POSSIBILITY OF USING A RING ACCELERATOR FOR IONIZATION COOLI

Restriction by scattering A possibility of using a racetrack-like ring accelerator as the first stage of a cooler for muon collider is considered. The ring cooler includes bending magnets with field index X 0.5, bent solenoids, and straight sections with a

POSSIBILITYOFUSINGARINGACCELERATORFORIONIZATION

COOLINGOFMUONS

V.I.Balbekov,FNAL,Batavia,IL

Abstract

Apossibilityofusingaracetrack-likeringacceleratorasthe rststageofacoolerformuoncolliderisconsidered.Theringcoolerincludesbendingmagnetswith eldindex0.5,bentsolenoids,andstraightsectionswithacceleratingcavitiesandsolenoids.LiHrodsplacedinstraightsectionsareusedfortransversecoolingwhereaswedgeabsorbersinbendingpartsprovidetransverse-longitudinalemittanceex-change.ResultsofanalyticalcalculationsandMonteCarlosimulationswithscatteringandstragglingarepresented,andproblemofsuppressionofnonlinearandchromaticef-fectsisdiscussed.

1INTRODUCTION

Thisreportexaminesthepossibilityofusingaracetrack-likeringacceleratorinthecoolingstageofmuoncollider(Fig.1).Themainmeritofsuchacoolerislowerprojectedcostbecausethesameacceleratingandfocusingsystemisusedrepeatedly(about20turnsinatypicalscenario)

[1].

Figure1:Schematicofaringcooler.

’Usual’ringacceleratorcouldprovidethecoolingwhichisschematicallyshownonFig.2,left.Boundaryofabeamonphaseplane(X X )isaphasetrajectorydependingonβ-functionandconservingtheshapeifcompressionbyacoolingexist.ButX sizeisrestrictedbymultipleCoulombscatteringtypically300mradon3σ-level.Initialsizecan-notbesigni cantlymorebecauseofaperturerestriction,soadeepcoolingisimpossibleinsuchascheme.Topro-videit,itisnecessarytogetindependentmotioninX andX directionsonphaseplaneasshownonFig.1,right.Itmeansthattransfermatrixis±I;anotherwords,betatronfrequencyoftheringcoolermustbeintegerorhalf-integer.Itreferstosynchrotronmotion,too,butitisverydif culttogetsynchrotronfrequency0.5atlowRF.Butthecon-sideredversionofaringcoolerisfocusedoninitialstageofcoolingwhenbunchlengthisseveralmeters[2,3],andusingofhighRFisimpossible.Hencesuchacoolermustoperateattransitionenergywhichformallycorrespondstosynchrotronfrequency0.Bunchersareneededonlyforlon-gitudinalcompressionofthe

bunch.

Restriction by scattering A possibility of using a racetrack-like ring accelerator as the first stage of a cooler for muon collider is considered. The ring cooler includes bending magnets with field index X 0.5, bent solenoids, and straight sections with a

wasconsideredinpreviousversionofaringcooler[1].Inthatcasebeamsizeinthebendingpartwasessentiallymoreresultingstrongnonlineardistortions.Drawbackofnewsystemislessdispersionfunctionresultingdecreaseofmo-mentumcompactionfactorandgrowthoftransitionenergywhichisoperatingenergyoftheringcooler.Otherparam-etersofthecoolerarelistedinTable1.

100

Dispersion function, cm

50

X

Y

50

100

0306090120150180

Bending angle, deg

Figure4:Dispersionfunctioninbendingpartofthering.

Table1:MainparametersofthecoolerMuonmomentum,MeV/c

42.47

Revolutionfrequency

120

Muondecay,%/turn

Restriction by scattering A possibility of using a racetrack-like ring accelerator as the first stage of a cooler for muon collider is considered. The ring cooler includes bending magnets with field index X 0.5, bent solenoids, and straight sections with a

Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

non-equilibriumparticles.Theygiveanadditionalemit-tanceblowupon10-

15%.

Energy deviation, mc^2

0.40.30.20.10.0 0.1 0.2 0.3 0.4 100

50

50

100

150

Energy deviation, mc^2

0.40.30.20.10.0 0.1 0.2 0.3 0.4200 100

50

50

100

150

200

60

4020

0 cm

Longitudinal coordinate, cmLongitudinal coordinate, cm

Figure8:Beamenvelopbetweentherodandthewedgeab-sorber(1/4ofaturn,schematically).Figure11:Longitudinalphaseplaneafter16turns:linear(left)andnonlinearapproximations.

atailappearswhichispartiallycutontheplot.After16turnsthecoreofthebunchcontinuestocompressbutr.m.s.sizedoesnotchangebecausethetailgrowsandthedistri-butionbecomesnonGaussian.ResultingemittancesandtransmissionarepresentedinTable2.

Table2:Effectofdifferentfactorsonthecooling(16turns)

εz,cm

Trans.

45.7

2.22.42.73.8

0.730.620.570.50

1.76

Linearapx.+chromaticity+trans.nonlin.+long.nonlin.

1.0

16 MeV

Horizontal momentum, mc

33 MeV

E = 0

16 MeV 33 MeV

0.5

0.0

0.5

1.0

10

50510

Horizontal coordinate, cm

Figure9:Phaseellipseafter1periodatdifferentenergyde-viation.Initialellipseiscanonical,σE=11Mev.

1.0

6CONCLUSION

Thelow-frequencyringcoolerappearscapableofsatisfac-torycoolingamuonbeambothintransverseandlongitudi-naldirections.Theachievableemittancesuggestsitsuseasaprecoolerinamuoncollidercomplexespeciallyforeffec-tivebunchshorteningwhichisnecessaryinanyscenario.Themostseriousproblemsare:

Chromaticeffectsareverystrongyet.Probably,acom-binedsystemwithsolenoids,quadsandsextupolecorrec-torsshouldbedevelopedtoreduceit.

Time-amplitudecorrelationsarethemostlimitingfac-torforthelongitudinalcooling.Itispossible,specialformofabsorberscanhelptosuppressit.

Developmentoflow-frequencyhighgradientacceler-atingsystemisnecessaryinanycase.

Horizontal momentum, mc

0.5

0.0

0.5

1.0

5 4 3 2 1012345

Horizontal coordinate, cm

Figure10:Nonlineardistortionsby1period.Dashedlines–phaseellipsesinthebeginning(1,2,3σ-levels),solidlines–intheend.

5LONGITUDINALNONLINEARITY

7REFERENCES

Alldemonstratedresultsareobtainedwithaccelerating eldofharmonicnumberh=1,andalmostthesameturnsoutath=2.Butdependenceofatrajectorylengthonam-plitudeofbetatronoscill …… 此处隐藏：3905字，全部文档内容请下载后查看。喜欢就下载吧 ……