arXiv:hep-ex/0306044v1

20Jun2003CriticalIssuesinLinearCollidersValeryTelnovInstituteofNuclearPhysics,630090Novosibirsk,RussiaAbstractLinearcolliders(LC)ontheenergy0.
5–1TeVareconsideredasthenextstepintheparticlephysics.
Highaccelerationgradients,smallbeamsizes,precisiontolerances,beamcollisioneectsaremainproblemsforlinearcolliders.
Inthispaperwediscussphysicsmotivation,parametersandstatusofcurrentLCprojects,e+e,γγandγemodesofoper-ation,physicallimitationsontheenergyandluminosity.
Presenttechnologiesallowtoreachenergiesabout5TeVwithadequateluminosities.
Advancedtechniquebasedonplasmaandlasermethodofaccelerationcanprovidemuchhigheracceleratinggradients,however,perspectivesofthesemethodsforhighenergycollidersarestillunderbigquestion.
Linearcolliderswithenergiesabove10TeVarehardforanyaccelerationtechnology.
SpeculationsonpossibilityofPeVlinearcollidersbasedonponderomotivelaseraccelerationarejustnotseriousandcontainseveralmistakesonconceptuallevel.
Itisshownthatduetoradiationinthetransverselasereld,methodsofaccelerationbasedonlaserbunch"pressure"donotworkathighenergies.
1Introduction:nextstepsinparticlephysicsProgressinparticlesphysicsinthelastseveraldecadeswasconnectedwiththeincreaseofacceleratorenergies.
Historically,twotypesofcollidersco-existedandgavemainresults,pp(pp)ande+e.
Protoncollidersgiveaccesstohigherenergies,bute+ecollidershavesimpleinitialstate,smallerbackgroundandallowmuchbetterprecision.
Atprotoncollidersc,b,tquarksandW,Zbosonshavebeendiscovered,whileate+ecollidersc-quark,τ-lepton,gluon.
Inaddition,ate+ecollidersc,b,W,Z,τphysicshasbeenstudiedwithahighaccuracyprovidingaprecisiontestoftheStandardModel.
ThenextprotoncolliderLHCwiththeenergy2E0=14TeVwillstartoperationinabout2007.
Itwillcertainlybringnewdiscoveries.
But,asbefore,fordetailstudyofnewphysicsandit'sunderstandingae+ecolliderisverydesirable.
Suchprojectsontheenergy2E0=0.
5–1.
5TeValreadyexist,but,unfortunately,approvalisdelayedduetoahighcostandnecessityofinternationalcooperation.
Accordingtopresentunderstandingtheconstructioncanstartinabout2007.
Asforlong-termperspectivesofparticlephysics,thefutureisevenlessclear.
Threekindoffacilitiesareunderdiscussion:VeryLargeHadronicCollider(VLHC)withppbeamsontheenergyupto200TeV,Compacte+eLinearColliderCLIContheenergy2E0=3–5TeVandmuoncolliderswhichpotentiallycanreachac.
m.
s.
energyevenhigherthaninppcollisions.
TalkatWorkshoponQuantumAspectsofBeamPhysicsandOtherCriticalIssuesofBeamsinPhysicsandAstrophysics,January7–11,2003,HiroshimaUniversity,Higashi-Hiroshima,Japan1Physicsmotivationfornextgenerationofcolliders(LHC,LC)isverystrong,twoexamplesaregivenbelow.
IftheStandardModelisvalidanewparticle,theHiggsboson,shouldexist.
DirectsearchatLEPandmeasurementsofloopcorrectionsindicatethattheHiggsbosonmasslaysintheregion115–200GeV.
Suchaparticleshouldhaveveryspecialproperties,theircouplingconstantswithotherparticlesareproportionaltoparticlemasses.
LinearcollidersallowustomeasureHiggsbranchingswithahighaccuracy,So,experimentsatLHCandLCcanshedalightontheoriginofparticlemasses.
Thesecondphysicsgoalisasearchofasupersymmetrywhichassumestheexistenceofanewclassofparticles,superpartnersofknownparticlesbutwithdierentspins:particleswiththespin1/2havepartnerswiththespin0andviceversa.
Itispossiblethatthedarkmatterintheuniverseconsistsofthelightestneutralsupersymetricalparticles.
Atcolliders,onecouldproduceanykindofsuchparticles,chargedandneutral.
Adiscoveryofa"parallel"world(whichaccordingtoastronomicaldatahasadensityevenhigherthanthatofthebarionicmatter)wouldmeananewrevolutioninphysics.
Belowweconsiderexistingprojectsoflinearcolliders,theirproblems,energyandluminositylimitations,prospectsofadvancedacceleratormethods.
2ProjectsoflinearcollidersItwasrealizedalready30yearsagothattheenergyofcirculare+elinearcollidersislimitedbysynchrotronradiationlossesatalevelof100–200GeVandfurtherprogressisonlypossibleusinglineare+ecolliders[1].
Attheendof1980-ththe2-mileelectronlinacatSLAChasbeentransformedintoa(semi)linearcolliderSLCwiththec.
m.
s.
energyof90GeV.
Itgavenicephysicsresultsandagreatexperienceofworkattherstlinearcollider.
AtthesametimeaninternationalstudyonlinearcolliderleadbySLAC,KEK,DESY,CERNandBINPhasbeenlaunchedwithambitiousgoaltodevelopalinearcolliderwithanenergyaboutoneTeVandaluminositybyafactorof103–104higherthanitwasattheSLC.
SincethattimealotofdevelopmentshavebeendoneandnowthreeprojectsTESLA(Eu-rope)[2],NLC(US)[3],JLC(Japan)[4]arealmostreadyforconstruction.
AfourthprojectCLIC(CERN)[5]isfocusedonmulti-TeVenergiesandisconsideredasthenext-to-nextlinearcollider.
SchemesofcollidersareshowninFig.
1,mainparametersarepresentedinTable1.
Eachprojecthassomedistinctivefeatures:TESLA:Lband,1.
4GHz,superconducting,Gmax35MeV/m,agoodeciency,alowwakeeld,arelaxedalignmenttolerances,alargedistancebetweenbunches;NLC/JLC:X-band,11.
4.
GHz,warmcavities,ahighgradient(55MeV/mloaded);CLIC:30GHz,atwo-beamaccelerator(oneofbeamsproducesRFpower),averyhighgradient,150MeV/m,costeectiveatmulti-TeVenergies.
So,therearethreemaintechnologiesforLCdevelopedbylargeteams,eachprojecthavecertainadvantages.
Itwouldbegoodtobuilttwocollidersalmostsimultaneously:TESLAforenergiesbelow0.
5TeV,NLC/JLCfortheenergyregionupto1.
5TeVandathirdcollider,CLIC,ontheenergy3–5TeVonedecadelater.
However,duetoahighcostonlyonegloballinearcolliderisseeninthevisiblefuture.
2electronsources(HEPandx-raylaser)linearacceleratorlinearacceleratorx-raylaserelectron-positroncollisionhighenergyphysicsexperimentspositronsourceaux.
positronand2ndelectronsourcedampingringdampingringpositronpreacceleratore-e+e-33kmFigure1:SchemesoflinearcollidersTESLA,NLC,JLCandCLIC(fromuptodown).
3Table1:ParametersoflinearcolliderTESLAJLC/NLCCLIC2E0GeV50080050010005003000SiteLkm–33–32–40TwolinacLkm303012.
625.
8527.
5Beamdel.
Lkm3.
23.
23.
83.
855G(un.
l/load)MeV/m23.
43570/5570/55172/150172/150TotalACMW95160120240100300AC-beame.
%232110108.
58.
5RFfreq.
GHz1.
31.
311.
411.
43030Rep.
rateHz54120120200100bunch/train28204886192192154154Coll.
ratekHz14.
119.
5232330.
815.
4Bunchsepar.
ns3371761.
41.
40.
670.
67Trainlengthsec9508600.
2670.
2670.
10.
1Part.
/bunch101021.
40.
750.
750.
40.
4σzm3003001101103030εnx/εnymm·mrad10/0.
038/0.
0153.
6/0.
043.
6/0.
042/0.
020.
68/0.
02βx/βymm15/0.
415/0.
48/0.
1113/0.
1110/0.
158/0.
15σx/σynm553/5391/2.
8243/3219/2.
3200/2.
543/1Dx/Dy0.
2/250.
2/270.
16/12.
90.
08/100.
12/7.
90.
03/2.
7Υ00.
060.
090.
140.
290.
38.
1δ%3.
24.
34.
78.
93.
831nγ/e21.
51.
31.
30.
72.
3ne+e/e0.
17L(withpin.
)1034cm2s13.
45.
8231.
410.
3L(w/opin.
)1034cm2s11.
62.
81.
21.
9L(1%)/L%66646725.
5L(5%)/L%91858640.
83GeneralfeaturesoflinearcollidersAtstoragerings,eachbunchcollidesmanytimes,theRFpowerisspentmainlyforcompensa-tionofsynchrotronradiationlosses.
Atlinearcolliders,eachbunchisusedonlyonce,radiationlossesduringtheaccelerationarenegligible,butalotofenergyisneededforproductionandaccelerationofbuncheswithahighrate.
ThetotalRFpowerconsumptionatLEPandat0.
5TeVlinearcollidersarecomparable,oftheorderof100MWfromthewallplug.
ThenumberofacceleratedparticlesislimitedbytotalACpowerwhichisproportionaltothebeampowerP.
Duetothedependenceofcrosssectionsontheenergyasσ∝1/E2theluminosityshouldincreaseasE2,asaresulttherequiredtransversebeamsizesatTeVenergiesshouldbeverysmall.
Beamswithsmallsizeshaveverystrongeldsthatleadtolargeradiationlossesduringbeamcollisions(beamstrahlung).
Thiseectdoesnotallowustousebeamswithsimultaneouslysmallhorizontalandverticalbeamsizes(σx,σy)(onlyveryatbeams)andtogettherequiredluminositythebeampowershouldbeadditionallyincreased.
Thisleadstothe"energycrisis"4atthebeamenergyofabout2E05TeV,seeSec.
4.
Intheγγmodeofoperation(Sec.
5)onlysomewhathigherenergiesarepossibleduetoconversionofhighenergyphotonstoe+epairsintheeldoftheopposingbeam(coherentpaircreation).
Besidetraditionallinearaccelerators,thereareideasofusingplasmaandlaserhighgradientacceleratortechniquesforlinearcolliders.
Therearesomespeculationsaboutcolliderswith100TeVandevenPeVenergies.
Certainly,developmentofthesetechniqueswillleadtosomepracticalapplications,butobtainingcollidingbeamsisveryproblematicduetorequiredqualityofbeamsandcollisioneects.
SomeconsiderationsandcriticalremarksonplasmaandlaseraccelerationaregivenSec.
6.
4CollisioneectsrestrictingluminosityandenergyoflinearcollidersInordertoobtainasucientluminosityatlinearcollidersthebeamsizesshouldbeverysmall.
Thiscausestwosortsofproblems:a)generationandaccelerationofbeamswithverysmallemittancesandfocusingtoatinyspot,b)beam-beamcollisioneectswhichleadtodegradationofthebeamquality.
Therstproblemisverydicultbutnotfundamental,inprinciple,onecanobtainemit-tancesmallerthangivedampingringsusing,forexample,lasercooling.
Thesecondproblemisevenmoresevere:beamcollisioneectsputrestrictionsonattainableluminosityand,cor-respondently,onthemaximumenergyoflinearcolliders.
IntheabsenceofcollisioneectstheluminosityofacolliderL≈N2f4πσxσy=P4πE0*Nσxσy.
(1)For2P=20MW(200MWACpower),N=2*1010,σx=σy=1nmitgivesL=1037/E0[TeV],cm2s1,thisluminosityissucientforproductionof103leptonpairsper107secupto2E0=25TeV.
Belowweconsiderseverallimitationsduetocollisionseects.
4.
1PincheectandinstabilityofbeamcollisionsDuringthecollisionbeamsattract(e+e)orrepulse(ee)eachother.
Thecharacteristicdisruptionparameter[6,7]Dy=2Nreσzγσxσy.
(2)ForatbeamandDy10,theattractionleadstoincreaseofthee+eluminositybyafactorofHD2.
AtDy≥25beamsbecomeunstable,thecorrespondingluminosityLPmc2reσz.
(3)ForP=10MWandσz=100mL5*1034cm2s1.
So,thisputlimitontheluminosityforagivenbeampowerandbunchlength.
54.
2BeamstrahlungAstrengthofabeameldischaracterizedbytheparameterΥ[8,7]Υ=23ωcE=γBB0,B0=αer2e=4.
4*1013G.
(4)ForatbeamsΥav≈5Nr2eγ6ασxσz.
(5)Themaximumvalueofσzisdeterminedbydisruption.
Ideally,increasingσxtoinnityandsimultaneouslydecreasingσytozeroonecangetarbitrarysmallΥforanyluminosity.
However,ifσyhassomeminimumvalue(therearemanyreasons),thenΥ∝L2γ2σy/P2Dy.
AsPisalwayslimited,DyE=4√315ΥU1(Υ)U0(Υ)=0.
462Υ(Υ→0),0.
254(Υ→∞),(8)δE=EE=1.
24α2σzΥreγΥU1(Υ);(9)Υ1isthe"classic"regime;Υ0.
2–200the"transition"regime(ΥU1(Υ)≈0.
1–0.
20.
15);Υ200the"quantum"regime.
CollidersintheTeVregionbelongtothetransitionregime,multi-TeVLCwithdenseshortbunchescanreachthequantumregime.
Theluminosity(1)canbeexpressedviaδE.
Inthetransitionregimeitdoesnotdependonthebunchlengthσz:L6.
45δE4παreγσyPmc2=1.
5*1034P[MW]δEE0[TeV]σy[nm]cm2s1;(10)InthequantumregimeL1.
954πα2σyδ3EreσzγPmc2=5*1034P[MW]σy[nm]δ3EE0[TeV]σz[m].
(11)Forexample,forP=10MWperbeam(about200MWfromwallplug)σy=1nm,2E0=5TeV,δE=0.
2weget(accuracyisaboutfactorof2–3)L=1.
2*1034cm2s1inthetransitionregime(doesnotdependonσz)andL=3*1034cm2s1inthequantumregime6(forσz=1m),anadditionalfactorof1.
5cangivethepincheect.
Weseethatthequantumregime(shortbunches)helpsbutnottoomuch.
Inordertoproduce103characteristicreactionse+eper107secattheenergy2E0=5TeVtherequiredluminosityis3*1034,thatisclosetotheabovelimitduetobeamstrahlung.
So,ifσy,min1nm(seeSec.
4.
5),themaximumreasonableenergyoflinearcollidersisabout2E05TeV.
Inprinciple,thereisapossibilitytocancelbeameldsbycollidingfourbeams(e+efromeachside),thenbeamstrahlungisabsent.
Thebeamsinstabilitythresholdremainsatthesamelevelofluminosityormaybeonlysomewhathigher.
Thisschemecangivesomegaininluminosity,buttechnicallyitlooksunrealistic.
4.
3Coherente+epaircreationAtκ=(ω/E0)Υ>1abeamstrahlungphotoncanconvertintoe+epairsintheeldoftheopposingbeam[9].
Atκ1theratioofbeamstrahlung/paircreationprobabilitiesisabout3.
8.
ThenumberofbeamstrahlungphotonsatlinearcollidersNγNe(inordertoincreseluminositythehorizontalsizeisdecreaseduntileachelectronemitaboutonephoton).
Thereforethenumberofe+epairsatκ1(orΥ1),Ne+e/Ne=O(0.
1).
Forexample,atCLIC(3000)Ne+e/Ne0.
085.
Theminimumenergyofproduceparticles(importantfromabackgroundpointofview)Emin0.
05E0/Υ.
4.
4DeectionofsoftparticlesThelowestenergychargedparticlesproducedinprocessofcoherentpaircreationwiththesamesignofthechargeasthatoftheopposingbeamaredeectedbytheopposingbeamontheangle[9]θ4πNe2σzEmin1/2170Nσzr3eσx1/2.
(12)Forexample,atCLICθ15mrad.
Toavoidbackgroundfromtheselargeangleparticlesoneshouldusethecrab-crossingscheme[10].
Belowwewillseethatcrab-crossinganglesbelow20–30mradareacceptable,butlargeranglesleadtotheincreaseoftheverticalbeamsize.
So,deectionofsoftparticlesputanadditionalconstraintonthebeamparameters.
Beam-strahlungandinstabilitiesmaybeOK(incaseofveryshortbunches),butdisruptionanglesaretoolarge.
4.
5MinimumvalueofσyTheminimumverticalbeamsizeattheinteractionpoint(atβyσz)σy=εnyσz/γ.
Limi-tations:Attainablevalueofthenormalizedverticalemittancefromaninjector;Radiationinnalquadrupoles(Oideeect)[11].
Minimumachievablebeamsizeσmin[m]≈1.
7*104εny[m]5/7.
ForεnyconsideredinthecurrentLCprojectsσmin0.
5nm;Radiationinthedetectorsolenoideldduetothecrabcrossing[12,13,14]7σ2y=55r2e480√3αeBsθcL2mc25.
(13)ForBs=4T,L=4mσy=0.
74nmforθc=20mradand2nmforθc=30mrad.
Moreaccuratesimulationofthiseect(thenumberofemittedphotonisaboutone)wasdoneinRefs[13,14].
Asalinearcolliderwithoutadetectorhasnosensethiseectputalimitonaminimumverticalbeamsizeattheinteractionpointatthelevelof0.
5nmatθc=20mrad.
4.
6ResumeonmaximumenergiesoflinearcollidersForareasonablewallplugACpower100–300MWthemaximumenergyoflineare+ecolliderswithaluminositysucientforexperiments,accordingtopresentunderstanding,islimitedbycollisioneectsatthelevelof2E0=5–10TeV.
5PhotoncollidersInadditiontoe+ephysics,linearcollidersprovideauniqueopportunitytostudyγγandγeinteractionsathighenergiesandluminosities[15,16].
HighenergyphotonscanbeobtainedusingComptonbackscatteringoflaserlightohighenergyelectrons.
Thisoptionisforeseeninallotherprojectoflinearcolliders[2,3,4,5,18].
ThemaximumenergyofphotonsafterComptonscatteringωm=xx+1E0;x≈4E0ω0m2c415.
3E0TeVω0eV.
(14)Forexample:E0=250GeV,ω0=1.
17eV(λ=1.
06m)x=4.
5andωm=0.
82E0=205GeV.
Thevaluex=4.
8isthethresholdfortheprocessγγL→e+eintheconversionregion.
Thisdeterminetheoptimumlaserwavelength:λopt4E0[TeV]m[19].
NonlineareectsinComptonscatteringincreasethethresholdvalueofxbyafactorof(1+ξ2),whereaparameterofnonlinearityξ20.
5isacceptable[18].
Mostpowerfulsolidstatelaserwithλ1.
05mcanbeuseduptotheenergies2E0800GeV.
Detaileddiscussionofphysics,andtechnicalproblemofphotoncolliderscanbefoundelsewhere[18,3,28].
Belowweconsideronlythemostcriticalissues:luminosity,energy,lasersystem.
5.
1CurrentprojectsofphotoncollidersParametersofthephotoncollidersatTESLA[18](asanexample)arepresentedinTable2,forcomparisontheluminosityine+ecollisionsisalsogiven.
Otherparameters,constantforallenergies,are:λ=1.
06m,N=2*1010,σz=0.
3mm,frep*nb=14.
1kHz,εnx/εny=2.
5/0.
03*106m·rad,βx/βy=1.
5/0.
3mm.
ForthesameenergytheγγluminosityinthehighenergypeakoftheluminosityspectrumLγγ(z>0.
8zmax)≈(1/3)Le+e,(15)wherez=Wγγ/2E0.
Note,thatcrosssectionsinγγcollisionsaretypicallylargerthenine+ebyoneorderofmagnitude.
AmoreuniversalrelationLγγ(z>0.
8zm)≈0.
1Lee(geom)(fork2=0.
4).
Expectedγγ,γeluminosityspectraatTESLAcanbefoundelsewhere[20,18,21].
8Table2:ParametersofthephotoncollideratTESLA2E0,GeV200500800Wγγ,max122390670Wγe,max156440732σx/y[nm]140/6.
888/4.
369/3.
4b[mm]2.
62.
12.
7Lee(geom)[1034]4.
81219Lγγ(z>0.
8zm,γγ)[1034]0.
431.
11.
7Lγe(z>0.
8zm,γe)[1034]0.
360.
941.
3Lee(z>0.
65)[1034]0.
030.
070.
095Le+e,[1034]1.
33.
45.
8TheγγluminosityatTESLAislimitedbyattainableelectronbeamsizes.
Havingbeamswithsmalleremittances(especiallythehorizontalone)onewouldgetahigherluminosity.
Inordertoincreasethegeometricluminosityoneshoulddecreasetheβ-functionsasmuchaspossible,downtoaboutabunchlength.
Inthecurrentschemeofthenalfocusitwasnotpossibletomakeβxbelow1.
5mmduetochromo-geometricabberations[18].
Itisnotclearwhetherthisisafundamentalorjustatemporarytechnicalproblem.
5.
2UltimateluminosityofphotoncollidersThoughphotonsareneutral,γγandγecollisionsarenotfreeofcollisioneects.
Electronsandphotonsareinuencedbytheeldoftheoppositeelectronbeamthatleadstothefollowingeects[19]:inγγ:conversionofphotonsintoe+epairs(coherentpaircreation);inγe:coherentpaircreation;beamstrahlung;beamdisplacement.
Beamcollisioneectsine+eandγγ,γecollisionsaredierent.
Inparticular,inγγcollisionstherearenobeamstrahlungandbeaminstabilitieswhichlimitthehorizontalbeamsizeine+ecollisionsonthelevel550(350)nmforTESLA(NLC/JLC).
Asimulation,whichincludesallcollisioneectshasshownthatinγγmodeatTESLAonecanusebeamswiththehorizontalsizedowntoσx=10nm(atsmallerσxmaybeproblemswiththecrab–crossingscheme)andinuenceofcollisioneectswillberathersmall[22,20,18].
Theγγluminosity(inthehighenergypart)canreach1035cm2s1.
NotethatnowinTESLAprojectσx≈500nmine+ecollisionsandabout100nmintheγγcollisions.
Havingelectronbeamswithmuchsmalleremittancesonecouldbuildaphotoncolliderfactorywithproductionrateofnewparticlesbyafactorof10–50higherthanate+ecolliders.
Alasercoolingofelectronbeamsisoneofthepossiblemethodsofreductingbeamemittancesatphotoncolliders[23,24],butthismethodisnoteasy.
Notethatsmallrateofcoherente+epairproductionatTESLAenergiesispartiallyexplainedbythebeamrepulsionwhichreducestheeldactingonthephotons.
Formulti-TeVenergiesandshortbunchessuchsuppressionisabsentandphotoncollidersreachtheirenergylimit(withadequateluminosity)approximatelyatthesameenergiesase+ecolliders[25,26,27].
95.
3TechnicalaspectsofphotoncollidersAkeyelementofphotoncollidersisapowerfullasersystemwhichisusedforthee→γconversion.
Requiredparametersare:afewJoulesashenergy,afewpicoseconddurationand10–20kHzrepetitionrate.
Toovercomethe"repetitionrate"problemitisquitenaturaltoconsideralasersystemwhereonelaserbunchisusedforthee→γconversionmanytimes.
AttheTESLA,theelectronbunchtraincontains3000buncheswith337nsspacing,heretwoschemesarefeasible:anopticalstorageringandanexternalopticalcavity[20,18,21].
Withtheopticalcavityarequiredlaserpowercanbelowerthaninthecaseofaone-passlaserbyfactorof50–100.
Thereisnodetailedschemeofsuchlasersystemyet.
AtNLC,theelectronbunchtrainconsistsof96buncheswith2.
8secspacingthereforeexploitingoftheopticalcavityisnoteective.
Acurrentsolutionisaone-passlaserschemebasedontheMercurylaserdevelopedforthefusionprogram.
Thelaserproduces100–200Jpulseswhichaftersplittingto96pulsescanbeusedfore→γconversionofonetrain[3,21].
Alasersystemforaphotoncollidercancertainlybebuiltthoughitisnoteasyandnotcheap.
6AdvancedacceleratorschemesConventionalRFlinearcollidershaveacceleratinggradientsupto150MeV/m,correspondinglengthsabout30–40kmandattainableenergiesupto5TeV(Sec.
2).
Ontheotherhands,peopleworkingonplasmaandlasermethodsofaccelerationhaveobtainedgradientsof100GeV/m!
Somepeoplearethinkingalreadyabout100TeVandeven1PeVlinearcollidersorabout1–5TeVLCwithlessthanonekmlength.
Certainly,newmethodsofaccelerationwillmakefurtherprogressandndcertainappli-cations,butitislessclearaboutpossibilityofsuperhighenergycollidersbasedonthesetechnologies.
Firstofall,collisioneectsrestricttheenergyoflinearcollidersatabout10TeV(Sec.
4);secondly,thequalityofelectronbeamsshouldbeveryhigh;andthirdly,itisverylikelythatinconsiderationsofveryhighaccelerationgradientssomeimportanteectsarejustmissed.
Drivenbymycuriosityandforself-educationIhavespentsometimeforrandomcheckoftheseconceptionsandsomeremarksarepresentedbelow.
Situationinthiseldisnotbad,butsomeofexistingproposalsarecertainlywrong.
6.
1PlasmaaccelerationLaserorparticlebeamscanexcitewavesinplasmawithalongitudinalelectricaleld[29].
TheacceleratinggradientGmcωp104np[cm3]MeVm.
(16)Typicalparametersconsidered:np1015cm3,G2GeV/m.
106.
1.
1MultiplescatteringLetusconsiderthecasenbnpwhenallplasmaelectronsarepushedoutfromtheacceleratedbeam.
Thebeamstravelthroughionswithdensitynpandexperienceaplasmafocusingwiththeβ-function[30]β2πγ/renp=√2γλp.
Ther.
m.
s.
angleduetomultiplescatteringθ2≈8πZ2r2endzγ2dρρ,ρminRN,ρmaxRD,(17)whereRD=(kT/4πne2)1/2istheDebairadius.
Theincreaseofthenormalizeemittanceεn2=γ2r2θ2=εnγβθ2.
Afterintegrationontheenergywegetthenalnormalizedemittanceεn8π√2πZ2(npr3eγf)1/2(mc2/G)L,(18)whereL=lnρmax/ρmin20.
Substitutingn=1015cm3,G=2GeV/m,Z=1,γf=5*106(2E0=5TeV)wegetεn3*107cm.
NotethattheresultdoesnotdependontheplasmadensitybecauseG∝√np(Eq.
16).
InpresentLCdesignstheminimumverticalemittanceεny=2*106cm,somultiplescatteringinanidealplasmaacceleratorslookacceptable.
Itisassumedthatsectionswithplasmahavesmallholesforbeamssinceanywindowswillgivetoolargescatteringangles.
6.
1.
2SynchrotronradiationDuetoastrongfocusingbyions(plasmaelectronsarepushedoutfromthebeam),beamelectronslosetheirenergytoradiation,theradiationpowerP=(2/3)cr2eγ2E2⊥,whereE⊥=2πenpZr(asbeforeweassumenbnp),rεnβ/γ,β=2πγ/renp.
Afterintegrationontheenergywendthedierenceofenergiesfortheparticleontheaxis(noradiation)andoneatther.
m.
sdistanceformtheaxisE/E25r5/2en3/2pZ2γ3/2f(mc2/G)εn.
(19)ForG=2GeV/m,np=1015cm3,εnx104cm(emittancefromdampingringsorfromphoto-guns),γf=5*106(2E0=5TeV)wegetE/E103,thatisacceptable.
Forseveraltimeslargerenergyspreadstherearechromaticityproblemsinnalfocussystems.
Note,thatG∝√np,thereforetheenergyspreadisproportionaltotheplasmadensity.
InRef.
[31]thecaseoftheoverdenseplasma(nb1/θ,thenintheelectronrestframelaserphotonscomefromtheforwardhemisphereandthereforetheelectronisdeaccelerated!
Forλ=1mandZR=100m,Emax15MeVonly!
2.
Ponderomotiveacceleration.
Inastronglasereldanelectronexperiencesacollectiveforcefromthewholelaserbunch,socalledaponderomotiveforce[37,38,39],Fimc2γdξ2dxi,ξ2=e2E2m2c2ω20=2nγr2eλα.
(21)Thisopensawaytotransfertheenergyfromlargebody(laserbeam)toonemicroscopicparticle(electron).
Thereisanidea[40]tocollidethelaserpulsepropagatinginararegas(tohavevAccordingtoaboveRefs,forthelaserpower4.
3EW(EW=1018W)γ=1.
6*106andγ0=1400,theenergyofreectedelectronsinthelaboratorysystemis1PeV≡1000TeV!
ThelengthofthecollideristhelaserbunchlengthoralmostZERO!
Unfortunately,theideaiswrongduetomanyreasons:TheinteractionlengthisnotthebunchlengthbutLintllaser/(1v/c)llaser*(γ)2102*1012105km!
Radiationofelectrons(seebelow),andmanyother"NO".
6.
2.
3RadiationduringaponderomotiveaccelerationDuringtheponderomotiveaccelerationelectronsradiateinthetransverselasereld.
ThiscanbetreatedasComptonscattering.
Radiatedenergyperunitlength:dE/dxn(1cosθ)σT.
Substitutingθ2λ/(2πZR),ω0γ2θ2,n=αξ2/(2r2eλ)wegetdEdxξ2γ2reZ2Rmc2.
(22)Forexample:E0=1TeV,ZR=100m,andξ2=100(ashenergy100J),dE/dx=200GeV/cm.
Forthementioned1PeVprojectwithξ2=2*106,dE/dx=109PeV/cm!
So,ponderomotiveaccelerationcanbeusefulforlowenergyapplication,butnotforlinearcollidersduetothedecreaseoftheforcewiththeincreaseoftheenergyandahugeradiation.
7ConclusionLineare+e,ee,γγ,γecollidersareidealinstrumentforstudyofmatterintheenergyregion2E0100–1000GeV.
Threeprojectsarealmostreadyforconstruction,awisechoiceandpoliticaldecisionareneeded.
Alinearcolliderisnotasimplemachine,veryhighaccuracies,stabilitiesandcleaverbeamdiagnosticsareneeded.
Manycriticalelementshavebeentestedexperimentally.
13Accordingtopresentunderstandingamaximumattainableenergyoflinearcolliderswithadequateluminosityisabout2E05TeV.
Thereistechnologyforsuch"last"LC,thatisCLIC.
Advancetechnologies(plasma,laser)cangivehigheracceleratinggradientsbuttheirap-plicationforhighenergylinearcollidersisunderbigquestion.
Furthercomplexstudiesofnewacceleratingmethodsinthiscontextareneeded.
AcknowledgementIamgratefultoPisinChenforagreatworkonorganizationofseriesofworkshopsonQuantumAspectsofBeamPhysics,whichmotivatedpeopletolookdeeplyintopicsrelatedtobeamphysicsatEarthandCosmosandtoAtsushiOgatafororganizationofthepresentworkshopinHiroshima.
ThisworkwassupportedinpartbyINTAS(00-00679).
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