Particle-in-cell charged-particle simulations, plu

IEEETRANSACTIONSONPLASMASCIENCE,VOL.19,NO.2,APRIL1991Particle-in-CellCharged-ParticleSimulations,PlusMonteCarloCollisionsWithNeutralAtoms,PIC-MCCC.K.Birdsall,LifeFellow,IEEE(InvitedPaper)Abstract-Many-particle(meaning1000's)charged-particleplasmasimulationsusingspatialmeshesfortheelectromagneticfieldsolutions,particle-in-cell(PIC)mergedwithMonteCarlocollision(MCC)calculations,arecomingintowideuseforapplicationtopartiallyionizedgases.ThispaperemphasizesthedevelopmentofPICcomputerexperimentssincethe1950'sstartingwithone-dimensional(I-D)charged-sheetmodels,theadditionofthemesh,andfastdirectPoissonequationsolversfor2-Dand3-D.Thefinite-sizeparticle-in-mesh(finiteAX,At)theoryofLangdon[51]-[53]ispresentedinparttodisplaytheeffectsoftoosmallAD/Ax,evenforMaxwellianvelocitydistributions,asacaution,forexample,whensomeionsarecooledtobackgroundgastemperaturesbychargeexchange.Earlyworkonaddingcollisionsto1-Dcharge-sheetmodelsbyBurger[28]andShannyeta1.[76]arepresented,withmanyoftheelementsofcurrentMonteCarlocodes.BoundedplasmamodelingispresentedwithelectrodechargesandexternalR,L,C,andV(t),Z(t)sourcesnowinuseonfastdesktopcomputersasreal-timecomputerexperiments,complementinganalyticmodelingandlaboratoryexperiments.TheadditionofMonteCarlocollisions(usuallydonewithirregulartimesteps)toPIC(usuallydonewithuniformAt's)isdisplayedasadevelopingart,relyingonexperimentaltotalcrosssectionsandapproximateanalyticaldifferentialcrosssectionstoproducechangesincharged-particlespeedanddirectionduetocollisionswithneutrals,sofarincludingelastic,excitation,ionization,chargeexchange,andattachmentprocesses.THEplasmamedium,consistingofelectrons,ions,neutralatomsandmolecules,andparticles,isverycomplicatedtounderstand.Theoryandmodelingprovideguide-linesfordesignofdevices;experimentsprovideavarietyofmeasurements.Simulationsprovideinsight,andnumbers,computerexperiments.Interactionsamongthistriohaveproveneffectiveandefficientinadvancingplasmascienceandengineering.Thisreportleadsthereaderthroughthedevelopmentoverthepastfourdecadesofmany-particleparticle-in-cell(PIC)simulationsandintoincludingcharged-particlecollisionswithneutralatomsusingMonteCarlomethods.SomementionwillbemadeofdoingCoulombcollisionsusingPICcodes.Wethenprovidesomedetailsofaddingthecollisionsbetweenthechargedparticlesandneutralatoms.Theresultismany-particlesimulationswithmanyofthefeaturesmetinlow-temperaturecollisionalplasmas;forexample,withapplicationstoplasma-ManuscriptreceivedAugust6,1990;revisedNovember30,1990.ThisworkwassupportedbytheU.S.DepartmentofEnergy,OfficeofFusionEn-ergy,AppliedPlasmaPhysicsunderContractNo.FD-DE-FG03-90ER54079,andtheOfficeofNavalResearchunderContractNo.FD-N00014-90-J-1198.SomeofthisworkbeganwithsupportfromVarian,throughDr.J.Helmer,withaCaliforniaMICROmatchinggrant.TheauthoriswiththePlasmaTheoryandSimulationGroup,DepartmentofElectricalEngineeringandComputerSciences,UniversityofCalifornia,Berkeley,Berkeley,CA94720.IEEELogNumber9042658.assistedmaterialsprocessing,butalsorelatedtowarmerplasmasattheedgesofmagnetizedfusionplasmas.Collisionlessmany-particleplasmasimulationisrichinhistoryandmayrateasoneofthesuccessstoriesinphysicsandengineeringusingthemoderndigitalcomputer,alongwithsuchadvancesasnumericalwindtunnelsandspacecraftcontrolandcommunications-bothcomplementingtheoryandexperimentand,insomecases,beingthemainingredient.Thisrichnessextendsalsotothebreadthofmethods,makingitdifficulttomentionhereallthebitsandpiecespractitionersliketohaveattheirfingertips.Thisreviewhasthefollowingorganization.SectionI1coversearlyone-dimensionalsheetmodels,roughlyfromthe1950'stomid1960's.SectionI11coversearlvtwo-andthree-dimensionalmodelswithmathematicalgrids(meshes),labeledparticle-in-cell(PIC)orcloud-in-cell(CIC),fromaboutthemid1960'sonwards.SectionIVcoversthetheoryofsimulationwithparticle-shapefactorsandsoon,fromabout1970onwards.SectionVcoversearlyworkonelectron-neutralelasticcollisions.SectionVIcov-ersearlyworkonelectron-ionCoulombcollisions.SectionVIIcoversmoreearlyCoulombcollisionwork.SectionVIIIcoverstheboundedmodelsthatweandothershavedevelopedforstudyingplasmasheathsandedges.SectionIXintroducesthedetailedtreatmentofseveralkindsofcollisionprocessesbetweenthechargedparticlesandneutralgasatoms.Severalbooksonplasmaandmany-particlesimulationsarereferredtofrequently:TheyappearinthereferencesasBirdsallandBridges[7],Dunn[37],HockneyandEastwood[50],BirdsallandLangdon[12],Tajima[82].Therearethreereviewbooks(vols.9and16ofMethodsofComputationalPhysics,Alderetal.,Eds.,1970and1976,respectively,andMultipleTimeScales,BrackbillandCohen,Eds.,1985).AnexcellentgeneralcoverageisPotter's1973book[70],coveringPICmethodsinfluidsaswellaswithparticles.Therearealsonumerousintroductoryorreviewarticlesorchapters:Forexample,BunemanandDunn[23],BirdsallandDawson[Ill,DenavitandKruer[36],andDawson[34].Lastly,therearetheProceedings(severalpagearticles)oftheConferencesonNumericalSimulationsofPlasmas,begunin1967,uptothe14thAnnualConferencein1990.Awordonthegeneraltemperamentofthefieldofmanycharged-particlesimula