等离子体中灰尘颗粒带电和等离子体边缘电子损耗
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Dustparticlechargeinplasmawithionflowandelectrondepletionnearplasmaboundaries
AngelaDouglass,VictorLand,LorinMatthews,andTruellHydea)CenterforAstrophysics,SpacePhysics,andEngineeringResearch,BaylorUniversity,Waco,Texas76798-7310,USA
(Received9June2011;accepted21July2011;publishedonline19August2011)Thechargeonmicrometer-sizeddustparticlessuspendedinplasmaabovethepoweredelectrodeofradio-frequencydischargesisstudied.Usingaself-consistentfluidmodel,theplasmaprofilesabovetheelectrodearecalculatedandtheelectrondepletiontowardstheelectrode,aswellastheincreasingflowspeedofionstowardtheelectrodeareconsideredinthecalculationofthedustparticlefloatingpotential.Theresultsarecomparedwiththosereportedinliteratureandtheimportanceofthespatialdustchargevariationisinvestigated.VC2011AmericanInstituteofPhysics.[doi:10.1063/1.3624552]
I.INTRODUCTIONDusty,complex,orcolloidalplasmaphysicsispartofthefieldofsoftcondensedmatter,similartogranularmate-rialphysicsandthephysicsofcolloidalsuspensions.1,2In
dustyplasmaexperiments,smallparticles,typicallymicro-meter-sized,areimmersedinplasma.Duetothecollectionofelectronsandionsfromtheplasma,theparticlesobtainalargenegativecharge.Asaresult,theycanbemanipulatedwithelectricfieldsandexhibitinter-particleinteractions.Duetothelargedustparticleinertia,dustyplasmasystemsallowthestudyofsolidstatephenomena,fluiddynamics,turbulenceandmuchmore,onlength-andtimescalesacces-siblewithordinaryopticaltechniques.3,4
Inlaboratorydustyplasmaexperiments,thestrongelec-tricfieldpresentinfrontofthepoweredelectrodeallowsthedustparticlestobelevitatedagainsttheforceofgravity.Theoretically,thechargingofmicro-particlesinplasmaisdescribedbyorbitalmotionlimitedtheory(OML)5andthe
electricfieldinwhichtheparticlesaresuspendedisusuallyassumedtovarylinearlywiththeheightabovetheelec-trode.6Manyexperimentalstudieshavebeenperformedto
determinetheparticlecharge,mostofwhichdependonper-turbingtheplasmaparametersorperturbingthedustpar-ticlesintheplasma,sinceprobemeasurementsindustyplasmasystemsarenotreliable.7–9
Tworecentexperiments,however,wereperformedtomeasuredustparticlechargewithoutperturbingtheplasmaparameters.Bothexperimentswereperformedinradio-fre-quency(RF)plasmadischargesandusedonlyafewdustpar-ticlestoactastracerparticleswithintheplasma.Thefirstemployedarotatingelectrode,causingrotationofthesus-pendedparticlesduetorotationalflowoftheneutralgas.10
Multipleparticlesizeswereusedtoprobedifferentpositionswithinthedischarge.ThisexperimentconcludedthatthedustchargebecomesmorenegativethanpredictedbyOMLtheoryastheparticlesmoveclosertotheelectrodesurface.
Thesecondinvolvedplacementoftheentiredischargecellontoacentrifuge,allowingtheeffectivegravitationalforcetobeenhancedandtheparticlestobepushedclosertotheelectrodesurface.11Thisexperimentconcludedthatthedust
chargebecomeslessnegativeastheparticlesmoveclosertotheelectrodesurface.Notonlydotheresultsfromtheseexperimentsseemtocontradicteachother,theyalsobringtheusualassumptionsaboutdustparticlechargingandlevi-tationindustyplasmaexperimentsintoquestion.Wewillpresentaself-consistentfluidmodel12whichshowsthatthe
twoaboveresultsareinfactconsistentwithoneanother.Thismodelallowsustocomputethedustpotentialand,inturn,thedustchargeasafunctionofheightaboveapoweredelectrodebytakingtheeffectsofionflowandelectrondepletionduetotheplasmaboundaryintoaccount.
II.DUSTCHARGINGINCLUDINGIONFLOWANDELECTRONDEPLETIONNEARAPLASMABOUNDARY
Adustparticleinplasmacollectsionsandelectrons,which,fortypicallaboratorysettings,isthedominantcharg-ingprocess.13Theparticlewillreachitsequilibriumchargewhenthecollectedplasmacurrentscancel
IeþXiIi¼0;(1)
wherethesubscriptedenoteselectronsandidenotesthedif-ferentionspecies.Inthispaper,weconsiderionizedargonastheonlyionspecies.Thesecurrentscanbecalculatedbyintegratingoverthevelocitydistributionoftheplasmaspecies,fe,i(ve,i),including
thecrosssectionforcaptureoftheplasmaparticlebythechargeddustparticle,re,i(ve,i),whichiscalculatedusingOMLtheory5
Ie;i¼Çeðve;ife;iðve;iÞre;iðve;iÞd3ve;i:(2)Intheplasmaabovetheelectrodewherethedustislevi-tated(usuallyassumedtobethesheathregion),theelectrona)
Electronicmail:Truell_Hyde@baylor.edu.
1070-664X/2011/18(8)/083706/6/$30.00VC2011AmericanInstituteofPhysics18,083706-1
PHYSICSOFPLASMAS18,083706(2011)Downloaded 22 Aug 2011 to 129.62.200.177. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions