comsol等离子体放电二维模型.docx
- 文档编号:10380201
- 上传时间:2023-02-10
- 格式:DOCX
- 页数:28
- 大小:27.19KB
comsol等离子体放电二维模型.docx
《comsol等离子体放电二维模型.docx》由会员分享,可在线阅读,更多相关《comsol等离子体放电二维模型.docx(28页珍藏版)》请在冰豆网上搜索。
comsol等离子体放电二维模型
SolvedwithCOMSOLMultiphysics5.2
DCGlowDischarge
Introduction
DCglowdischargesinthelowpressureregimehavelongbeenusedforgaslasersand
fluorescentlamps.DCdischargesareattractivetostudybecausethesolutionistime
independent.ThismodelshowshowtousetheDCDischargeinterfacetosetupan
analysisofapositivecolumn.Thedischargeissustainedbyemissionofsecondary
electronsatthecathode.
ModelDefinition
TheDCdischargeconsistsoftwoelectrodes,onepowered(theanode)andone
grounded(thecathode).Thepositivecolumniscoupledtoanexternalcircuit:
1000Ω
CathodePlasmaAnode
1pF
V
Figure1:
SchematicoftheDCdischargeandexternalcircuit.
DOMAINEQUATIONS
Theelectrondensityandmeanelectronenergyarecomputedbysolvingapairof
drift-diffusionequationsfortheelectrondensityandmeanelectronenergy.
Convectionofelectronsduetofluidmotionisneglected.Fordetailedinformationon
electrontransportseeTheoryfortheDriftDiffusionInterfaceinthePlasmaModule
User’sGuide.
∂n
()+∇⋅[–ne(μe•E)–De•∇ne]=Re
∂t
e
∂n
()+∇⋅[–nε(με•E)–Dε•∇nε]+E⋅Γe=Rε
ε
∂t
where:
1|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
Γe=–(μe•E)ne–De•∇ne
TheelectronsourceReandtheenergylossduetoinelasticcollisionsRεaredefinedlater.Theelectrondiffusivity,energymobilityandenergydiffusivityarecomputedfromtheelectronmobilityusing:
De=μeTe,με
5
μ
=--,Dε=μεTe
e
3
Thesourcecoefficientsintheaboveequationsaredeterminedbytheplasmachemistry
usingratecoefficients.SupposethatthereareMreactionswhichcontributetothe
growthordecayofelectrondensityandPinelasticelectron-neutralcollisions.In
generalP>>M.Inthecaseofratecoefficients,theelectronsourcetermisgivenby:
Re=xjkjNnne
j=1
wherexjisthemolefractionofthetargetspeciesforreactionj,kjistheratecoefficient
forreactionj(m3/s),andNnisthetotalneutralnumberdensity(1/m3).ForDCdischargesitisbetterpracticetouseTownsendcoefficientsinsteadofratecoefficientstodefinereactionrates.Townsendcoefficientsprovideabetterdescriptionofwhat
happensinthecathodefallregionRef1.WhenTownsendcoefficientsareused,the
electronsourcetermisgivenby:
Re=xjαjNnΓe
j=1
whereαjistheTownsendcoefficientforreactionj(m2)andΓeistheelectronfluxas
definedabove(1/(m2·s)).TownsendcoefficientscanincreasethestabilityofthenumericalschemewhentheelectronfluxisfielddrivenasisthecasewithDC
discharges.Theelectronenergylossisobtainedbysummingthecollisionalenergyloss
overallreactions:
Rε=xjkjNnneΔεj
j=1
whereΔεjistheenergylossfromreactionj(V).Theratecoefficientsmaybecomputed
fromcrosssectiondatabythefollowingintegral:
2|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.2
∞
kkγεσk(ε)f(ε)dε
=
0
whereγ=(2q/me)1/2(C1/2/kg1/2),meistheelectronmass(kg),εisenergy(V),σk
isthecollisioncrosssection(m2)andfistheelectronenergydistributionfunction.InthiscaseaMaxwellianEEDFisassumed.WhenTownsendcoefficientsareused,the
electronenergylossistakenas:
Rε=xjαjNnΓeΔεj
j=1
Fornon-electronspecies,thefollowingequationissolvedforthemassfractionofeach
species.Fordetailedinformationonthetransportofthenon-electronspeciessee
TheoryfortheHeavySpeciesTransportInterfaceinthePlasmaModuleUser’s
Guide.
∂wρ
()+ρ(u⋅∇)wk=∇⋅jk+Rk
∂t
k
Theelectrostaticfieldiscomputedusingthefollowingequation:
–∇⋅ε0εr∇V=ρ
Thespacechargedensityρisautomaticallycomputedbasedontheplasmachemistry
specifiedinthemodelusingtheformula:
nρ=qZknk
–
e
k=1
FordetailedinformationaboutelectrostaticsseeTheoryfortheElectrostaticsInterfaceinthePlasmaModuleUser’sGuide.
BOUNDARYCONDITIONS
UnlikeRFdischarges,themechanismforsustainingthedischargeisemissionof
secondaryelectronsfromthecathode.Anelectronisemittedfromthecathodesurface
withaspecifiedprobabilitywhenstruckbyanion.Theseelectronsarethenaccelerated
bythestrongelectricfieldclosetothecathodewheretheyacquireenoughenergyto
initiateionization.Thenetresultisarapidincreaseintheelectrondensityclosetothe
cathodeinaregionoftenknownasthecathodefallorCrookesdarkspace.
3|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
Electronsarelosttothewallduetorandommotionwithinafewmeanfreepathsof
thewallandgainedduetosecondaryemissioneffects,resultinginthefollowing
boundaryconditionfortheelectronflux:
–n⋅Γe
=
1
γ
-p(Γp⋅n)
-νe,thne
–
2
p
(1)
andtheelectronenergyflux:
–n⋅Γε
=
5
ε
--νe,thnε–pγp(Γp⋅n)
6
p
(2)
Thesecondtermontheright-handsideofEquation1isthegainofelectronsduetosecondaryemissioneffects,γpbeingthesecondaryemissioncoefficient.ThesecondterminEquation2isthesecondaryemissionenergyflux,εpbeingthemeanenergyofthesecondaryelectrons.Fortheheavyspecies,ionsarelosttothewallduetosurfacereactionsandthefactthattheelectricfieldisdirectedtowardsthewall:
–⋅jk=MwRk+MwckZμk(E⋅n)[Zkμk(E⋅n)>0]
n
PLASMACHEMISTRY
Argonisoneofthesimplestmechanismstoimplementatlowpressures.The
electronicallyexcitedstatescanbelumpedintoasinglespecieswhichresultsina
chemicalmechanismconsistingofonly3speciesand7reactions:
TABLE1:
TABLEOFCOLLISIONSANDREACTIONSMODELED
REACTIONFORMULATYPE
Δε(eV)
1e+Ar=>e+ArElastic0
2e+Ar=>e+ArsExcitation11.5
3e+Ars=>e+ArSuperelastic-11.5
4e+Ar=>2e+Ar+Ionization15.8
5e+Ars=>2e+Ar+Ionization4.24
6Ars+Ars=>e+Ar+Ar+Penningionization-
7Ars+Ar=>Ar+ArMetastablequenching-
4|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.2
InaCCPreactortheelectrondensityanddensityofexcitedspeciesisrelativelylowso
stepwiseionizationisnotasimportantasinhighdensitydischarges.Inadditionto
volumetricreactions,thefollowingsurfacereactionsareimplemented:
TABLE2:
TABLEOFSURFACEREACTIONS
REACTIONFORMULASTICKINGCOEFFICIENT
1Ars=>Ar1
2Ar+=>Ar1
Whenametastableargonatommakescontactwiththewall,itrevertstotheground
stateargonatomwithsomeprobability(thestickingcoefficient).
ResultsandDiscussion
Theelectricpotential,electrondensityandmeanelectronenergyareallquantitiesof
interest.Mostofthevariationineachofthesequantitiesoccursalongtheaxiallength
ofthecolumn.Figure2plotstheelectrondensityinthecolumn.Theelectrondensity
peaksintheregionbetweenthecathodefallandpositivecolumn.Thisregionis
sometimesreferredtoasFaradaydarkspace.Theelectrondensityalsodecreases
rapidlyintheradialdirection.Theiscausedbydiffusivelossofelectronstotheouter
5|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
wallsofthecolumnwheretheyaccumulateasurfacecharge.Thebuildupofnegative
chargeleadstoapositivepotentialinthecenterofthecolumnwithrespecttothewalls.
Figure2:
Surfaceplotofelectrondensityinsidethecolumn.
InFigure4theelectricpotentialisplottedalongtheaxiallengthofthecolumn.Notice
thatthepotentialprofileismarkedlydifferentfromthelineardropinpotentialwhich
resultsintheabsenceoftheplasma.Thestrongelectricfieldinthecathoderegioncan
leadtohighenergyionbombardmentofthecathode.Heatingofthecathodesurface
6|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.2
occurswhichmayinturnleadtothermalelectronemissionwhereadditionalelectrons
areemittedfromthecathodesurface.
Figure3:
Plotofelectron“temperature”alongtheaxiallengthofthepositivecolumn.
7|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
Figure4:
Plotoftheelectricpotentialalongtheaxiallengthofthepositivecolumn.
8|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.2
Figure5:
Plotofelectricpotentialalongtheaxiallengthofthepositivecolumn.
Figure6:
Plotoftheelectrontemperaturealongtheaxiallengthofthepositivecolumn.
9|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
Figure7:
Plotoftheelectrondensityalongtheaxiallengthofthepositivecolumn.
Figure8:
Plotofthenumberdensityofexcitedargonatoms.
10|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.2
Figure9:
Plotofthenumberdensityofargonions.
Reference
1.M.A.LiebermanandA.J.Lichtenberg,PrinciplesofPlasmaDischargesand
MaterialsProcessing,JohnWiley&Sons,2005.
ApplicationLibrarypath:
Plasma_Module/Direct_Current_Discharges/
positive_column_2d
ModelingInstructions
FromtheFilemenu,chooseNew.
NEW
1IntheNewwindow,clickModelWizard.
11|DCGLOWDISCHARGE
SolvedwithCOMSOLMultiphysics5.1
MODELWIZARD
1IntheModelWizardwindow,click2DAxisymmetric.
2IntheSelectphysicstree,selectPlasma>DCDischarge(dc).
3ClickAdd.
4ClickStudy.
5IntheSelectstudytree,selectPresetStudies>TimeDependent.
6ClickDone.
GEOMETRY1
Rectangle1(r1)
1OntheGeometrytoolbar,clickPrimitivesandchooseRectangle.
2IntheSettingswindowforRectangle,locatetheSizeandShapesection.
3IntheWidthtextfield,type0.05.
4IntheHeighttextfield,type0.4.
Rectangle2(r2)
1OntheGeometrytoolba
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- comsol 等离子体 放电 二维 模型