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.