IBSFOR IONDISTRIBUTIONUNDER ELECTRON COOLING

Standard models oftheintra-beam scattering (IBS) are basedonthegrowth ofthermsbeamparameters fora Gaussian distribution. Asaresult ofelectron cooling, the coreofbeamdistribution iscooled muchfaster thanthe tails, producing adenser core. Inthis paper, wecompare various approaches toIBStreatment forsuchdistribution. Itsimpact ontheluminosity isalso discussed. CORE-TAILMODEL Formation ofadense coreduetocooling anddiffusion ismodeled usingthemacro-particle approach which allowsvariable withtimebeamdistribution. The individual-particle kicksduetocooling andIBSare applied inthevelocity space.Suchapproach wasthe basis oftheSIMCOOLcode(1)andwasalsorecently implemented intheBETACOOL codeasa "Model Beam"approach (2). To account fora corecollapse (which directly impacts luminosity inacollider) ofion distribution, the"core-tail" modelfortheIBSwas proposed. Ingeneral, todescribe dynamics ofsuch distributions anaccurate kinetic simulation isrequired whichwill beaddressed inthefuture work. Withthecore- tail modelweattempt tocapture only basic features ofthe coreformation inorder toestimate theluminosity. Inthis model, theindividual-parti cle kickinthevelocity space duetoIBSisapplied basedondiffusion coefficients whicharedifferent forparticles inside andoutside ofthe core. Cooling process fortypical RHICparameters (3)is showninFigs. 1-4. Figure 1showsthat anrmsemittance undercooling staysapproximately constant forthese parameters, while there isafast formation ofadistinct coreinthebeamprofiles.