Time-of-Arrival Applied to the Spatially Distributed ELF/VLF Source Region above HAARP

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Time-of-Arrival Applied to the Spatially Distributed ELF/VLF Source Region above HAARP
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Fujimaru,Shuji
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Master's ( M.S.)
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University of Florida
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Electrical and Computer Engineering
Committee Chair:
Moore, Robert Christian
Committee Members:
Lin, Jenshan
Uman, Martin A

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electromagnetics -- elf -- ionosphere -- time -- vlf -- wave
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, M.S.
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Electromagnetic waves in the Extremely Low Frequency (ELF, 3--3000~Hz) and the Very Low Frequency (VLF, 3--30~kHz) bands may be generated by modulated High Frequency (HF, 3--30~MHz) heating of the lower ionosphere in the presence of the naturally-forming auroral electrojet currents. This investigation experimentally studies high power radio wave interactions in the lower ionosphere and focuses on the dynamics of ELF/VLF wave generation, which has been utilized across a broad spectrum of applications such as submarine communications and ionospheric remote sensing. This thesis melds Time-of-Arrival (TOA) analysis with ELF/VLF wave generation experiments in order to estimate the location of the dominant ELF/VLF source region and to distinguish between various ELF/VLF signal paths to the receiver. These accomplishments are a first step toward mapping the ELF/VLF source regions currents, which in turn may provide a means to increase ELF/VLF wave generation efficiency in the future. In this thesis, the application of linear TOA analysis to the non-linear ELF/VLF wave generation process is described in full detail. Experimental observations performed during research campaigns at the High Frequency Active Auroral Research Program (HAARP) in Gakona, Alaska, are compared with the predictions of an HF heating model to demonstrate that the TOA analysis method is a valid and useful measurement technique at ELF/VLF frequencies. Lastly, TOA analysis is applied to experimental observations to extract geophysically meaningful information regarding the ionospheric absorption of modulated HF waves.
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by Shuji Fujimaru.
Thesis:
Thesis (M.S.)--University of Florida, 2011.
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Adviser: Moore, Robert Christian.

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TIME-OF-ARRIVALANALYSISAPPLIEDTOTHESPATIALLYDISTRIBUTEDELF/VLF SOURCEREGIONABOVEHAARP By SHUJIFUJIMARU ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2011

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c 2011ShujiFujimaru 2

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Tomyparentsandbrother,Akio,IkuyoandYoshikiFujimaru,andtomygrandparents, MitsuyoshiandYukoFujimaruandShinakoHosozawa 3

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ACKNOWLEDGMENTS Firstofall,Iwouldliketoexpressmyappreciationtomyadviser,Dr.RobertMoore, forhisencouragement,guidance,andhelpthroughoutmygraduatestudies.Thisthesis wouldnotpossiblyhavebeencompletedinaprofessionalmannerwithouthispatient andunselshsupport.IalsowouldliketothankDr.MartinUmanandDr.JenshanLin forservingasmembersofmythesiscommitteeandforprovidingpreciseandprompt feedbackstothisthesisdespitetheirbusyschedules. IamgratefultoallmycolleagueswithwhomIhavesharedafulllingresearch experiencethroughmygraduateschoollife.Especially,Iwouldliketoshowmygratitude toTongWang,forprovidinghelpfuladviceonsignalprocessingproblems;toDivya Agrawal,forfruitfuldiscussionsonplasmaphysicsandelectromagnetics;andtoMichael Mitchel,forunfailingsupportofobservationalinstruments. Lastly,IowemydeepestgratitudetomyparentsandfamiliesinJapanforbeingmy lifesupport,withtheirunconditionallove. ThisworkissupportedbyONRgrant#N000141010909totheUniversityofFlorida andbyBAESystemscontract#709372totheUniversityofFlorida. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS..................................4 LISTOFTABLES......................................7 LISTOFFIGURES.....................................8 ABSTRACT.........................................9 CHAPTER 1INTRODUCTION...................................11 1.1IonosphereandExtremelyLowFrequency/VeryLowFrequencyELF/VLF Waves......................................12 1.2ELF/VLFWaveGenerationandPropagation................13 1.2.1HighFrequencyHFPropagationandAbsorption.........14 1.2.2ELF/VLFSignalPropagation.....................16 1.3ELF/VLFWaveCurrentSources.......................17 1.4ObservationalInstrumentation........................18 1.4.1HighFrequencyActiveAuroralResearchProgramHAARP....18 1.4.2ELF/VLFReceivers...........................19 2EXPERIMENTALMETHOD:TIME-OFARRIVALTOATECHNIQUE.....24 2.1TOATransmissionDescription........................24 2.2Time-of-ArrivalMethod.............................24 2.3AlternativeTime-of-ArrivalDerivation.....................28 2.4TOAProperties.................................31 2.4.1TimingAccuracy............................31 2.4.2TimingResolution...........................33 2.4.3PreviousTOAAnalysis.........................33 3TOAOBSERVATIONANDANALYSIS.......................37 3.1ComparisonwithModel............................37 3.2BeamDirection.................................39 4GEOPHYSICALINTERPRETATION........................43 4.1Dual-BeamExperiment............................43 4.1.1ExperimentDescription........................43 4.1.2ExperimentalResults..........................44 4.2TOAvsVLFFrequency............................45 4.2.1ExperimentDescription........................45 4.2.2ExperimentResultsandAnlaysis...................45 4.3TOAvsHighFrequencyHFandPower...................46 5

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4.3.1ExperimentDescription........................46 4.3.2ExperimentResultsandAnlaysis...................46 5SUMMARYANDFUTUREWORK.........................51 5.1Summary....................................51 5.2FutureWork...................................51 5.2.1TOAAnalysisforHFbeamsatDifferentAzimuths..........51 5.2.2TOAAnalysisforDifferentHFBeamPatterns............52 5.2.3TOAAnalysisforDifferentModulationTechniques..........52 REFERENCES.......................................53 BIOGRAPHICALSKETCH................................55 6

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LISTOFTABLES Table page 1-1Radiospectrum....................................20 4-1ExtremelyLowFrequency/VeryLowFrequencyELF/VLFsourceregion...48 7

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LISTOFFIGURES Figure page 1-1Electrondensityintheionosphere.........................20 1-2Electroncollisionfrequency.............................21 1-3CartoondiagramofELF/VLFwavegenerationattheHighFrequencyActive AuroralResearchProgramHAARP........................21 1-4HAARPantennaarrays...............................22 1-5GeographicmapoftheELF/VLFreceiversites..................22 1-6ELF/VLFantenna..................................23 2-1Time-of-ArrivalTOAobservationsandsincfunctionsusingonlypositivefrequencycomponentsandusingpositiveandnegativefrequencycomponents.35 2-2Cramr-RaoLowerBoundCRLBofthestandarddeviationofthetimedelay forthepeakamplitude................................35 2-3ExperimentalObservationsoftheamplitudesofthereceivedELF/VLFwaves and`apparentsourceheight'atTroms......................36 3-1TOAobservationswithnoiseapproximation....................40 3-2Comparisonbetweenmodelpredictionandobservations............41 3-3TOAvsHFbeamdirection.............................42 4-1Cartoondiagramofthedual-beamexperiment..................47 4-2Dual-beamheatingobservations..........................47 4-3DominantELF/VLFsourceregionmap.......................48 4-4TOAvsELF/VLFfrequency.............................49 4-5TOAvsHFfrequencyandpower..........................50 8

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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience TIME-OF-ARRIVALANALYSISAPPLIEDTOTHESPATIALLYDISTRIBUTEDELF/VLF SOURCEREGIONABOVEHAARP By ShujiFujimaru August2011 Chair:RobertC.Moore Major:ElectricalandComputerEngineering ElectromagneticwavesintheExtremelyLowFrequencyELF,3Hzand theVeryLowFrequencyVLF,3kHzbandsmaybegeneratedbymodulatedHigh FrequencyHF,3MHzheatingofthelowerionosphereinthepresenceofthe naturally-formingauroralelectrojetcurrents.Thisinvestigationexperimentallystudies highpowerradiowaveinteractionsinthelowerionosphereandfocusesonthedynamics ofELF/VLFwavegeneration,whichhasbeenutilizedacrossabroadspectrumof applicationssuchassubmarinecommunicationsandionosphericremotesensing. ThisthesismeldsTime-of-ArrivalTOAanalysiswithELF/VLFwavegenerationexperimentsinordertoestimatethelocationofthedominantELF/VLFsourceregionand todistinguishbetweenvariousELF/VLFsignalpathstothereceiver.TheseaccomplishmentsarearststeptowardmappingtheELF/VLFsourceregionscurrents,whichin turnmayprovideameanstoincreaseELF/VLFwavegenerationefciencyinthefuture. Inthisthesis,theapplicationoflinearTOAanalysistothenon-linearELF/VLFwavegenerationprocessisdescribedinfulldetail.Experimentalobservationsperformedduring researchcampaignsattheHighFrequencyActiveAuroralResearchProgramHAARP inGakona,Alaska,arecomparedwiththepredictionsofanHFheatingmodeltodemonstratethattheTOAanalysismethodisavalidandusefulmeasurementtechniqueat ELF/VLFfrequencies.Lastly,TOAanalysisisappliedtoexperimentalobservationsto 9

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extractgeophysicallymeaningfulinformationregardingtheionosphericabsorptionof modulatedHFwaves. 10

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CHAPTER1 INTRODUCTION Thisworkappliestime-of-arrivalTOAanalysistoexperimentalobservationsof ExtremelyLowFrequencyELF,3HzandVeryLowFrequencyVLF,3kHz electromagneticwavesgeneratedbymodulatedHighFrequencyHF,3-30MHz heatingofthelowerionosphere.Theexperimentalobservationspresentedhereinwere performedneartheHighFrequencyActiveAuroralResearchProgramHAARPHF transmitterinGakona,Alaska.TheHAARPHFtransmitterispresentlytheworld'smost powerfulionosphericheater,andwith3.6MWoftotaltransmitterpower,itiscapableof broadcastingsignalswithmorethan1GWofeffectiveradiatedpowerERP,depending onHFfrequency.Whilealargevarietyofionosphericmodicationexperimentsare regularlyperformedatHAARP,thisthesisfocusesonHAARP'sabilitytogenerate electromagneticwavesintheELF/VLFbandbymodulatedheatingoftheauroral electrojetcurrentsystem,whichispresentinpolarandsub-polarregionsoftheworld. Modulatedheatingofthelowerionosphereinthepresenceofnaturally-forming currentsystems,suchastheauroralelectrojet,hasbeenrecognizedasameansfor producingELF/VLFwavessincethe1970's[e.g., Getmantsevetal. ,1974].Recent technologicaladvanceshaverenewedeffortstoincreasetheefciencyofELF/VLF wavesgeneratedinthismanner.Onemethodtodosofocusesonmappingthespatial distributionELF/VLFsourceregioncurrentswithinthelowerionosphere.Inorderto maptheELF/VLFsourceregioncurrents,twoproblemsmustbeaddressed:1the wavelengthsoftheELF/VLFfrequenciesusedareseveral10'sofkilometerslong, limitingthespatialresolutionattainablebystandardinterferometricmethods,and2 experimentalobservationsarecomplicatedbythefrequency-dependenteffectsofthe Earth-ionospherewaveguide,whichsignicantlyaffectsELF/VLFwavepropagation. Thisthesisprimarilyaddressesthesecondproblem:itisdemonstratedthatTOA analysismaybeemployedtodistinguishbetweenline-of-sightELF/VLFpropagationand 11

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ionospherically-reectedELF/VLFpropagation.Separatingthetwotypesofpropagation enablestheexperimentaldeterminationoftheamplitudeandphaseofthereceived ELF/VLFsignalasafunctionoftime.Thisthesisleavesforfutureworktheeffortto convertTOAobservationsatmultiplereceiversitestoaspatialmapofELF/VLFsource regioncurrents. ThisintroductorychapterprovidesanoverviewoftheELF/VLFwavegeneration phenomenonanddescribestheobservationalinstrumentationemployedduringexperimentalcampaignsatHAARP.Chapter2detailstheTOAsignalprocessingtechnique asitisappliedtoELF/VLFobservations.Chapters3and4demonstratetheutilityof ELF/VLFTOAanalysisusingobservationsperformedduringseveralproof-of-concept experimentsandduringseveralmoreelaborateexperiments.Lastly,Chapter5summarizesthisthesisandsuggestsfuturedirectionsforthisresearch. 1.1IonosphereandExtremelyLowFrequency/VeryLowFrequencyELF/VLF Waves TheionosphereistheportionoftheEarth'supperatmospherethatischaracterized bylargeconcentrationsofionsandelectrons[ Budden ,1985].Figure1-1,adaptedfrom Davies [1990],showstheelectrondensitydistributionwithaltitudeonasummerday atmid-latitudes.Theionosphereextendsfromabout60kmto1000kmaltitudeandis dividedintothreegeneralregions:the D -region,rangingfrom 60kmto100km,the E -region,rangingfrom 100kmto140km,andthe F -region,rangingabove 140km. Thechargedparticleswithintheionosphereaffectthepropagationofradiowaves asafunctionofthewavefrequency.Anabbreviatedsummaryofpropagationfeatures fordifferentfrequencybandsisprovidedbyTable1-1.AscanbeseenfromTable1-1, adaptedfrom[ Davies ,1990],lowerfrequencywavesmaypropagatelargedistances withintheEarth-ionospherewaveguidewithrelativelylowattenuation.Asaresult,ELF andVLFwaveshavebeenusedforsuchpurposesassubmarinecommunications[e.g., Wait ,1972]andionosphericremotesensing[e.g., Cummeretal. ,1998]. 12

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Theinteractionbetweenelectromagneticwavesandthe D -regionionosphereis scienticallyinteresting.TheEarth-ionospherewaveguideisformedbythegroundon onesideand D -regionionosphereontheother.Inaddition,asisshowninFigure1-2, the D -regionhashighelectron-neutralcollisionfrequenciesthatresultintheabsorption ofelectromagneticwavesbytheionosphere.Wewillexploretheseionosphericplasma andwavepropagationcharacteristicsusingELF/VLFwavegenerationexperimentsat HAARP. 1.2ELF/VLFWaveGenerationandPropagation ThecartoondiagramshowninFigure1-3depictstheprocessofELF/VLFwave generationbymodulatedHFheatingofthelowerionosphere.ThemodulatedHFsignal broadcastupwardbytheHAARPHFtransmitterisabsorbedbythecollisional D -region ionosphereat 60kmaltitude.Thewaveenergyabsorbedbytheionosphere modiesthetemperatureoftheconstituentelectronsoftheionosphere.Becausethe waveenergyismodulated,theelectrontemperatureisalsomodulated.Theconductivity ofthelowerionospherestronglydependsontheelectrontemperature.Asaresult,the conductivityofthelowerionosphereismodulatedwiththesamefundamentalperiodicity oftheHFsignalmodulation.Thispropertyhastwosignicanteffects:1thetimevaryingconductivityleadstoatime-varyingrateofabsorptionoftheHFwavei.e.,the absorptionoftheHFwavemodiestherateofabsorptionoftheHFwaveanonlinear processknownasself-absorption,and2thetime-varyingconductivitytogether withthebackgroundelectrojetelectriceldyieldsanELF/VLFsourcecurrentdensity ~ J = ~ E .ThespatiallydistributedELF/VLFsourcecurrentsexcitetheEarth-ionosphere waveguideandproducewavesthatmaypropagatetolargedistancesaroundthe globe.Forlong-distancepropagation,itistypicaltomodelEarth-ionospherewaveguide propagationusingmodalsignalanalysis,inwhichadiscretenumberofwaveguide modespropagatewithvaryinggroupvelocities,phasevelocities,andattenuation rates.Forshort-distancepropagation,asisthecaseforthelocationofthereceivers 13

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usedinthiswork,aray-basedanalysismethodisemployed.Thetwomethodsare mathematicallyequivalent.Atlargedistances,fewerwaveguidemodesarenecessaryto calculatethereceivedsignal,whereasatshortdistances,fewerraypathsarerequiredto calculatethereceivedsignal. ThefollowingsubsectionsprovidebriefdescriptionsoftheHFpropagationand absorptionprocessesandtheresultinggenerationandpropagationofELF/VLFwaves. 1.2.1HighFrequencyHFPropagationandAbsorption TheHFwavebroadcastbyHAARPpropagatestothelowerionosphere,inwhich itisrefractedandpartiallyreected.Theamountofrefractionandthepercentageof reectionaredeterminedbythevariationintheionosphericrefractiveindexalong thepropagationpath.Therefractiveindexoftheionosphericplasmadependsonthe localelectrondensity,electrontemperature,andthedirectionandmagnitudeofthe Earth'smagneticeldatthatlocation.AdetaileddescriptionofHFpropagationthrough thelowerionosphereisprovidedby Moore [2007].Forthepurposesofthiswork,it sufcestostatethattheraypathandgroupvelocityoftheHFwavemaybedetermined accuratelyusingambientionosphericparametersi.e.,theeffectsofHFheatingon thesepropertiesmaybeneglected,whiletheamplitudeandphaseoftheHFwave dependsensitivelyonthemodulatedelectrontemperatureviaconductivity. Themodulationofionosphericelectrontemperaturemaybedescribedbythe localizedenergybalanceequationadaptedfrom MooreandAgrawal [2011]: 3 2 N e B dT e dt =2 k T e S )]TJ/F41 11.9552 Tf 11.956 0 Td [(L T e T 0 Thelefthandsideoftheequation, 3 2 N e B dT e dt ,representsthechangeinthermal ionosphericenergyasafunctionoftimeforagivenelectrondensity, N e ,andelectron temperature, T e B istheBoltzmannconstant.Thersttermoftherighthandside, 2 k T e S representsthepoweroftheHFwavethatisabsorbedbytheionosphere, withanabsorptionrate T e andHFPoyntingux S .Thesecondtermoftheright 14

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handside, L T e T 0 istheelectronenergylossrateasafunctionof T e andtheambient electrontemperature T 0 .Forthemodelingresultsusedinthiswork,theequations describing T e and L T e T 0 arepresentedby Moore [2007]. Themodulatedelectrontemperatureresultsinamodulatedionosphericconductivity.Inthelowerionosphere,conductivityisrepresentedasatensorbecausethe relationshipbetween ~ J and ~ E dependsonthedirectionoftheelectriceldwithrespect totheEarth'smagneticeld.Theconductivitytensoristypicallyexpressed: = 2 6 6 6 6 4 P )]TJ/F27 11.9552 Tf 9.298 0 Td [( H 0 H P 0 00 jj 3 7 7 7 7 5 where P H ,and jj denotethePedersen,Hall,andparallelconductivities,respectively. Usingakineticformulation,theconductivitycomponentscanbedescribed[ Tomko 1981]: P = 4 3 j q 2 e m e Z 1 0 U U 2 )]TJ/F41 11.9552 Tf 11.956 0 Td [(Y 2 v 3 e @ f e ,0 @ v e dv e H = )]TJ/F24 11.9552 Tf 9.298 0 Td [(4 3 j q 2 e m e Z 1 0 U U 2 )]TJ/F41 11.9552 Tf 11.955 0 Td [(Y 2 v 3 e @ f e ,0 @ v e dv e jj = 4 3 j q 2 e m e Z 1 0 1 U v 3 e @ f e ,0 @ v e dv e where q e istheelectroncharge, m e istheelectronmass,and istheangularfrequency. U and Y aregiven: U =1 )]TJ/F41 11.9552 Tf 11.955 0 Td [(j v e Y = ce v e istheeffectiveelectron-neutralcollisionfrequencyand ce isthecyclotronfrequency. f e ,0 istheMaxwellianelectronvelocitydistributionfunction: 15

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f e ,0 = N e m e 2 B T e 3 = 2 exp )]TJ/F41 11.9552 Tf 9.298 0 Td [(m e v 2 e 2 B T e Hencetogetherwithauroralelectrojetelectriceld, ~ E ,themodulatedconductivities becomecurrentsourcesi.e., ~ J = ~ E ,andconstituteasourceforelectromagetic radiationatELF/VLFfrequencies,asdescribedinthenextsubsection. 1.2.2ELF/VLFSignalPropagation Theradiationofelectromagneticwavesfromaspatiallydistributedcurrentsourcein free-spacecanbeexpressedas[ Balanis ,1986]: B fs x y z = )]TJ/F27 11.9552 Tf 13.645 8.088 Td [( 4 ZZZ V ^ R J 1+ j R R 3 exp )]TJ/F42 7.9701 Tf 6.586 0 Td [(j R dx 0 dy 0 dz 0 where x y ,and z representthelocationofthereceiver, x 0 y 0 ,and z 0 representthe locationofthesource, R isthedistancebetweenthereceiverandsource, isthe permeabilityoffree-space,and isthewavepropagationconstant. InordertoaccountforEarth-ionospherewaveguideeffects,however,boundary conditionsmustbeincluded.AreasonablerstapproximationoftheEarth-ionosphere waveguideisaparallel-platewaveguidewithperfectlyconductingwallsandaplate separation, h ,representingthereectionheight.Insuchawaveguide,thereceived signalmaybemodeledusingimagetheory.Althoughthisrepresentationdoesnot accountforfrequency-dependentreectionheightsorreectioncoefcients,itwillserve thepurposesoftheworkpresentedherein.Usingthisparallel-platerepresentation oftheEarth-ionospherewaveguide,theline-of-sightpropagationpath,whicharrives atthereceiverearliest,isequivalenttoadistributedcurrentsourceaboveaground plane.Infact,allsubsequentreectionsmayberepresentedsimilarly,althoughsourced atdifferentaltitudes.The B -elddetectedonthegroundresultingfromaspatially distributedcurrentsourceoveragroundplanemaybeexpressed: B x =2 B fsx 16

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B y =2 B fsy B z =0 1.3ELF/VLFWaveCurrentSources ThespatialdistributionofELF/VLFsourcecurrentsisofprimeinteresttothework presentedinthisthesis.Hereweprovideabackgroundrelatingpreviousresearch effortstoexperimentallydetectELF/VLFsourcecurrentdistributions. Rietveldetal. [1984]analyzedthespatialdistributionoftheauroralelectrojet electriceldbysweepingthedirectionoftheHFbeamandcomparingELF/VLFwave observationswiththedirectionoftheelectriceldmeasuredbytheSTAREradar. ThisexperimentrecognizesthatthedetectedELF/VLFwavescanpossiblybeused toestimatethespatialdistributionoftheauroralelectrojetelectriceld.Usingfareld measurements, Barretal. [1998]and Cohenetal. [2008]showthataimingHFbeam towardthereceiverincreasestheELF/VLFwaveamplitudedetectedatthereceiver. Whilethisresultisexpectedsincethesourceisclosertothereceiver,theamountof amplitudeincreasewasunexpectedlyhigh,indicatingamoreefcientexcitationofthe Earth-ionospherewaveguideusingobliqueHFheatingoftheionosphere,ratherthan asimplesource-to-receiverdistancereduction.Ontheotherhand, Barretal. [1998] explainsthatreductionsofamplitudeswiththeHFbeamaimedawayfromthereceiver maybecausedbyphasespreadingduetotheincreasingdifferenceofpropagation distanceindifferentpaths. Anumberoftheoreticalandexperimentaleffortshavebeenperformedtodetermine theELF/VLFwavecurrentsourcelocation.Forexample, James [1985]theoretically computesthemodulatedionosphericpropertiesasafunctionofaltitudewithgivenappropriateionosphericparametersanddeterminesthedominantaltitudeoftheELF/VLF wavesource.Ontheotherhand, Rietveldetal. [1986]experimentallyestimatesthe sourceheightusingpulsedionosphericheating. Rietveldetal. [1989]and Riddolls [2003]useamethodsimilartotime-of-arrivalanalysistodeterminetheELF/VLFsource 17

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heightsthedifferencefromourTOAanalysisisdiscussedinSection2.4.3.These analyseswereconductedassumingthedominantELF/VLFsourceregionwaslocated directlyabovetheHFtransmitteranddidnotattempttoseparateionosphericallyreectedsignalsfromtheline-of-sightsignals.Mostrecently, Payneetal. [2007] attemptedtomaptheELF/VLFsourcecurrentstructureusinganELF/VLFinterferometerchain.TonalELF/VLFtransmissionswereemployed,however,andhedemonstrated thatinthiscasetheproblemisill-conditionedi.e.,notsolvable. Ionospherically-reectedsignalshavebeendirectlyobservedinELF/VLFrecordings[e.g., Papadopoulosetal. ,2003; Rietveldetal. ,1986].Itisthuspossiblethat theexperimentalobservationslistedabovemaybecontaminatedbyionosphericallyreectedsignals,affectingtheanalysis.TheTOAmethodpresentedinthisworkis capableofseparatingtheline-of-sightandtheionospherically-reectedcomponentsof theobservedELF/VLFwave,andtheseexperimentshaveprovidedthemotivationtoexperimentallyseparateline-of-sightpropagationfromionospheric-reectionpropagation. 1.4ObservationalInstrumentation 1.4.1HighFrequencyActiveAuroralResearchProgramHAARP TheHighFrequencyActiveAuroralResearchProgramHAARPisajointly-funded AirForce/NavyresearchfacilitylocatedatGakona,Alaska.39 N,145.15 Wwith thepurposetostudyupperatmosphere.TheprimaryresearchinstrumentatHAARP istheHFphasedarraytransmitter,consistingof180crosseddipoleantennasaligned ina12x15grid.Thetotaltransmitterpoweris3.6MW,andthearrayiscapableof broadcastingERPs > 1GW.TheavailableHFfrequencyrangeis2.8to10MHz. HAARPaccommodatesanumberofmodernobservationalinstruments,suchasradars, magnetometers,andopticaldetectors. TheHAARPHFtransmitteriscapableofbroadcastingHFwaveswithvarious wavepolarizationse.g.,circular,linear,ellipticalandusingvariousmodulationformats 18

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e.g.,AM,FM,PM.Anumberofmodulationwaveformsareavailable,suchassquarewave,sinusoidal,triangular,saw-tooth,andpulsemodulation.Themainlobeofthe transmissionmaybedirectedupto30 offzenithatanyazimuthalangle,andthe directionofthebeammaybechangedanywherewithin15 ofagivencenterpointin 5secintervals.ItisalsopossibletodividetheHFarrayintotwosub-arraysthatmay beusedtoindependentlybroadcastatdifferentfrequenciessimultaneously. Fortheexperimentspresentedinthiswork,HAARPbroadcasta3.2MHzXmodepolarizedsignalthatwasamplitudemodulatedusingasquare-wavemodulation waveform. 1.4.2ELF/VLFReceivers DuringexperimentalresearchcampaignsatHAARP,ELF/VLFwaveobservations areperformedatground-basedreceiverslocatedatSinonaCreekinChistochina, Alaska 33kmfromHAARPandatMilepost71oftheTokCutoff 96kmfrom HAARPasshowninFigure1-5.AftertherecentcampaigninJuly2010,receiversare locatedatSinonaCreekandatSportsmanParadiseLodgea.k.a.,Paradise, 100km fromHAARP. Eachreceiversystemrecordssignalsfromtwoorthogonal,triangularloopantennas orientedinNorth-SouthNSandEast-WestEWdirectionstodetectthehorizontal magneticeldatgroundlevelasisshowninFigure1-6.Theantennaoutputsare connectedtoaweather-proofedpreamplierbox.Usinga200-ftcable,the detectedsignalsarefedtoalinereceiveranddigitizedandstoredonacomputerat 100kHzsamplingfrequencywith16bitresolution.Thefrequencysensitivityofthe systemisbetween500and49kHz. 19

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Figure1-1.Exampleelectrondensityproleasafunctionofaltitude.Adaptedfrom Davies,K.1990.IonosphericRadio,PeterPeregrinusLtd.,London,UK. Table1-1.RadiospectrumadaptedfromDavies,K.1990.IonosphericRadio,Peter PeregrinusLtd.,London,UK.Note:thefrequencyrangesspeciedbelow varyslightlytheliterature. NameFrequencyRangePrimaryPropagationModes ExtremelyLowFrequencyELF<3kHzEarth-ionospherewaveguide, Penetratesseawater VeryLowFrequencyVLF330kHzEarth-ionospherewaveguide, Groundwave LowFrequencyLF30300kHzWaveguide,Groundwave MediumFrequencyMF3003000kHzE-regionreectionnight, Groundwave HighFrequencyHF330MHzReectionfromEandFregions VeryHighFrequencyVHF30300MHzLineofsight,Scatterfromionosphere UltraHighFrequencyUHF3003000MHzLineofsightaffectedbyionosphericirregularities SuperHighFrequencySHF330GHzLineofsighttropospheric, affectedbyionosphericirregularities 20

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Figure1-2.ElectroncollisionfrequencyasafunctionofaltitudeadaptedfromBudden, K.G.1985ThepropagationofradiowavesPage12,Figure1-2,Cambridge UniversityPress,Cambridge,UK. Figure1-3.AcartoondiagramofELF/VLFwavegenerationatHAARP. 21

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Figure1-4.PictureoftheHAARPantennaarraylocatedinGakona,Alaska Source:http://www.haarp.alaska.edu/haarp/images/ovhead.jpg Figure1-5.GeographicmapshowingthelocationoftheELF/VLFreceiversitesusedin thisworkinrelationtotheHAARPfacility.SCreferstoSinonaCreek;MP71 referstoMilepost71;andPDreferstoParadise. 22

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Figure1-6.PictureoftheELF/VLFantennadeployedatSportsmanParadiseLodge, Alaskaa.k.a.,Paradise.A1000-ftcable,connectingthepre-amplierand linereceiver,whichislocatednexttothedataacquisitionsysteminanearby cabin. 23

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CHAPTER2 EXPERIMENTALMETHOD:TIME-OFARRIVALTOATECHNIQUE ThischapterdescribestheHFtransmissionschemesusedforTOAanalysis,togetherwithmathematicalderivationsoftheTOAtechnique.Furthermore,theTOA's timingaccuracyandresolutionarediscussedtogetherwithit'sphysicalandmathematicallimitations. 2.1TOATransmissionDescription TheHAARPHFtransmitterisusedtomodulatetheauroralelectrojetcurrentsusing square-waveamplitudemodulationwithlinearmodulationfrequencyramps.Forthe typicalexperiment,theHFcarrierfrequencyis3.2MHzwithX-modepolarization, whilethemodulationfrequencyrangeslinearlyfrom1kHzto5kHzover4seconds. TheHFbeamisorientedvertically.Overthecourseofseveralexperiments,however, theseparametersweremodiedindifferentcombinationstoinvestigatetheireffecton theTOAresults.TheprimarytransmissionparameterrelevanttoTOAanalysisisthe frequency-timecharacteristicoftheimposedmodulationwaveform. 2.2Time-of-ArrivalMethod ThegoaloftheTOAmethodistoestimatetheamplitudeandphaseofELF/VLF wavesarrivingatthereceiverasafunctionoftimeinsuchawayastorevealcharacteristicsoftheELF/VLFwavesourceregion.As Payneetal. [2007]demonstrated,thisis notpossibleusingasingle-tonemodulationfrequency.Instead,weutilizeafrequencytimerampmodulationformatasisdescribedintheprevioussection.Thistypeofsignal isbroadlyknownasFrequencyModulatedContinuousWaveFMCWinradarapplications[e.g., Barrick ,1973; Schusteretal. ,2006]andiscommonlyreferredtoaschirp modulation. Thetime-dependenceofthemodulationfrequencyprovidesameanstodifferentiate betweensignalsarrivingatdifferenttimes:theimpulseresponseofthesystemmaybe 24

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directlycalculatedfromtheobservations,providingatime-domainestimateofthemultipathpropagationdelaysandothersignalproperties.Itshouldbenotedatthispoint thattheELF/VLFwavegenerationprocessisinherentlynonlinear,whereastheTOA analysismethodpresentedislinear.Forinstance,ELF/VLFharmonicsatmodulation frequenciesthatarenottransmittedareregularlyobservedinELF/VLFrecordings.The implementationoftheTOAanalysisrstseparatesthereceivedELF/VLFharmonics andconsidersthemindividually.Additionally,becauseELF/VLFwavegenerationis nonlinearwithHFpowerandsignicantlyvarieswithHFfrequencyandpolarization, itisexpectedthatthecalculatedimpulseresponseappliesonlyforagivenHFpower, frequency,andpolarization.Lastly,becausedifferentmodulationwaveformsproduce differentharmoniccontentwhendrivingtheionosphericconductivitymodulation,we donotexpectthecalculatedimpulsetoapplytoallmodulationwaveforms.Instead, theintentistointerpretagivenTOAimpulseresponsetoyieldinformationaboutthe ELF/VLFsourceregionforagivensetoftransmissionparameters. Webeginbyexpressingthetime-averagedHFPoyntinguxofthetransmission, whichhasasquare-waveenvelope,asthesumofharmoniccomponents: h P t i = X n h P n t i = X n A n cos 2 n f 0 t + f 2 t 2 + 0 n where h P n t i representsthetime-averagedPoyntinguxofthe n th harmonic, f 0 isthe initialfrequencyoftheramp,and f istheslopeofthefrequency-timeramp. A n and 0 n aretheamplitudeandphaseofthe n th harmonic,bothofwhichareassumedtobe constantwithfrequencyinthiswork. Foragivenharmonic,thereceivedsignalmaybeexpressed: r n t = h P n t i g n t p t = h P n t i h n t where g n t istheeffectiveimpulseresponseconvertingHFpowertoionospheric currentmodulationforthe n th harmonic, p t istheimpulseresponsecharacterizing 25

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ELF/VLFwavepropagationtothereceiver,and denotesconvolution.TOAanalysis nds h n t ,theeffectiveimpulseresponsecombiningtheeffectsofcurrentgeneration andwavepropagationforagivenharmonic. ThetotalreceivedELF/VLFsignal, R t ,maythusbeexpressed: R t = X n A n cos 2 n f 0 t + f 2 t 2 + 0 n h n t u t = T )]TJ/F24 11.9552 Tf 11.955 0 Td [(1 = 2 X F s t where T isthedurationofthefrequency-timeramp, F s isthesamplefrequencyofthe dataacquisitionsystem,and u and X aredened: u t = 8 > < > : 1 j t j < 1 2 0 j t j > 1 2 X t = 1 X n = t )]TJ/F41 11.9552 Tf 11.955 0 Td [(n Theprocessingofthe n th harmonicbeginsbymixing-downandlteringthereceived signal.Themixingkernelforthe n th harmonicmaybeexpressed: m n t = e )]TJ/F42 7.9701 Tf 6.586 0 Td [(j 2 n f 0 t + f 2 t 2 u t = T )]TJ/F24 11.9552 Tf 11.955 0 Td [(1 = 2 The100-Hzbandwidthlow-passlter, b t ,isimplementedusinga2000-tap, 8 th -order Kaiserwindow.Afterapplyingthelowpasslter,thebase-bandsignalismixed-uptoits originalfrequencyrangeusingthecomplexconjugateof m n t ,andtherealcomponent oftheresultingcomplex-valuedsignalrepresentstheisolated n th harmonic. Theisolated n th harmonicofthefrequency-timeramp, y n t ,maythenbedescribed: y n t =
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x n t =cos 2 n f 0 t + f 2 t 2 u t = T )]TJ/F24 11.9552 Tf 11.956 0 Td [(1 = 2 X F s t h n t = F )]TJ/F25 7.9701 Tf 6.587 0 Td [(1 F y n t F x n t u f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 nT f )]TJ/F24 11.9552 Tf 13.15 8.087 Td [(1 2 where F denotestheFouriertransformand F )]TJ/F25 7.9701 Tf 6.586 0 Td [(1 denotestheinverseFouriertransform. Notethat fT representsthefullbandwidthtraversedbythefrequency-timeramps. Then, h n t reducesto: h n t = A n t e j n t e j 2 f c t sinc nT ft nT f where A n t and n t representthebandwidth-averagedamplitudeandphaseofthe receivedsignalasafunctionoftime,and f c isthecenterfrequencyofthefrequency-time ramp.Here, h n t iscomplex-valuedinordertodirectlyassessthephase n t .This resultisachievedbyeliminatingthenegativefrequencycomponentsinEquation2 9[ Gabor ,1946]. Anexample h n t isshowninFigure2-1.AsseeninEquation2,theTOA resultconsistsofthecomplex-weightedsumofsincfunctions.Eachsignalarriving atthereceiveratdifferenttimesisconvolvedwithasincfunctionandformstheTOA result.Figure2-1alsocomparesTOAresultsforcalculationsperformedusingonly positivefrequencycomponentsandthoseperformedusingbothpositiveandnegativefrequencycomponents.Whilethecombinedfrequencyformproducesanarrower mainlobe,itdoesnotdirectlyprovidephasinginformationitisentirelyreal-valued. Additionally,thepositive-frequencycomplex-valued h n t representsthesameinformationasthecombined-frequencyreal-valued h n t ,duetoconjugateHermitian symmetry[ Boashash ,2003].Thecomplex-valuedformof h n t isusedthroughoutthis work. 27

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AscanbeseenintheEquation2,weapplyarectangularwindowinthefrequencydomainandtransformittothesincfunctioninthetimedomain.Inthefuture,this windowmaybereplacedbyadifferentwindowsuchasaHammingorKaiserwindow, whosesidelobesaresuppressedtoagreaterextentthanthoseoftherectangularwindow.Inthisthesis,therectangularwindowisusedasamatterofsimplicity.Thewidth ofthesincfunctionisdeterminedbythebandwidthofthefrequencyramps, fT ,andit dictatestheTOApropertiessuchasthetimingaccuracyandresolution. 2.3AlternativeTime-of-ArrivalDerivation Thefrequency-timerampemployedbyourTOAmethodproducesinteresting andcomplicatedintegralsintheFourierdomain.Thusfar,wehaveomittedproviding theactualFourierTransformsofourtransmission,asthesetransformsmayeasilybe calculatednumerically.Forcompleteness,weprovidethefollowingderivationinthe continuousratherthanthediscretetimedomainandshowthattheresultisequivalentto Equation2. LetusstartwithEquation2andassume h n t hassometimedelay, ,andan amplitudeandphase, A n e j n y n t = A n cos 2 n f 0 t )]TJ/F27 11.9552 Tf 11.955 0 Td [( + f 2 t )]TJ/F27 11.9552 Tf 11.955 0 Td [( 2 + n u t )]TJ/F27 11.9552 Tf 11.955 0 Td [( T )]TJ/F24 11.9552 Tf 13.151 8.088 Td [(1 2 NowwetakeaFouriertransformwithrespecttotime, t : Y n f = F [ y n t ] = Z + T y n t e )]TJ/F42 7.9701 Tf 6.587 0 Td [(j 2 ft dt 28

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UsingEuler'sformula, Y n f = A n 2 Z + T e j f n ft 2 +2 n f 0 )]TJ/F25 7.9701 Tf 6.587 0 Td [( f t )]TJ/F25 7.9701 Tf 6.586 0 Td [(2 nf 0 + n f 2 + n g e )]TJ/F42 7.9701 Tf 6.587 0 Td [(j 2 ft dt + A n 2 Z + T e )]TJ/F42 7.9701 Tf 6.586 0 Td [(j f n ft 2 +2 n f 0 )]TJ/F25 7.9701 Tf 6.586 0 Td [( f t )]TJ/F25 7.9701 Tf 6.587 0 Td [(2 nf 0 + n f 2 + n g e )]TJ/F42 7.9701 Tf 6.586 0 Td [(j 2 ft dt Weknowthat, Z e )]TJ/F25 7.9701 Tf 6.587 0 Td [( at 2 +2 bt + c dt = 1 2 r a e b 2 )]TJ/F43 5.9776 Tf 5.756 0 Td [(ac a erf p at + b p a + C where C isanarbitraryconstantand erf istheerrorfunction,denedas, erf t = 2 p Z t 0 e )]TJ/F42 7.9701 Tf 6.587 0 Td [(u 2 du From2, Y n f = A n 2 Z + T e )]TJ/F25 7.9701 Tf 6.586 0 Td [( a 1 t 2 +2 b 1 t + c 1 + e )]TJ/F25 7.9701 Tf 6.586 0 Td [( a 2 t 2 +2 b 2 t + c 2 dt where a 1 = )]TJ/F41 11.9552 Tf 9.299 0 Td [(j n fa 2 = )]TJ/F41 11.9552 Tf 9.299 0 Td [(jn f b 1 = )]TJ/F41 11.9552 Tf 9.299 0 Td [(j nf 0 )]TJ/F41 11.9552 Tf 11.955 0 Td [(n f )]TJ/F41 11.9552 Tf 11.955 0 Td [(f b 2 = j nf 0 )]TJ/F41 11.9552 Tf 11.955 0 Td [(n f + f c 1 = )]TJ/F41 11.9552 Tf 9.299 0 Td [(j f n f 2 )]TJ/F24 11.9552 Tf 11.956 0 Td [(2 nf 0 + n g c 2 = j f n f 2 )]TJ/F24 11.9552 Tf 11.955 0 Td [(2 nf 0 + n g 29

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Hence, Y n f = A n 2 1 2 r 1 )]TJ/F41 11.9552 Tf 9.298 0 Td [(jn f e j f )]TJ/F25 7.9701 Tf 6.586 0 Td [(2 f )]TJ/F28 7.9701 Tf 6.587 0 Td [( f )]TJ/F42 7.9701 Tf 6.587 0 Td [(nf 0 2 = n f + n g erf j f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 )]TJ/F41 11.9552 Tf 11.955 0 Td [(nT f p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f )]TJ/F41 11.9552 Tf 11.955 0 Td [(erf j f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f + A n 2 1 2 r 1 )]TJ/F41 11.9552 Tf 9.298 0 Td [(jn f e )]TJ/F42 7.9701 Tf 6.586 0 Td [(j f )]TJ/F25 7.9701 Tf 6.587 0 Td [(2 f )]TJ/F28 7.9701 Tf 6.586 0 Td [( f + nf 0 2 = n f + n g erf j f + nf 0 + nT f p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f )]TJ/F41 11.9552 Tf 11.955 0 Td [(erf j f + nf 0 p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f Similarlyto Y n f ,wetakeaFouriertransformof x n t fromEquation2. X n f becomes X n f = 1 2 1 2 r 1 )]TJ/F41 11.9552 Tf 9.299 0 Td [(jn f e j f )]TJ/F28 7.9701 Tf 6.586 0 Td [( f )]TJ/F42 7.9701 Tf 6.586 0 Td [(nf 0 2 = n f g erf j f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 )]TJ/F41 11.9552 Tf 11.956 0 Td [(nT f p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f )]TJ/F41 11.9552 Tf 11.955 0 Td [(erf j f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 p )]TJ/F41 11.9552 Tf 9.299 0 Td [(j n f + 1 2 1 2 r 1 )]TJ/F41 11.9552 Tf 9.299 0 Td [(jn f e )]TJ/F42 7.9701 Tf 6.586 0 Td [(j f )]TJ/F28 7.9701 Tf 6.587 0 Td [( f + nf 0 2 = n f g erf j f + nf 0 + nT f p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f )]TJ/F41 11.9552 Tf 11.955 0 Td [(erf j n f + nf 0 p )]TJ/F41 11.9552 Tf 9.298 0 Td [(j n f Therefore, H n f = Y n f X n f = A n e j f)]TJ/F25 7.9701 Tf 10.821 0 Td [(2 f + n g u f )]TJ/F41 11.9552 Tf 11.955 0 Td [(nf 0 nT f )]TJ/F24 11.9552 Tf 13.15 8.087 Td [(1 2 Thentheimpulseresponse, h n t ,is h n t = F )]TJ/F25 7.9701 Tf 6.587 0 Td [(1 [ H n f ] = Z 1 H n f e j 2 ft df = Z nf 0 + nT f nf 0 A n e j )]TJ/F25 7.9701 Tf 6.586 0 Td [(2 f + n e j 2 ft df = A n e j n Z nf 0 + nT f nf 0 e j 2 f t )]TJ/F28 7.9701 Tf 6.586 0 Td [( df = A n e j n e j 2 f c t )]TJ/F28 7.9701 Tf 6.586 0 Td [( sinc f nT f t )]TJ/F27 11.9552 Tf 11.955 0 Td [( g nT f 30

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where f c isacenterfrequencyofthefrequencyramp. Sowend h n t by, h n t = Z 1 A n e j n e j 2 f c t )]TJ/F28 7.9701 Tf 6.586 0 Td [( sinc f nT f t )]TJ/F27 11.9552 Tf 11.955 0 Td [( g nT fd Recognizingtheconvolutionintegral,wemayexpress h n t as: h n t = A n t e j n t e j 2 f c t sinc f nT ft g nT f whichisequivalenttoEquation2. 2.4TOAProperties 2.4.1TimingAccuracy OnemainconcernregardingtheTOAmethodisthetimingaccuracyofthedetected peakamplitude.Theeffectiveimpulseresponseisasampledversionofthecontinuous impulseresponseconvolvedwithasincfunctionwhosewidthisdeterminedbythe bandwidthofthetransmission.Whilethedetectedpeakamplitudemaybeinterpolated intimeusingstandardFouriertechniques,thedetectedpeakamplitudemaynotexactly coincidewiththetimingoftheactualpeakamplitudeincidentuponthereceiver,dueto convolutionwiththesincfunction.Toassessthisaccuracy,wecalculatetheCramr-Rao LowerBoundCRLB[ Schusteretal. ,2006,andreferencetherein]usingtheoutputofa modulatedHFheatingmodelthatpredictsthetimedistributionofamplitudeandphase generatedbymodulatedHFheatingofthelowerionosphere.WenowdescribetheHF heatingmodelandhowitisusedtocalculatetheCRLB. TheHFheatingmodelemployedwasdevelopedby Moore [2007],anditrequiresas inputtheHFfrequency,modulationfrequency,andHFpower.Electrontemperatureand densityproles,togetherwithmolecularnitrogenandmolecularoxygendensityproles, arealsoprovidedasinput.Weapplytheelectrondensityprolesusedinprevious ELF/VLFstudies[e.g., Lev-Tovetal. ,1995; Moore ,2007]andtherestoftheionospheric parametersareavailableinMSISE-90ModelprovidedbytheGoddardSpaceFlight 31

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CentersSpacePhysicsDataFacilityonthewebsiteathttp://modelweb.gsfc.nasa.gov/. Usingthisinput,themodelcomputesthemodulatedconductivitiesPerdersen,Halland Parallelateach1kmgridin3-Drectangularcoordinates.Lastly,themodelassumesa constantElectrojetelectriceldparalleltogroundthroughoutthe D -regionionosphere topredictthemagneticeldincidentuponagivenreceiverlocationasafunctionof timeassumingfree-spacepropagation[ Payneetal. ,2007].Forexample,themodel maybeusedtopredicttheamplitudeandphaseofthemagneticeldincidentupona receiverasafunctionoftimeusingamodulationfrequencyof2.5kHz,anHFpowerof 85.7dBW,andanHFfrequencyof3.2MHzwithX-modepolarization.Thepropagation modelemployedneglectsEarth-ionospherewaveguideeffects,however.Forthe receiverlocationsusedinthisworkeachlessthan 100kmawayfromtheHAARP transmitter,thisassumptionisreasonableashasbeendemonstratedby Payneetal. [2007],whichshowedexcellentagreementbetweensimpleray-tracingandfull-wave modelingresultsatthesedistances.ApplyingtheTOAtechniquetothepredicted magneticeldtimeseries,weareabletoassessthetimingaccuracyofourpeakTOA measurement.Eachtimebinhasthreeunknownparameters:amplitude,phase,and timedelay.WecreatetheFisherinformationmatrix[ Schusteretal. ,2006,andreference therein]whichmaybeusedtodirectlycomputetheCRLBfordifferentwhiteGaussian Noiselevels.Figure2-2showstheCRLBofthestandarddeviationofthetimedelay forthepeakamplitudeinthemodelasafunctionofthesignal-to-noiseratioSNR. Typically,theSNRofourobservationsis5dBorhigher,andFigure2-2indicatesa best-caseaccuracyof 1 secat5dBSNR.Whilemodelpredictionsusingother ionosphericprolesmayyieldslightlydifferentresultsthanpresentedhere,weexpect the 1secaccuracyguretobegenerallyrepresentativeoftheaccuracyofthe TOAmeasurement.AlthoughELF/VLFdataisalsosensitivetoimpulsivenoisefrom lightning,forexampleandtopowerlineradiationintheELF/VLFrange,theCRLBis stillareasonablebenchmarkfortimingaccuracy,sincetheintegrationperiodislarge 32

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typically > 100seconds.Inadditiontotheerrorfactorsdiscussedabove,thereisa 27.5 2.5 sectransmissiondelayduetotheHAARPtransmissionand 30 n secGPS accuracy,whichhavebeenaccountedforinouranalysis. ToexperimentallyevaluatetheSNRofthemeasurement,weperformthesame TOAanalysisonthedatasetstartingwithanoffsetof2seconds.Becausethe frequency-timerampis4secondsinduration,wedonotexpectHAARP-generated ELF/VLFwavestocontaminatethismeasurement,yieldinganeffectivemeasurementof thenoiseoor.Fromamongthemanynoise-oormeasurementsthattheTOAanalysis produces,wepickthehighestnoisemeasurementasthenoiseoor.Asanexample, Figure3-1exhibitsanapproximateSNRof 12dBmarkedwithahorizontallinefor thepeakamplitudeatSinonaCreekandanapproximateSNRof 25dBmarkedwith ahorizontallineforthepeakamplitudeatMilepost71,bothevaluatedusing2.5minutesofdata.Thenullsinthenoiselinemaybecausedbythehumnoiseinterference. WenotethattheSNRofthemeasurementincreasessignicantlybyrepeatingthe frequency-timerampsforafewminutes. 2.4.2TimingResolution Althoughthetimingaccuracyisnotsignicantlylimiting,thetimeresolutionofthe TOAmethodismoresignicant.Timingresolutionmaybeanalyzedusingstandard Fouriertechniques,anditislimitedbythebandwidthofthereceivedsignal.Forexample,asignalbandwidthof4kHzprovidesatimeresolutionof250 sec,sinceonly positivefrequenciesareusedintheanalysis.Asaresult,thisTOAmethodcannotfully resolvesignalsarrivingwithin250 secofeachother.Nonlineardeconvolutiontechniquesareavailableandhavebeenemployedtosurpassthislimit,however,aswillbe discussedinSection3.1. 2.4.3PreviousTOAAnalysis TheTOAmethodpresentedhereinissimilarinmanyregardstopreviouswork analyzingtheeffectivesourceheightofELF/VLFwavesgeneratedbymodulatedHF 33

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heating. Rietveldetal. [1989]demonstratedamethodtodeterminethegroupdelay oftheELF/VLFsignalreceivedonthegroundasafunctionofmodulationfrequency. MeasurementsofELF/VLFsignalsgeneratedusingalinearfrequency-timemodulation formatwereusedtocalculatethechangeinreceivedphaseperchangeinfrequency, whichisdirectlyrelatedtotheoverallgroupdelay.AssumingtheELF/VLFsourceis locateddirectlyabovetheHFtransmitter, Rietveldetal. [1989]calculatedthe`apparent sourceheight'oftheELF/VLFsourceregionasafunctionofmodulationfrequency, althoughtheapplicationofthismethodtoexperimentaldataproducedsourceregion altitudesvaryingrapidlyasafunctionoffrequencybetween60and130kmasisshown inFigure2-3. Riddolls [2003]appliedasimilarTOAmethodtoELF/VLFharmonics generatedduringtheHFheatingprocess,buttheunderlyingmethodremainedthesame asthatdescribedby Rietveldetal. [1989]. ThenewTOAmethoddescribedinthisworkutilizeslinearfrequency-timemodulationramps,similarto Rietveldetal. [1989],butdoesnotdirectlyrelyuponacalculation ofthemeasuredphasedifferentialwithfrequency.Instead,thepresentedmethod focusesonthecalculationofaneffectiveimpulseresponseofthesystem.Thetime resolutionattainedissufcienttodistinguishbetweenline-of-sightELF/VLFsignalsand ionospherically-reectedELF/VLFsignalsandourresultsindicatethationosphericallyreectedpropagationpathslikelyaffectthecalculationspresentedbyboth Rietveldetal. [1989]and Riddolls [2003]. 34

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Figure2-1.ATOAobservations:TheamplitudesofthereceivedELF/VLFsignalasa functionoftimeatMilepost71NSantenna.BConvolvedsincfunctions: TheamplitudesofsincfunctionsbeingconvolvedshowninEquation2. Eachbluelineisaresultofusingonlypositivefrequencycomponentin Equation2andeachredlineisaresultofusingbothpositiveand negativefrequencycomponents. Figure2-2.Cramr-RaoLowerBoundCRLBofthestandarddeviationofthetime delayforthepeakamplitudecomputedbytheHFheatingmodel. 35

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Figure2-3.ExperimentalObservations.AtheamplitudesofthereceivedELF/VLF waves.B`apparentsourceheight'atTromsonNovember8,1984 presentedbyM.T.Rietveldetal. TOnthefrequencydependenceofELF/VLF wavesproducedbymodulatedionosphericheating T,RadioSci.,vol.24,no.3, pp.270-278,1989 36

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CHAPTER3 TOAOBSERVATIONANDANALYSIS Inthischapter,weprovidetheTOAanalysisofELF/VLFsignalobservationsfor variousHFheatingschemes.WedemonstratethattheELF/VLFTOAtechniqueisa validexperimentalmeasurementoftheamplitudeandphaseofthereceivedELF/VLF signalsasafunctionoftime.Section3.1comparesexperimentalTOAobservationswith modelpredictionsandSection3.2experimentallydemonstratestheTOAsensitivityto differentHFheatingparameters. 3.1ComparisonwithModel ExampleTOAresultsareprovidedinFigure3-1fordataacquiredon29July 2008.Duringthisexperiment,a7x7elementsub-arrayoftheHAARPfacilityradiated at3.2MHzX-modemodulatedwithfrequency-timerampsfrom1to5kHzovera periodof4seconds.Thesefrequency-timerampswererepeatedsequentiallyfor150 seconds.Figure3-1showstheTOAobservationsatSinonaCreekSCandMilepost71 MP71intheNorth-SouthNSantennatogetherwiththeapproximatednoiseoor, demonstratingthatthetransmissionsequencemaybeusedtoproduceobservations withsignicantSNR 12dBatSCand 25dBatMP71.Figure3-2compares thesesameobservationswithmodelpredictions.Thesolidbluelinesareexperimental observations;thesolidredtracesarethepredictedamplitudesasafunctionoftime withoutprocessing,butincludingionosphericreectionwiththereectionheightsetat 65kmandtheeffectivereectioncoefcientsetat0.3 150 ;andthedashedredlines representthepredictedamplitudesasafunctionoftimefollowingTOAprocessing.The solidgreenspikesinFigure3-2arederivedfromobservationsandcalculatedusinga nonlineardeconvolutionmethodknownastheCLEANmethod[ SegalovitzandFrieden 1978],andthedashedgreentracesaretheresultsofTOAprocessingontheseCLEAN methodextractions.TheCLEANmethoditerativelysubtractsaportionofthelargest amplitudesignalfromtheTOAobservationsuntilthenoiseoorisreached.TheCLEAN 37

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methodthusdecomposestheobservedTOAintoaseriesofcomplex-valued functions. Weinterpretearlierarrivaltimese.g., 573 secondsatSCand 673 secondsat MP71astheresultofline-of-sight,ordirect-path,propagation,whereasweinterpret laterarrivaltimese.g., 900 secondsatSCand 1.04millisecondsatMP71asthe resultofionospherically-reected-pathpropagation. Afterde-convolvingusingtheCLEANmethod,severaloutliersmayexistthatdefy physicalinterpretation.Forinstance,atintermediatestages,theprocessofsubtracting thelargestamplitudesincfunctionmaycreatefalsepeaksattimesearlierthanthe speed-of-lightpropagationtimefromthetransmittertothereceiver.Weremovethese timesfromtheCLEANoutputanddeterminetheamplitudeandphaseatpermissiblearrivaltimesusingaregularizedleast-squaresttothecomplex-valuedimpulseresponse. Forexample,atMilepost71inFigure3-2,theCLEANmethodextractsseveralpulses fromtheobservedTOA.Pulsesarrivingearlierthan320 seccorrespondingtothe 96kmline-of-sightpropagationpathfromHAARPtothereceiverareremovedfromthe series.Theamplitudeandphaseoftheremainingpulsespulsesarethendetermined usingaregularizedleast-squaresttotheimpulseresponsesolidbluetrace. Figure3-2showsthatthemodeleddirect-pathTOAreasonablymatchesthe observedTOAatbothSCandMP71.TheTOAoftheionospherically-reectedcomponentsatMP71alsocloselymatchthetimingofthemodelresults,althoughatSC, themodelandobserveddataarenotalignedintime.Thisispossiblyduetothelow SNRoftheionospherically-reectedcomponentinSCdataseeFigure3-1.Itmay alsobepossiblethattheionospherically-reectedcomponentsobservedatSCand MP71havereectionheightsand/orreectioncoefcientsduetothedifferentangles ofincidenceattheionosphericboundary.Thisexample,andparticularlytheMP71observation,demonstratestheabilityoftheTOAtechniquetodiscernbetweendirect-path andionospherically-reectedpathcomponentsoftheELF/VLFwavesobservedatthe receiver.Italsodemonstratestheabilitytoassignamplitudeandphase,notshown 38

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valuesasafunctionoftime.BothexperimentalobservationsandtheHFheatingmodel indicatethatthetimedifferencebetweenthedirectandionospherically-reectedsignal pathsisgreaterthan 400 sec,implyingabandwidthof 2.5kHzissuitabletoresolve thetwopeaks. 3.2BeamDirection DuringtheSummerStudentResearchCampaignSSRCatHAARPonAugust 6thand7th,2009,theUniversityofFloridaconductedELF/VLFwavegeneration experimentstoevaluatetheELF/VLFTOAasafunctionofHFbeamdirection.Unlike theTOAexperimentsdiscussedabove,themodulationformatconsistedoffrequencytimerampsrangingbetween1.5and3.5kHzoveraperiodof4secondsi.e.,asmaller bandwidth.TheHFtransmitteraimedinthreedirections:5 off-zenithtowardSinona Creek,vertical,and5 off-zenithawayfromSinonaCreekazimuth56.8 .A5 shift inthelocationoftheELF/VLFsourceregioncorrespondstoa 9kmlateraloffset at100kmaltitude,andonlya2kmdifferenceintotalrangingfromHAARPtothe ionospheretothereceiver.Thisexperimentwasdesignedtoinvestigatewhetherthe TOAmethodissensitivetothisrelativelysmallspatialshiftintheELF/VLFsource location. ThetoppanelofFigure3-3showstheTOAresultsforindividualantennasat SinonaCreekandMilepost71.AtMilepost71,thearrivaltimesforeachoftheHFbeam directionsareintheorderexpected.AtSinonaCreek,however,ontheNSantenna, ELF/VLFwavesgeneratedusingtheverticalHFbeamarriverst,followedbythose generatedusingtheAwaybeam,followedbythosegeneratedusingtheToward beam:acounter-intuitiveresult.Thisdiscrepancyresultsfromtheinterferencebetween TOAresultsfortheHallandPedersencurrents,andthusonthedirectionoftheauroral electrojet.Forinstance,thebottompanelofFigure3-3showsthe magnitude ofthe TOAanalysisandyieldstheintuitiveresultatbothSinonaCreekandMilepost71:the dominantTOAisintheorderoftheshortestpropagationtimetothelongest.Inaddition 39

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totheorderingbeingcorrect,theTOAdifferencesbetweenthetracesareclearly evident,indicatingthattheTOAmethodisabletodetectthepeakarrivaltimewithhigh rangingaccuracy < 2km. Figure3-1.TOAobservations:TheamplitudesandphaseofthereceivedELF/VLF signalasafunctionoftime.AandCSinonaCreekNSantenna.BandD Milepost71NSantenna.Thedashedlineineachcaseshowsthe approximatenoiselevelforeachsite.Thehorizontalwidedashedlineisour noisereferenceleveldeterminedthepeakapproximatednoiselevel.The referencenoiselevelisusedtoestimateSNRofthedetectedELF/VLF signals. 40

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Figure3-2.AComparisonbetweenmodelpredictionandobservations:ASinona Creek.BMilepost71.Onthisplot,weusetheCLEANmethodwiththegain loop0.4. 41

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Figure3-3.TOAvsHFbeamdirection:TOAusingasingleantenna.ASinonaCreek. BMilepost71.TOAoftheELF/VLFsignalmagnitude.CSinonaCreek.D Milepost71. 42

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CHAPTER4 GEOPHYSICALINTERPRETATION Thusfar,wehavedescribedthedetailsofTOAsignalprocessing,andwehave providedproof-of-conceptexperimentalresultsusingsimpleexperiments.Inthischapter,weuseTOAprocessingtoprovidegeophysicalinterpretationsofmorecomplicated experiments. 4.1Dual-BeamExperiment TheDual-BeamHFheatingexperimentutilizesanovelHFtransmissionschemeat HAARPtogetherwithTOAanalysistoestimatethelocationofthedominantELF/VLF sourceregionin2-D.InadditiontotheTOA,thisexperimentestimatestheoff-zenith angleofthedominantsourcelocation.TheDual-Beamheatingexperimenttransmits twodifferentHFsignalstowardtheionosphereatthesametime.AsisdepictedinFigure4-1,onesideoftheHAARPtransmitterarrayheatstheionosphereusingAmplitude ModulationAMwhiletheothersideheatsusingaContinuousWaveCWbeamwith varyingoff-zenithangles. MooreandAgrawal [2011]provedthatCWheatinginaddition tomodulatedheatingreducedtheELF/VLFamplitudereceivedontheground.TheCW beameffectivelyprobesthelargermodulatedregiontodeterminetheoff-zenithheating anglethatreducesthereceivedELF/VLFamplitudethemost,identifyingthedominant ELF/VLFsourceregion. 4.1.1ExperimentDescription TheDual-BeamexperimentwasperformedonJuly29th,2008followedbythe TOAexperimentintroducedinSection3.1inthepreviouschapter.TheDual-Beam experimentsplitthe12x15transmitterarrayintotwosub-arrays.One7x7sub-array modulatestheelectrojetcurrentsat2485Hzusingsquare-waveAmplitudeModulation AMat3.2MHzX-modewhiletheother8x8sub-arraysimultaneouslyheatssmaller portionsofthemodulatedregionusinga9.5MHzContinuousWaveCWbeamXmode.Thezenithangleofthe9.5MHzCWbeamissteppedbetween0 and15 .For 43

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30seconds,astheCWbeamturnsonandoffeverytwoseconds,theoff-zenithangles changediscretelyfortwosecondintervalsinthefollowingvalues:0 ,2 ,4 ,6 ,9 ,11 13 and15 .TheazimuthsEastofNorthoftheCWbeamweredirectedtowardeach receiversite,48.84 forSinonaCreek,and56.76 forMilepost71. 4.1.2ExperimentalResults Figure4-2showsthevariationsinthenormalizedELF/VLFamplitudeasfunctionoftheCWheatingbeamangle.Theoff-zenithanglethatminimizesthenormalizedamplitudesaredifferentatSinonaCreekandMilepost71.Weapproximatethe amplitude-minimizingzenithangleas2.5 -5.0 forSinonaCreekandas9.5 -12.0 for Milepost71asisshownasgrayswathsinFigure4-2. UsingthesimplegeometryshowinFigure4-1,theamplitude-minimizingzenith anglefromtheDual-BeamHeatingexperiment,andthetotalpropagationdelaytime fromtheTOAexperiment,wemaydeterminetheELF/VLFgenerationsourceregion. Theheight h andradialdistance r oftheELF/VLFsourcelocationisexpressedby h = R 2 )]TJ/F41 11.9552 Tf 11.955 0 Td [(D 2 cos 2 R )]TJ/F41 11.9552 Tf 11.955 0 Td [(D sin r = h tan = R 2 )]TJ/F41 11.9552 Tf 11.955 0 Td [(D 2 sin 2 R )]TJ/F41 11.9552 Tf 11.955 0 Td [(D sin where R isthetotalpropagationdistanceand isthezenithangle. D isthedistance betweenthetransmitterandreceiver. R isdeterminedassumingspeed-of-lightpropagationandusingthearrivaltimeofpeakTOAmagnitudeinFigure3-1withtheknown errorsdiscussedinSection2.4.1.TheerrorfromthezenithangleandtotalpropagationdistanceresultsindifferentrangingaccuraciesatSinonaCreekandMilepost71 showninTable4-1.TheerrorinTable4-1isanaveragesidelengthoftheapproximate ELF/VLFsourceregion.Additionally,theintersectionoftheapproximatedzenithangleandtheellipsedrawnbytheELF/VLFtotalpropagationdistancedetermines2-D ELF/VLFwavesourceregionasisshowninFigure4-3.ThelledareasinFigure4-3 correspondtothedominantELF/VLFsourceregionineachcase. 44

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Fromtheseexperimentalresults,wemaketwoobservations:Thedominant ELF/VLFsourceregionsarelocatedatapproximatelysamealtitude,andtheyincrease withradialdistancefromthecenterofthemodulatedHFbeamthefartherawaythe receiverisfromthetransmitter.Thedominantsourcealtitudeisinarangeofprevious observations James [1985]and Rietveldetal. [1986].Fromtheseexperimentalresults, weexpectthelateraldominantsourcelocationisafunctionofreceiversite. 4.2TOAvsVLFFrequency Intheprevioussections,weappliedTOAanalysistoestimatethedominant ELF/VLFsourcelocation.Inthissection,welimitthefrequencyrangeandanalyze thereceivedsignaldependenceonmodulationfrequency. 4.2.1ExperimentDescription On22July2010,duringthe2010PolarAeronomyandRadioSciencePARS SummerSchool,thefull12x15HFarraybroadcastat3.25MHzX-modefrequencytimemodulationrampsrangingfrom1to5kHzoveraperiodof8secondsrepeated 10times.ObservationswereperformedatSinonaCreekandatParadiseusingTOA analysis.Forthisanalysis,welimitedthebandwidthto3kHzandcalculatedtheTOA attributedtothecenterfrequencyofthebandwidthforcenterfrequenciesbetween2.5 and3.5kHz. 4.2.2ExperimentResultsandAnlaysis Figure4-4showstheTOAvariationsasafunctionofcenterfrequencyforSinona CreekandParadisetogetherwiththemodeledHallconductivitiesasafunctionofheight inthebottompanel.TheplottedtimesinthegurearecomputedbytheCLEANmethod andregularizedttingasaredescribedinSection3.1toensureavalidseparationofthe directandionospherically-reectedpathsignals.Thenwendthearrivaltimesofthe dominantdirectpathsignalwiththeidealinterpolation. TheTOAclearlydecreaseswithincreasingcenterfrequencyatbothSinonaCreek andParadise.Thisrelationshipisnotunexpected.Toillustratethiseffect,thebottom 45

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panelofFigure4-4showsthealtitudeproleofconductivitymodulationdirectlyabove theHAARPtransmitterfor1kHzand5kHzmodulation.Thevariationinthetwotraces isalmostexactlythesamebelow85kmaltitude.Above85km,1kHzmodulationis relativelystrongerthan5kHzmodulation.ThemodulationofthePedersenconductivity notshownexhibitssimilareffects.Anoverallreductioninaltitudewithincreasing modulationfrequencyresults,andthisreductioninaltitudebringsaboutashorter propagationdelaytothereceiver. 4.3TOAvsHighFrequencyHFandPower 4.3.1ExperimentDescription DuringtheBasicResearchonIonosphericCharacteristicsandEffectsBRIOCHE CampaignatHAARPinJune2010,theUniversityofFloridaconductedELF/VLF generationexperimentstoinvestigatetheTOAasafunctionofHFfrequencyandHF power.Thefrequency-timerampsinthiscaserangedfrom1to5kHzoveraperiod of4seconds.Every4secondperiod,theHFpoweralternatedbetween25%,50% and100%power,andeachperiodrepeatedfor5minutes.Every5minutes,theHF frequencyswitchedbetweeen3.2MHzX-modeand5.8MHzX-mode.Observations wereperformedatSinonaCreekandatMilepost71,buttheintroductionofcommercial powerlinesnearMilepost71sitehassignicantlyreducedthedataqualityatthatsite.In thissection,onlyobservationsfromSinonaCreekwillbediscussed. 4.3.2ExperimentResultsandAnlaysis Figure4-5showstheTOAforthemaximumpeakmagnitudeasafunctionof HFpowerat3.2MHzandat5.8MHz.ThevariationsinTOAaresmall,lessthan 10 seconds,whetherintermsofHFfrequencyorintermsofHFpower.TheexperimentalresultspresentedinFigure4-5donotdenitivelyexhibitamonotonicincrease intheTOAintermsoftheHFpower,andneitherdotheydenitivelyshowanincrease intheTOAfrom3.2MHzto5.8MHz.Nevertheless,itisclearthattheeffectsofHF frequencyandpowerarerelativelysmallcomparedtootherparameters,suchastheHF 46

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beamdirection.ItwillbenecessarytocompleteafullstatisticalanalysisofHFpower andHFfrequencyTOAobservationstodeterminewhetheraconsistentdependence maybederivedfromthisdataset. Figure4-1.CartoondiagramoftheDual-beamexperiment.AHalfofthetransmitters heatstheionosphereusingtheamplitudemodulationwhiletheotherhalf simultaneouslyheatswiththeCWbeam.BSimplegeometryfordirect propagationpath Figure4-2.Dual-beamheatingobservations:Normalizedamplitudesoftheobserved ELF/VLFsignalsasafunctionoftheoff-zenithCWheatingangle.ASinona Creek.B.Milepost71.TheazimuthoftheCWbeamwasalignedwith SinonaCreekbetween2146:30and2147:00UTandwasalignedwith Milepost71between2147:30and2148:00UTon29July2008 47

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Figure4-3.DominantELF/VLFsourceregionmap:TOAmaximummagnitudeellipse drawntogetherwithdual-beamminimizationzenithanglesforSinonaCreek redandforMilepost71bluerespectively.Thelledcoloredareas representthedominantELF/VLFregionineachcasewhilethegrayarea representstheHFheatedregion. Table4-1.ELF/VLFsourceregion ReceiverAltitudekmRadiuskmErrorkm SinonaCreek83.3-84.63.65-7.402.21 Milepost7184.3-86.214.1-18.32.82 48

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Figure4-4.ATOAasafunctionofELF/VLFfrequency:TheGreenlineistheTOAfor SinonaCreekandtheBluelineforParadise.BHallconductivitymodulation amplitudeasafunctionofheightwithdifferentVLFfrequencies:Theblue lineiswiththeVLFfrequencyof1kHzandtheredlineisof5kHz.This modelisgeneratedbyusingamediumelectrondensityprole,3.2MHzHF frequencyandfullHFpowerwith12x15arrayatHAARP. 49

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Figure4-5.TOAasafunctionofHFfrequencyandpoweratSinonaCreek.TheTOAof themaximummagnitudeisplottedasafunctionofHFpowerwithdifferent HFfrequencies. 50

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CHAPTER5 SUMMARYANDFUTUREWORK 5.1Summary ThisthesisexaminesELF/VLFwavegenerationbymodulatedHFhatingofthe lowerionosphere.AnewTOAanalysistechniquehasbeenappliedtoELF/VLFwave observations. Utilizingfrequency-timerampmodulations,wemeasuretheamplitudeandphase oftheELF/VLFwavesasafunctionoftimeatthereceiver.Thissignalschemehas beenappliedinradarapplicationsandareknowntobehighlyaccuratemeasurements[ Schusteretal. ,2006].TheELF/VLFTOAanalysissucceedsin1distinguishing adirectandionospherically-reectedpathsignalsand2estimatingthedominant ELF/VLFsourceregion,whichisshowntobedependentonthereceiverlocation andtheELF/VLFmodulationfrequency,butnotsignicantlyontheHFpowerand frequency. 5.2FutureWork 5.2.1TOAAnalysisforHFbeamsatDifferentAzimuths AsisdiscussedinSection3.2,theTOAobservationsaresensitivetotheHFbeam direction.Infutureexperiments,wemayalsotilttheHFbeamatdifferentazimuths andapplytheTOAanalysis.As Payneetal. [2007]predictsfromhisHFheatingand ELF/VLFpropagationmodel,thecurrentsourcedirectionsmaybefoundasthebeam rotatesinazimuthusingELF/VLFverticalElectricelddata.Healsomentionedthat aHAARP-collocatedreceiverwouldestimatethecurrentsourcedirectionsusingthe groundbasedmagneticelddata.HissuggestionisderivedfromthefreespacepropagationinEquation1,therefore,isolationofdirectpathsignalsfromionosphericallyreectedpathsignalsusingTOAanalysismaybehelpfultohisestimationmethod. 51

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5.2.2TOAAnalysisforDifferentHFBeamPatterns HAARPiscapableoftransmittingvariousHFbeampatterns,suchasbroad-, narrow-,anddonut-shapedpatterns[ Cohen ,2009; Leyseretal. ,2009].Asisintroduced in Cohen [2009],thebroadshapedHFbeamscanextendintodifferentdirections. DifferentHFbeampatternsresultindifferentELF/VLFwavegenerationefciencies,and itisatpresentnotwellunderstoodwhythisisthecase.TOAanalysismaybeappliedto determinehowthedominantELF/VLFsourceregiondependsontheHFbeampattern. ConsideringsaturationeffectintheELF/VLFgeneration[ Moore ,2007],thebroadHF beamsmaybemoreefcientthanthenarrowHFbeams.However,thebroadHFbeams causemoreinterferenceofthegeneratedELF/VLFsignalsduetothephasespreading inthelagerheatedregion[ Barretal. ,1998].Thedonut-shapeHFbeam,ontheother hand,hasthepeakHFenergyawayfromthebeamcenter.TOAanalysiswiththeability torangethesourcelocationandtoseparatemulti-pathswillbeaconvenientdiagnostic tooltoevaluatetheELF/VLFgenerationefciencyonthesedifferentHFbeamshapes. 5.2.3TOAAnalysisforDifferentModulationTechniques Inthisthesis,weapplyTOAanalysistoamplitudemodulatedwaveforms.Asan alternativemodulationmethod,theHFbeammaymoverapidlyatthemodulationfrequencyusingtheContinuousWaveformCW[ Cohenetal. ,2008; Papadopoulosetal. 1990].Comparedtotheconventionalamplitudemodulation,thisalternativemodulation hasalargerheatedregionandtheinterpretationofthesignalinterferencebecomes morecomplex.Although Cohenetal. [2008]claimsthegeometricmodulationincreasestheELF/VLFwavegenerationefciency,theTOAanalysismaybeusefulto experimentallyre-evaluatetheefciencyincludingtheinterferenceeffectsandthe dominantsourceregions. 52

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REFERENCES Balanis,C.A., AdvancedEngineeringElectromagnetics ,JohnWiley&SonsInc,New York,1986. Barr,R.,M.T.Rietveld,P.Stubbe,andH.Kopka,IonosphericHeaterBeamScanning:A RealisticModelofThisMobileSourceofELF/VLFRadiation, RadioSci. 23 ,1073, 1998. Barrick,D.E.,Fm/cwradarsignalsanddigitalprocessing, Tech.Rep.ERL283-WPL20 NOAA,1973. Boashash,B., Timefrequencysignalanalysisandprocessing:acomprehensive reference ,743pp.,Elsevier,Oxford,UK,2003. Budden,K.G., Thepropagationofradiowaves:thetheoryofradiowavesoflowpower intheionosphereandmagnetosphere ,CambridgeUniversityPress,Cambridge,UK, 1985. Cohen,M.B.,Elf/vlfphasedarraygenerationviafrequency-matchedsteeringofa continuoushfionosphericheatingbeam,Ph.D.thesis,StanfordUniversity,2009. Cohen,M.B.,U.S.Inan,andM.G.kowski,Geometricmodulation:Amoreeffective methodofsteerableelf/vlfwavegenerationwithcontinuoushfheatingofthelower ionosphere, Geophys.Res.Lett. 35 ,L12101,doi: 10.1029/2008GL0340610 ,2008. Cummer,S.,U.Inan,andT.Bell,Ionospheric D regionremotesensingusingvlfradio atmospherics, RadioSci. 33 ,1781,1998. Davies,K., IonosphericRadio ,PeterPeregrinusLtd.,London,UK,1990. Gabor,D.,Theoryofcommunication., J.IEE 93 ,429,1946. Getmantsev,G.G.,N.A.Zuikov,D.S.Kotik,L.F.Mironenko,N.A.Mityakov,V.O. Rapoport,V.Y.T.Y.A.Sazonov,andV.Y.Eidman,Combinationfrequenciesin theinteractionbetweenigh-powershort-waveradiationandionosphericplasma, JETPLett 20 ,101,1974. James,H.G.,TheELFspectrumofarticiallymodulatedd/e-regionconductivity, J. Atmos.Terr.Phys. 47 ,1129,1985. Lev-Tov,S.J.,U.S.Inan,andT.F.Bell,Altitudeprolesoflocalized D regiondensity disturbancesproducedinlightning-inducedelectronprecipitationevents, J.Geophys. Res. 100 A11,21,375,383,1995. Leyser,T.,L.Norin,M.McCarrick,T.Pedersen,andB.Gustavsson,Radiopumpingof ionosphericplasmawithorbitalangularmomentum, Phys.Rev.Lett., 102 ,2009. Moore,R.C.,ELF/VLFwavegenerationbymodulatedHFheatingoftheauroral electrojet,Ph.D.thesis,StanfordUniversity,Stanford,CA,2007. 53

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Moore,R.C.,andD.Agrawal,ELF/VLFwavegenerationusingsimultaneouscw andmodultedhfheatingoftheionosphere, J.Geophys.Res 116 ,A04217,doi: 10.1029/2010JA015902 ,2011. Papadopoulos,K.,C.Chang,P.Vitello,andA.Drobot,Ontheefciencyofionospheric elfgeneration, RadioSci. 25 ,1990. Papadopoulos,K.,T.Wallace,M.McCarrick,G.M.Milikh,andX.Yang,Ontheefciency ofELF/VLFgenerationusinghfheatingoftheauroralelectrojet PlasmaPhys.Rep. 29 ,2003. Payne,J.A.,U.S.Inan,F.R.Foust,T.W.Chevalier,andT.F.Bell,Hfmodulated ionosphericcurrents, Geophys.Res.Lett. 34 ,L23101,doi: 10.1029/2007GL031724 2007. Riddolls,R.J.,Structureofthepolarelectrojetantenna,Ph.D.thesis,Massachusetts InstituteofTechnology,Cambridge,MA,2003. Rietveld,M.T.,R.Barr,H.Kopka,E.Nielsen,P.Stubbe,andR.L.Dowden,Ionospheric heaterbeamscannning:AnewtechniqueforELFstudiesoftheautoralionosphere, RadioSci. 19 ,1069,1984. Rietveld,M.T.,H.Kopka,andP.Stubbe, D -regioncharacteristicsdeducedfrompulsed ionosphericheatingunderauroralelecrojetconditions, J.Atmos.Terr.Phys. 48 311,1986. Rietveld,M.T.,P.Stubbe,andH.Kopka,OnthefrequencydependenceofELF/VLF wavesproducedbymodulatedionosphericheating, RadioSci. 24 ,270,1989. Schuster,S.,S.Scheiblhofer,L.Reindl,andA.Stelzer,Performanceevaluationofalgorithmsforsaw-basedtemperaturemeasurement, IEEETrans.Ultrason.,Ferroelectr., Freq.Control 53 ,1177,2006. Segalovitz,A.,andB.R.Frieden,ACLEAN-typedeconvolutionalgorithm, Astron. Astrophys.Suppl. 70 ,335,1978. Tomko,A.A.,Nonlinearphenomenaarisingfromradiowaveheatingofthelower ionosphere,Ph.D.thesis,ThePennsylvaniaStateUniversity,1981. Wait,J.,Thesanguineconcept,in EngineeringintheOceanEnvironment,Ocean72IEEEInternationalConferenceon ,pp.84,doi: 10.1109/OCEANS.1972.1161183 1972. 54

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BIOGRAPHICALSKETCH ShujiFujimaruwasborninJapanin1986.Hereceivedabachelor'sdegreein electricalandcomputerengineeringfromtheUniversityofFloridain2009.Withthe AlumniFellowshipawardfromtheUniversityofFlorida,heenteredthePh.Dprogram inelectricalandcomputerengineering.Hereceivedhismaster'sdegreeontheway tothePh.D.withguidancefromDr.RobertMoore.HisresearchfocusesonELF/VLF generationusingmodulatedHFheatingofthelowerionosphere.Hisstudiesaremainly appliedtoelectromagnetics,plasmaphysics,andsignalprocessing. 55