comsol等離子體放電二維模型

1、DCGlowDischargeIntroductionDCglowdischargesinthelowpressureregimehavelongbeenusedforgaslasersandfluorescentlamps.DCdischargesareattractivetostudybecausethesolutionistimeindependent.ThismodelshowshowtousetheDCDischargeinterfacetosetupananalysisofapositivecolumn.Thedischargeissustainedbyemissionofseco

2、ndaryelectronsatthecathode.Figure1:SchematicoftheDCdischargeandexternalcircuit.DOMAINEQUATIONSTheelectrondensityandmeanelectronenergyarecomputedbysolvingapairofdrift-diffusionequationsfortheelectrondensityandmeanelectronenergy.Convectionofelectronsduetofluidmotionisneglected.Fordetailedinformationon

3、electrontransporThe eeryfortheDriftDiffusioninnt teefaclesmaModuleUserGuide.?n()+?Fe(ve?E)De?ne=Re?te?n()+?Fe(？E)De?5+E?Te=Rewhere:1|DCGLOWDISCHARGEre=-(p,e?E)neDe?neTheelectronsouraaRtheenergylossduetoinelasticcolhsiOnSnRdlater.Theelectrondiffusivity,energymobilityandenergydiffusivityarecomputedfro

4、mtheelectronmobilityusing:De=VeTeg5g=-,Dg=gsTee3Thesourcecoefficientsintheaboveequationsaredeterminedbytheplasmachemistryusingratecoefficients.Supposethatrea而而oneWhichcontributetothegrowthordecayofelectrondensityaBtitelectron-neutralcollisions.IngeneralPM.Inthecaseofratecoefficients,theelectronsourc

5、etermisgivenby:Re=XjkjNinej=1whereixthemolefractionofthetargetspeciesjifothre earcti1coekficientforreactiom3fs),andnliithetotalneutralnumberdens3(dischargesitisbetterpracticetouseTownsendcoefficientsinsteadofratecoefficientstodefinereactionrates.Townsendcoefficientsprovideabetterdescriptionofwhathap

6、pensinthecathodefallregionRef1.WhenTownsendcoefficientsareused,theelectronsourcetermisgivenby:Rs=XjajNnFej=1wherexjistheTownsendcoefficientfor(mactnonjeistheelectronfluxasdefinedabove2s()mTownsendcoefficientscanincreasethestabilityofthenumericalschemewhentheelectronfluxisfielddrivenasisthecasewithDC

7、discharges.Theelectronenergylossisobtainedbysummingthecollisionalenergylossoverallreactions:Re=XjkjNhneAjj=1whereejistheenergylossfromreacThejratecoefficientsmaybecomputedfromcrosssectiondatabythefollowingintegral:2|DCGLOVDISCHARGEkkT6k()f()d0where=(2q；e)1/2(C/2kg/2,neistheelectronmasse(ki(s)energy(

8、V)kisthecollisioncrossse2)tiond(mitheelectronenergydistributionfunction.InthiscaseaMaxwellianEEDFisassumed.WhenTownsendcoefficientsareused,the1IIelectronenergylossistakenas:Re=xjajNnrejj=1Fornon-electronspecies,thefollowingequationissolvedforthemassfractionofeachIIspecies.Fordetailedinformationonthe

9、transportofthenon-electronspeciesseeTheoryfortheHeavySpeciesTranspoirttheePfa asmaModUsersGuide.?wp()+P(u?)w0nPLASMACHEMISTRYArgonisoneofthesimplestmechanismstoimplementatlowpressures.Theelectronicallyexcitedstatescanbelumpedintoasinglespecieswhichresultsinachemicalmechanismconsistingofonly3speciesa

10、nd7reactions:TABLE1TABLEOFCOLLISIONSANDREACTIONSMODELEDREACTIONFORMULATYPE(eV)1e+Ar=e+ArElastic02e+Ar=e+ArsExcitation11.53e+Ars=e+ArSuperelastic-11.54e+Ar=2e+Ar+Ionization15.85e+Ars=2e+Ar+Ionization4.246Ars+Ars=e+Ar+Ateinningionization-7Ars+Ar=Ar+ArMetastablequench-ing4|DCGLOVDISCHARGEInaCCPreactort

11、heelectrondensityanddensityofexcitedspeciesisrelativelylowsostepwiseionizationisnotasimportantasinhighdensitydischarges.Inadditiontovolumetricreactions,thefollowingsurfacereactionsareimplemented:TABLE2TABLEOFSURFACEREACTIONSREACTIONFORMULASTICKINGCOEFFICIENT1Ars=Ar12Ar+=Ar1Whenametastableargonatomma

12、kescontactwiththewall,itrevertstothegroundstateargonatomwithsomeprobability(thestickingcoefficient).ResultsandDiscussionTheelectricpotential,electrondensityandmeanelectronenergyareallquantitiesofinterest.Mostofthevariationineachofthesequantitiesoccursalongtheaxiallengthofthecolumgureplotstheelectron

13、densityinthecolumn.Theelectrondensitypeaksintheregionbetweenthecathodefallandpositivecolumn.ThisregionissometimesreferredtoasFaradaydarkspace.Theelectrondensityalsodecreasesrapidlyintheradialdirection.Theiscausedbydiffusivelossofelectronstotheouter5|DCGLOWDISCHARGEwallsofthecolumnwheretheyaccumulate

14、asurfacecharge.ThebuildupofnegativeFigure 2:Surfaceplotofelectrondensityinsidethecolumn.InFiguret4eelectricpotentialisplottedalongtheaxiallengthofthecolumn.Noticethatthepotentialprofileismarkedlydifferentfromthelineardropinpotentialwhichresultsintheabsenceoftheplasma.Thestrongelectricfieldinthecatho

15、deregioncanleadtohighenergyionbombardmentofthecathode.HeatingofthecathodesurfaceTifnTifn = =chargeleadstoapositivepoitentialin一一ecenterofthecolumnwithrespecttothewalls.0.150.15*io*ioL L* *6|DCGLOVDISCHARGEoccurswhichmayinturnleadtothermalelectronemissionwhereadditionalelectronsFigure 3:Plotofelectto

16、mperaOUregtheaxiallengthofthepositivecolumn.Figure4:Plotoftheelectricpotentialalongtheaxiallengthofthepositivecolumn.30302020Q Q DCDischarge(dc)3ClicAdd4ClicStudy范lEfrlEfr古一皆切口5InthCelectstutree,selectesetStudiesTimeDependent6ClicDoneGEOMETRY1Rectangle1(r1)1OnthGeomettoolbar,clicrmitivandchoos!ectan

17、gle2InthCettingsindowforRectangle,locateandShapetion.3IntheWidttextfield,typ054IntheHeigHfextfield,typeRectangle2(r2)1OnthGeomettoolbar,clRikmitiveundchoosfectangle2Inth金金 ettingsindowforRectangle,locateandShapetion.3IntheWidttextfield,typ03754Inthedeigrtfextfield,type35Locatetlfitesitionection.In出出

18、extfield,typ01Rectangle3(r3)1OnthGeometryolbar,clRjkmitivondchoos!ectangle2IntheettingsindowforRectangle,locateandShapetion.3IntheWidttextfield,typ03754IntheHeigHfextfield,type35Locatetlfitesitionection.Intttextfield,typ384Compose1(co1)1OnthGeometroolbar,clMoleansandPartannschooCempose2Selecttheobje

19、cnly.3IntheettingsindowforCompose,locaomtheection.4IntheetformUextfield,好陋好陋 2-13BzierPolygon1(b1)1OnthGeometryolbar,cllCkmitivesidchooBezierPolygon2Inth金金 ettingwindowforzferPolygon,locaPotyge3nSegmencSion.3FindthAddedsegmentbsection.CUddtLinear4FindthControlpoistsbsection.In1;cse1zto0.025Inrow；set

20、rtoO.03756InrowsetztoO.O27ClicktheuildAllObjebustton.MeshControlEdges1(mcel)1OnthGeometryolbar,clWiktualOperationschooMeshControlEdges2OntheobjectselectBoundary7only.3OnthGeometryolbar,clickldAllDEFINITIONSVariables11OnthHomdoolbar,clVkriablerndchoosecalVariables2InthCettingsindowforVariables,loVate

21、ableection.3Inthetable,enterthefollowingsettings:NameExpressionUnitDescriptionmueN1E251/(m*V*s/Vns)ReducedelectronmobilityVO125VVAppliedvoltageWf5WorkfunctionpO0.5torrPaGaspressureExplicit11OnthDefinitionsolbar,clEXplicit2IntheModelBuildeindow,right-EXpkcitandchooRename3Inth歌歌 enameExpuctogbox,typeh

22、odethdewlabtextfield.4ClicOK5Inth金金 ettingwindowforExplicit,loctetputhentitsesction.6FromtheeometricentitylieVechoosieundary7SelectBoundaries3,5,and1Oonly.Explicit21OnthDefinitiohsolbar,clEXplicit2IntheodelBuildendow,right-EXpkcitandchooRename3Inth參參 enameExpUiaiogbox,tpedetheNewlabtelxtfield.4ClicO

23、K5IntheSettingwsindowforExplicit,locIantpeuthEentitiseesction.6FromthteeometricentitylfisVechooBeundary7SelectBoundaries6,8,and11only.Explicit31OnthDefinitiotoolbar,clExplicit2Inth期期 odelBuildendow,right-bxpkcitandchooRename3Inth嶇嶇 enameExpSiatogbox,typallntheJewlabtextfield.4ClicOK5IntheSettingwsin

24、dowforExplicit,locIantpeuthEentitiseesction.6FromtheeometricentityKstechooSeundary7SelectBoundaries2,9,and12only.Explicit41OnthDefinitiotoolbar,clExplicit2Inth和和 odelBuildeindow,right-cxpkcitandchooRename3Inth參參 enameExpUcHogbox,tApeWansthUewlabtextfield.4CliclOK5IntheSettingwsindowforExplicit,locIa

25、ntpeuthEentitiseesction.6FromthSeometricentitylfisVechoosieiundary7SelectBoundaries2,3,5,32aoidly8Explicit51OnthDefinitiotoolbar,clExplicit2InthdModelBuildeindow,right-ExpkcitandchooRename3Inth嶇嶇 enameExpdjiatogbox,typnCathodeWahsNewlabtextfield.4ClicOK5IntheSettingwsindowforExplicit,locIantpeuthEen

26、titiseesction.6FromtheeometricentitylisVeChooBeundary7SelectBoundaries2,6,8,9,11,and12only.DCDISCHARGE(DC)CrossSectionImport11OnthPhysicteolbar,clldobaindchooCeossSectionImport2IntheettincwindowforCrossSectionImport,QocssteeicejonImportsection.3ClicBrowse4Browsetothe)licatioApplicbtionLibraryfoldera

27、nddouble-clickthefileAr_xsecs.txt5IntheodelBuildeindow,cDckDischarge.(dc)6IntheettingsindowforDCDischarge,locasmtineropeGtection.7Selectthesereducedelectrontransportchecktbox.PlasmaModel11IntheModelBuildeindow,unComponent1(comp1)DCDischage(dc)PlasmaModel12InthCettingsindowforPlasmaModel,locaHelthpui

28、ection.3Intheptextfield,type4LocatetheectronDensityandEnctgyn.IntheeNitextfield,typeeNYounowchangethewaythesourcecoefficientsforelectronicexcitationandionizationarespecified.Bydefault,COMSOLcomputesratecoefficientsbasedonthecrosssectiondatayousupplied.ForDCdischarges,Townsendcoefficientsprovideamore

29、accuratedescriptionofthecathodefallregionsotheyshouldbeused.TheTownsendcoefficientsaretypicallycomputedusingtheBoltzmannEquation,Two-TermApproximationinterface.2:e+Ar=e+Ars1InthModelBuilwendow,unCemponent1(comp1)DCDiscbferge(dc)e+Ar=e+Ars2IntheettingindowforElectronImpactReactioCOtiicateCnien.3Fromt

30、hepecifyreactionustngchooUeelookuptable4LocatetSourceCoefficientsecfon.FromRheconstantfsmchooseTownsendcoefficient5ClicLoadfromFile6BrowsetoOneolicatioAppliCationLibraryfolderanddouble-clickthefiletown2.txt.7:e+Ar=2e+Ar+1InthModelBuildeindow,urtdemponent1(comp1)DCDisohfergfe(dc)e+Ar=2e+Ar+2Inth金金 et

31、tingsindowforElectronImpactReactiorCotticatnethien.3FromthSpecifyreactioniliisingphooiseelookuptable4LocatetSeurceCoefficientsectaon.FromRhteconstantfistmchooseTownsendcoefficient5ClicLoadfromFile6BrowsetoapplicatioApplidationLibraryfolderanddouble-clickthefiletown4.txt.Reaction11OnthPhysictoolbar,c

32、lickmainsndchooReaction2IntheettingindowforReaction,locaeedhsnFornseletion.3Inth+ormutextfield,tyAr+Ars=e+Ar+Ar+4LocatethefReaction21OnthPhysicoolbar,clickmainandchooReaction2Inth金金 ettingsindowforReaction,locaiedtioniFornsefetion.3Inth+ormutextfield,tyArs+Ar=Ar+Ar4LocatethKneticsExpressionsion.Inth

33、teXtfield,type7Whensolvingareactingflowproblemtherealwaysneedstobeonespecieswhichisselectedtofullfillthemassconstraint.Thisshouldbetakenasthespecieswiththelargestmassfraction.Species:Ar1Inth和和 odelBuildeindow,unComponent1(comp1)DCDischarge(dc)Species:.Ar2InthCettingsindowforSpecies,locateaieeFormsec

34、tion.3SelecttHreommassconscheckbox.4LocatethfeneralParametecsion.FromPhesetspeciesdstachooAeSpecies:Ars1IntheodelBuildendow,unComponent1(comp1)DCDischOicJe(dc)Species:Ars2Inth金金 ettingwindowforSpecies,locaenthelParametecsion.3FromthPresetspeciesdstachooAeWhensolvingaplasmaproblemtheplasmamustbeiniti

35、allychargeneutral.COMSOLautomaticallycomputestheinitialconcentrationofaselectedionicspeciessuchthattheelectroneutralityconstraintissatisfied.Species:Ar+1InthdModelBuildendow,unCemponent1(comp1)DCDischage(dc)Species:A.r+2IntheSettingwindowforSpecies,locapeaheFormsection.3Selecttheitialvaluefromelectr

36、oneutralityc：leecta：iok.4LocatetGeneralParametection.FromPtresetspeciesdatachooAeWall11OnthPhysidoolbar,clBoundariandchooWall2IntheSettingwsindowforWall,locaBtoeutnhdearySelecsteiocntion.3FromthSelectidiist,chooAeWallsGround11OnthPhysicteolbar,clBoundariandchooeund2IntheSettingwsindowforGround,locBa

37、oteunthdearySelecsteiocntion.3FromthSeelectiolinst,chooCseathod.eMetalContact11OnthPhysidoolbar,clBoundariandchoosfetalContact2Inth金金 ettingsindowforMetalContact,lecaiecthrySelesortion.3FromthSelectidiist,chooAnode4Locatethejrminsection.IntheeVtfield,type5LocatetlQiickCircuitSetsegsion.FromCtbekcirc

38、uittypt,chooseSeriesRCcircuitDielectricContact11OnthPhysidoolbar,clBoundariandchoostelectricContact2InthSettingwindowforDielectricContact,BecatferylSelectie(rtion.3FromthSelectiOist,chooSeallsNowyouaddasurfacereactionwhichdescribestheneutralizationofArgonionsontheelectrode.Secondaryemissionofelectro

39、nsisrequiredtosustainthedischarge,soyouentertheemissioncoefficientandanestimateofthemeanenergyofthesecondaryelectronsbasedontheionizationenergythresholdandtheworkfunctionofthesurface.SurfaceReaction11OnthPhysictoolbar,cl&kundariasdchooserfaceReaction2IntheSettingwindowforSurfaceReaction,Reaceoh6

40、ornseetion.3Inthdrormutextfield,typr+=：Ar4LocatetBoundarySelectection.FromStetectioist,choosethodeMakethesecondaryemissioncoefficient0.25andsetthemeanenergyofthesecondaryelectronstobetheionizationenergy(givenbytheexpressiondc.de_4)minustwicetheworkfunctionoftheelectrode.5LocatetISecondaryEmissionPar

41、amctiois.Inthetextfield,typ256Intheetextfield,typcede_4-2*WfSurfaceReaction21OnthPhysictoolbar,clBoundariesdchoosurfaceReaction2Inth金金 ettingwindowforSurfaceReaction,ReaceohWornseation.3Inth+ormutextfield,typr+=Ar4LocatetBoundarySelectioction.FromSthlectidiist,choosonCathodeWalisSurfaceReaction31Ont

42、hPhysictoolbar,clickundariasdchoosurfaceReaction2Inth金金 ettingwindowforSurfaceReaction,ReateohWornseation.3Inth隼隼 ormutextfield,typrs=Ar4LocatetIBoundarySelectioction.FromSthlectidiist,chooAeWallsMESH1Edge11Inth期期 odelBuildeindow,unComponent1(comght-clickeshandchoosMoreOperationsEdge2SelectBoundarie

43、s3,5,6,8,10,11,and14only.Size11Right-cliComponent1(comp1)Mesh1artEdgeolOSize2Inth金金 ettingwindowforSize,locatlemhentSsection.3Fromtheredefinest,chooEetremelyfine4ClickthCustorbutton.5LocatetHEtementSizeParansstetion.SelecMtaeimumelemencheekbox.6IntheassociatedtextfiekQQype7ClicktheoomExtebtsttononth

44、eaphidoolbar.FreeTriangular1InthModelBuildeindow,right-MlisikiandchoosreeTriangularSize11InthdModelBuildeindow,unCemponent1(comp1)Mgst-cliFkeeTriangulara1ndchooSsieze.2IntheSettingwsindowforSize,locaEtelemtheentSiszeection.3FromthPeredefinelidst,chooEsextrafin.eBoundaryLayerProperties1Inth和和 odelBui

45、ldeindow,right-MleshandchooBoundaryLayers2IntheettingwindowforBoundaryLayerPropertiBeuleateSeeJctionsection.3FromthSelecticJist,chooAeWalls4LocatetBeundaryLayerProsrtie!on.Inthemberofboundarytextersfield,typ4.e5ClicktheuildAbutton.STUDY1Step1:TimeDependent1InthdModelBuildendow,expanStthynode,thencSt

46、ep1：TimeDepende.nt2IntheSettingwsindowforTimeDependent,lSotcuadtyeStheettinsgesction.3Intherimetextfield,type4ClickRang.e5Intheangdialogbox,chooseberofvalfrosntheEntrymethodlist.6IntheStartextfield,type7IntheStopextfield,type8Intheumberofvaluesfield,type9FromthFunctiontoapplytoallVstucS)ooex31010Cli

47、cAdd11OnthHomeoolbar,cCompuiteRESULTSSelectionOnthResultS)olbar,clSkectionDataSets1Inth金金 ettingwindowforSelection,loGeeritieericEntitySelsetcikon.2FromthteeometricentitylfisVechooBoundary3FromthSelectidiist,chooAeWallsCutLine2D1OntheResulttsoolbar,clCicuktLine2.DDataSets1IntheettingwindowforCutLine

48、2D,locateDasection.2InroWoint,1seZto0.0163InroWoint2settoQ4InroWoint2seZto0.384Mirror2D1OnthResulfloolbar,clMkreDataSatsdchooisiarror2DElectronDensity(dc)1Inth和和 odelBuildeindow,uridessultsliclElectronDensity.(dc)Intheettin(windowfor2DPlotGroup,loDcaattaseetchteion.3FromthDatasest,chooserror2D14Onth

49、ElectronDensitytoodbar,clRlbt5ClicktheoomExtebtsttononGeaphicoolbar.ElectronTemperature(dc)1InthdModelBuildeindow,undesultsliclElectronTemperature(dc)3FromthDatasest,chooMrror2D14OnthElectricPotentialtooibar,clP:101t5Clickthe)omExtebtsttononGeaphidoolbar.1DPlotGroup41OnthHomeoolbar,clAkdPlotGroundch

50、oosDPlotGroup2IntheSettingwsindowfor1DPlotGroup,loDcaattaseetchteion.3FromthTimeselection,chooLas.t4LocatetPotSettingsction.SelecX-axis1abeieckbox.5IntheassociatedtextfieDdsttypce.(x)6Selecttlyeaxislabsheckbox.7IntheassociatedtextfieEdecypePotential(V)8LocatetlDataection.FromDatasetst,chooeitLine2D1

51、LineGraph1Onth1DPlotGroupoolbar,clLhkeGraph1DPlotGroup41InthettingwindowforLineGrapRecliakeExpresisidheupper-rightcornerofty-axisdasection.Fromthemenu,M;booComponent1DCDischarge(Electrostatics)ElectricV-Electricpotential2Inth和和 odelBuildendow,clickPlotGroup43Onth1DPlotGroupoolbar,clPlkt4ClicktheoomE

52、xteibtsttononGeaphidoolbar.1DPlotGroup51OnthHomeoolbar,clAkdPlotGroundchoosDPlotGroup2IntheSettingwindowfor1DPlotGroup,locatsethton.3Fromthemeselection,chooLas.t4LocatetheotSettingsction.SelecX-heslabcheckbox.5IntheassociatedtextfieDdstance.(x)6Selecttlyeaxis1absheckbox.7IntheassociatedtextfieEdecyp

53、eTemperature(V)8LocatetDatasection.FromDthtasetst,choogeitLine2D1LineGraph12IntheSettingwindowfor2DPlotGroup,lOCatteethteon.3FromthDatasest,chocMlerror2D14OnthElectronTemperaturoodcar,clIClot5ClicktheoomExtebtsttononGeaphidoolbar.ElectricPotential(dc)1IntheModelBuildendow,unidsultslickzlectricPotent

54、ial(dc)Inth金金 ettingwindowfor2DPlotGroup,loDcaattaseetcchteion.Onth1DPlotGroupoolbar,clLikeGraph1DPlotGroup51IntheettincwindowforLineGrapReplceExpresisidheupper-rightcornerofty-axisdasection.Fromthemenu,MhdelComponent1DCDischarge(DriftDiffusion)Electronenergydensitydc.Te-Electrontemperature2Onth1DPlotGroupoolbar,clPlkt3ClicktheoomExtebtsttonontGeaphictoolbar.1DPlotGroup61OnthHomtoolbar,clAkdPlotGroundchoosDPlotGroup2InthCettingsindowfor1DPlotGroup,ldDOtsettteon.3FromthTimeselection,chooLas.t4LocatetheotSe