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NUCLEARPHYSICSAELSEVIERNuclearPhysicsA595(1995)346-382Relativistichydrodynamicsforheavy-ioncollisions.I.Generalaspectsandexpansioninto~rvacuumDirkH.Rischkea,j,StefanBernardb,JoachimA.MaruhnbaPhysicsDepartment,PupinPhysicsLaboratories,ColumbiaUniversity,538W120thStreet,NewYork,NY10027,USAblnstitutfiirTheoretischePhysikderJ.W.Goethe-Universitiit,Robert-Mayer-Str.10,D-60054Frankfurt/M,GermanyReceived21April1995;revised11July1995AbstractWepresentalgorithmstosolverelativistichydrodynamicsin(3+1)-dimensionalsituationswithoutapparentsymmetrytosimplifythesolution.Insimulationsofheavy-ioncollisions,thesenumericalschemeshavetodealwiththephysicalvacuumandwithequationsofstatewithafirstorderphasetransitionbetweenhadronmatterandaquark-gluonplasma,i.e.ratherspecialconditionsfluid-dynamicalalgorithmsareusuallynotconfrontedwith.Therefore,priortoapplyingthemdirectlytothesimulationofheavy-ioncollisions,oneshouldinvestigatetheirperformanceinwell-controlledsituations.Weconsiderheretheone-dimensionalexpansionofbaryon-freenuclearmatterintothevacuum,whichisananalyticallysolvabletestproblemthatincorporatesboththeaspectofthevacuumaswellasthatofaphasetransitionintheequationofstate.Thedependenceofthelifetimeofthemixedphaseontheinitialenergydensityisdiscussed.1.IntroductionHydrodynamicsrepresents(local)energy,momentumandchargeconservation[1,2].Becauseofitssimplicityithasfoundwidespreadapplicationinstudyingtheevolutionof*ThisworkwassupportedbytheDirector,OfficeofEnergyResearch,DivisionofNuclearPhysicsoftheOfficeofHighEnergyandNuclearPhysicsoftheUSDepartmentofEnergyunderContractNo.DE-FG-02-93ER-40764.]PartiallysupportedbytheAlexanderyonHumboldt-StiftungundertheFeodor-Lynenprogram.0375-9474/95/$09.50(~)1995ElsevierScienceB.V.AllrightsreservedSSDI0375-9474(95)00355-XD.H.Rischkeetal./NuclearPhysicsA595(1995)346-382347nuclearmatterinheavy-ioncollisions.Thephysicalinputisthenuclearmatterequationofstate(EoS).Therefore,hydrodynamicsallowstostudynuclearmatterpropertieslikethephasetransitiontothequark-gluonplasma(QGP)[3]inasimple,straightforwardmanner.Oneofthefirstapplicationsofhydrodynamicstoheavy-ioncollisionswasthestudyofmulti-particleproductionbyFermiandLandau[4]2.Simplehydrodynamicalmod-els[5]predictedtheoccurrenceofnuclearshockwaves[6]intheearlyseventies.Full(3+1)-dimensionalcalculationsforheavy-ioncollisionsatBEVALACenergies(E[~b=0.1-2A.GeV)wereperformedabouttwentyyearsago(seetheverydetailedreviewofthistopicinRef.[1]andRefs.therein).Itwasfoundthatthecompressionalshockwavescreatedinthecollisionleadtocollectiveflowphenomenalikesidewarddeflectionofmatterinthereactionplane(side-splashandbounce-off)aswellasazimuthaldeflectionoutofthereactionplane(squeeze-out).Oneofthemainsuccessesofthefluid-dynamicalpicturewastheconfirmationofthesecollectivefloweffectsbyBEVALACexperiments[7].Moredetailedinvestigationsoftheflow,however,haverevealed[8]thatviscositymightbeimportanttoexplainthesephenomenaquantitatively.Also,systematichydrodynamicalstudiesweredoneonlyinthenon-relativisticlimit.Therefore,idealanddissipativerelativistichydrodynamicalinvestigationsforBEVALACenergiesaremandatory.AcomparisonwithrecentexcellenttripledifferentialdatafromtheEOScollaboration[9]wouldhelptounderstandinhowfarthehydrodynamicalpictureisquantitativelyapplicableattheseenergies.(3+l)-dimensionalidealrelativistichydrodynamicswasappliedtostudyheavy-(j~'kinioncollisionsatAGS¢/Tkin,.~11A-GeV)andCERN-SPSenergies~Lab-~60-~,L,Lab--200A.GeV)[10].Sinceidealhydrodynamicsassumesthatmatterisinlocalequilib-riumateveryinstant,collidingfluidelementsareforcedbymomentumconservationtoinstantaneouslystopandbyenergyconservationtoconvertalltheirkineticenergyintothermalenergy(compressionandheatingviashockwaves).However,thelongitudinalrapiditylossinindividualnucleon-nucleoncollisionsislimited.Thus,immediatecom-pletestoppingisnotachievedinrealityand,forhigherbeamenergies,itisnolongerjustifiedtotreattheinitialstageofthereactioninanidealhydrodynamicalpicture.Idealhydrodynamicsmightneverthelessbeapplicableintheexpansionstageofthecol-lision[11],wheretheconditionsoflocalthermodynamicalequilibriumaremorelikelytobeestablished.Inordertodescribetheinitialstage,however,onehastoextendthehydrodynamicaldescriptiontoaccountfornon-equilibriumeffects.Whiledissipativehydrodynamicsinprincipleprovidesthetheoreticalframeworkforthestudyofnon-equilibriumeffects,itsviabilityasacausaltheoryisstillunderde-bate[2].Moreover,allknownformulationswhicharerigorouslyderivedfromkinetictheoryrelyontheassumptionthatnon-equilibriumeffectscanbetreatedaspertur-bations,orinotherwords,thatthemomentumdistributionofparticlesdeviatesonly2OverthepastyearstheoriginalLandaumodelandalsosimplifiedversions(so-calledfireballmodels)havebeenfrequentlyappliedtoexplainheavy-ioncollisiondata.Todiscusstheseapproachesingreaterdetailisoutofthescopeofthispaper.348D.H.Rischkeetal./NuclearPhysicsA595(1995)346-382slightlyfromitslocalequilibriumform.Thisisnotthecaseintheinitialstageofheavy-ioncollisionswhereincidentenergiescanbemuchlargerthantheFermi-momentumofthenucl
本文标题:重离子碰撞的相对论流体力学I一般方面和扩展到真空中Relativistichydrodynamics
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