Analysis of hot dense plasmas and consideration of Stark broadening theory applied to transitions involving continuum radiator wavefunctions PDF
Preview Analysis of hot dense plasmas and consideration of Stark broadening theory applied to transitions involving continuum radiator wavefunctions
ANALYSISOFHOTDENSEPLASMASAND CONSIDERATIONOFSTARKBROADENING THEORYAPPLIEDTOTRANSITIONSINVOLVING CONTINUUMRADIATORWAVEFUNCTIONS By DONALDARTHURHAYNES,JR. ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1997 Causalatet, visestnotissima. ACKNOWLEDGEMENTS Iwouldliketotakethisopportunitytogratefullyacknowledgethesupport andencouragementofProfessorCharlesF.Hooper,Jr.,andtothankhimfor allowingmetheopportunitytoparticipateintheexcitingworkdonebyhis groupduringmytimeattheUniversity. Also,IwouldliketothankDrs. J. W. Dufty, R. C. Mancini, and D. P. Kilcreaseformanyhelpfuldiscussions. Aspecial thanks isdue Dr. R. L. Coldwell for hisguidance inallmatters numerical. Thecomputercodeusedtocalculatetheiondynamicslineshapesusedin Chapter3wasdevelopedbyMr. D.ThorGarber,whosehardwordandkind assistancearebothherebyacknowledged. Iwouldalsoliketothankmywife,Karen,mychildren,CaitlinandDonald, my parents, Mr. and Mrs. Donald Arthur Haynes, Sr., and my brother, Matthew E. Haynes. Without theirsupport and encouragement, this work wouldhaveneverbeenundertakenoraccomplished. iii TABLEOFCONTENTS Page ACKNOWLEDGEMENTS iii ABSTRACT v 1 INTRODUCTION 1 2 STARKBROADENINGTHEORY 10 3 THEANALYSISOFHOTDENSEPLASMAS 21 Introduction 21 CalculationofTheoreticalSpectra 22 StarkBroadenedLineProfilesIncludingtheEffectsofIonMotion . 23 OpacityBroadening 25 Non-LTERelativeIntensities,RadiativeTransferEffect 27 ExperimentalData 33 Analysis 36 Comments 43 4 ABSORPTIONSPECTROSCOPY 47 StarkBroadenedAbsorptionLineProfiles 48 OpticalDepthofaUniformAbsorbingRegion 56 AnalysisofAbsorptionSpectra 60 Recapitulation 66 5 STARKBROADENINGTHEORYAPPLIEDTO CONTINUUMRADIATORWAVEFUNCTIONS 69 MicrofieldConstrainedAverages 71 Radiator-PlasmaIonInteraction 73 ADifferentTruncation 77 6 ILLUSTRATIVEMODELSYSTEMS 79 CalculationoftheResolvent 79 AnAuto-ionizingTransition 82 Comments 84 7 CONCLUSIONSANDDISCUSSION 87 REFERENCES 92 BIOGRAPHICALSKETCH 97 iv AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ANALYSISOFHOTDENSEPLASMASAND CONSIDERATIONOFSTARKBROADENING THEORYAPPLIEDTOTRANSITIONSINVOLVING CONTINUUMRADIATORWAVEFUNCTIONS By DonaldArthurHaynes,Jr. August1997 Chairman: C.F.Hooper,Jr. MajorDepartment: Physics TheuseofStarkbroadenedlineshapesintheanalysisofhotdenseplasmas isstudied. Analysisofemissionspectrafromexperimentsperformedatthe LaboratoryforLaserEnergeticsattheUniversityofRochesterincludingthe eflFectsofiondynamicsandopacityispresented. Amethodfortheanalysis ofinhomogeneous absorbing regions is explored. The importance ofauto- ionizingsateUitesintheseanalysesmotivatesanexaminationoftheappUcation ofStarkbroadeningtheorytothosetransitionsinvolvingcontinuumradiator wavefunctions. Transitionsinvolvingcontinuumradiatorwavefunctionshavebecomees- sentialdiagnostic features ofx-ray spectra from inertial confinement fusion experiments. AnalysisofemissionspectraincludingargonK-shelltransitions andauto-ionizingsatellitesispresented,withemphasisontheintertwinedef- fectsofiondynamicsandopacity. Also, amethodofanalysisofabsorption spectraisdiscussed,andamodelforabsorptionbyanon-homogeneousplasma isexplored. V TheapplicationofStarkbroadeningtheorytotransitionsinvolvingcon- tinuumradiatorwavefunctionsisstudied. Techniquesandapproximationsap- propriatetothisapplicationaredevelopedandcontrastedwiththoseusedin theanalysisoftransitionsinvolvingonlyboundradiatorwavefunctions. For instance,fortransitionsamongboundstatestheresolventisfrequentlycalcu- latedbysimpletetradicinversion. Fortransitionsinvolvingcontinuumradia- torwavefunctions,thecalculationisaccomplishedbydiscretizingtherelevant continuaandinvertingtheresulting tetradic. Fortransitions amongbound states, theinteractionoftheradiatorwiththeplasmaionsisoftenapproxi- matedbytruncatingamultipoleexpansion. Here,Iintroduceanapproxima- tionappropriatefortransitions involvingcontinuumradiatorwavefunctions. Thisapproximationretainsthecalculationalsimplicityoftheionmicrofield formulationofStarkbroadeningtheory,reducestothedipoleapproximation fortightlyboundstates,andaccountsforthespatialvariationintheplasma ionmicrofield. These techniques and approximations areillustrated by the useofmodelsystems,constructedtohighlightthenewfeaturesintroducedin thisworkwhileavoidingtheobscuringcomputationalcomplicationsofactual atomicphysics. Theeffectofcontinuumstatesonsometransitionsofcurrent interestwillbediscussed. vi CHAPTER INTRODUCTI1ON The radiation emitted by ions embedded in a plasma from transitions amongboundstatesdifferssignificantlyfromthatemittedbyanisolatedra- diator. Theplasmaenvironment,interactingwitheachradiatorthroughthe combined electric field ofthe constituents ofthe plasma, changes the level structureofeachradiator. Theamountandcharacterofthatchangediffers foreachradiator. Thedistributionofchange,andthustheemittedspectrum, isdependentonafewplasmaparameters,suchasthedensityandtemperature oftheions, andelectrons. Thisdissertationexamines the process ofinfer- ringplasmaconditions from the spectrum emitted by embedded radiators, anddiscussestheapplicationofthisprocesstotransitionsbetweenboundand unboundstates. Attheoutset,itisappropriatetoparsethetitleofthiswork,asitcontains sometermsofart: "TheAnalysisofHotDensePla.smasandConsiderationof StarkBroadeningTheoryAppliedtoTransitionsInvolvingContinuumRadi- atorWavefunctions". Thesubjectmatterofthisdissertationisthusdivided intotwobroadcategories. Forthepurposeofthiswork"denseplasmas"arethoseplasmaswherethe electronandionnumberdensitiesaresufficientlyhighsothatplasmapertur- bationscauselinewidthsgreaterthanthesumofboththenaturalwidthand theDopplerwidthoftheline. So, "Hot" cannotbetoohot,butratherindi- catesthattheplasmaelectronsarenon-degenerate. "Hotdenseplasmas" are 2 thenthosenon-degenerateplasmasforwhichStarkbroadeningisthedominant causeoftheshapeoftheobservedhneprofiles. "Analysis" hereindicatesthe comparisonofspectraldatafromsuchplasmaswithcalculatedspectracom- posedofStarkbroadenedlineprofiles. Theshapesofthecalculatedspectra dependonthetemperature,densityandsizeoftheplasma. Thoseparameters usedtocalculatethespectrumwhichbestfitsthedataprovidetheinferences fortheparameterswhichcharacterizetheplasma. Thisdissertationdiscusses twodistinctanalyticalmethods: theanalysisofdatafromlaser-implodedgas filled microballoons usingthe emitted line spectra, and the analysis ofthe detailedstructureofabsorbingregions. "Starkbroadening" refers to the effect that plasmamicrofields have on theenergylevelstructureofanimmersedradiatorandtheresultingbroad- eningofthespectrallineprofile. "Transitionsinvolvingcontinuumradiator wavefunctions" arethosewhereeithertheinitialstateand/orthefinalstate ofthetransitionconsideredhasatleastoneunboundelectron. Starkbroaden- ingtheoryisamaturediscipline^''^'^''*'^'^whichfordecadeshasbeenapplied successfullytoanalyzeplasmabroadenedtransitionsinvolvingonlyboundra- diatorwavefunctions. Theapplicationofthattheorytotransitionsinvolving unbound-aswellasbound-radiatorelectronsisthesubjectmatterofthefinal partofthisdissertation. ThisIntroductionwillgiveanoverviewofonemethodofproducinghot denseplasmasandonemethodofrecordingtime-resolvedx-rayspectra. (While thisisnotanexperimentaldissertation,itisimportanttodiscusssomedetails oftheexperimentswhichproducetheplasmasofinterest.) Also,samplespec- trawillbepresented forthepurpose ofestabUshingthe nomenclature that willbeusedtodenotevariousspectralfeatures. Withthiscontextestabhshed, thesubsequentchaptersofthisdissertationwilldiscussStarkbroadeningthe- ory,analysisofemissionandabsorptionspectra,andtheapplicationofStark broadeningtheorytodiagnosticallyusefulautoionizingsateUites;thelatterne- cessitatesthedevelopmentofsomedifferentapproachestothecalculationof theirlineshapes. Typicaloftheplasmasaddressedinthisdissertationarethosecreatedusing theprocessoflaser-drivenimplosion'^,illustratedinFigure1. Figure 1. Laser-drivenimplosion. Indirectdrivelaser-drivenimplosions, as currentlyimplementedattheLaboratoryforLaserEnergeticsattheUniversity ofRochester, aspherical microballoonofapproximately 1mmdiameterand 15/imshellthickness,filledwithacoregas,orfuel,isimplodedbythereaction forcetotheablationofshellmaterialbythelaser. Inthisprocess,thelasersymmetricallyilluminatesthesphericalmicroballoon, depositingenergy,mainlythroughinversebremsstrahlung,intheexteriorre- gionoftheshellmaterial. Thematerialinthisregionablates,andthereaction forcedrivestheremainingpartoftheshellinwards,compressingthefuelgasto densitiesmanytimessohddensityandtemperaturesnearthoseoftheinterior oftheSun^. TheprecedingPanglossianparagraphdiscussesanidealseldomapproached inactualexperiment. Therearemanyexperimentalrealitieswhichhavesofar preventedimplosionsfromachievingthecompressionspredictedbyspherically symmetrictheories. Forexample,animportantnemesisistheRayleigh-Taylor instability.^'^^'^-^Thishydrodynamicinstabilitycausesanynon-uniformitiesin aninterfacewherealess-dense fluidispushingagainst (i.e., accelerating) a more-densefluidtogrowexponentially. Therearetwosuchinterfaces inan ablativelydrivenimplosion,theinterfacebetweentheablatingmaterialandthe remnantoftheshell,andtheinterfacebetweenthefuelgasandtheinteriorof theshell. TheRayleigh-Taylorinstabilitycanundersomecircumstanceslead toshellbreak-upbeforetheimplosioniscomplete, limitingtheconvergence oftheimplosion. Anynon-uniformitiesintheilluminationoftheshellbythe lasercanseedthisinstabilityevenintheabsenceofshellnon-uniformities. Thetime-resolvedx-rayspectraanalyzedlaterinthedissertationaremea- suredusingcrystalspectrometersattachedtostreakcameras. Thegeometry ofthese instruments isillustratedinFigure 2. Inthespectralrangeofthe ArK-shelltransitionswhichwillbeafocusofthisdissertation(approximately 3-4keV),theseinstrumentsoperatewitharesolutionE/AE^ 1000,witha timeresolutionofapproximately40ps. Asthetimeduringwhichdiagnostically usefulx-raysareemittedfromtheplasmaisapproximatelyhalfananosecond, thistimeresolutionsufficesforthe analysisofacoarsetimehistoryofthat partoftheimplosion. Aswillbeseeninthenextchapter, theStarkbroad- enedlinewidthsforthelinesofinterestareontheorderoftensofeVforthe lowestdensitiesconsidered, andthustheinstrumentalwidthassociatedwith theresolutionofthespectrometerdoesnotpreventStarkbroadeninganalysis.
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