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A Novel Final Focus Design for High Energy Linear Colliders

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SLAC-PUB-9722April 2003
A Novel Final Focus Design for High Energy Linear Colliders *
Pantaleo Raimondi and Andrei SeryiStanford Linear Accelerator Center; Stanford University, Stanford, California 94309 USAAbstractThe length, complexity and cost of the presentFinal Fo-cusdesignsor linearcollidersgrowsvery quickly with the
beamenergy. In this letter, a novel final focus system spresented nd comparedwith the one proposed or NLC[ 11. This new design s simpler,shorterand cheaper, ithcomparable andwidth, olerances nd tunability. More-over, he engthscales lower han inearly with energyal-lowing for a more lexible designwhich is applicable vera much argerenergy ange.
1 INTRODUCTION
The designof a final focus system or linear colliders sdrivenprimarily by the necessityo compensatehromatic-
ity of the final doublet (FD). This chromaticity scalesasL*/@‘, whereL* (typically 2-4 m) is thedistance rom theinteraction oint (IP) to the FD and ?* (about -O.lmm) isthe betatron unction at the IP. As an example, he “tradi-tional” designof the NLC Final Focus l] with L* = 2 m,& = 10 mm and 3; = 0.12 mm s shown n Fig.1.Figure 1: Opticsof the raditionalFinal Focus or theNLC.
The major disadvantage f the “traditional” final focussystem s that the chromaticity of the FD is not locallycompensated. s a direct consequencehereare ntrinsiclimitations on the bandwidthof the systemdue o the un-avoidable reakdown f theproperphaseelationsbetween
the sextupolesand the FD for different energies. Thisprecludeshe perfectcancellation f the chromaticaberra-
tions. Moreover, he system s very sensitive o any distur-banceof the beamenergy n between he sources f chro-maticity, whetherdue to longitudinalwake-fieldsor syn-
chrotron adiation. In particular, he bends n the systemhave o be long and weak to minimize the additionalen-ergy spread enerated. n addition, he phase lippageofthe off-momentum articlesdrastically imits the dynamicaperture f the system.Therefore ery ong andproblem-atic collimation sections re equired n order o eliminate
* Work supported y the U.S. Department f Energy,ContactNumberDE-AC03-76SF00515.
these articles hat would otherwise it the FD and/orgen-eratebackgroundn the detector.The collimation section
optics tself alsobecomes source f aberrations inceverylargebetaand dispersion unctionsare required. As a re-
sult of all these imitations, he engthof the beamdeliverysystembecomes significant raction of the lengthof theentireaccelerator, ndscaling o higherenergiess difficult.
2 “IDEAL” FINAL FOCUS SYSTEM
Taking nto account he disadvantages f the traditionalapproach, ne can formulate he requirementsor a more“ideal” final focus: 1)Thechromaticityshouldbecorrected
as ocally as possible. 2) The numberof bendsshouldbe
minimized. 3) The dynamicaperture r, equivalently, hepreservation f the inearoptics shouldbe as argeaspossi-
ble. 4) The systemshouldbe as simpleaspossible.5) The
system houldbe optimized or flat beams 3].Figure2: Optical ayout of the new inal focus.It is straightforward, tarting rom the IP, to build sucha system:1) A Final Doublet s required o provide ocus-ing. 2) The FD generates hromaticity,so two sextupolesinterleaved ith thesequadrupoles nda bendupstreamo
generate ispersionacross he FD will locally cancel hechromaticity. 3) The sexupoles enerate eometricaber-rations, so two more sextupolesn phasewith them andupstream f the bendare equired.4) In general our morequadrupoles re needed pstream o match the incomingbeta unction (see he schematicn Fig.2).The second rderaberrations re cancelledwhen he xandy-pairsof sextupoles reseparated y matrices:
whereall nonzero arameters rearbitrary. The sextupoleintegrated trengths S aredetermined y the equations:
KSFS = -F3&~l ;KSD~ = -D3Ksol
Kz andZ’ are he beam oordinates t the IP, &i is the hor-izontal chromaticityof the systemupstream f the bend,&s is the chromaticitydownstream, , is the vertical chro-maticity. RF, RD are he ransfermatrices efined n Fig.2.The angular ispersion t the IP, Q’, s necessarily onzeroPresented t the 7th European articleAcceleratorConferenceEPAC 2000),
Vienna,Austria,June26-30,200O
in the new design,but can be small enough hat it doesnot significantly ncreasehe beamdivergence. art of thehorizontalchromaticitymustbe generated pstream f the
bend n order o cancel he second rderdispersion.The third order geometricaberrations enerated y thesextupoles-are:
1222
= K~DK~F&R$&~~
U3444
= K~DKs&,,R:,,~C~I~
VI244 = u3224
= -KsDKsF[~I&,&~~
+Y~R~,,,R$,,
- 4~34R~lzRo34R~12R~34]/2
where $12 and $34 are elementsof transfer matrix be-tween SF1 and sol. The term us444 s small if the lastquadrupoles defocusing. CT1222s negligible or typicalparameters f flat beams.
CT1244
and us224 an be madeto vanish.Similar constraints old for third orderchromo-geometric berrations. ll these onstraints anbe satisfiedwith the simplesystem escribed bove.A systemwith the
samedemagnification s he NLC FF andcomparable p-tical performance anbe built in a lengthof about300 m.
1~I III I IIFigGe 3: O$cs of ;h”,new EC Fin? Focu?&%&.
3 PERFORMANCE OF THE NEW FF
The new FF systemhas potentially much better perfor-mance han the traditionaldesign. The “minimaI” opticsconcept an be further mproved y addingmoreelementsto minimize residualaberrations.An additionalbend up-
streamof the second extupole air decreaseshromatic-ity through he system. An additionalsextupole pstreamand n phasewith the last one further reduces berrationsin x-plane. Sincesuchsystem s “ideal” up to third order,additionaldecapoles an give further mprovements.Thenew optics is shown n Fig.3. The flat beamparametersaregiven n Table1. The new systemhasan L* = 4.3 m,
which is twice the srcinal value. This allows the use oflargebore superconductinguadrupoles ndsimplifies he
designof the detector.Although he chromaticity s dou-bled due o the argerL*, the performance f the system sstill better han or the srcinal NLC FF design.Table1: BeamparametersBeamenergy,GeV500Normalizedemittances ee IYQ, @m>4 IO.06Beta-functions& / pa,at IP (mm)9.5 JO.12Beamsizes6, / a, at IP (nm)19712.7Beamdivergence 2: 8, at IP brad)21123Energyspread ~ ( 10w3)3Dispersion’11;at IP (10m3)5.4Figs.4,5,6 omparehebandwidth f the NLC FF and henewdesign.Figs.45 show he P beamsize sa functionof
energy nd he uminosity eduction sa functionof energyspread.Beamsize and uminosity n Fig.5 were mprovedwith two additionaldecapoles. ig.6 shows he bandwidthin terms of the beamsize t the final doublet. The band-width is derived rom the variationof the beta unctionandthe beam sizes as they actually contribute o luminosity,which s determined y tracking.Thebeamsizebandwidth
is narrower han the beta function bandwidthbecause fhigherordercross-plane hromaticaberrations.While the
IP bandwidth or these wo systemss comparable,he FDbandwidth s muchwider for the new FF.Fig.7 shows he halo particle distribution at the face ofthe final doublet for the traditional FF and for the newFF. The beam s very distorted n the traditionalFF whilethe nonlinear ermsarestill negligible or the new FF. Thenonzero ispersion cross he FD in the new system as it-tle affect on the dynamicaperture. n addition, he designaperture f the NLC final doublet s about ra = 10 mmwhile for the new FF with twice longer L” this aperturecanbe as argeas r. =40 mm. Therefore he collimationrequirementsor the new FF may be relaxedby a factorof at leastone hundred n the IP phase, ndby a factor ofat least 3 for the FD phase nd energywithout increasingparticle osses t the FD.Due o the shorter engthof the system, herewould alsobe ess egenerationf thebeam alo n the inal focus tselffrom beam-gas cattering, educing n additionalsource fbackground.
- (P, fPJ' I2(P, fPJ' I2-----(fj/pJ"----(fj/pJ".ax 'a"x 'a"cll0QY =oY =on- UL,UL,1.1-0OooOOOOOC1.0D*P----------0.9t 8---__ ___%\0.60.5 ,-0.010 -0.005 O.&O OiO5 O.dlO
Figure4: IP bandwidth f the raditionalNLC Final Focus.Normalizedbetatron unctionsandnormalized uminosity
equivalent eam izeversus nergy ffset A El E, andnor-malized uminosity versus ms energy pread ~.
1.6-o1.5- 0-(i-j, ,$'2c----<p,/p~"z000.6 AJ3E.5 , , -* ***Bc1-0.010 -0.005 0.000 0.005 0.010
Figure5: IP bandwidthof the New NLC Final Focus.
I ’
- Traditional FF. x--o-- TraditionalFF.Y- NewFp.X---- NewFF,Y
Figure6: FD bandwidth f the Traditional ndNew NLCFinal Focus. Normalized etatron unctionsat the finaldoublet ersus nergy ffsetA El E.
lOO-0 0SO-D-100, , I . I I I I . I . I I t-1M) -80 -60 40 -20 0 20 40 60 80 100
Figure7: Beamat the entrancef the inal doublet or the
traditionalNLC FF and or thenewFF.Particles f the n-
comingbeam replaced n a surface f an ellipsoidwith
dimensionsN,(z, z’, y, y’, E) = (800,8,4000,40,20)times arger han henominal eam izes.
4 SCALING WITH E AND ENERGY
To maintain ptimalperformancef the systemwith larger
incomingbeamemittances,he bend ield must ncrease
like Bu cx 4. The ncreasedield is necessaryo holdconstanthe contribution f high orderaberrationso the
IP beam ize,aswell as he contribution f the P angulardispersion,$ to thebeam ivergence.The scaling o higherenergiess mucheasierwith the
new design. For a wide range f parameters,he IP spotsizedilution s dominated y theenergy pread reated ysynchrotronadiationn thebends. his scalesike
ab,; gK y&3j2gll
L2I pJ3 (5)"" gwhere & is the angular ispersion roduced y the bendswhere hebend ength s assumedo beproportionalo the
total lengthof the system . The erms n the parenthe-sis areconstantf the P angular ispersions proportional
to the beamdivergence nd f we conservativelyssumethat the normalized mittance ill be the same t higherenergies.n this case he engthof the system caleswith
energy s L c( y7/ro. If, however,he achievableormal-izedemittance cales pproximatelynversely ith energy,as s assumedn [2], then he scaling ecomes o( y2i5.In this case,with thenewdesign,heFF or a 3 TeVcenter
of mass nergy ollidercouldbeonly about 00m ong.
1.0“1TeV” parameters“5Tev” parameters
- OhOn’y\
+ cvE+synch.rad0.72505001000Beam energy. GeV
\
\*- 2500
Figure8: Luminosity s beam nergyor thenewFF,bend
field optimizedat eachenergy, eamwith energy pread.
With andwithout synchrotronadiation.The “1TeV” pa-
rametersorrespondo Table. , he STeV”set orresponds
to [2] with YE = 50/l . 10vs m, p* = 9.5/0.14 mm,nE = 0.2%andc*(at 2.5TeV/beam)=1/0.54nm.
The beam also emits synchrotron adiation in thequadrupoleshich becomes oreof a problemat higher
energies. This can be reducedn the new designbe-cause he argerbandwidth
llows
the FD quadrupolesobe engthenedo minimize he synchrotronadiation en-eratedn them.For hepresentedptics, hedependencef the uminos-
ity onbeam nergys shownn Fig.& Clearlya ixed ength
final focushasa wide range f energies heret couldop-
erate. f thebeam arametersrom 2] areassumed,his FF
canoperate lmost p o 5TeV n thecenter f mass.
5 CONCLUSION
We have eveloped newFinal Focus ystemhat hasbet-
ter propertieshan he systems o ar consideredndbuilt.
It
is muchshorter, rovidinga significant ost reductionfor thecollider.Thesystem as imilarbandwidth nd ev-
eral orders f magnitudesargerdynamicaperture.This
reduceshebackgroundsnd elaxeshedesign f thecol-
limation section. t is alsocompatiblewith an L' whichis twice as ong as hat n the raditionalNLC FF design,which simplifiesengineeringf the nteraction oint area.Finally, ts favorable calingwith beam nergymakest at-
tractive or multi-TeV olliders.We believe hat further mprovements f the perfor-mance f the system repossible.We would ike to thank N. Phinney, . Raubenheimerand ? Tenenbaumor veryusefuldiscussions.
6 REFERENCES
[l] NLC ZDR Design Group, A Zeroth-Order esign Reportfor the Next LinearCollider”, SLAC Report-4741996).[2] J.P Delahaye,G. Guignard,J. Irwin, T.O. Raubenheimer,R.D. Ruth, . Wilson,P.B.Wilson, “A 30 GHz 5-TeVLinear
Collider”, PAC 1997Proceedings,1998).p.482.
[3] P. Raimondi,A. Seryi A novelFinal Focus esign or futureLinear Colliders”, SLAC-PUB-8460,May 2000, submittedto Phys.Rev.Lett.

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