Table Of ContentANALYSISOFHOTDENSEPLASMASAND
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.
