A method for conditioning electron beams is proposed, making use of the TM{sub 210} mode of microwave cavities, to reduce the axial velocity spread within the beam, in order to enhance gain in resonant electron beam devices, such as the free-electron laser (FEL). Effectively, a conditioner removes the restriction on beam emittance. The conditioner is analyzed using a simple model for beam transport and ideal RF cavities. Analysis of an FEL is employed to evaluate performance with reduced axial velocity spread. Examples of FELs are presented showing the distinct advantage of conditioning

Sessler, Andrew M.

Whittum, D.H.

Yu, L.

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',JLBL-31006PreprintLawrence Berkeley LaboratoryUNIVERSITY OF CALIFORNIAAccelerator & FusionResearch DivisionSubmitted to Physical Review LettersRadio-Frequency Beam Conditioner for Fast-WaveFree-Electron Generators of Coherent RadiationA.M. Sessler, D.H. Whittum, and L.-H. YuJuly 1991·1Prepared for the U.S. Department of Energy under Contract Number DE-AC03-76SF00098LBL-31006RADIO-FREQUENCY BEAM CONDITIONER FOR FAST-WAVEFREE-ELECTRON GENERATORS OF COHERENT RADIATION'OAndrew M. Sessler and David H. Whittum'O'OLawrence Berkeley Laboratory, University of California,Berkeley, California 94720Li-Hua YuBrookhaven National Laboratory, Upton, New York 11973July 1991* Work at LBL was supported by the U.s. Department of Energy under Contract Number DE-AC03-76SF00098; work at BNL was supported by the US. Department of Energy underContract Number DE-AC02-76CHOOOI6; work at KEK was supported by the Japan Society forthe Promotion of Science and the National Laboratory for High Energy Physics (KEK).'O'O Present address: Accelerator Division, National Laboratory for High Energy Physics,KEK, 1-1 Oho, Tsukuba, Ibaraki, 305, Japan.RADIO-FREQUENCY BEAM CONDITIONER FOR FAST-WAVEFREE-ELECTRON GENERATORS OF COHERENT RADIATIONAndrew lYt. Sessler and David H. Whittum(a)Lawrence Berkeley Laboratory, University of California, Berkeley, California94720Li-Hua YuBrookhaven National Laboratory, Upton, New York 11973July 1991A method for conditioning electron beams is proposed, making use ofthe TM210 mode of microwave cavities, to reduce the axial velocity spreadwithin the beam, in order to enhance gain in resonant electron beam devices,such as the free-electron laser (FEL). Effectively, a conditioner removes therestriction on beam emittance. The conditioner is analyzed using a simplemodel for beam transport and ideal RF cavities. Analysis of an FEL isemployed to evaluate performance with reduced axial velocity spread.Examples of FELs are presented showing the distinct advantage ofconditioning.PACS numbers: 42.55.Tb, 41.80.Ee, 52.75.MsThe performance of fast-wave resonant electron devices for the production ofcoherent radiation, such as free-electron lasers (FEL) or cyclotron auto-resonantmasers (CARM), is limited by the intrinsic spread in longitudinal velocity of theelectrons. 1,2,3,4 For the purpose of this note we limit the discussion to FELs. Inpractice, to limit the spread in longitudinal velocity the energy spread and theemittance of the electron beam are carefully limited. In fact, it is the very difficultyof reducing these two features of a beam, while still maintaining high beam current,which produces the limit on gain in fast wave devices. Often electron beam sourceshave the feature that the energy spread of the particles is exceedingly small. In thiswork, we shall consider only this situation.Small energy spread, alone, is not enough to make a fast-wave device workoptimally, for the non-zero angular spread of the beam, measured by its emittance,produces longitudinal velocity spread; i.e., "effective energy spread". However, onecan consider a device, placed between the accelerator producing the electron beamand the fast-wave coherent radiation generator, that "conditions the beam"; i.e.,converts the beam to particles all moving with the same longitudinal velocity. Sucha device need not "cool" the beam; i.e., the phase volume after the device can equalthat before the device, but it builds upon the fact that the beam has a very smallenergy spread and "pushes phase space around"; Le., introduces a tight correlationbetween transverse oscillation energy and total particle energy. In this note weanalyze the performance of such a device, and show that it can significantly increasethe gain in fast-VI/ave devices.In Ref (1) it is shown that FEL behavior is governed by the equation(1)(2)2provided~«1pkw (3)In this formula, E is the electromagnetic field, the wiggler wave number is kw , thebetatron wave number is kfJ, and the central beam energy is Yomc2. Resonance at thesignal wave number kr occurs when y = Yr' The FEL parameter, is p and qll is theFourier transform variable of ~ = (kr + kw) Z - VQ t. The variables k = kfJ/ kw, r = -V2kskwR, R is the radial coordinate, and p =dr / d(kwz).The usual inequalities for FEL behavior are obtained from Eq. (1) by requiringthat the energy spread and the emittance effect are small. Thus2 (r-rv)!rv « 2p, (1/4) (k2r2+p2) « 2p, or(J-« p ,Y(4)(5)where £. =kpR2, the emittance, and cr, the energy spread, have been introduced. Eq.(1) now becomes(6)where W(r) is dependent only upon r.Transverse effects can be ignored if V~ « 2p, which is3LRay » LCain (7)where LRay = ksR2 and LCain = 1/2pkw . The usual inequalities are Eqs. (3), (4), (5), (7),which result from taking fa = fa «Y-YO) Iyo, (1 14) (p2+k2r2» having a small spread in itstwo arguments.For a conditioner we have(8)still having a small spread in its two arguments, but now we have introduced acorrelation between total energy and transverse energy. In this case it is obvious,from Eq. (2), that there is no longer a restriction on transverse energy. Thus FELbehavior is only limited by the inequalities Eqs. (3), (4) and (7). In the microwaverange, where there is a wave guide, only the conditions of Eqs. (3) and (4) remain.A device, or "conditioner", that introduces a correlation between transverseoscillation amplitude and particle energy is shown in Fig. 1. It consists of a focusingFODO channel and suitably phased RF cavities operating in the TM210 mode. For aFODO channel, and in the thin-lens approximation, in the absence of RF cavities amatched beam will have maximum (x2)+ at the focusing lenses and minimum (x2).at the defocusing lenses where, in terms of the lens strength f and separation L wehave(9)where Ex is the beam emittance. The orthogonal (y2) will be exactly the same, but (y2)will be largest at the defocusing lenses.4Since in the TM210 mode, at the appropriate phase, there is predominantly Ez,and no deflecting fields (we ignore fringe fields), to a good approximation a particlepassing through the RF cavity at the focusing lens has its transverse motionunaffected, but gains energy /:i.y+ = a (x2 - y2), with a. a constant that depends oncavity parameters. Similarly, with a 1800 phase change, at the defocusing lens /:i.y_ =-a (x2 - y2). It is clear that in passing through N periods of a conditioner, a particle ofinitial amplitude of oscillation characterized by emittance E and initial phase ([Jox and<flay will gain energy(10)where Ji, the phase advance for a period is given by cos Ji = 1 - ~ L2 / f. If theconditioner has an infinite number of periods, is "perfect", then(11)There results an averaging over oscillations, as we expected, so that energy, L1y, isexactly correlated with amplitude of oscillation, E. The requirement for aconditioner is given by Eq. (8) and results in(12)5where the first factor only contains FEL parameters, and the second only conditionerparameters.In practice, a conditioner has only a finite number of periods. How manyperiods are necessary to obtain a rather good averaging; i.e., for particles to be mostlyat the extreme of oscillations when going through the RF cavities? A bit of analysisshows that for N periods the maximum deviation of L1y is:L1y sin Nil r 11 4P. 211]1/21-----'---- - 1 < 1------1 COs2 - + - SIn -L1 I - Nsin 11 2 L2 2 'Y perfect L(13)so that the spread in energy drops off inversely with N and can be made zero if Nfl isa multiple of 1t. As a good practical example, L = 50 em, f = 100 em, fl = 0.505, f3+ =258 em, f3- = 155 em, and for N = 6 we have L1y/L1yl perfect = 5.2 x 10-2 so that with only6 periods the induced correlation is good to 5%, which for the examples given is anegligible correction.A complete analysis of an FEL with conditioner, such analysis taking intoaccount energy spread, emittance and focusing of the electron beam, and thediffraction and guiding of the radiation, may be given following the work of Yu,Krinsky and Gluckstern.5 In fact, the analysis results in the same scaling laws. Theonly change is to delete the term 3is (K/D) (krE) in Eq. (0) of Ref. 5. Now Fig. 1 ofRef. 5 is replaced with Fig. 2 of this Letter. Thus the e-folding length of the electricfield, Lc, is given by(14)where, in terms of the wiggler parameter K, and the beam current I6[2 ]1/2o = 4eL; K L [J JJ '""""'r2 ... rr 2 'V-/.;;,~ 1+1\. I\J(15)and the factor un, a difference of Besel functions is given in Ref. 5, but is close tounity. The dependence of G upon its first three arguments is given in Fig. 2. For allcases the detuning was taken as zero; i.e., [(w - wr) / wrD] = O. (The gain was close tooptimum for zero detuning.) With the formula for Lc and Fig. 2 one can readilyevaluate the performance of an FEL with conditioned beam.Some examples of a conditioner are given in Table 1. The examples havebeen arrived at by using the scaling laws and then checked by numerical simulation(they gave the same result). The parameters of the examples are all realistic; thebeam current, energy spread, and emittance in the examples corresponds to lessdemanding performance than that of the LANL photo cathode gun.6 The amountof conditioning required, /j:y Ic, which is the average energy increment across thebeam, is given by !1yc = kskpEn /2 kw , and is indicated in Table 1. It can be seen thatgain from conditioning is considerable; for example, in the infra red (10 IJ.m)example the gain length is reduced by a factor of 5, while in the ultra-violet examplethe energy of the beam is reduced by a factor of 3 (thereby reducing the cost of theaccelerator by essentially the same factor) while the gain length is reduced by morethan a factor of 2 (thus reducing the cost of the wiggler by this factor). The saving incost is even larger than these numbers indicate, for with the shorter wiggler, magneterrors are less important and therefore manufacturing tolerances are reduced.In the analysis of this paper, and in all the examples, the betatron wavelengthA~ has been determined by the "natural" focusing of the FEL. That doesn't have tobe the case and, in particular, ion focusing (the use of a plasma) can be used todecrease Ap.3 Such reduction is quite advantageous, for FEL performance, but islimited by the very condition, on the emittance, that a conditioner removes.If Ap is reduced by an ion channel, one can design a conditioner so that theaverage longitudinal velocity spread across the beam is zero, but there will still beoscillations (at frequency 2kpC> in the longitudinal velocity. In Table II we havepresented examples whose performance has been evaluated under the assumptionthat longitudinal velocity modulations are unimportant. (Numerical simulationconfirms the essential correctness of the assumption.) The example of the 30 A FEL7operates in the "water window" where wet biological samples are transparent andwhere an intense coherent source would be of great interest for imaging.Presumably such a short wavelength FEL is obtained by seeding a 1000 A FEL at (say)3000 A with an excimer or dye laser and then cascading FELs. The second examplein Table II, based upon the proposed Brookhaven National Laboratory VUV Facility,is a set of parameters which might be used to experimentally study conditioning andion focusing. Operation at very short wavelengths requires two things which havenot yet been achieved, but which appear to be possible; namely, operation of aconditioner and operation of an FEL with ion focusing.This work was supported by the U.s. department of Energy under ContractNumbers DE-AC03-76SF00098 and DE-AC02-76CH00016, the Japan Society for thePromotion of Science, and the National Laboratory for High Energy Physics (KEK).References(a) Present address: Accelerator Division, National Laboratory for High EnergyPhysics, KEK, 1-1 Oho, Tsukuba, Ibaraki, 305, Japan.1. Li-Hua Yu and Samuel Krinsky, Physics Letters A 129,463 (1988).2. C. Pellegrini, Nuclear Instruments and Methods in Physics Research A 272, 364(1988); Li-Hua Yu and Samuel Krinsky, Ibid, A 272, 436.3. W.A. Barletta and A.M. Sessler, Proceedings of the INFN International Schoolon Electromagnetic Radiation and Particle Beams Acceleration, Varenna, Italy,North-Holland Physics, 211 (1989); K. Takayama and S. Hiramatsu, Phys. Rev. A~ 143 (1988).4. K.D. Pendergast, B.G. Danby, R.J. Temkin and J.s. Wurtele, IEEE Trans. onPlasma Science 16, 122 (1988); D. Whittum, A.M. Sessler, and J. Dawson, Phys.Rev. Lett. M, 2511 (1990).,J. L.-H. Yu, S. Krinsky and R.L. Gluckstern, Phys. Rev. Lett. M, 3011 (1990).6. Richard L. Sheffield, Proc. of the 1989 IEEE Particle Accelerator Conference L1098, Chicago, IL, March 20-23, 1989; D.W. Feldman et aI, "Performance of the LosAlamos HIBAF Accelerator at 17 MeV", Proceedings of the 12th InternationalFEL Conference, Sept. 1990, Paris (to be published).8Table 1. Parameters for a 10 ).lm, 300 A and 500 A FEL, with, and without, a conditioner. For each case thewiggler wavelength (Au) was varied and determined so that the growth length (Lc) was minimum.10 ).lm 3000 A- 500 A10 ).lm FEL with FEL with FEL withFEL conditioner 3000 A FEL conditioner 500 A FEL conditionerElcctron BcamEnergy yomc2 (MeV) 54.2 54.2 483 153 1004 304Electron Beam ;Peak Current I (A) 300 300 300 300 300 300Electron Beam NormalizedEmittance En (rms) (m) 8xl0-4rc 8xl0-4rc 5xl0-5rc 5x10-5rc 2x10-5rc 2xl0-5rcElectron Beam BetatronWave-length Ap (m) 8.91 8.91 20.1 12.4 33.5 19.2'-0 Electron BeamRadius (rms) (mm) 4.6 4.6 0.58 0.81 0.33 0.46Electron Beam Energy4.4xl0-4 4.4xl0-4 4.4x10-4 4.4x10-4 4.4x10-4 4.4xl0-4Spread aly (rms)Wiggler Wave-length2rc/kw (cm) 8.0 8.0 4.8 2.8 3.7 2.0Maximum MagneticField B (T) 0.25 0.25 1.0 0.52 1.26 0.66Power e-foldingLength LC 12 (m) 7.95 1.58 3.09 1.38 4.64 2.12Beam conditioning (rms)6'YdlTlc2 iMeV) --- 0.12 --- 0.61 --- 0.67Table II. Parameters for a "water window" FEL assuming one can have ion focusing and a conditioned beam.Parameters are also given for an experiment at the proposed BNL facility.30 A FEL withExperiment 1000APEL with plasma30 AFELplasma focusing and VUV facili ty focusing andconditioning 1000 AFEL conditioningElectron BeamEnergy yomc2 (MeV) 1562 1240 250 250Electron BCLlm PcakCurrent I (A) 80 80 300 30Electron BeamNormalized Emi t-tance £n (rms) (m) 2x10-6 n 2x10-6 n 8x10-6n 8x10-61tElectron BeamBetatron Wave-length A~ (m) 82.9 0.62 14.0 0.23Electron Beam Radiusf-' (rms) (mm) 0.13 0.013 0.27 0.0350Electron Beam Energy4.4x10-4 4.4x10-4 4.4x10-4 4.4x1Q-4Spread a/y (rms)wi~gler Wavelength2n kw (cm) 2.3 2.0 2.2 2.2Maximum MagneticField B (T) 0.79 0.66 0.75 0.75Power e-folding LengthLc/2 (m) 25.6 1.54 1.07 0.76Beam condi tioning(rms) !:!.yc/mc2 (MeV)(a) --- 17.3 --- 6.2(i1) For strong ion focusing, c..'Yc is given by 1/2 of the formula used in Table I.Figure CaptionsFig. 1.Fig. 2.A diagram showing the location of the beam conditioner Oa), and thenshowing one period of the conditioner (1 b). A period consists of twofocusing lenses (each of strength //2), two defocusing lenses (each ofstrength -//2), and three RF cavities each operating in the TM210 mode.Scaling functions versus scaled emittance for several values of kfJ/ kwDcorresponding to scaled energy spreads (a) (5/ D = 0, (b) (5/ D = 0.1 and(c) (5/ D =0.2.11(a) Accelerator Condi tioner ~~-~ Free-Electron LaserL ----:l>~ ....oll(E----- LRF cavity(-1/21) t (1/2 I)RF cavityr- ,.... .-~ \l 17 /Iv L ~ \-'- '-t(1/2 I)RF cavity(b)120.80.6"..-.....::i'EO 0.4-0.2o0.01 0.1131 10XBL 917-60880.7 (J(b) -=0.100.60.5,..--, 0.4::i..'-.-./ 0E 0.31----'4 I0.20.1o0.01 0.1141 10XBL 917·60900.60.50.4~ 0.3"-'0E.-0.20.1o0.01 0.1151(c) (J =0.2D10XBL 917-6089

Radio-Frequency Beam Conditioner for Fast-Wave Free-Electron Generators of Coherent Radiation

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Radio-Frequency Beam Conditioner for Fast-Wave Free-Electron Generators of Coherent Radiation

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