Strong collisions in the electron broadening of spectral lines from charged radiators in hot, dense plasmas PDF
Preview Strong collisions in the electron broadening of spectral lines from charged radiators in hot, dense plasmas
STRONGCOLLISIONSINTHEELECTRONBROADENINGOFSPECTRAL LINESFROMCHARGEDRADIATORSINHOT,DENSEPLASMAS By MARKALLENGUNDERSON ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA ACKNOWLEDGMENTS Iwouldliketoacknowledgethecontinuoussupport,encouragement,andpatienceof ProfessorCharlesF.Hooper,Jr.duringthecourseofthisresearchworkandtothank himforsuggestingthisresearchtopic. Iwouldalsoliketogratefullyacknowledgethe supportofProfessorJ.W.Duftyforhisguidancethroughthecourseofthisresearch, especiallyduringthetryingtimesofthelastyear. IwouldliketothankDr.D.A.Haynes andDr. G. C. Junkel-Vivesformanyhelpfuldiscussionsandcollaborations,without whichthisresearchwouldnotbepossible. Finally,Iwouldliketothankmyparents, Mr.andMrs.RussellGunderson,forprovidingsupportandencouragementthroughout myeducation. n TABLEOFCONTENTS ACKNOWLEDGMENTS ii ABSTRACT iv CHAPTERS 1 INTRODUCTION 1 2 LINEBROADENINGINHOTDENSEPLASMAS 9 3 ELECTRON-BROADENINGMODEL 22 3.1 Electron-RadiatorInteraction 22 3.2 CalculationoftheWidth-and-ShiftOperator 25 3.2.1 Classical-PathApproximation M 26 3.2.2 RadiatorBasisandtheMatrixElementsof (u>,e) 30 4 COMPUTATIONALANALYSIS 39 4.1 ComputationalMethods 39 4.2 AnalysisofLineWidthsandShifts 42 4.3 ComparisonwithOtherModels 47 5 CONCLUSIONS 63 APPENDICES A EQUATIONOFMOTIONFORD{u,e) 66 B ELECTRON-BROADENINGOPERATOR 73 C DEUTSCHPOTENTIALANDTHEQUANTUMCUTOFF 78 D IRREDUCIBLETENSOROPERATORSAND3N-JSYMBOLS 81 REFERENCES 85 BIOGRAPHICALSKETCH 88 iii AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy STRONGCOLLISIONSINTHEELECTRONBROADENINGOFSPECTRAL LINESFROMCHARGEDRADIATORSINHOT,DENSEPLASMAS By MarkAllenGunderson December2001 Chairman: CharlesF.Hooper,Jr. MajorDepartment: Physics Themodelpresentedinthisdissertationincorporatesstrongcollisioneffectsinthe electronbroadeningofspectrallinesfromchargedradiatorsinhot,denseplasmas. This modelisanextensionofanexistingmodel,oftenreferredtoastheunifiedtheory,that wasoriginallydevelopedtocalculatefrequency-dependentelectron-broadeningeffects consistentlyfromspectrallinecentertothefarlinewingsforneutralhydrogenradiators andlateradjustedforsingly-chargedheliumradiators. Specifically,theextensionallows fortheconsistentcalculationofelectron-broadeningeffectsonlinespectraemittedfrom mid-Zradiators(i.e.,argon). Thisisaccomplishedthroughtheuseofrelativisticradiator statedataandalsotheinclusionofstrongcollisioneffectsbyincorporating,inaddition tothedipolecontribution,theeffectsofthemonopoletermandallothercontributing higher-order“multipole”termsintheelectron-radiatorinteraction. Thismodelpreserves thesemiclassicaltreatmentoftheoriginalmodelwheretheperturbingelectronsmovein classicaltrajectoriesandtheradiatoristreatedthroughquantummechanicalmeans. It alsopreservesthecalculationoftheelectron-broadeningoperatortoall-ordersinterms oftheelectron-radiatorinteraction. IV Line spectra using the full-Coulomb, semiclassical, all-order electron-broadening model are compared to line spectra from a dipole-approximation version of this model. Theselinespectraarealsocomparedtolinespectrafromfull-Coulomband dipole-approximationversionsofafullquantummechanicalelectron-broadeningmodel expandedtosecond-orderin aBorn-likeexpansionintermsoftheelectron-radiator interaction. Significantshiftsanddistortionsinthefull-Coulombline-shapecalculations ascomparedtothedipole-approximationline-shapecalculationsatelectrondensities greaterthan1x1024cm-3showthatadipoleapproximationoftheelectron-radiator interactionisnolongerreasonable. Differencesintheamountofshiftanddistortion inthecomparisonsoffull-Coulombcalculationsbetweenthesemiclassical,all-orderand quantummechanical, second-ordermodels, specificallyinthecalculationofmerging spectrallinesatelectrondensitiesabove1x1024cm~3,suggestthatanall-ordermodel isneededasthedensityincreases. v CHAPTER 1 INTRODUCTION Whenaradiatingionisimmersedinadenseplasma,theenergylevelsofitsbound statesaremodifiedbyinteractionswiththesurroundingionsandelectrons.Thisresults inspectrallinesthat aresignificantlybroadened and shiftedfromthespectrallines ofanisolatedradiator [1,2], Themagnitudeofthiseffectdependsontheidentityof theradiatorandthedensityandtemperatureoftheions andelectrons. Therefore, thewidthandshiftofthelinesprovideausefuldiagnosticmeasurementofthedensity andtemperatureofhot, denseplasmas [3-5]. Asthedensityofaplasmaincreases, modelsdescribingthebroadeningandshiftingofthespectramustbemodifiedtomore accuratelyaccountforhigh-densityeffects. Thisdissertationspecificallyexaminesthe effectsofstrongelectroncollisionsonthespectraofaradiatorimmersedinaplasma ofionsandelectronsandthepotentialuseoftheresultingspectraasadensityand temperaturediagnosticintheanalysisofexperimentaldata. Aspecialfocusisplaced onplasmaconditionsinwhichsomeofthespectrallinesbegintomergetogether. Itisappropriateatthispointtoparsethetitleofthiswork,asitcontainssometerms thatneedtobeexplained. Inthecontextofthiswork,a“strongcollision”referstothose collisionsinwhichthestrengthoftheinteractionbetweentheradiatorandaperturbing electronislargeenoughandoccursoverasufficientperiodoftimetodisruptaradiative transitionfromanupperstatetoalowerstate. Thisworkdoesnotincludetheeffectsof ionizingcollisionsandelectroncapture. “Electronbroadening”referstothebroadening effectsofperturbingelectronsthroughtheirmodificationstotheboundstatesofthe radiator. “Chargedradiators”correspondstoionsintherangeof6<Z<36thatare undergoingradiativetransitionsandemittingspectra. “Hot,denseplasmas” refersto 1 2 nondegenerateplasmaswheredensitybroadeningeffects,specificallyStarkbroadening andelectronbroadening,arethedominantbroadeningmechanismsonthespectraand arelargeenoughtocausespectrallinestooverlap,or“merge”,together. Improvementsinlasertechnologyoverthepast20yearsledtothecreationofplas- maswithincreasinglyhigherdensitiesandtemperatures[6-8]. Toanalyzeandunder- standtheseplasmas, originaltheoreticallinebroadeningmodelshavebeenadvanced andimprovedupon. EarlymodelsbeganwiththeStarkbroadeningofspectrafrom neutralradiatorsinthepresenceofanelectricfieldfromthedistributionofthesur- roundingions,commonlyreferredtoastheionmicrofield[9,10],alongwithanelectron- broadeningmodel utilizing adipoleinteraction approximation. Asthedensityand temperatureoftheplasmasincreased,thestudyofspectrafromionicradiatorsbecame necessary[11-13]becausethehydrogenatomsbecamecompletelyionized,thusrequiring amultipole,orfull-Coulombcalculationoftheinteractionbetweenthechargedradiator andtheperturbingplasmaelectronsintheelectron-broadeningcalculation[14,15]. The inclusionofthemonopoletermintheinteractionledtothepredictionofanexperi- mentallynoticeableredshiftinthelocationofthespectrallinesasthedensityofthe plasmasincreased [16-19]. Thisshiftwasshowntoincreasewithincreasingprincipal quantumnumberandelectrondensityandtodecreasewithincreasingtemperature. Asacontextualaidforthemodelpresentedinthisdissertation,webeginbybriefly describingtheexperimentalprogramcurrentlyunderwaytogeneratetheexperimental linespectrathatareusedtoprobetheplasmaconditionsachievedintheexperiment throughcomparisonswiththeoreticallinespectrafromdifferentmodels. Inorderto generateplasmaswiththehighelectrondensitiesneededtoobservehigh-densityeffects, ahigh-poweredlaser,specificallythe64beamOMEGAlasersystemattheLaboratory forLaserEnergeticsattheUniversityofRochester,isusedtoimplodeasmallplastic shell(CHmicroballoon)filledwithagasconsistingofdeuteriumwithtraceamountsof amid-Zelement(i.e.,argon). Themainvariablesofinterestinourexperimentsinclude 3 theshellthicknessoftheCHmicroballoon,themicroballoon’sdiameter,thepressure andcompositionofthefillgas,thelaserbeampulseshape,andthetotalenergydelivered ontarget. ForourmostrecentlyanalyzedexperimentsthroughourNLUF(NationalLaserUser Facility)campaign,theCHshell,orablator,thicknessgenerallywas20microns,and theCHinnershelldiameterwas940microns. Thecompositionandpressureofthe fillgasrangedfrom0.3%to2%atomicfractionargonin7-20AtmofD2. Thelaser- beampulseshapewaseithera1nsrampto1nsflat-toppulseora1nsflat-toppulse. Thetotalultravioletlaserenergydeliveredontargetwasintherangeof19-24kJ.The energydeliveredontargetwouldgenerallybeabitlarger,butsometotalbeamenergy was sacrificedtoachieveexcellent beam balanceofabout AE/E ~ 3% RMS. The experiments,withafewexceptions,weresuccessful. Theframingcameraimagesand thestaticpinholeimagesallshowednearlycircularcoreimages,showingnosignificant excursionsfromasphericalimplosion. GoodargonK-shelldatawereobservedinmost oftheexperimentalshots. Ourprimarydiagnosticwasastreakedx-raycrystalspectrometer,orSSCA,operat- ingwithaflatRbAP(rubidiumacidphthalate)crystalandanAuphotocathode. The instrumentprovidedapproximatelya1.9nswindowwitharesolutionof25ps. The spectrawererecordedonfilmandthendigitized. Becausetheisolatedlineposition isveryimportantindeterminingimportantdense-plasmaeffects,includinglineshifts andline-mergingeffects,correctionsforfilmsensitivity,filtering,photocathoderesponse, streak-cameradistortionsincludingcurvatureofisotemporallinesandstreakangle,and crystal/photocathodeirregularitieswereperformedonthedata. Lineoutsaveragingover 25pswerethenextractedfromtheimages,andtheresultingtime-dependentspectra exhibitedtime-varyingArK-shelldata. Spectraldispersionwasdeterminedusingearly- timelineoutswhentheelectrondensitywassmall. 4 Ouranalysisofthedataproceedsbyperformingaleastsquares(y2)fittothespectral datausingourgroup’sfittingmodel. ThemodelcontainsStarkbroadenedlineshapes, NLTEpopulationdistributions,andcorrectionsforthetransferofthethickalphalines andtheopacityofthediagnosticlines. Thefreeparametersinourfittingmodelarethe emissivity-averagedcoreelectrontemperaturesanddensities. Thisfittingprocessleads toaninferenceoftime-dependentcoreconditions,somethingusefulinitsownright. Thefittinganalysisofourmostrecentlyanalyzedexperimentsconfirmedthatthe experimentalshotsprovidedplasmaconditionsapproachingthoseneededforourinvesti- gationofdense-plasmaeffects. Weregularlyreacheddensitiesjustabove2x1024cm-3. Atthisdensity,high-densitydeviationsfromalinearStark-broadeningtheorythatdoes notincludemixingbetweentheupper-statemanifoldsofadjacentspectralseriesmem- bers,specificallyinlinemergingbehaviorandstrong-collisioneffects,aresubtle. How- ever, wesawindicationsinthedatathat anonlinearStark-broadeningtheorythat includesmixingbetweentheupper-statemanifoldsofadjacentseriesmembersyielded fitswithasomewhatlowery2thanthosefromthelineartheory,especiallyintheregion oftheLy-yline,asisshowninFigure1.1. AsourNLUFcampaignprogresses,weare confidentthatchangesintheshellthickness,fillgaspressure,andpulseshapeshould givedensitiesontheorderof4x1024cm-3wherethedifferencesarenotsosubtle. Aswasjustnoted,wecancurrentlygenerateelectrondensitiesofamagnitudesuch thatstrongcollisionsarebeginningtoaffectthespectrafromhydrogenicandhelium- likeargon. Inotherwords,thespectrabecomesufficientlybroadandshifttotheextent thatthecontributionsfromstrongcollisionsmustbestudiedingreaterdetail. Previous modelsthatlimittheeffectsofstrongcollisionsbyincludingonlythosecontributions tosecond-orderintheperturbingelectron-radiatorinteractionarevalidoverarange ofAu) < Zujpiasma, whereAujisthefrequencyseparationfromlinecenter [20]. For example,withcurrentelectrondensities,theLyman-5lineofArgonbroadensandshifts totheextentthatithasalreadymergedwiththeLyman-qline. Infact,theLyman-q5 5 stratesthataquantum-mechanicalnonlinearmodeltosecond-orderinthefull-Coulomb electron-radiatorinteractiongivesaslightlybetterfitthanthelinearversionofthis modelatanelectrondensityof1.9x1024cm-3andatemperatureof1.15keV.The valueofx2isslightlysmallerforthenonlinearfit. spectralfeatureisalreadyaffectingtheLyman-/!linesignificantly. Inaddition,these mergedspectralfeaturestendtobesignificantlybroaderthan2upiasma. Toincorporatestrongcollisions, asdefinedabove, intothetheoreticalfoundation ofplasmalinebroadeningformid-Zionicradiators,wedevelopanelectron-broadening modelsimilartoamodeldevelopedbyVidal, Cooper,andSmith (VCS)backinthe late1960sandearly1970sforneutralradiators[21-24],andextendedafewyearslater byGreeneandCooperforionizedhelium[25-27]. TheVCSmodelwasoriginallydevel- opedtocalculatespectrallinesofneutralhydrogenradiatorsfromlinecenterallthe wayouttothefarlinewingconsistently. Thismodelissometimesreferredtoasthe unifiedtheoryoflinebroadeningbecauseit consistentlyjoinedtheimpactmodelof linebroadeningthatisappropriatearoundlinecentertotheone-electronmodelofline broadeningthatisappropriateinthefarwingsofaline. TheVCSmodelisafrequency- dependent,binary-collisionelectron-broadeningmodelthatincludestermstoall-order
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