Strong collisions in the electron broadening of spectral lines from charged radiators in hot, dense plasmas

94 Pages·2001·3.6 MB·English

by  Gunderson, Mark Allen, 1969-

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