A REVIEW OF DIFFICULTIES IN ACHIEVING SHORT BUNCHES IN STORAGE RINGS. 1. C.Limborg, SSRL/SLAC PO Box 4349, MS 69, Stanford, CA, , USA

Transcription

1 A REVIEW OF DIFFICULTIES IN ACHIEVING SHORT BUNCHES IN STORAGE RINGS. 1 C.Limbog, SSRL/SLAC PO Box 4349, MS 69, Stanfod, CA, , USA Abstact Duing the last few yeas, the otential of electon stoage ings fo the oduction of shot bunches has been thooughly investigated. The beam-wall inteaction in geneal was econsideed fo 3 d geneation synchoton souces. The mechanism of the so-called "micowave" instability, esonsible fo bunch lengthening and enegy widening, was claified in all details fom a theoetical oint of view. Pedictions wee confimed with esults fom tacking code simulations and exeimental data. A esult of these studies is that hamonic cavities ae ineffective fo eithe shotening the bunch o substantially aising the instability theshold. Extensive investigations wee efomed on quasi-isochonous lattices. Many ings wee oeated with vey low momentum comaction otics, above and below tansition enegy. Exeimental esults in full ageement with theoetical ediction confim that unfotunately shot bunches ae vey had to oduce. 1 INTRODUCTION By the time the fist 3 d geneation stoage ings wee commissioned, the quasi-isochonous tuning of ings aeaed omising to oduce shot electon bunches and accodingly shot and intense X-ay ulses. The quasi-isochonous egime has now been tested. Unfotunately, the bunch lengthens stongly with cuent and its length becomes indeendent of both the momentum comaction and the enegy. The stong defocusing effect of the self-induced voltage can be evesed when the momentum comaction is negative. But, a negative mass instability then stats develoing, blowing u the enegy sead. Fo a ositive momentum comaction, the enegy sead will stat widening above the micowave instability theshold. The micowave instability mechanism was thooughly investigated again to detemine if, imlementing hamonic cavities o a assive cavity-like stuctue, would hel to each highe eak billiance on stoage ings. Unfotunately, none of these stuctues will allow to boost the eak billiance to the level of efomances announced fo linac diven souces. SHORT BUNCHES HISTORY Small alha imlicitly fom high billiance 3 d geneation synchoton adiation stoage ings have been designed to ovide high quality synchoton light with a billiance exceeding by 4 odes of magnitude that of nd geneation machines. Such an imovement was made ossible by the extensive use of undulatos and wiggles. Undulato secta ae highly eaked when the tansvese emittances ae small. Accodingly emhasis was ut to each the smallest ossible emittances on 3 d geneation ings, tyically below 1 nm fo the hoizontal emittance and less than 1% of that value fo the vetical one. A eduction of the hoizontal emittance is achieved by minimizing the amlitude of the disesion function in the diole magnets. As the amlitude of the disesion behaves as a aabolic function along the diole length, shot diole magnets wee imlemented. As a consequence of the eduction of the disesion amlitude, the momentum comaction α, α = dl L d = 1 D ds (Equ.1) was deceased by L dioles ρ at least one ode of magnitude. The natual bunch length E 3 α scales like (Equ.), with ff the RF fequency, f f Vf V f the RF voltage, and E the enegy of the electon beam. The bunch lengths, tyically of s in Full Width Half Maximum (FWHM) on nd geneation stoage ings, wee shotened to a few tens of s on 3 d geneation ings. Incidentally, the need fo moe RF voltage to comensate fo inceased synchoton losses also contibuted to futhe educe the natual bunch length. As claimed duing the Stanfod Woksho on 4 th geneation light souces [1], thee is a stong case fo shot electon bunches, and shotening the electon bunch length by gaining odes of magnitude on α seemed attactive by the advent of the 3 d geneation of machines. Stong case fo shot bunches Vaious synchoton adiation use communities would benefit fom the eduction of the electon bunch length. 1 * Wok suoted by the Deatment Of Enegy, contact DE-AC3-76SF1 11

2 Thee is a stong scientific case fo intense X-ay ulses in the subicosecond ange to efom dynamic studies. FEL uses would aeciate the eduction of bunch length by one o two odes of magnitude since the FEL gain is ootional to the eak cuent. With a bunch length in the ange o smalle than the wavelength of the adiation emitted, the emission becomes coheent, and the intensity is then ootional to N, the squae of the numbe of aticles e bunch, wheeas fo the sontaneous emission the flux is only ootional to N. The temendous enhancement of hotons flux has aleady been demonstated exeimentally fo fa infa-ed adiation. The ossibility to stoe subicosecond bunches would boost the efomances of infa-ed souces. Otimized luminosity is obtained fo an ms bunch length σ τ aoximately of the ode of β* the betaton value at the inteaction oint. B-factoies and daming ings used to inject in linea collides ae good candidates fo smalle bunches. Finally, the muon collide will be oeated with bunches in the mm ange and in a quasiisochonous egime. 3 QUASI-ISOCHRONOUS REGIME When the evolution eiod of aticles become nealy indeendent of enegy, the ing is said to be quasiisochonous. The hase-sliage facto η = 1 γ dl L d, is then vey small. In electon machines, the hasesliage facto η is aoximately the momentum comaction α = dl L d = α + α d/+ α 1 3 (d/), and the quasi-isochonous egime is eached when α is small u to highe ode tems in d/. Histoically, difficulties to un an acceleato in the quasi-isochonous egime wee aleady met as it coesonds to the situation of tansition enegy cossing on oton and heavy ion machines. By efoming the Q- jum, difficulties to un in the quasi-isochonous egime ae avoided. Fo unning a ing steadily in the quasi-isochonous egime, the highe ode tems of α, need to be minimized emanently. 4 SMALL α AND NEGATIVE α TUNING Lattice tuning To educe the momentum comaction α, the disesion function needs to be educed along the diole. By focing the disesion to be negative within the two dioles, the momentum comaction, integal (1) can vanish and even be made negative. At the ESRF, the lattice is a DBA of the Chasman- Geen tye. The focusing quaduoles of the achomat, allow to adjust the amlitude of the disesion function in the dioles. By focing the disesion function to have its minimum taking a negative value in the middle of the diole, one can tune α 1 to any small ositive o negative value and get a small hoizontal emittance at the same time. Necessity of deceasing the nd ode tem α Non-linea tems aising fom bending magnets and thei finging fields as well as fom sextuoles contibute to the geneation of an α tem. α is the longitudinal chomaticity. Thee diffeent families of sextuoles ae needed to coect at the same time the two tansvese and the longitudinal chomaticities. The RF bucket size follows 1 α 1 when nd ode tems can be neglected. When the nd ode tems ae not negligible, the RF bucket size emains smalle than α 1 ( α 3). With the ESRF exeiment, fo an α 1 in the.1 -, α needed to be deceased below to kee an RF accetance above the quantum limit of 6.6 σ δ. In figue 1, RF buckets ae deicted fo thee diffeent combinations of (α 1,α ). Obviously, with shote bunches the bunch density is inceased ceating moe fequent Touschek collisions. The enegy excusion occuing fom a Touschek collision can easily each 1% of the beam enegy. Consequently, the RF bucket size must be huge to get a decent Touschek lifetime. D/ D/ D/ Esf V RF =. α =.1 Esf V RF = e α =.1 Esf V RF = e α = Phase in adians / Φ s =.398 (ad) Figue 1- Necessity of deceasing α NB: RF bucket sizes ae also futhe squeezed due to enegy indeendent tems inceasing the sead in cicumfeence length. This tem is a function of both tansvese emittances. Accodingly, a small emittance lattice is also mandatoy to each vey small α values while maintaining a viable RF bucket size. 1

3 ESRF exeiment with shot bunches In ode to each bunch lengths of 1s in ms value on the ESRF ing, attemts wee made to lowe α 1 down to the 1-6 ange. Only with α 1 =.1 -, the eduction of α was successful leaving a decent lifetime fo measuements. The bunch lengths wee measued with a s esolution steak camea. They show that as soon as a substantial cuent is stoed, the bunch length is indeendent of both the momentum comaction and the enegy. The imedance of the ing makes the bunch lengthen stongly due its stong self-induced voltage. Incidentally, but as an exeimental difficulty to be mentioned, the RF system must be vey clean down to vey low fequencies to avoid diving coheent longitudinal oscillations. Indeed, fo vey small momentum comaction, the synchoton fequencies eached ae small since they ae in the few hunded Hz.. COLLECTIVE EFFECTS Caeful attention was aid to smooth the vacuum chambe and educe the imedance of 3 d geneation ings. Stee ste tansitions and cavity-like stuctues have been avoided as much as ossible. Vacuum ots ae attached to ante-chambes and bellows ae RF shielded. The stong lengthening with cuent, the indeendence of the bunch length with both the enegy and the momentum comaction at high cuents, can be exlained by an inductive imedance model. In 3 d geneation machines, exeiments have shown that the theoetical model of an inductive imedance matches nicely bunch lengths measuements [ESRF, Sue-Aco[], ALS[4] ]. Howeve, a uely inductive imedance model can not justify the enegy widening obseved above eak cuent of 4 A in the ESRF case. Only, a high fequency esistive inteaction can be at the oigin of an enegy sead blow-u. The mechanism involved is then the well-known micowave instability. The natue of the imedance of 3 d geneation ings makes them inaoiate to the oduction of shot and intense bunches, and in aticula not in the quasiisochonous egime. The ath followed to daw this conclusion of majo imotance is esented in []. A shot oveview is given hee below. The esolution of the Haissinski equation [3], a multiaticle tacking code of the longitudinal motion and analytical deivations wee used when ossible. The simlified and academic case of a uely inductive imedance is studied fist. a- Inductive imedance Fo a uely inductive imedance, the self-induced voltage is the deivative of the bunch line density which is gaussian at zeo cuent. Positive α When the momentum comaction is ositive, with inceasing cuent, the sloe of the effective voltage subsides aound the synchonous hase. The bunch is defocused and lengthens. Fo inceasing cuent, the bunch ofile becomes moe and moe like a aabola. The Haissinski equation is a tanscendental equation, fo which an exlicit solution can not be witten in the case of a uely inductive imedance. Howeve, one can demonstate that thee always exists a solution whateve the cuent fo the case of a ositive momentum comaction and an inductive imedance[]. As fo the coasting beam, fo a uely inductive imedance and fo a ositive momentum comaction, the beam is always stable. The bunch lengthens in a ue otential well egime and its enegy distibution emains unchanged and equal to the natual one. Witing the Haissinski equation xλ( x) πi( Lω ) as λ '(x) = with = o 1+ λ( x) Vf hcosϕs( ωoσ o) 3,x = τ/σ τo τ a Runge-Kutta algoithm allows to comute aidly the temoal distibution λ(τ). At high cuents, the bunch length becomes indeendent of both the momentum comaction α and of the enegy, but deends on the owe 1/3 of atio between the induced voltage and the extenal voltage. The quasi-isochonous egime is then useless in that to oduce shot and intense bunches. Negative momentum comaction The stong defocusing effect can be evesed when the momentum comaction takes a negative value. The synchonous hase is then on the ising sloe of the RF wave. The self-induced etubing voltage now tends to incease the RF gadient aound the synchonous hase, and the bunch self-focuses. Unfotunately, this selffocusing effect is limited. is now negative as cos ϕ s is negative. Thee is a theshold limit =-1., at which, the Haissinski equation esents a singulait. It coesonds to a cuent theshold at which the effective gadient field would take infinite values []. Beyond this value, a negative mass instability fo bunched beam stats develoing. The ms enegy sead σ δ and the ms bunch length σ τ both widen in aallel, such that the coefficient emains constant. This esult was also confimed by unning the multiaticle tacking code, a simila theshold was found []. Above that theshold, the bunch lengthens and bunch distibutions kee the shae esented at theshold. The line density shows a high density coe and long low density tails. The enegy sead ofile emains gaussian. This mechanism of the negative mass instability is a well known mechanism. Its aeaance in 3 d geneation ings was oved exeimentally and unfotunately uins the hoes of using negative momentum comaction to oduce shot and intense bunches. 13

4 NB: The uely inductive model is not fully satisfying fo fitting exeimental esults when the momentum comaction is negative. Indeed, the naow high density eak inteacts with the high fequency tems. The imedance esents some esistive comonents in the high fequencies. The high fequency esistive tem is the souce of additional enegy widening and it also geneates a stong skewness on the bunch ofile. b- Boadband esonato imedance A uely inductive imedance can not coectly eesent a the tue imedance of a ing. Unavoidable discontinuities catue some fields, the owe of which is dissiated in the walls. Of the few diffeent eesentations commonly used[8],[9], the boadband esonato model oved to be mathematically handy while ossessing the coect hysical featues. It eesents an imedance which is inductive u to a esonant fequency, f, at which the inductive at falls and whee the stong esistive comonents ae esent. A micowave instability develos in the esence of a high fequency esistive inteaction. As deicted in figue, the self-induced etubation voltage oscillates with a wavelength λ c/f and accodingly the amlitude of the longitudinal focusing foce oscillates with that wavelength along the bunch. We fist conside the situation in which the bunch length contains moe than one wavelength. This ceates some local stability islands o fixed oints on the isohamiltonian cuves. The isohamiltonian cuves eesent the motion in the longitudinal hase sace in the absence of adiation daming and quantum fluctuation. Paticles gathe in mico-bunches and glide along those stability islands. The mico-bunch stuctue is then diluted due to the global synchoton motion geneated by the extenal RF voltage (See figue 3). Vey small dos kee eaeaing which ae immediately diluted. The bunch density stabilizes with a temoal distibution of a aabolic shae and an enegy distibution of gaussian shae both with FWHM values which incease with the owe 1/3 of the cuent. An analytical fomula fo the theshold of the micowave instability has been deived fom a disesion elation deduced fom the lineaization of the Vlasov equation. The stability citeion, hee below, also gives the bunch dimensions above theshold: $ Λ R eff ~ Z ( ) ωo λ ( ) < 1. with σ τ & with ) Λ = Zeff = Reff = α I π E e ωσ τ ~ λ and σ τ & = ω s σ τ. () The effective imedance Z eff = R eff is only esistive since the etubation λ ~ of the stationay distibution is centeed aound ( =f /f o ) and the ovela with the eactive at of the imedance is globally zeo. This citeion was fist deived by Keil & Schnell fo a coasting beam and alied to oton beams by Boussad. The extensive deivation fo electon bunched beams can be found in [], [6],[7]. The validity of the fomula was confimed by the esults fom the tacking code. E nomalized E nomalized Distibution in hase Sace τ nomalized Time Distibution 1 τ nomalized Phase with oigin at φ s Figue Micowave mechanism 1 tuns late, i.e. 3 ms 1 Distibution in hase Sace 1 τ nomalized Dilution via Synch. Motion 1 1 Nomalized Figue 3 Dilution of mico-stuctue 6 HIGH PEAK BRILLIANCE IN STORAGE RINGS No Possibility of bunch shotening The condition of aeaance of the micowave instability is that the hase advance of the wake field is lage than π ove the bunch length of σ τ leading to the condition: ω στ> π with f the esonant fequency and σ τ the ms bunch length (the bunch eventually lengthens due to its inteaction with the inductive at of the esonato). Vf (MV) Enegy Distibution Effective Voltage Dilution afte 1 Ts 1 14

5 When the condition ω στ> π is not fulfilled, the esistive inteaction leads to a bunch self-focusing. Howeve, the bunch beaks into two subbunches o a shot bunch with a long tail. The enegy sead can stat widening; indeed the aticles of the tail of the bunch have a vey slow synchoton seed. The enegy sead ofile is eventually not any moe gaussian but the sueosition of two gaussian distibutions with diffeent ms values. The stong diffusion ocess eithe to the tail o to a second sub-bunch, makes the assive cavity like stuctues unusable fo the oduction of shot and intense bunches. NB: At that oint, it is woth mentioning that while unning the ESRF at GeV, the bunch length, fo the lowest cuents allowing steak camea measuements was aleady close to 1s, to be comaed with the s theoetical zeo cuent value at that enegy and fo an RF voltage of 8 MV. Hamonic cavity Reaching small and intense bunches is not ossible in stoage ings, since the bunch eithe lengthens and ossibly widens in enegy. One could nevetheless exect eaching high eak cuent since the eak cuent incease with the owe /3 o the cuent. In 3 d geneation ings, the tansvese single bunch cuent limit can be aised eithe by inceasing the chomaticity o by using a feedback system. The incease of the chomaticity is not a good solution as it deteioates the off-momentum dynamic aetue and accodingly educes the Touschek lifetime. By means of an hamonic cavity, the bunch can be lengthened to at least a facto 3 and the Touschek lifetime aised by the same amount. The RF voltage sloe is made about flat aound the synchonous hase along the desied width of the bunch. Fo a long bunch, the etubing voltage is sead ove a wide ange, and has consequently a smalle amlitude. The cuent theshold is fo that eason highe. Howeve, with a lengthened bunch, the sectum is shinked, accodingly the effective esistance R eff is lage. Moe detailed analysis ae in eaation [1]. The hamonic cavity fullfills its goal as to incease the Touschek lifetime but the micowave instability theshold is not aised by moe than a facto of fo a bunch lengthened by a facto of 3[7]. Hamonic cavities ae not the solution eithe to incease the eak billiance by odes of magnitude. 7 CONCLUSIONS It has been demonstated that stoing subicosecond bunches with high cuent cannot be achieved on stoage ings. In the ange of bunch length exloed on 3 d geneation ings, the bunch lengthens in its inductive wakefield. A micowave instability stats aeaing at high cuents due to the esence of high fequency esistive comonents, which mechanism has been fully analyzed. Running the ing with a negative momentum comaction is also not a solution since a negative mass instability develos which blows the enegy sead of the electon beam. Futue ossibilities Peak billiance of u to 1 1 kev in standad units ae announced fo the linac diven souces (LCLS[11], Tesla). The 8 odes of magnitude diffeence, above efomances achieved esently on stoage ings, have two oigins. Two odes come fom the eduction of the bunch length down to 67 fs in ms value. The othe six come fom a new incial, SASE (Self Amlified Sontaneous Emission). The adiation will be coheent as the bunch micobunches itself at the otical wavelength of its own adiated field. If SASE woks as edicted, the linac diven souces will constitute genuine 4 th geneation souces fo which the figue of meit will be th eeak billiance. ACKNOWLEDGEMENTS I m vey gateful to JL.Laclae and G.Besnie fo the valuable discussions. I want to thank L.Favacque, K.Scheidt, A.Roet, P.Elleaume fo thei assistance duing the exeiments efomed at ESRF. I m gatefully to A.Hofmann fo his encouagement and suggestions. Finally, I thank M.Conacchia fo suoting this wok. REFERENCES [1] ICFA Poceedings, 4 th Geneation Light Souces woksho, Stanfod, 199 [] C.Limbog, Potential of Stoage Rings in the oduction of Shot and Intense X-Ray ulses, PhD thesis, ESRF 1996 [3] J. Haissinski Exact Longitudinal Equilibium Distibution of Stoed Electons in the Pesence of Self-Fields, IL Nuevo Cimento Vol.18 BN1, 1973 [4] C.Pellegini, D.Robin, Quasi-Isochonous stoage ing, Nucl. Inst. &Methods A31, 7-36, 1991 [] A.Nadji et al. Exeiments with low and negative momentum comaction facto with Sue-Aco, EPAC 96 [6] M.Month, A esistive theoy of bunch lenghtening, IEEE,Tans.on Nucl. Science, Vol. NS4, No3, June77 [7] G. Besnie Pivate Communications, Uni.of Rennes, Fance. [8] Micowave Instabilities in Electon Stoage Rings wih Negative Momentum Comaction Facto, SX. Fang et al. KEK Peint Febuay 199 [9] K.Oide, K.Yokaya, Longitudinal Single Bunch Instability in Electon Stoage Rings, KEK Peint 9-1 KEK Ail 199 [1] C.Limbog, SSRL Note July 98, In eaation [11] M.Conacchia et al. Linac Coheent Light Souce (LCLS) Design Reot, SSRL/SLAC