrostatic accelerator Induction linac Stanford, Los Alamos, Boing / Spectra Techno... Santa-Barbara, 6 GeV, 2 A 120-800 µm L. Elias et al.,The UCSB electrostatic accelerator free electron laser: First operation, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 237, Issues 1–2, 15 June 1985, Pages 203-206 ETA, Lawrence Livermore Nat. Lab. 3.5 MeV, 9 mm, 40 % efficiency operated as amplifier T. J. Orzechowski et al. Phys. Rev. Lett. 54, 889 (1985) T. J. Orzechowski et al. Phys. Rev. Lett. 57, 2172 (1986) Microtron ERL M.Tigner Nuovo Cimento 1965 ENEA Frascati 2.3 MeV, 2-3.5 mm Ciocci, F., Doria, A., Gallerano, G. P., Giabbai, I., Kimmitt, M. F., Messina, G., ... & Walsh, J. E. (1991). Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser. Physical review letters, 66(6), 699. Jefferson Lab. 2.3 MeV, 2-3.5 mm S. Benson et al., NIM A (1999) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com III. The first Free Electron Laser experimental results FEL oscillator properties Temporal properties Gain reduction (u. a.) Transverse modes Desalignement (u. a.) M. E. Couprie et al., NIMA 304 (1991) 47-52 VEPP3 (Russia) λ/∆λ = 10-5 Optical cavities for storage ring FELs in the UV, M.E. Couprie, D. Garzella, M. Billardon, 1995, Nucl. Inst. Meth. A 358, 382-386 (1995) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 e!ects due to the nanosecond and sub-nanosecond timescale dynamics of the process have been obTABLE II. Fluorescence measurements of NADH performed with the super-ACO FEL. www.lunex5.com served by scanning the FEL-to-SR delay with an ! , ns c ! , ns ! , ns ¯! , ns Temperature c optical delay line on the FEL path. Photochemistry and beam Photobiology, 2005, 81 717 #0.01 #0.02 c #0.2 #0.01 (°C) #1% #1% , 3216 Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 Edwards et al. 10 61% 0.30 38% 0.70 1% 1.7 0.47 1.30 Fig. 2 shows the SPV intensity #uctuations as 20 68% 0.28 32% 0.62 %0.1% 1.8 0.39 1.20 a function of the delay between the two pulses for 40 78% 0.24 22% 0.55 %0.01% 2.1 0.31 1.24 0.8 three di!erent surface qualities of cleaved Arrhenius fits for different fluorescence decays. Human surgery 0.6 Photon echo Si(1 1 1)2!1. The long-time behavior is due to the ! ! ¯! E 1.4#0.3 kcal/mole 1.5#0.1 kcal/mole 2.6#0.3 kcal/mole steady-state regime of photocarrier relaxation as 4#3$10 s 0.4 2#1$10 s 2#1$10 s A observed in the bulk. In contrast, the strongly oscilThermodynamical parameter K!c /c !exp("%G/RT) with others techniques. Edwards, G. S., Austin, R. H., Edwards, G. S., Allen, S. J., 0.2 lating transient regime, observed during the "rst Carroll, F. mole# E., Copeland, M. "kcal/mole# R. F., Nemanich, Technique %H "kcal/mole# %S "cal/K G Haglund, Fluorescence "5.0#0.2 "18.5#0.7M. E., Gabella, 0 &0.1#0.4 is attributed to the ! (bonding) L., Couprie, R. J., Redlich, B.,half-nanosecond, Simon, J. D., NMR ("5.6#0.2) ("17.5#1) ("0.8#0.2) (&0.4#0.1) -10 0 10 20 30 40(2005). 50 60!H70(anti-bonding) electronic surface states [11]. W. E., ... & Joos, K. M. & Yang, W. C. and Time (ps) of One (2003). Free-electron-laserApplications Free‐ can then understand the very di!erent behavsample, on an X – Y – Z manipulator. The pump beam can the emissions process, which is related to rotational BrownFigure 10. Vibrational photon echo decay data taken W(CO)6 in 2based biophysical and Electron Lasersior in ofthe observed on a surface showing many defects MTHF at 16 K. The inset is a semilogarithmic plot showing the data decay ian motion of the moleculesbiophysical in solution.instrumentation The decay of anisotbe moved instrumentation. and focused precisely in the region where the FEL-based 3233 then biomedical exponentially. Reprinted with pemission from reference 28. Biological and Material ropy of a chromophore rigidly attached to a sphere can be probe beam intersects the sample. This region where the two known to accelerate the electronic relaxation (curve scientific FIG.Review 8. Positionof of the patient prior to incision. The arrow shows location of Photochemistry Sciences. described by r(t)!r 0 exp("t/!) where r 0 is the static anisot- thephoton beams‘‘T’’" intersect isdata optimized with the signal obtained tumor !circled based on from the neuronavigational system. FIG. 7. Preoperative MRI scan !axial T1 weighting with gadolinium conMetal carbonyl solutes and in glassy and liquidcsolvents in the "gure). These results, as well as recent data instruments, 74(7), photobiology, 81(4), ropy related to the angles between the moments associated to by a charge coupled device "CCD# camera in steady-state trast". The arrow points to the tumor and its compression of the right temVibrational photon was echo,performed pump-probe at anda transient-grating experiabsorption 3207-3245. operation. The time-resolved experiment 711-735. poral lobe. and to emission and ! is the relaxation coefficient, on other silicon interfaces [16], are very temple to expose the skull ments over the tumor, rather than the mode ofobtained of kHz, the asymmetric CO-stretch tungsten hexacarwhich is inversely proportional to the rotational diffusion typically lower repetition rate, i.e., 83.2 than the normal one large skin flap one bony1 uses just to ensure that the tumor (w[co]6) in various solvents have provided a foundation for for the understanding of surface recomimportant coefficient a sphere. The measurements of fluorescence is"8.32 MHz# using a Pockel’s A. Humanof neurosurgery within the exposed area.understanding A 5cell. cm bone flap was raised, the dynamics of molecular vibrations in condensedanisotropy decay lead to very fast depolarization of the nico- exposing Acridine from Prolabo, used without further purification, bination phenomena and their role in the dynamics the underlying dura, which linesThe the inside of the matter systems. seminal experiment investigated the asymThe first patient had a suspected meningioma of at least tinamide ring, independent of the rest of the NADH mol- skull. was studied. Absorption spectra were recorded using a Cary -5 0 5 10 15 20 25 2 The tumor, attached tometric the CO-stretch deep, or brain of the mode side, of W(CO)6 in 2-methyltetrahydrofuran (23 cm We in size, in hydrodynamic Fig. 7, and wasvolume neurologically of photon-induced electron/hole pairs. ecule. find asanshown average of 1000 dura, 210 was "Varian Inc.# spectrophotometer. Typically, a 0.1 cm or a MTHF) (28). The FELneuronavigawas tuned to 5.10 pm and the micropulse Time (ps) easily located using the wand of the 3234 III. The first Free Electron Laser experimental results Edwards et al. Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 1 1 2 2 3 2 3 User applications started 1 a 2 10 2 "1 10 "1 11 "1 1 0 °C 3 stableÅprior the procedure. patient was operated by fortoNADH, which The would correspond to a on sphere #100 an experienced neurosurgical in Vanderbilt’s Keck with radius of 6.2 Å. This isteam in good agreement withFEL the Center. While this was the first human operation in this fa3 volume of a folded configuration (836 Å ) given by a van cility utilizing the Mark-III FEL, the facility had been perder Waals model. The spatial conformations deduced are forming both conventional laser and nonlaser human surgery shown in Fig. 38 in folded and open conformations. These !primarily orthopedic procedures" on a daily basis for several results are in agreement with those obtained from previous months prior to this operation. There are extraordinary needs nuclear magnetic resonance "NMR# studies of aqueous for a 81neurosurgical operation of this complexity. It became NAD. clear early on in the design of these operating rooms that was 2.7around psconcentration at athe repetition rate of 1 kHz. Because the 1 cmsystem. quartz A optical used. Itscut final tional 1 cm cell cuff was ofduration dura was borderwas Figure 11. Beating evident in photon echo decays and fits for the of vibrations to the heat bath, i.e. mechanical degrees of coupling First use of the UV Super-ACO Free asymmetric CO-stretching mode for W(CO)6 in DBP as a function of $ M and 1.6 mM, giving an absorbance of about 0.5 116 of the tumor and then folded back to expose the tumor. The at freedom external to the molecule, is substantially weaker than that temperature. Reprinted with permission from reference 37. Electron Laser : fluorescence 350 nm and absorbance about 1 at 363 nm,any respectively, surrounding normal brain of was protected from possible in of electronic states, the dephasing times are relatively long for the decays rotational dynamics of the 0.1 cm path of amoistened quartz cuvette. stray laserand energy by cottonoids !Fig. 9". vibrational photon echo, and there are little or no solvation The beats are interpreted as multilevel coherence of the anharmonic surgically exposed, 1500 macropulses ofpulses are appropriate for this The absolute intensity of a differential transient absorptheOnce NADH coenzyme , M.dynamics. E.about Consequently, picosecond oscillator. Figure 11 exhibits beats in the photon-echo decay curve, m radiation 32 mJ/macropulse were deliv6.45 tion#spectrum %A(&,t) isinvestigation. directly proportional to the popuThe temperature was varied from 300 to 16 K, taking Couprie, P.Tauc, F.averaging Merola, A. which are accounted for by a three-level model with a modulation ered through an articulated arm toM.the outer surface ofthat the theliquid and then to a glass. the sample from a liquid to a supercooled lation of theD. molecule in an excited state. Assuming Delboulbé, Garzella, T. Hara, frequency of 2.3 ps and a vibrational anharmonic splitting of Photon echoes observed from 16 to 140 K, where T, is 90 K, tumor. armonly terminates awere hand piece, where pumpThe beam via65(5) theintransition S 0 →S 1 , the Billardon ,articulated Rev.interacts of Scient. Inst., 14.7 ? 0.3 cm-'. and the photon-echo decay curve at 16abK is shown in Fig. 10. The a saturation calcium fluoride lens with a focal length of 12.5 cm fo!1/ ' (&) where ' (&) is the fluence is F Vibrational spectral diffusion has been investigated with pumpS (0 a0 great care was required to minimize the likelihood of forgetMay 1994, 1485-1495 constant for decay is# m. 15 ps, A2 )theathomogeneous dephasing cused the cross FEL section beam to atime spot sizestate of the 310!20 probe and transient-grating techniques using 1.3 ps pulses from the sorption of the ground "in units of cm ting a seemingly insignificant device, medicine, supply, or is 60 and the the homogeneous linewidth is 5.2 GHz, which B. Transient absorption experiments helium–neon beam wastime used to ps guide excision. By Surface States and Space FEL and 10 ps pulses from an optical parametric amplifier (38). An wavelength pilot &. The pulse fluence the pump be of part. Thus a track record was established of successful, roushould beofcompared withshould the inhomogeneous linewidth of 540 practicing one final time with some sterile paper on a side ensemble of solute molecules will sample all possible solvent 39 shows transient absorption experimental Charge Layer Dynamics on Si the same order as the saturation fluence in order to excite a to the homogeneous tineFigure cases using these the operating rooms prior to the first FEL GHz. The pure dephasing time contribution environments and thus a distribution of transition energies on some table, the surgeon was able linewidth, to then position hand piece of conformational fluctuasetup ofpower theElectron influence aThe measure case. employed at Super-ACO. Control of the spatial overlap large fraction of the molecules. on the (111)2x1 :FEL athe Free timescale. Consequently, the homogeneous line spectrally diffuses with the visible pilot beam tions to keep thevibrational focus on the tumor on the level spacing, is 1.6 GHz. between pulses critical.toToa holding monitor area this,from we mounted The the patient wasisbrought the main a sample is limited to a maximum of 100 mW,energy which correLaser-Synchrotron radiation throughout the full inhomogeneous line on a timescale that is long controlling FEL-beamSubsequent delivery measurements with a foot-pedal10 investigated W(CO)6 in 2-methylquartz lens,where whichanesthesiologists was used to focusprepared the pump ontofor the surface, hospital, thebeam patient photons/ sponds to energy of 12 nJ per pulse "i.e., 2$10 with respect to the homogeneous dephasing time. Measurements of study , M.from Marsi, M. E.expoCouprie, actuated beam block. In the pentane first operation, total FEL (2-MP) room temperature to 10 K (36). The FEL was general anesthesia. The patient was prepped and brought into transient spectral hole demonstrate spectral diffusion and pulse#. The pump beam istuned focused onto about theand sample to within to 5.04 thes,pulse sure administered in multiple passes tookpm, 50 ablatL. Nahon, D. Garzella, A. duration was -1.5 ps. These aorientational one of the two operating rooms fitted for use of the FEL. motion of the asymmetric CO-stretching mode for $ m, leading to the possibility of fluence a diameter of )20 results suggest that the asymmetric CO-stretch mode can be ing approximately a cubic centimeter ‘‘divot’’ from the outer Delboulbé, T. Hara, R. Bakker, G. W(CO)6 in 2-MP. Intriguingly, the lifetime increases with Once under anesthesia, the patient was positioned in a supine approximately equal The to theremainder saturationoffluence. In the simplest . 37. Single photon counting data obtained with the Super-ACO SRsurface inhomogeneously broadened in liquid solutions and that inof the tumor. the tumor was retemperature. Indlekofer, M. Billardon, A. Talebposition with a shoulder roll under her right shoulder, thus broadening occurs at toroom temperature. The L: !A" Total fluorescence decay F(t) of NADH at pH 8, 10 °C, $ exc 350sected situation, the !Fig. pump/probe signal observed is proportional en bloc 10". homogeneous allowing to be easilyinstrumental positioned function nearly horizontally 1.6 ps, the homogeneous linewidth was apparent decay time was Ibrahimi, , Appl. Phys. Lett. $ em 460 nm,her andhead corresponding g(t); !B" residu- theOnce population thattheistumor not inwas thedivided groundand state. Thus, if the removed, a portion of 70(7) Native and mutant myogiobins !Fig. 8". 49 (1997) GHz and the inhomogeneous linewidth was -300 GHz. The obtained from maximum entropy method analysis of the decay in !A"; ground state is the only absorbing 895-897 state, then thefor pump/probe the tumor that did not include the defect was sent neuroroom temperature observation of the photon echo is attributable to Investigation of the dynamics of the CO-stretching mode in A standard neurosurgical autocorrelation of the residuals. approach was used in the right A is a linewidth conobservable is given by S(t)!A * P ex(t) + where the relatively sharp homogeneous of asymmetric COmyoglobin provided insight 2016 into protein dynamics (39). temporal area, guided by a Pickar® neuronavigational sysM. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs 31 has !May –10 !June, stant determined by experimental parameters such as theand la- !ERLs), Hamburg, Germany, 2-MP. stretch mode for W(CO)6 in O2 in muscle tissue. CO or O2 Myoglobin stores and transports tem which utilized a computer topography !CT" scan that ser intensity and the probability that the system is found in Infrared photon-echo beats have been observed with -700 fs binds to the iron atom located in a symmetric protoheme, i.e. for Fig. 2. SPV intensity as a function of the FEL/SR delay 2 contrast juin 2016 showed obtained the dayneither prior to the procedure. This in %. jeudi The oxided form (NAD") absorbs nor emits www.lunex5.com III. The first Free Electron Laser experimental results Wavelength limits of oscillator configuration • Storage rings VEPP3 (Russia) Super-ACO (France) NIJI-IV (Japan) UVSOR (Japan) Duke (USA) ELETTRA (Italy) - limited straight section length - planar undulator : mirror degradation due to harmonic content • Linacs Stanford Los Alamos FELI (Japan) ..... • ERLs : Jefferson Lab JAERI Novosibirk Limits in mirror performances M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com High gain studies Strong signal case : Case of «long» undulator, «high» current : The change of electric field in one pass can not be neglected treatment with a set of generalised Bloch equations F. A. Hopf, P. Meystre, M. O. Scully,W. H. Louisell, Strong-signal theory of a Free Electron laser, Phys. Rev. Lett 17 (30) (1976) 1342-1345 Hamiltonian despcription G. Dattoli, A. Marino, A. Renieri, F. Romanelli, Progress in the Hamiltonian Pictoure of the Free-Electron l Laser, IEEE journal of Quantum Electronics QE17 (8) 1371-1387 (1981) N. M. Kroll, P. L. Morton, M. N. Rosenbluth, in Free Electron generators of coherent radiation, edited by S. F. Jacobs et al. Physics of Quantum Electronics 7 (Addison_Wesley), 147 (1980) A. Gover, P. Srangle, IEEE J. Quantum Electron. 17, 1196 (1981) Collective instability the electron communicate with each other through the radiation and the space charge field. => electron «self bunching» on the scale of the radiation wavelength periods. The electrons have nearly the same phase and emit collectively coherent synchrotron radiation. Exponential growth of the radiation. Ex of cooperative effect in radiation-matter interaction R. Bonifacio et al., Cooperative and chaotic transition of a free electron laser Hamiltonian model, Optics Communications 40(3), 1(1982), 219-223 R. Bonifacio, Pellegrini C. and L.M. Narucci, Collective instabilities and high-gain regime in a free electron laser, Opt. Comm. 50, 376 (1984) Sprangle, P.,Tang, C. M., & Roberson, C.W. (1985). Collective effects in the free electron laser. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 1-18. Bonifacio, R., Casagrande, F., Cerchioni, G., de Salvo Souza, L., Pierini, P., & Piovella, N. (1990). Physics of the high-gain FEL and superradiance. La Rivista del Nuovo Cimento (1978-1999), 13(9), 1-69. Start-up from spontaneous emission First considered by Saldin and Kondratenko in order to amplify the emission in the high gain regime until saturation. Considered cases : infra-red FEL @ 10 MeV, shorter wavelengths (20 GeV, 0.25 keV). A.M. Kondratenko et al, Sou Phys. Dokl. 24 (12), 1979, 989 Kondratenko A.M., Saldin E.L.: Generation ofCoherent Radiation by a Relativistic Electron Beam in a Undulator. Part. Accelerators 10, 207–216 (1986) Y.S. Derbenev, A.M. Kondratenko, E.L. Saldin: On the possibility of using a free electron laser for polarisation control in a storage ring, Nucl. Instr. Meth. A 193, 415–421 (1982) K. J. Kim et al, PRL57, 1986, 1871 C. Pelligrini et al, NIMA475, 2001, 1 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com IV. The high gain Free Electron Laser Self Amplified Spontaneous Emission (SASE) High density electron beam and long undulator : • a strong bunching takes place (space charge) • the change in electric field can no more be neglected => - coupled pendulum equation, describing the phase space evolution of the particules under the combined undulator magnetic field and electric field of the optical wave - evolution of the optical field - evolution of the bunching coupled to the longitudinal sapce charge forces => evaluation of the electronic density and current evaluation of the light wave evolution Undulator Magnetic field B electron equations of motion J Maxwell wave equation for the radiation field Er Collective instability the electron communicate with each other through the radiation and the space charge field The FEL parameter defines the growth rate, measured in undulator periods Review papers : Z. Huang, K. J. Kim, Review of the free-electron laser theory, Physical Review Special Topics-Accelerators and Beams, 10(3), 034801. Pellegrini, C., A. Marinelli, and S. Reiche. "The physics of x-ray free-electron lasers." Reviews of Modern Physics 88.1 (2016): 015006. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com Evolution of the light wave in the High gain regime SASE : Self Amplified Spontaneous Emission start-up from spontaneous emission noise exponential growth due to a collective instability (self-organisation of the electrons from a ramdon initial state) At saturation, the amplification process is replaced by a cyclic energy exchange between the electrons and the radiated field. Light Start-up 4 1) energy modulation Exponential gain regime 2) density modulation 3) Coherent emission Energy 1 2 eEnergy 3 Saturation Optical guiding • gain guiding (quadratic gain medium, Kogelnick 1965) • refractive index => undulator longer than a few Rayleigh lengths is possible Phase Scharlemann, E.T., A.M. Sessler and J.S.Wurtele, 1985, Physical Review Letters 54, 1925. Scharlemann, E.T., Sessler, A. M., & Wurtele, J. S. (1985). Optical guiding in a free electron laser. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 29-35. Z. Huang, K. J. Kim, A Review of X-ray Free-Electron Laser theory, Phys. Rev. Spe.Topics AB, 10, 034801 (2007) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com Evolution of the light wave in the High gain regime SASE : Self Amplified Spontaneous Emission start-up from spontaneous emission noise exponential growth due to a collective instability (self-organisation of the electrons from a ramdon initial state) At saturation, the amplification process is replaced by a cyclic energy exchange between the electrons and the radiated field. Light Start-up 4 1) energy modulation Exponential gain regime 2) density modulation 3) Coherent emission Energy 1 2 eEnergy 3 Saturation Optical guiding • gain guiding (quadratic gain medium, Kogelnick 1965) • refractive index => undulator longer than a few Rayleigh lengths is possible Phase Phase Scharlemann, E.T., A.M. Sessler and J.S.Wurtele, 1985, Physical Review Letters 54, 1925. Scharlemann, E.T., Sessler, A. M., & Wurtele, J. S. (1985). Optical guiding in a free electron laser. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 29-35. Z. Huang, K. J. Kim, A Review of X-ray Free-Electron Laser theory, Phys. Rev. Spe.Topics AB, 10, 034801 (2007) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 FELs as part of the Star Wars program, and promised a much higher electron IV. The high gain Free Electron Laser beam brightness. Robert Palmer and I, at the Center for Accelerator Physics at www.lunex5.com Brookhaven National Laboratory, decided in 1986-87 to develop this new Limits in storage rings and electron gun development technology for application in laser acceleration and FELs. An S-band version of the Los Alamos gun, optimized for high peak power and small emittance, was Limits in storage ring designed at Brookhaven. J. B. Murphy and C. Pellegrini, J. Opt. Soc. Am. B, 2 (1985) Batchelor, K., H. Kirk, K. McDonald, J. Sheehan Developments of photo-injectors and M. Woodle. 1988. Development of a High Fraser, J.S. and R.L. Sheffield. 1987. High- brightness injectors for RF-driven freeBrightness Electron Gun 1489-1496. for the Accelerator Test electron lasers. IEEE J. Quantum Electron. QE-23: Batchelor, K.,Facility H. Kirk, K. McDonald, J. Sheehan and M.Woodle.Laboratory. 1988. Development at Brookhaven National Proc. of a High Brightness Electron Gun for the Accelerator Test Facility at Brookhaven of the Proc. 1988 European Particle Accelerator Conf., National Laboratory. of the 1988 European Particle Accelerator Conf., Rome, pp. 54–958.Rome, pp. 54–958. with a linac and a photoinjector it is possible to reach the nm region at a beam energy of 1.5 GeV, with about 6 mJ/pulse starting from noise in an 11 m long Later work onundulator photo-injector development was done at UCLA and a program was started later at SLACNuclear by Herman Winick, andA272, continued with a BNL-SLAC-UCLA collaboration. C. Pellegrini Instruments and Methods 364-367 (1988). Sigtuna, June 14-18, 2015 C. Pellegrini 10 fs-10 ps, εα1/E 10-30ps, εαE2 25 Energy spread : 0.01 % Repetition rate : depending on the linac (room temperature or superconducting) Energy spread : 0.1 % M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com Historical observations of SASE SASE at saturation mm waves (80’s: LLNL, MIT) T. Orzechowski et al. Phys. Rev. Lett 54, 889 (1985) SASE at start-up µm (CLIO, L. A., Stanf.) Prazeres, R., Ortega, J. M., Glotin, F., Jaroszynski, D. A., & Marcouillé, O. (1997). Observation of self-amplified spontaneous emission in the mid-infrared in a free-electron laser. Physical review letters, 78(11), 2124 Saturation at 100 nm (TESLA-TTF, 2001) Ayvazyan,Valeri, et al. "A new powerful source for coherent VUV radiation: Demonstration of exponential growth and saturation at the TTF free-electron laser." The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics 20.1 (2002): 149-156. Bunching (CESTA, 8mm) SASE operation of the VUV FEL at 30 nm (DESY, 2005), 4 nm (2007) Gardelle, J., Lefevre,T., Marchese, G., Rullier, J. L., & Donohue, J.T. (1997). High-power operation and strong bunching at 3 GHz produced by a 35-GHz free-electron-laser amplifier. Physical review letters, 79(20), 3905. Ackermann,W. A., Asova, G., Ayvazyan,V., Azima, A., Baboi, N., Bähr, J., ... & Brinkmann, R. (2007). Operation of a free-electron laser from the extreme ultraviolet to the water window. Nature photonics, 1(6), 336-342. 5 orders of magnitude of amplification (IR, UCLA/Los A.) and Saturation at 12 µm (UCLA/L. Alamos, 1998) SCSS Test Acceletator at 60-40 nm M. J. Hogan et al., Phys. Rev. Lett. 80, 289 (1998) M. J. Hogan et al., Phys. Rev. Lett. 81, 4867 (1998) Saturation at 530 nm, 385 nm (LEULT, 2000) Milton, S.V., Gluskin, E., Biedron, S. G., Dejus, R. J., Den Hartog, P. K., Galayda, J. N., ... & Sereno, N. S. (2000). Observation of self-amplified spontaneous emission and exponential growth at 530 nm. Physical review letters, 85(5), 988. S.V. Milton et al, Exponential gain and saturation of a Self-Amplified Spontaneous Emission Free- Electron Laser, www.sciencexpress.org / 17 May 2001 / Page 1/ 10.1126/science. 1059955 Saturation at 800 nm (UCLA, 2001) Shintake,T.,Tanaka, H., Hara,T.,Tanaka,T.,Togawa, K.,Yabashi, M., ... & Goto, S. (2008). A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region. Nature Photonics, 2(9), 555-559. SASE operation of the LCLS at 0.15 nm Emma, P., Akre, R., Arthur, J., Bionta, R., Bostedt, C., Bozek, J., ... & Ding,Y. (2010). First lasing and operation of an ångstrom-wavelength free-electron laser. nature photonics, 4(9), 641-647. SASE operation at SACLA at 0.08 nm Ishikawa,T., Aoyagi, H., Asaka,T., Asano,Y., Azumi, N., Bizen,T., ... & Goto, S. (2012). A compact X-ray free-electron laser emitting in the sub-angstrom region. Nature Photonics, 6(8), 540-544. Tremaine, A.,Wang, X. J., Babzien, M., Ben-Zvi, I., Cornacchia, M., Nuhn, H. D., ... & Rosenzweig, J. (2002). Experimental characterization of nonlinear harmonic radiation from a visible self-amplified spontaneous emission free-electron laser at saturation. Physical review letters, 88(20), 204801. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 the theinput inputofofthe theFEL FELamplifier amplifierisisamplified, amplified,typically typicallyup uptotosaturation saturationininaasingle singlepass passafter afteraaregime regimeofofexponential exponential wth. growth. growth. IV. The high gain Free Electron Laser www.lunex5.com SASE : Conditions for amplification 3.4 Conditions amplification Conditions forfor amplification 3.4 Conditions for amplification Conditions for amplification discuss now the for SASE amplification. Let’s discuss now theconditions conditions for SASE amplification. sLet’s discuss now the conditions for SASE amplification. • The electron beam should be rather "cold", its energyspread spreadshould should be be smaller smaller than the bandwidth, i. e.i. e. The electron beam should be rather "cold", its energy than the bandwidth, The electron beam should rather "cold",itsitsenergy energyspread spread should should be bandwidth, i. e.i. e. The electron beam should be be rather "cold", besmaller smallerthan thanthethe bandwidth, σγ σσγ γ <<ρρFEL FEL γγ < ρFEL γ (172) (172) εεn n λλ << γ λ εnγ 4π 4π (173) (173) (172) There should bebeaaproper matching (size, divergence) between the beam and the There propertransverse transversematching matching (size, divergence) between theelectron electron beam thephoton photon • Thereshould should be a proper transverse (size, divergence) between the electron beam and the and photon beam There should beundulator a properprogression transversefor matching (size, divergence) between the beamshould and the photon beam along insuring aaproper interaction. ItItthat means the be beam along the undulator progression for insuring proper interaction. means thatelectron theemittance emittance should not be along thethe undulator progression for insuring a proper interaction. It means thethat emittance should not be toonot large mtoo along the undulator progression forundulators, insuring aintermediate proper interaction. It means that the segments. emittance should large atatshort For long between undulator segments. at short wavelength. For long undulators, intermediate focusing isfocusing then put is between undulator It writes : not be too large shortwavelength. wavelength. For long undulators, intermediate focusing isthen thenput put between undulator segments. ItItwrites : : wavelength. For long undulators, intermediate focusing is then put between undulator segments. large at short writes rites : < (173) ItItonly γ 4πbecause onlybecame becamepossible possibletotoreach reachFEL FELatatshort shortwavelenght wavelenght becauseofofthe theprogresses progresseson onelectron electronguns. guns. The radiation diffraction be than the FEL i.e. length should be It only became possible tolosses reach should FEL at short wavelength ofgain, the progresses on electron guns. The radiation diffraction losses should besmaller smaller thanbecause thebecause FEL gain, i.e.the theRayleigh Rayleigh should belarger larger t only became possible to reach FEL at short wavelenght of the progresses onlength electron guns. than thanthe thegain gainlength. length. The radiation diffraction losses smallerthan than the Rayleigh length should • The radiation diffraction lossesshould should be be smaller thethe FELFEL gain, gain, i.e. thei.e. Rayleigh length should be larger thanbe thelarger gain length. n the gain length. (174) Zr > Lgo Zr > Lgo Corrections Correctionsterms terms(from (fromthe the3D 3Dtheory) theory)can canbe beintroduced introduced XXXREF REFM. M.XieXXXX XieXXXX Zr > LgoXXX Corrections terms (from the 3D theory) canCorrections be introduced XXX REF M. XieXXXX terms M. Xie Nucl. Inst. Meth. A 445, 59 (200) M. Xie, Porceedings PAC 1995, 183 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 (174) (174) IV. The high gain Free Electron Laser 1 Seeding FELS with HHG www.lunex5.com 13 while an FEL amplifier has a relative amplification bandwidth of the order SASE properties and coherence: only the noise infrom the noise, FEL bunching amplification spectral f ∼ Limited 2ρf el [31] temporal start-up on different trainsrange of the bunch will be amplified. We need to calculate the fluctuations in a frequency => “spikes” in spectral andthen temporal distribution : slippage over one gain length the portion of beam that we have to consider for the angeCooperation ∆ω ∼ 2ωρflength el and Nberhas of spikes = bunch lengthof/ cooperative length length, lc ∼ λ/4πρf el . The verage, to be of the order the cooperation umber of electrons in a cooperation length is Spikes : separated nec by one cooperative length We may therefore spectral width :ρ .12, 1.14 and 1.15 Statistics : Gamma distribution = Ipeak lc /e0 c = Ipeak λ/ (4πe0 cρf el ) (1.15) estimate the shot noise intensity combining equations Isn ∼ 18e− √ 2 ρ f el 3 ω γm0 c2 ∼ 3 ωρ2f el γm0 c2 Σb (1.16) • jitterfunction from This is proportional to the square of the ρf el parameter, grows pulse to nearly with the frequency and with the electron beam energy. Assuming pulse ypical values for the main parameters (ρf el ∼ 10−3 , λu = 3 cm and K = 2) we have plotted in Fig. 1.5 the power corresponding to the intensity 1.16 over transverse mode area equivalent to the electron beam transverse size. Handling : single spike taper seeding and self seeding S. Reiche et al., NIMA 593 (2008) 45-48 L. Giannessi et al., Phys. Rev. Lett. 106, 144801 (2011) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com SASE properties FLASH SCSS Test Accelerator : 60-40 nm M. Kuhlmann et al, FEL06 P. Mercère et al, , Optics Letters, 28 (17), 1534-1536 (2003) A. Singer et al. PRL 101, 254801 (2008) Single-shot wavefront analysis of SASE harmonics in different FEL regimes, R. Bachelard, P. Mercere, M. Idir, M. E. Couprie, M. Labat, O. Chubar, G. Lambert, P. Zeitoun, H. Kimura, H. Ohashi, A. Higashiya, M.Yabashi, N. Nagasono,T. Hara,T. Ishikawa, accpeted in Phys. Rev. Lett. 2011 Wavefront quality : ability to properly focus M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com IV. The high gain Free Electron Laser SASE Versus seeding and echo SASE (Self Amplified Spontaneous Emission) : no laser - electron interaction • short wavelength operation (1 Å) • good transverse coherence => low emittance required=> gun, energy • spike • single spike (low charge, chrip/taper), self-seeding S. Reiche et al., NIMA 593 (2008) 45-48 R. Bonifacio et al, Opt. Comm. 50, 1984, 376, K. J. Kim et al, PRL57, 1986, 1871, C. Pelligrini et al, NIMA475, 2001, 1, A.M. Kondratenko et al, Sou L. Giannessi et al., Phys. Rev. Lett. 106, 144801 (2011) Phys. Dokl. 24 (12), 1979, 989 Seeding : one laser-electron interaction • temporal coherence given by the external seed laser • improved stability (intensity, spectral fluctuations and jitter) => pump-probe experiments • quicker saturation => cost and size reduction L. H.Yu et al, Science 289, 2000, 932 • good transverse coherence L. H.Yu et al, PRL912003, 074801 • Seed : laser and HHG ( 60 nm) T. Saftan APAC 2004, Gyeongu Echo : Echo Enable Harmonic Generation : two laser - electron interactions 1 "echo = 1 1 + ! "1 "2 G. Stupakov., PRL 102, 074801 (2009) high order harmonics reached in a compact manner Zhao et al., Proceed FEL conf, Mamö (2010) D. Xiang et al., PRL 105, 114801 (2010) ! !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com X-ray FELs FLASH. FLASH2 Operation Started 2 mJ, 1.4 Å LCLS Free-Electron Laser in Hamburg SACLA 1.5 Å saturation at 65 m (of 112 m) now 6 mJ, 96.7 % availability > Official permission for FLASH2 beam operation February-7, 2014 Electron beam on 4FL2EXTR March-4, 2014 > Electron beam operation started in March 2014 first electron beam in extraction March-4, 2014 first beam to dump May-23, 2014 Electron beam on 3FL2DUMP May-23, 2014 only few days available for FLASH2 beam operation before simultaneous operation established > Simultaneous operation of FLASH1 (SASE) and FLASH2 (electron beam) starting end of May 2014 !"#$%&'()*(+*,-./0*1'&2*/2($&*/./34,3-* FLASH2 runsFLASH now in parallel to FLASH1 whenever possible, 5%6'%&'()*789:#:* mainly during FLASH1 photon user <1A9$BC38D$ experiments =>$<989:1-4$ J/191-$ 6..'7'389:-;$<93,.9,3'4$ E-F,789134$ 4>?6<G$ ĺWLPHDYDLODEOHIRUFRPPLVVLRQLQJLQFUHDVHGVLJQLILFDQWO\ LGM$ K:8;-149:.4$ Photon beam on FL2_CE_YAG August-20, 2014 !"#$%&' dedicated FLASH2 beam time reserved as well =>$@,-$ ?84'34$ +,-./$01%23'44134$ #$&'($ "#)$&'($ "*#)$&'($ 2014 > First lasing:5#)$&'($ August-20, +'8%$K,%2$ >H?$HI2'3:%'-94$ !"#$%$ FERMI Katja Honkavaara | FEL Conference 2014 | August-27, 2014 !" to come : E XFEL, PAL FEL, Swiss FEL .... M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 IV. The high gain Free Electron Laser www.lunex5.com LETTER Applications of FELs in the X-ray domain RESEARCH LETTER Jet (10 m/s) Towards imaging of living cells using the program RADDOSE14) and a peak power density in excess of 1016 W cm22 at 70-fs duration. In contrast, the typical tolerable dose in conventional X-ray experiments is only about 30 MGy (ref. 1). A single LCLS X-ray pulse destroys any solid material placed in this focus, but the stream replenishes the vaporized sample before the next pulse. The front detector module, located close to the interaction region, recorded high-angle diffraction to a resolution of 8.5 Å, whereas the rear module intersected diffraction at resolutions in the range of 4,000 to 100 Å. We observed diffraction from crystals smaller than ten unit 200 μm cells on a side, as determined by examining the data recorded on the Rear pnCCD es rear pnCCDs (Fig. 2). A crystal with a side length of N unit cells gives (z = 564 mm) rise to diffraction features that are finer by a factor of 1/N than the Front pnCCD Interaction Bragg spacing (that is, with N 2 2 fringes between neighbouring Bragg (z = 68 mm) point peaks), providing a simple way to determine the projected size of the nanocrystal. Images of crystal shapes obtained using an iterative phase second nanocrystallography. Nanocrystals flow in their retrieval method15,16 are shown in Fig. 2. The 3D Fourier transform of 21 a gas-focused, 4-mm-diameter jet at a velocity of 10 m s the crystal shape is repeated on every reciprocal lattice point. However, Liquid the pulsed X-ray FEL beam that isjet focused on the jet. Inset, the diffraction condition for lattice points is usually not exactly satisfied, anning electron micrograph of the nozzle, flowing jet and so each recorded Bragg spot represents a particular ‘slice’ of the Ewald wo pairs of high-frame-rate pnCCD detectors12 record lowpnCCD s FEL repetition sphere through the shape transform, giving aRear sethe variety of Bragg spot lat ffraction from single X-ray FEL pulses, u p (z = 564 mm) y -raorientations stals arrive at random times in the beam, and profiles in a pattern; these are apparent in Fig. 2. The sum of counts Xand S L LC hitting one is proportional to the crystal concentration. in each Bragg spot underestimates the underlying structure factor square modulus, representing Front pnCCD a partial reflection. Interaction Figure 3a shows of the X-ray pulses was 1.8 keV (6.9-Å wavelength), with (z = 68strong mm) single-crystal diffraction to the highest point photons per pulse at the sample and pulse durations of angles of the front detector. The nanocrystal shape transform is also s (ref. 13). An X-ray fluence of 900 J cm22 was achieved apparent in many patterns at the high angles detected by the front FEL beam to a full-width at half-maximum of 7 mm, detector, giving significant measured intensities between Bragg peaks Figure nanocrystallography. Nanocrystals flow in their as is noticeable in Supplementary Fig. 3a. These mid-Bragg intensities o a sample dose of up to1 700| Femtosecond MGy per pulse (calculated 21 using the program RADDOSE14) and a peak power density in excess of Mimivirus (Acanthamoeba polyphaga) : le plus 1016 W cm22 at 70-fs duration. In contrast, the typical tolerable dose in conventional X-ray experiments only about 30 MGy (ref. connu 1). A single RESEARCH isLETTER virus (diamètre de 0.75 µm) LCLS X-ray pulse destroys any solid material placed in this focus, but the stream replenishes the vaporized sample before the next pulse. a b The front detector module, located close to the interaction region, Diffraction pattern recorded high-angle diffraction to a resolution of 8.5 Å, whereas the rear module intersected diffraction at resolutions in the range of 4,000 to 100 Å. We observed diffraction from crystals smaller than ten unit cells on a side, as determined by examining the data recorded on the rear pnCCDs (Fig. 2). A crystal with a side length of N unit cells gives rise to diffraction features that are finer cby a factor of 1/N than the Bragg spacing (that is, with N 2 2 fringes between neighbouring Bragg peaks), providing a simple way to determine the projected size of the nm nanocrystal. Images of crystal shapes obtained200 using an iterative LETTERphase RESEARCH Membran protein photosystem 1 15,16 Diffraction pattern d retrieval method are shown in Fig. 2. The 3D Fourier transform of e buffer solution in a gas-focused, 4-mm-diameter jet at a velocity of 10 m s Micrographie the crystal shape is repeated on every reciprocal lattice point. However,électronique 1 perpendicular to the pulsed X-ray FEL beam that is focused on the jet. Inset, Upper font detector a a b b for lattice points is usually not exactly satisfied, ¯the 21 11 0 diffraction condition 0 1¯ 1 ¯ ¯2 15 20 environmental scanning electron micrograph of the nozzle, flowing jet and ¯0 22 6 ¯ 4¯ 14 24 002 so each recorded Bragg spot represents a particular ‘slice’ of the Ewald focusing gas30. Two pairs of high-frame-rate pnCCD detectors12 record low¯ 13 12 0 19 2 0 and high-angle diffraction from single X-ray FEL pulses, at the FEL repetition sphere through the shape transform, giving a variety of Bragg spot ¯ 2̄ 16 ¯ and 12 1 1 profiles in a 7pattern; these are apparent in Fig. 2. The sum of counts rate of 30 Hz. Crystals arrive at random times and orientations in the beam, ¯0 79 11 0 1 ¯ 2̄ 4 14 ¯ 0 Bragg 57 the probability of hitting one is proportional to the crystal concentration. in each spot underestimates the underlying structure factor ¯ 0 921 811 19 10 3 5¯ 0 square modulus, representing a partial reflection. 1,000 nm 010 Lower font detector ¯ 2¯ 6¯ Figure 3a shows strong single-crystal diffraction to the highest 14 photon energy c*of the X-ray pulses was 1.8 keV (6.9-Å wavelength), with ¯ 17 4̄ 13 ¯ 21 4¯ 10 020 1¯4 9 4̄ of the front detector. The nanocrystal shape transform is also per pulse at the sample and pulse durations of 14¯angles more than 1012 photons 14 4̄ 010 010 22 715 nm 620 nm the front 10, 70, and 200b*fs (ref. 13). An X-ray fluence of 900 J cm was achieved apparent19¯in 9 7¯ many patterns at the high angles detected by Reconstruction f Unconstrained Sphere Icosahedron g Unconstrained Sphere Icosahedron ¯ 20 14 7̄ by focusing the FEL beam to a full-width at half-maximum of 7 mm, detector, giving significant measured intensities between Bragg peaks ¯ ¯ 19 19 7 ¯ 26 7¯ 15 c corresponding to a sample dose d in¯ Supplementary 100 Fig. 3a. These mid-Bragg intensities of up to 700 MGy per pulse (calculated ¯ 22 7¯ as is noticeable 18 2¯3 9 10 gros 1 0 1 0 1 0 c a 100 b 0 1¯ 1 1¯ 1 0 20 Å d h 1.0 i 1.0 0.8 M.0.8M. Seibert Single particles and PRTF = 0.5 intercepted PRTF = 0.1 PRTF = 0.5et al.,PRTF = 0.1 mimivirus 0.6 0.6 imaged with an X-ray laser,0.4Nature, 470, 2011, 78 0.4 PRTF = 0.5 PRTF 002 a* 0.2 32 nm 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 b* 160 nm 290 nm 0 200 nm PRTF = 0. 1 PRTF 010 Resolution shell (nm–1) Figure 2 | Single-shot diffraction patterns on single virus particles give 0.2 32 nm 32 nm 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Resolution shell (nm–1) modes19 and two averaged images after fitting unconstrained low-res corresponding high-angle pattern. In c we count seven fringesand in the b* Figure 3 | Diffraction intensities electron density of photosystem I. 73patterns, displayed on the linear colour scale shown on the right. c, d, Region of H. Chapman et al., Femtosecond X-ray protein nanocrystallography, Nature, 470, 2011, interpretable results. a, b, Experimentally recorded far-field diffraction modes to a spherical or an icosahedral profile, respectively. The orien direction, corresponding to nine unitpattern cells, or 250 nm. Insets, images a, Diffraction recorded onreal-space the front pnCCDs with a single 70-fs pulse the 2mF 2 DF electron density map at 1.0s (purple mesh), calculated from ent crystal diffraction. Low-angle diffraction patterns ear pnCCDs, revealing coherent diffraction from the structure m I nanocrystals, shown using a logarithmic, false-colour indices of the peaks in a were identified from the c patternso(inand false-colour representation) from individual virus particles the icosahedron2016 was determined from the diffraction data. The resul of the nanocrystal, by phase retrieval (using the Shrinkwrap M. E. Couprie, CAS determined School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs !ERLs), Hamburg, Germany, 31 !Mayofat–10 70-fs data (c) and from conventional synchrotron data truncated a small!June, background subtraction and correction of saturated pixels. Some peaks are the circled coherent Bragg shape transform. algorithm ) of theafter captured in two different orientations. c, Transmission electron micrograph differences between the spherical and icosahedral fits. h, i, The jeudi 2 juin 2016 VOL 470 | 3 FEB RUARY 2011 15 labelled with their Miller indices. 0 1 0 The resolution in the lower detector corner is 8.5 Å. b, Precession-style pattern of the [001] zone for photosystem I, obtained 7 resolution of 8.5 Å and collected at a temperature of 100 Kappearance (d) (Methods). The . an unstained Mimivirus particle, showing pseudo-icosahedral reconstructions where the unconstrained low-resolution modes were refined model is depicted in yellow. d, e, Autocorrelation functions for a (d) and b (e). The shape and size of each an icosahedron. All reconstructions gave similar resolutions. We cha Conclusion and prospects www.lunex5.com Conclusion 2011 2008 2009 EUV SASE FEL 2001 2002 VUV SASE FEL VUV FEL oscillator Seeded high Gain SASE FEL Visible SASE FEL 2000 1990 1983 Second FEL oscillator (visible) Free Electron Laser amplification 1976 First Free Electron Laser oscillator (infra-red) 1977 1980 1971 Free Electron Laser concept First laser (Ruby) Ubitron 1970 1958 1960 Undulator concept Laser invention 1946 1947 1951 1953 1954 1955 Undulator radiation observation Maser Undulator radiation observation HHG seeded FEL First X-ray FEL 2010 FERMI Seeded FEL user facility Second X-ray FEL X-ray FEL oriented History Energy loss Lab observation of synchrotron radiation 1950 1939 Varian brothers : klystron 1940 1930 1920 Einstein, black body radiation 1917 Historical survey of FELs : - exchange of ideas and concepts in various domains : creativity ! - attempting to show how the new ideas arise - subjective (apologize for cherished non cited papers...) C. Pellegrini,The history of X-ray free-electron lasers, Eur. Phys. J. H, 37(5), 659-708. DOI: 10.1140/epjh/e2012-20064-5 Maturity of X-FEL => X-ray FEL applications for new investigation of matter are blooming up Bostedt, C., Boutet, S., Fritz, D. M., Huang, Z., Lee, H. J., Lemke, H.T., ... & Williams, G. J. (2016). Linac Coherent Light Source:The first five years. Reviews of Modern Physics, 88(1), 015007. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Conclusion and prospects www.lunex5.com Approach diffraction and Fourier limits in a wide spectral range, with flexibility for users high High rep. rate : stability higher photon energies single spike, modified SASE, XFELO FEL property manipulations seeding, echo, up frequency conversion Compact accelerator : Laser wakefield acceleration, dielectric acceleration, inverse FEL Short FEL interaction superconducting linacs, rings as pulses / high energy resolution (BW : 10-6) multiple users Combinaison with lasers and THz (e.g. pump-probe...) Compact undulator Make «more compact» FELs Physics and applications of High Brightness Beams : towards a fifth generation light source, Puerto-Rico, March 25-28, 2013 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Poincare! sections are illustrated in Fig. 6b, for which the number of intercepts n of the attractor with the plane of the Poincare! section is a signature of the ‘‘nT’’ regime, and where a folded shape which does not fill the whole space corresponds to the chaos. From the observation of the attractors, the origin of the irregular patterns of the FEL can be attributed to the deterministic chaos rather than to noise. The evolution of the system when a given control parameter is varied can be followed by the observation of the bifurcation diagram, in which the intensity sampled at a definite time of Conclusion www.lunex5.com Various regimes and studies • MOPA • Chaos and control • Regerative FEL • Vortives Fig. 7. Bifurcation diagrams (a) for a change of f between 200 and 400 Hz, a ¼ 14:3 Hz and (b) for a change of a between 0 and 60 Hz, f=600 Hz. the modulation period is plotted versus the control parameter. As the stroboscopy is synchronized with the modulation, a nT regime delivers a nvalued output and random answers reflect the statistics of the chaos. Fig. 7 illustrates a 1T–2T bifurcation for a change of the frequency of the modulation in (a), and a 1T, 2T, chaos, 2T, 3T sequence for a modification of the amplitude of modulation. Bifurcation diagrams are powerful tools for the observation of the transitions between the different regimes. • Mode locking • Q-switching • Super-radiance 5. Conclusion • CPA • limit cycles • 2 color operation.... Fig. 6. (a) IðtÞcosð2pft), IðtÞsinð2pft), Iðt þ tÞ attractors reconstructed from intensity evolution of Fig. 3. 2T regime for a ¼ 12 Hz, chaos for a ¼ 20 Hz, 3T regime for a=46 Hz. (b) Corresponding Poincar!e sections. M. Billardon, PRL 65 (6) , 713 (1990) M. E. Couprie, NIM A 507 (2003) 1-7 Clear bifurcation and chaos sequences have been observed in the response of the FEL to a detuning modulation. In a further work, the sequences (period doubling, inverse cascade, logistic map, etc.) corresponding to various parameters set-ups should be studied, for the determination of the basins of attraction. Clear analysis of the data E. Hemsing et al. , Nature Physics 9, 549–553 (2013) M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com Question for the end Is FEL a real laser? M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 Question for the end www.lunex5.com Is FEL a real laser? Quantum description ? yes very heavy.... needed for some particular effects (electromgantic undulator...) no Macroscopical quantum system? Light Amplification by Stimulated Emission ? theoretically : yes if stimulated diffusion considered as stimulated emission experimentally : light amplifier (with optical resonator, SASE...) Spatial and longitudinal coherence properties yes M. Orzag, R. Ramirez, Quantum features of a fre electron laser, J. Opt. Soc. Am. B , 3 (6) , 895-900 (1986) C. B. Schroeder, C. Pelligrini, P. Chen, Quantum effects in high gain FELs, Phys. Rev. E (64), 056502 M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com Books.... Laser Handbook, Volume 6: Free Electron Lasers by W.B. Colson, A. Renieri, Claudio Pellegrini Noth Holland Free-Electron Lasers in the Ultraviolet and X-Ray Regime Physical Principles, Experimental Results,Technical Realization Authors: Schmüser, P., Dohlus, M., Rossbach, J., Behrens, C. The Physics of Free Electron Lasers Authors: Saldin, Evgeny, Schneidmiller, E.V., Yurkov, M.V. Introduction to the physics of Free electron laser and comparison with conventional laser sources, G. Dattoli et al., ENEA, RT / 2009 / 44/FIM Lectures on the Free Electron Laser Theory and Related Topics, G. Dattoli, A. Renieri, A.Torre, World Scientific, 1 janv. 1993 - 637 pages Principles of FreeElectron Lasers !H. P. Freund M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com Books.... Elleaume P., Onuki H. : Undulators, wigglers and their applications.Taylor and Francis, London (2003) Synchrotron Radiation, Polarisation, Devices and New Sources, M. E. Couprie, M.Valléau, in “Magnetism and Synchrotron Radiation:Towards the Fourth Generation Light Sources”, Proceedings of the 6th International School “Synchrotron Radiation and Magnetism”, Mittelwihr (France), 2012, edited by E. Beaurepaire, H. Bulou, L. Joly, F. Scheurer Springer Proceedings in Physics Volume 151, 2013, pp 51-94 S. Krinsky, M.L. Perlman and R.E. Watson Characteristics of Synchrotron Radiation and Its Sources "Handbook on Synchrotron Radiation",Vol 1 ... A. Hofmann, Proc. of CERN-Accelerator School (CAS) on Synchrotron Radiation and free Electron Lasers, 90-03, 115 (1990). M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 worldwide16–21. This mode of operation allows successfully tested in user experiments at Linac Coherent Light 1.4 he dynamics of ultra-fast processes triggered by a Source (LCLS) in a wide variety of fields. 1.2 -ray pump, with a time resolution on the order of 1.0 www.lunex5.com onds. For example, in the field of time-resolved 0.8 pectroscopy, two colour pulses allow the selective Results olecular and atomic processes, such as chemical Twin-bunch experiment at hard X-rays. The twin-bunch 0.6 and rearrangement. High-intensity two-colour method is schematically illustrated in Fig. 1. The electrons are 0.4 w the study of warm dense matter with time- generated by a photocathode illuminated by a train of two laser 0.2 pump/X-ray probe experiments22,23 as well as the pulses (generated with a pulse stacker, see the Methods section) 0.0 vestigation of X-ray-induced Coulomb explosion with a variable delay on the order of a few picoseconds, 10 11 12 13 rs and nanocrystals at the Instr. femtosecond scale.A407, generating two separate electron are R.Prazeres et al. Nuclear and Methods, 464 (1998), R.Prazeres, et al.,bunches. Eur. Phys.The J. D3,two 87 bunches (1998) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7369 A Photon energy (keV) field of coherent X-ray imaging, there is a accelerated up to 15 GeV in the LCLS linear accelerator and rest in extending multiple wavelength anomalous compressed from a peak current of 20 A to roughly 4 kA by a c Phase-space Phase-space at undulator exit (lasing on) bat undulator exit (lasing off) D) imaging24 to fourth-generation light sources means of two magnetic chicanes. As a result of the bunch com13.5 13.5 5 E = 5800 MeV and E = 1.5 keV b ! tosecond crystallography . 25 2.15 pression, the final arrival time difference of the electron bunches HEAD HEAD TAIL an intense electron bunch travels in a magnetic is on the order of a few tens of femtoseconds. As the acceleration/ TAIL 13.4 13.4 2.1 rating a high-power X-ray pulse (ranging form a compression system generates a time–energy correlation in the 20 Magnetic (between nd ral tens1stof GW) with narrow bandwidth 2 electron undulatorbeam, sectionthe two bunches also have different energies at the 2.05 undulator section Chicane 13.3 13.3 and duration between a few femtoseconds and a end ofK2the accelerator. Finally, the two compressed bunches are –40 –20 0 20 40 –40 –20 0 20 40 Time15 (fs) Time (fs) mtoseconds1. K1 The central wavelength lr is given sent into the undulator where they emit two X-ray pulses of 2.0 ee-formula25 Controlled b d different energies. Although we will present experimental data at Current distribution at undulator exit X-ray temporal profile 8 Delay 2 100 a photon energy x-ray of 8.3 keV, the scheme described can work at any 10 1 þ K2 x-ray 6 nd Color the available LCLS range (nominally from 300 lr ¼ lw ð1Þ photon energy 2in st; 2.05 2g2 1 Color 50 4 to 10 keV). 2 5 2.1 The recently developed X-band transverse deflector13 provides undulator period, g is the beam’s Lorentz factor 0 0 ed amplitude of the magnetic field. At X-ray an effective diagnostic tool for this two-bunch technique. + variants –40 –20 0 20 40 –20 0 20 40 K2 = 2.15 –40 Time (fs) Time (fs) ethods developed so far rely on generating two Figures 2a and 2c show the measured longitudinal phase-space 0 by- using twoslotted distinct emittance values of Kspoiler with a quasi of to the control two bunches for2 the double enabling the at the end of the undulator beamlineFigure | Time-resolved measurements. (a) Measured9.5 longitudinal phase-space of the 10.5 two unspoiled electron the end of th 10.0 11.0 bunches at11.5 16,20,21. Although this approach (theaFEL process being suppressed). (b) Associated current profile of the two bunches. (c) Measured longitudinal phase-space of the tw electron beam unspoiled beam (that is, suppressing the lasing process with large Photon energy (keV) delay (fresh bunch) A. A. Lutman et al.,, PRL 110,after134801 (2013) lasing. (d) Temporal profile of the two X-ray pulses reconstructed from the two phase-space measurements. The error bars are der beam control of the time and energy separation, the transverse perturbation in the electron orbit) and for the averaging of 100 unspoiled phase-space measurements, as discussed in ref. 13. The horizontal axis represents the arrival time with respe Marinelli Phys. Rev.for Lett. 111, 134801 spectra of the two-colour XFEL. (a) Spectrum after slightly the lasingdetuned process. TheA. peak currentetis al., roughly 5 kA a total h -pulses is lower the(phase saturation level because observer (the beam head is on the left). T.Figure Hara2 |etMeasured al., Nature Communications, 4, 2919, 2013 iSASE with than delay shifter), undulators measured by scanning a monochromator with K1 ¼ 1.7 and K2 ¼ 2.15. (2013)separation of 70 MeV. Figure 2d on bunch is used for lasing twice, yielding a total charge of 150 pC, with an energy (b) Consecutive single-shot spectra measured by an in-line spectrometer. to act 5asand phase (K1), power. U2 (K2),shows U1(K1), U2(K2)profile of the X-ray pulses reconstructed from the temporal between 15% shifters. of the full U1 saturation Intensity (a.u.) IV. The high gain Free Electron Laser Two-color operation (SASE) First two color operation at CLIO on a FEL oscillator Power (GW) I (kA) pulse stacking Undulator Chicane 2 Linac Chicane 1 SASE ARTICLE –5 0 The line at 11.4 keV is emittedb from the first undulator section and the 6 Average number of undulators is reduced5 from eight to seven atSingle around Shot 13 min on the ordinate. K2 is varied stepwisely from 2.15 to 2.0 in the lower part and 4 from 2.0 to 2.15 in the upper part of the figure. The accelerator was 3 operated at 10 Hz and the sampling frequency of the in-line spectrometer 2 was 1 Hz. Intensity (arb.units) Laser ∆ Eelectron (MeV) a LCLS with twin bunch ID 01– 08 Time (min) ID 02– 08 Energy (GeV) Energy (GeV) Delay by chicane and different K 5 1 0 NATURE COMMUNICATIONS | DOI: 10.1038/ 0 20 40 60 –60 –40 –20 Intensity (arb. units) ∆ Eelectron (MeV) Energy Energy 60 electron 20 40 the 0 second colour increases. In the TCDP operation, ∆ Ephoton (eV) ∆ Ephoton (eV) beam energy spread resulting a b 15 from the first-colour lasing affects 22 Average –3 the gain of the second colour Figure 3 | Spectral measurements: SASE. (a) Spectral intensity as a function of beam .energy and photon energy in the SASE regime. (b Single shot and single-shot spectrum for a–2 fixed beam energy (the data are binned over electron beam energy fluctuations). This relation is more clearly shown in Figure 3, in which the Beam Direction 10 –1 shot-to-shot intensity correlation between the first and second ~5 ps Spectral properties. the double-colour the longitudinal phase-space measurement (see the Methods 0 colour pulses is plotted. K and K were setToatillustrate 2.14 (9.75 keV) and Self-seeded 1 ~50 fs X-rays,2Fig. 3 shows X-ray spectra taken under th section and ref. 13). The two bunches emit two X-ray pulses the 1.95pulse (11and keV), and energies estimated from the i Time 5 conditions as Fig. were 2. Figure 3a shows the spectral with a peak power of 76 GW1for the head 62 GW for the the pulse integrated spectral area measured by the in-line spectrometer function of electron-beam energy and photon ener tail, and a full-width at half-maximum (FWHM) pulse duration of 2 A. Marinelli et al., High-intenisty double-pulse X-ray are binned in beam energythe using a single-shot me approximately 8 and 10 fs, 3respectively. Thea two pulses arefitnot Photon Energy using Gaussian (see methods). To vary electron beam Time free-electron laser, Nature Comm. 6:6369 (2015) Fourier transform limited as the FEL process is initiated by noise in the0average electron energy in order to deconvolve energy generated by the the 60 number of –60 –40 –20 0spread 20 40 60 –60 first-colour –40 –20 0 lasing, 20 40 the electron operation commonly referred shot-to-shot energy fluctuations. The peak-to-p tic representation of the experiment. Illustration not to scale. From right to left: a laser pulse train generates two electron bunches at a distribution, a mode of the ∆ Ephoton (eV)28 of the first section was (eV) ∆ Ephoton undulators changed between eight aro to as self-amplified spontaneous emission or SASE . The fine separation of the two colours is 90 eV centred right inset shows the measured longitudinal phase-space at the photo-injector exit). The two bunches are accelerated in the LCLS The photon energy of the two pulses is correlated spiky temporal structure of the two SASE pulses is not resolved by (ID01-08) and four (ID05-08) by opening the undulator gaps. Figure 4 | Spectral measurements: self-seeding. (a) Spectral intensity as a function of beam energy and photon energy in the self-seede energy and the colour separation is independentino this diagnostic, which atspectrum this energy time resolution of 4 are fs binned sed by means of two magnetic chicanes (the left inset shows the measured phase-space at the end of the beam line). Finally, (b) Average and single-shot for When ahas fixeda beam (the undulators data over electron beam energy fluctuations). allenergy eight were closed (brown diamonds beam 2016 energy variations (note that this implies that root mean squareHamburg, (RMS). For Germany, this data set,31 the !May pulse energy M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), –10 !June, re sent to an undulator for the emission of two X-ray FEL pulses. The two X-ray pulses have a tunable energy difference in averaged the range Fig.a 3), the first-colour was to saturation. Underarethis tions of theclose energies of the two bunches cor over 100 shots is 1.207 mJ with shot-to-shot fluctuation lasing ndjeudi a variable time delay of tens of fs. condition, the pulse energy of the first colour (9.75 keV) was bandwidth of the two pulses differs slightly. This level of 12%. These data illustrate the main advantage of this two2 juin 2016 –60 –40 –20 colour scheme, which ais that of generating peak power levels and b different features in the longitudinal phase-space www.lunex5.com electron-beam duration and by the possibility of generating long-enough (chirped) seed pulses characterized by significant local power at their tails. In the following, we concentrate on the analysis of the so-called low-gain regime. In this low-gain regime, the relative FEL gain bandwidth B (approximately equal to the relative maximum spectral separation) is proportional IV. The high gain Free Electron Laser Two-color operation (seeded) Pulse splitting P H Y S+I Cchirp A L R E@ V I FERMI EW LETTERS 801 (2013) week ending 8 FEBRUARY 2013 AR NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3476 FIG. 3. Projected spectral and temporal FEL intensities for sing focu different seed powers. Left panel:K–Bexperimental spectral splitting, matic layout of a seeded single-pass FEL s optic measured at FERMI@Elettra [7]; central and right panels: ration scheme). ne Onli eter simulated spectral and temporal splitting (using the code trom spec r ulato PERSEO ). The ∆tset of parameters, valid both for the experiment Und plifier m a L e propose overcomes all the issues related to FIG. 2.G. De Seed-electron interaction and resulting FEL (temporal FEand for the simulation, is the following: normalized energy Ninno et al. PRL, 110, 064801 (2013) mentioned schemes. 10FE3L, energy spread ð#$ Þ ¼ 2:544 & 10#1 , peak and spectral) outputs for different seed configurations: no chirp ð$0 Þ ¼ 2:544 & Twin es uls Ls can rely on different configurations and moderate seed intensity (left panel), no chirp and high current ðIpeak Þ ¼p 200 A, bunch duration ¼ 1 ps (rms); modulaCCD work, we focus on the so-called harmonic seed intensity (central panel), chirped seed with high intensity tor period ¼ 0:1 m, modulator length ðLu Þ ¼ 3 m, modulator detector Twin seed eme, in which a relativistic electron beam (right panel). The meaning of the symbols is explained in ∆tthe laser parameter ðKÞ ¼ 5:7144, radiator period ð&w Þ ¼ 55 & 10#3 m, pulses ΘPump periods ðN Þ ¼ 264, central modulator wavetext. number of radiator rough the static and periodic magnetic field u ΘProbe length ð’ 2%c=!0 Þ ¼ 261 nm, central radiator wavelength an undulator modulator) interacts M. Labat et(called al. Phys.aRev. Lett. 103 (2009) 264801 ð&rad Þ ¼ 32:6 nm, harmonic number ðnÞ ¼ 8; seed-laser power ar externally injected optical pulse (seed) Gaussian seed will have, at the radiator entrance, a bunch∆t ðP0 Þ ¼ 50–500 MW, strength of the dispersive section ðR56 Þ ¼ Ti dispersive ngth !0 ; see Fig. 1. The interaction modu37.2 37.3 37.4 37.5 ing larger than optimum (overbunching). Because of the 20 'm,1 µmlasergratingspot size in the 37.1 modulator ! (nm) ð#r Þ ’ 300 'm, tron-beam energy. Energy modulation Two delayed pulsesis @ large FERMI andenergy SPARC laser-induced spread, the FEL emission from ð!R ; !I Þ3 ¼ ð5 & 10#5 fs#2 ; 3:2 & 10#5 fs#2 Þ. nto spatial bunching, when the electron ! (nm) 37.0 this part of the bunch will be significantly attenuated. The 37.1 tes through a magnetic chicane (dispersive larger the seed peak intensity, the larger the overbunched 37.2 E. Allaria ethas al.,aNature Com. (2013). bunching (as the energy modulation) 064 37.3 zone will3476 be. The beam portions having optimum bunching ual to the seed wavelength. However, it Phys. also Rev.(seeded 37.4 A. Petralia et al., Lett. 115, (2015) by 014801 the lateral parts of the Gaussian seed) will be 37.5 ficant components at the harmonics of the located both at the right and at the left of that zone. As a 37.6 !0 (where !0 ¼ 2"c=!0 , c being the speed consequence, in these conditions the FEL pulse will be –500 0 500 1,000 1,500 2,000 2,500 an integer number). Finally, the bunched Delay (fs) characterized, in the time domain, by two lateral peaks m is injected into a long undulator chain 1 | Generation andintense characterization [(see Fig. 2(b)] or, if the seed Figure is sufficiently to of the twin-seeded FEL pulses and experimental set-up. (a) Energetically distinct two ultraviole pulses with an adjustable delay interact with a single electron bunch. Inside the FEL amplifier, the two seeded regions emit XUV radiation. The ator), where it emits coherently at one of suppress the emission from the central part,of generated by two and temporal separation twin FEL pulses are determined by the parameters of the seed laser pulses and the spectral purity, pulse onics. In the radiator, M. theE. electromagnetic and the widthsseed of!(FELs the pulses is monitored by an ‘online’ spectrometer. (b) Typical of the 2016 twin-FEL pulses. (c) Sequence of FEL spectra Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !ERLs), to Hamburg, Germany, 31 !Mayspectrum –10 !June, separated subpulses [8]. Because is and assumed during a temporal scan of the seed laser pulse pair with respect to the electron bunch. The zero time is defined as the instant when the first rated from bunched electrons is amplified, be monochromatic, the two subpulses have the same jeudi 2 juin 2016 interacts with the electron bunch. Increasing the arrival time delay of the laser pulses with respect to the electron bunch, the emission of th www.lunex5.com FEL configurations M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com Low gain regime of Free Electron Lasers First FELs : Linac based detuning curve M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 www.lunex5.com Low gain regime of Free Electron Lasers First FELs : storage ring based FEL, detuning curve Billardon, M., Garzella, D., & Couprie, M. E. (1992). Saturation mechanism for a storage-ring free-electron laser. Physical review letters, 69(16), 2368. M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 jeudi 2 juin 2016 4.4.5Synchrotron Limits of the classical approach : quantum effects radiation and Free Electron Laser 35 Even though first FEL theory approached quantum mechanics, subsequent classical theory approach Even though the the first FEL theory has has beenbeen withwith quantum mechanics, subsequent classical theory approach 4.4.5 Limits of the classical approach : approached quantum effects www.lunex5.com be applied majority of the experimental set-ups. consider quantum effects can influence the FEL cancan be applied for for the the majority of the experimental set-ups. Let’sLet’s consider howhow quantum effects can influence the FEL process. Even though the first FEL theory has been approached with quantum mechanics, subsequent classical theory approach process. Limits of the classical approach : quantum effects can be applied for the majority of the experimental set-ups. Let’s consider how quantum effects can influence the FEL process. Quantum recoil Quantum recoil Quantum recoil When a electron emits a photon h̄ω its energy is reduced by such an amount toquantum the quantum recoil. the energy When a electron emits a photon h̄ω ph , its is reduced by such an amount due due to the recoil. If theIfenergy ph ,energy Quantum recoil change to�the recoil of the order or larger the FEL bandwidth i.e. given by spontaneous the spontaneous emission change duedue to�the recoil is ofisthe order or larger thanthan the FEL gaingain bandwidth i.e. given by the emission When a electron emits a photon h̄ω ph , its energy is reduced by such an amount due to the quantum recoil. If the energy ∆ ω ∆ ω ≈ ∆ ω( ∆2ω )2 + ∆ ω( ∆2ω )2 , then the quantum recoil may significantly affect the FEL gain. Consider a typical width width ≈ ( ) + ( )inh , inh then may significantly affect thebyFEL gain. Consider a typical change due to the recoil is of orderthe or quantum larger thanrecoil the FEL gain bandwidth i.e. given the spontaneous emission h ω ω ω the ω ω h ω � h̄ω ∆ω ∆ ω−32 −3 ∆ ω 2 ph −6 , the ph h̄ωConsider −610 width ≈ ( ) + ( ) , then the quantum recoil may significantly affect the FEL gain. a typical bandwidth of 10 , for a short wavelength FEL, the fraction of the energy change is more than gaingain bandwidth of 10 , for a short wavelength FEL, the fraction of the energy change is more than 10 , the ω ω h ω inh E E h̄ω ph −3 −6 and high quantum electron recoil is then negligible. It FEL, can start toofplay a role with energy electron beams and high quantum electron recoil is, then It can thenthen start to play atherole withchange low low energy electron beams gain bandwidth of 10 for a negligible. short wavelength the fraction energy E is more than 10 , the energy emitted photons in the X-ray in using an optical undulator (created byoptical an optical energy emitted photons (foris(for example in the X-ray range), as inaasusing an optical undulator (created by an quantum electron recoil thenexample negligible. It can thenrange), startsuch to such play role with low energy electron beams and high wave). wave). energy emitted photons (for example in the X-ray range), such as in using an optical undulator (created by an optical wave). Quantum diffusion Quantum diffusion Quantum diffusion The emission of spontaneous emission radiation, if not affecting the electron energy a significant amount, The emission ofdiffusion spontaneous emission radiation, if not affecting the electron energy by aby significant amount, intro-introQuantum Theanemission of spontaneous emission radiation, not affecting the electron energy aemission significant amount, introduces an energy as described above. Inifif addition, thethe discrete nature ofbyby photon emission (over a wide duces lass as described justjust above. In addition, the discrete nature of photon (over aintroduces wide energy Theenergy emission oflass spontaneous emission radiation, not affecting electron energy a significant amount, anenergy duces an energy lass asthe described just above. In addition, the isdiscrete nature of photon emission (over in a wide energyring. The spectrum) increases uncorrelated energy spread. similar to the quantum excitation a storage spectrum) increases the uncorrelated spread. Itemission isItsimilar toa the quantum excitation in a storage ring. The energy loss. In addition, the discreteenergy nature of photon (over wide energy spectrum) increases the uncorrelated spectrum) increases the uncorrelated energy spread. It is similar to the quantum excitation in a storage ring. The energy spread. Itenergy is energy similar to the diffusion of the spread is given by :[?] : in a storage ring. diffusion raterate of the spread isquantum given byexcitation [?] diffusion rate of the energy spread is given by [?] : 2 >2 7 7 < (∆ γ) dd<<d(∆ γ) > 234 K 3 2 k3 F(K ) (∆ γ) >2 = −=7−r λ re λCompton 4γo4 K 2 uγ k e Compton o u uu) u ) u u F(K = − r λ γ K k F(K e Compton o u u ds 15 ds 15 ds 15 (96) (96) (96) −13 the Compton wavelength. In the LCLS 11 1 −13 −13 )==1.2K 1.2K + 1+1.33K and λ = h̄/m c ≈ 3.86 10 and λ = h̄/m c ≈ 3.86 10 the Compton wavelength. InLCLS the LCLS withwith F(KF(K o Compton and λ = h̄/m c ≈ 3.86 10 the Compton wavelength. In the with F(K 2 u) = u+ o Compton 2 uu) 1.2K u u+ o Compton 1+1.33K u +0.40K 1+1.33K u +0.40K u u2 u u +0.40K case, quantum diffusion process increases the uncorrelated energy spread in 110 the 110 m long undulator to more case, the the quantum diffusion process increases the energy spread m long undulator to more than than case, the quantum diffusion process increases the uncorrelated uncorrelated energy spread inin thethe 110 m long undulator to more than LCLS case, quantum diffusion process theDespite uncorrelated energy spread in is the longtoo undulator to than −4 −4the assuming anthe initial energy spread equal to zero. in asuch a the case, the effect ismtoo not themore quantum 10 assuming initial energy spread equal toincreases Despite ininsuch effect not too large, thelarge, quantum 10In assuming an an initial energy spread equal to zero. Despite such acase, case, the effect is110 not large, the quantum 1 1011−4 1 1084 assuming an initial energy spread equal to zero. Despite in such a case, the effect is not too large, the quantum diffusion diffusion process isis likely impose limits in achievable achievable wavelength forparameters. given beam parameters [?].[?]. [?]. diffusion process to impose limits in achievable wavelength for given beam parameters diffusion process is likely totoimpose in wavelength given beam parameters process is likely to likely impose limits inlimits achievable wavelength for given beamfor faut avoir laladiscussion surles lesvaleurs valeurs de la ladedispersion dispersion en dede l’mittance.....XXXXXXXXXXXXXXXXXX IlIl faut avoir fait discussion sur les valeurs la dispersion en nergie, de l’mittance.....XXXXXXXXXXXXXXXXX Il faut avoir faitfait la discussion sur de ennergie, nergie, l’mittance.....XXXXXXXXXXXXXXXXXX Dattoli M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016 cfcfDattoli cf Dattoli jeudi 2 juin 2016