TWO SAMPLE PROBLEMS ILLUSTRATING THERMAL BLOOMING USAGE IN WAVETRAIN 波列热晕应用的两个示例问题

专业文档，值得珍藏！优秀文档，值得收藏！TWOSAMPLEPROBLEMSILLUSTRATINGTHERMALBLOOMINGUSAGEINWAVETRAINT.Berkopec(NOTE:Thisdocumentisanextractfromalongerreport.Sectionnumberinginthepresentextractstartswith4.0)4.0ThermalBloomingUsageTwoexamplesoftheuseofthethermalbloomingcodearepresentedinthissection.Thefirstisasimplepropagationtothefar-fieldofaGaussianHELbeam.ItduplicatesinWaveTrainasimpleconfigurationcreatedbyLincolnLaboratoryandsimulatedusingtheirMOLLYcode.ThesecondusesthephasescreenscreatedbyaGaussianHELtodistortlightback-propagatedfromanincoherentlyilluminateddisk.ThisduplicatesaneffortofNahrstedt(Refs.[5])tostudythethermaleffectsonaback-propagatedbeam.4.1DiscussionandFeaturesThefirstconsiderationthatneedstobeaddressedintheconfigurationofathermalbloomingmodelistheplacementofthephasescreens.TheWaveTrainimplementationdoesnotprovidetheuserwithanyguidancefordeterminingtheplacementornumberofthermalscreensrequiredtoaccuratelymodelagivenpropagationpath.Wesuggestthatusersexperimentwithvaryingthenumberofscreensandtheirplacementalongthepathtodeterminewhatconstitutesa“good”approximationfortheirconfiguration.Becausethethermalbloomingalgorithmusesthetwo-cycleschemedescribedinsection2.0,therearesomeconstraintsimposedbytheimplementedalgorithmontheplacementofthescreens.Thisrequirementamountstothis:Thescreensmustbepositionedinafashioninwhichtheyarelocatedatthemidpointofsegments,whichpartitionthepropagationpath.Forexample,ifwehavea100kmpathandplacejustonephasescreenat90km;thisviolatesthesegmentmidpointrequirementandsoisnotapermissibleconfiguration.Usingjustonephase,onemustplaceitatthemidpointofthepath.Thereishoweverawayaroundthisrequirement.Consideragainlocatingthescreenat90km,then,ifweweretolocateasecondscreenat40km,themidpointrequirementwouldbesatisfied.So,dojustthatbutsettheabsorptioncoefficientforthisscreentobezero.Thisturnsoffthethermalbloomingandtheonlythermaleffectsarethoseappliedbythescreenlocatedat90km.However,something,whichmaybeundesirable,occurswhentheabsorptioncoefficientforthe40kmscreenissettozero;thebeamisnotattenuatedalongthefirst80kmofthepath.Thisleavesuswiththeproblem:Howdoweinsertthe40kmscreen,soastoconformwiththerequirementsofscreenpositioning,turnoffthethermalbloomingeffectsofthisscreen,andyetattenuatethebeamalongtheentirepath?Thereisahacksolutiontothisproblem.Settheabsorptioncoefficienttothedesiredvalue(probablythesameasthatofthe90kmscreen),andsetoneofthewindvelocitycomponentstoaveryhighnumber,say106,oranumber,whichguaranteesthattheentiretemperaturedistributionisblownoffofthemeshinatimecorrespondingtotheincrementalupdateDeltaTime.Thishastheeffectofapplyingthermalbloomingatthe40kmscreen,buttheeffectofthethermalbloomingisnegligiblesincethetemperaturedistributionduetotheHELheatingisnowoffthemeshonwhichthebeamcurrentlylies.Yet,theattenuationspecifiedbytheabsorptioncoefficientwillstillbeappliedtothebeam.Asmentioned,thismannerofpositioningscreenssatisfiesthe2-cycleschemeandconformstothewayinwhichbookkeepingiscurrentlydoneinthethermalbloomingcode.TheuseofnumberSavedStatesisperhapsbestillustratedviaanexample.Considerthesomewhatcontrivedexampleofanopticalpathof1000km,whichgivesapropagationtimeseconds,betweensourceandtarget.Furthermore,supposethattheupdatetimeofadetectorinthetargetplaneisandtheupdaterateofadetectorinthesourceplaneisLetthedetectorinthetargetplanerequestdataattimeTandthedetectorinthesourceplanerequestdataattime,+Also,supposethattherearethreescreenlocations:at250km,500kmandat750km.,asshowninfigure4.1-1.(NOTE:aftertheratherlengthydiscussionconcerningtheruleregardingthepositioningofthethermalscreens,thisexampleviolatesthatrule.Itistoberegardmerelyasanillustrationoftheuseoftheparameter,numberSavedStates,andtheselocationsservetosimplifythecalculationsinvolvingtime).WhenthedetectorinthetargetplanerequeststheHELattimeT,theHELissentfromitssourceattimeT-DuringitspropagationalongtheopticalpaththeHELmodifiesthethermalbloomingscreensasitencountersthem.Figure4.1.showsthetimesatwhichthethermalscreensareupdatedbytheHELandthetimeatwhichtheyareencounteredbytheback-propagatedbeam.Forinstance,thescreeninthemiddleisupdatedattimebytheHELcreatedatthesourceattimeandattimeTbytheHEL,whichstartsoutattime.Nowtheback-propagatedbeamBParrivesatthemidpointofthepropagationpathattime.ThismeansthatthescreenupdatedattimeTistheclosest,temporally,tothetothetimeatwhichtheback-propagatedbeamarrivesatthethermalscreen.Soitisthefirstsetofthermalsavedstatesthatareusedinupdatingtheback-propagatedbeamattime.Ontheotherhand,atthescreenlocatedat750kmonefindsthatitisthethermalstatescorrespondingtothetimethatgetsusedintheapplicationofphasetotheback-propagatedbeam,andthesethermalstatesaresavedinthesecondsetofsavedstates.Wefindforthisconfigurationatleasttwopastthermalstatesareneededtocorrectlyupdatetheback-propagatedbeam,i.e.numberSavedStatesmustbeequaltoatleast2.Figure4.1-1Showsthelocationsandcorrespondingtimesofvariousbeams.4.2ExamplesTheMOLLYconfigurationprovidesanelementaryexampleofthermalblooming.Thebasicconfigurationconsistsofapropagationpathof5000meters,withatelescopeaperturediameterof0.5meters.Thebeamprojectedtothefar-fieldisaGaussianbeamwithabeamsigma(thee-2point)equaltotheradiusofthetelescopeandaninitialpowerof300000.0Watts.Thewavelengthis3.8e-6meters.Thereare20thermalscreensalongthebeampathlocatedatthefollowingpositionsdistances=[214.03,634.885,1040.07,1427.165,1794.0,2138.75,2460.0,2756.805,3028.725,3275.8,3498.525,3697.8,3874.845,4031.265,4175.445,4318.645,4464.725,4613.8,4765.995,4921.445]inmeters.Notetheincreaseinspacingdensitytowardtheendofthepath.Also,thesepositionssatisfythemidpointrequirementmentionedabove.Thethreephysicalpropertiesofthescreens:absorptioncoefficient=,scattercoefficient=,andtemperature=0.0C,arethesameforeachofthescreens.Thereisnobeamslewingandtheplatformandtargetarestationary.Ateachofthethermalscreensthereisaconstantwindinthex-directionof10m/s.Thenumberofmeshpointstosamplethebeamandthethermalscreensisthesame,512X512andthemeshspacingis0.1meters.Theincrementalupdaterateis0.01seconds.ThisisalsotherequestrateoftheSimpleFieldSensormoduleinthefar-field.Thiscodewasrunfor.11seconds.ItisbelievedthattheMOLLYcodeusesmeshes,whicharesymmetricabouttheorigin,whereastheWaveTrainusesasymmetricmeshwiththeoriginatameshpoint.ThisisprobablythesourceofdiscrepancybetweenMOLLYandWaveTrain.Figure4.2-1TopleveloftheLincolnLaboratoriesthermalbloomingconfiguration.Figure4.2-1showsthemodules,whichcomprisetheWaveTrainsimulationmodel.TheTBAtmoPathmoduleisshownwithitsaccompanyinginputparameters.NotetheparametersacsSpecandmtbSpec,whichprovidetheinformationforconstructingthephaseandthermalbloomingscreens.MtbAtmSpec(512,0.1,-1.0,-1.0,.0.01,6.93e-5,6.820e-5,0.0,3.8e-6,distances,10.0,0.0,0.0,0.0,0.0,0.0,1)andacsSpecisspecifiedsimplyasAcsAtmSpec(5000.0).DescendingintothemoduleTBAtmoPathweseeinfigure4.2-2thatitconsistsofthetwoPropagationControllermodulesandaTurbBloomAtmospheremodule.Theinformationjustoutlinedisalsopresentedintheaccompanyingrunset,showninfigure4.2-3.Figure4.2-2DescentintoTBAtmoPath.Figure4.3-3TheRunsetspecificationaccompanyingtheMollyModelAsecondexampleofthethermalbloomingcodeisprovidedbytheconfigurationsoutlinesinNahrstedt’spaper[5].Nahrstedt’sstudyisdesignedtoinvestigatetheimpactofathermallybloomedatmosphereonabeamback-propagatedfromthetargetplane.ConfigurationspecificationsoutlinedintheNahrstedtstudyareasfollows:theHELwavelengthequals3.8e-6meters;theback-propagatedbeamwavelengthequals10.0e-6meters;thex-componentofthewindspeedequals100meterspersecond;thepropagationpathrangeequals107.85km;theFresnelnumberfortheconfigurationis3.833;thetelescopediameterequals1.0meters;theabsorptionnumberequals0.274;andthetransmissionequals0.760.Additionally,wearetoldthattheHELisGaussian(beamwaistunknown);thattheback-propagatedbeamisanincoherentuniformdiskcenteredatthepointinthetargetplaneatwhichtheintensityoftheHELismaximum,andwhichsubtendsanangleof~10mirco-radiansatthetelescope;thattheplacementofthescreensisnearlyuniform;andthatthegeometryforthesamplingmeshesisarectangulargridof64X64pointswithaspacingof0.0476meters.WemodeledtheincoherentdiskusingtheIncoherentDiscmodulewithfifteenspecklerealization.Fivethermalscreenswereplaceduniformlyalongthepath.Thesimulationwasrunforsixdifferdistortionnumbers[0.333,0.667,1.335,2.670,5.339,10.679],wherethedistortionnumberwasvariedbyvaryingthepoweroftheHEL.Herethecorrespondingpowerlevelsare,[0.1,0.2,0.4,0.8,1.6,3.2]Mega-Watts.FordistortionnumberNahrstedtuses=ThefactorsareP,theHELpower;a,thetelescoperadius,andR,thepropagationpathlength.Theotherfactorsareasdefinedinsection2.1.InordertogeneratethethermalscreensinWaveTrain,weneedtospecifythreephysicalquantities:theabsorptioncoefficient,thescattercoefficientandthetemperature.Fromthedataprovided,weknowthattheabsorptioncoefficientis0.274/107.85e3m-1,thescattercoefficientiszero,butweneedtoextractthetemperature.Rememberinsection3.3itwasshownthattbcoef=+temperature)=(Notethatthefactorn0wastakentobe1.0insection2.1).Usingthisequationandtheequationforthedistortionnumber,wefindthat===400000)()()(100)(.5)3),whichgivesthat+temperature)==hencethe=.Foreachdistortionnumber,twentyrealizationswerecreatedandtheimagesinthefocalplaneofacamerabehindthetelescopeaveraged.Theupdateratewas0.0005secondsandthestoptime0.015seconds,foratotalofthirtypassesthroughtheatmosphere,whichguaranteedthatasteady-statehadbeenachieved.5.0SimulationResultsThissectiongivesabriefcomparisonoftheresultsobtainedbythethermalcodeinWaveTraintothoseresultsobtainedbytheLincolnLaboratories’MOLLYcode.ItalsocomparesresultsfromtheNahrstedtstudytothosegeneratedwiththethermalbloomingsoftwareinWaveTrain.Theseresultsofcoursepertaintothesystemsdescribedinsection4.2.5.1MollyCodeResultsFigure5.1-1showsacomparisonofthefar-fieldintensityfootprintofthebeamontheeleventhiteration.TheimageontheleftisthatobtainedbyLincolnLabsandtheoneontherighttheimagegeneratedbyWaveTrain.Figures5.1-2and5.1-3areslicesthroughthepeakintensitylocationofthefar-fieldimages,whichagaincompareLincolnLabandWaveTrainresults.Whilethecomparisonsarereasonablygood,therearedifferences.Figure5.1-1Far-Fieldintensityfootprintsofthethermalbloomedbeam.Thesearesteady-stateresults.Fromfigures5.1-2and5.1-3againweseethatthesliceplottrackreasonablywellbutWaveTrainproducesagreaterpeakintensityvalue.Possiblereasonsforthesediscrepanciesare:therearepossiblydifferentfiltersbeingappliedduringthepropagation(weareunawareofthedetailsunderlyingtheMOLLYcode’spropagator),thiscouldexplainthesidelobevariation;also,webelievethattheMOLLYcode’smeshesaresymmetricwithrespecttotheorigin,whilethoseofWaveTrainareasymmetric,duetotheplacingofameshpointontheorigin,whichcouldexplainthepeakintensitymismatch.Figure5.1-4showsacomparisonofthetimehistoryofthepeakintensitiesfrombothsimulations.AsexpectedtheresultstrackwellbuttheWaveTrainpeakintensitiesarealwaysslightlylarger.Figure5.1-2X-sliceandY-sliceplotsthroughthepointofpeakintensityFigure5.1-3Comparisonofthepeakintensityofthefar-fieldversustime.5.2NahrstedtStudyResultsFigure5.2-1showstheintensityfootprintoftheforwardbeaminthefar-fieldforthesixdifferentdistortionnumbersconsideredinthestudy.Asexpected,asthelevelofthermalbloomingisincreasedthebeamdefocusingalsoincreases,causingitscentroidtomovefartheroff-axis.TheresultsoftheprinciplecomparisontotheNahrstedtstudyareshowninfigure5.2-2.(Relativeintensityistheratioofthepeakintensityofthefieldtotheidealintensityofthefield).Thecurvefortheforwardbeam(HEL)wasobtainedbycomputingtherelativeintensityofthefieldinthefar-fieldinsteady-state.Fortheback-propagatedbeam,20realizationsoftheback-propagatedbeamwerecomputedandtheintensitiesofthebeamswereaveraged.TheWaveTrainresultsseemtotrackwellwithNahrstedt’sresultsbutdonot