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Optimization of Beam Painting for ELF/VLF Wave Generation at HAARP Using Time-of-Arrival Analysis

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Title:
Optimization of Beam Painting for ELF/VLF Wave Generation at HAARP Using Time-of-Arrival Analysis
Creator:
Fujimaru, Shuji
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (102 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
MOORE,ROBERT C
Committee Co-Chair:
RAKOV,VLADIMIR ALEK SANDROVICH
Committee Members:
YOON,YONG KYU
UMAN,MARTIN A
ROY,SUBRATA
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Amplitude ( jstor )
Arc length ( jstor )
Azimuth ( jstor )
Bandwidth ( jstor )
Heating ( jstor )
Ionospherics ( jstor )
Paradise ( jstor )
Propagation delay ( jstor )
Signals ( jstor )
Wave generation ( jstor )
Electrical and Computer Engineering -- Dissertations, Academic -- UF
electromagnetics -- elf -- haarp -- ionosphere -- vlf
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Electrical and Computer Engineering thesis, Ph.D.

Notes

Abstract:
This dissertation experimentally and theoretically investigates the generation of radio waves in the extremely low frequency (ELF, 3-3000 Hz) and very low frequency (VLF, 3-30 kHz) bands by high frequency (HF, 3-30 MHz) heating of the lower ionosphere. ELF and VLF waves can propagate to large distances around the globe with little attenuation, making them ideally suited for long distance communications and ionospheric remote sensing. These waves may also propagate into near-Earth space, where they can control the population of energetic radiation belt particles. Improving the efficiency of this unconventional mechanism for ELF/VLF wave generation is the primary emphasis of this work. For the experimental observations presented herein, the ELF/VLF signal detected at the receiver is considered to be the sum of several multi-path components. These multi-path components are produced by reflections from the ground and the lower ionosphere. A novel time-of-arrival (TOA) analysis technique is applied to observations to distinguish between line-of-sight (LOS) and ionospherically-reflected (IR) components. This decomposition enables the experimental differentiation of HF heating (i.e., source) effects and Earth-ionosphere waveguide (i.e., propagation) effects. TOA analysis of experimental observations for various HF heating schemes are compared against a theoretical model to demonstrate the validity of the technique. TOA analysis is applied to evaluate the ELF/VLF source properties produced by rapidly scanning the HF beam across the ionosphere, a very efficient modulation technique known as beam-painting. By precisely controlling the duration of the HF pulse during the beam-painting experiments, the amplitude and phase of individual ELF/VLF array elements are experimentally measured. The influence of the source area, phasing distribution, heating and cooling time scales, and obliqueness of the HF beam on the received ELF/VLF amplitude are experimentally quantified for the first time. Based on these observations, a simple change to the modulation format is proposed to significantly increase the received ELF/VLF amplitude by >4 dB and the HF-to-ELF conversion efficiency by >7 dB. Lastly, a rigorous optimization method is applied to maximize the received ELF/VLF wave amplitude. The optimization is based on experimental observations, and utilizes the observed amplitudes, phases, and propagation delays associated with 8 different HF heating locations. The optimal heating pattern is predicted to increase the received ELF/VLF amplitude by ~7 dB and the HF-to-ELF conversion efficiency by ~11 dB, constituting a tremendous improvement over the current state-of-the-art modulation formats. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: MOORE,ROBERT C.
Local:
Co-adviser: RAKOV,VLADIMIR ALEK SANDROVICH.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-11-30
Statement of Responsibility:
by Shuji Fujimaru.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
11/30/2014
Resource Identifier:
907294831 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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OPTIMIZATIONOFBEAMPAINTINGFORELF/VLFWAVEGENERATIONATHAARP USINGTIME-OF-ARRIVALANALYSIS By SHUJIFUJIMARU ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2014

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c 2014ShujiFujimaru 2

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Idedicatethisdissertationtomyparents,AkioandIkuyoFujimaru,tomybrotherYoshiki Fujimaru,andtomygrandparents,MitsuyoshiandYukoFujimaruandShinakoHosozawa. 3

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ACKNOWLEDGMENTS Iwouldliketoexpressmyappreciationtomyadviser,Dr.RobertMoore,forhisencouragement,guidance,andhelpthroughoutmygraduatestudies.Thisdissertationwouldnotpossibly havebeencompletedinaprofessionalmannerwithouthispatientandunselshsupport.Ialso wouldliketothankDr.VladimirRakov,Dr.SubrataRoy,Dr.MartinUman,andDr.YKYoonfor servingasmembersofmyPhDcommitteeandforprovidingpreciseandpromptfeedbackonthis dissertationdespitetheirbusyschedules. IamgratefultoallmycolleagueswithwhomIhavesharedafulllingresearchexperience throughmygraduateschoollife.IamespeciallygratefultoDanielKotovskyforprovidinghelpful adviceonplasmaphysicsandelectromagnetics,toMichaelMitchelforprovidingunfailingsupport ofobservationalinstruments,toNealDupreeforsharingthehardworkofinstrumentdeployment, andtoalltheotherlabmemberswithwhomIhavehadthepleasuretowork:TongWang,Divya Agrawal,JerrodLangston,SydneyGreene,MatthewBell,andDianLi. WithoutthetremendoushelpIreceivedfromtheHAARPstaffandtheAlaskanlocalsto deployinstruments,performexperiments,andcollectdatainthetreacherousAlaskanwilderness, Iwouldnothavebeenabletocompletethisdissertation.IwouldliketoespeciallythankDr.Mike McCarrickforimplementingmytransmissionsequencesatHAARP,JayScrimshawforletting usoperatetheinstrumentsathishomesinGakonaandCopperLake,DougandJudyFrederick forkeepingourinstrumentwarmwiththeirgeneratoratParadise,BarbaraCharleyforsharing hercabinwithourinstrument,andNormaandDoyleTrawforprovidinguswarmhousingand breakfastinChistochina. Lastly,IowemydeepestgratitudetomyparentsandfamiliesinJapanforbeingmylife supportwiththeirunconditionallove. ThisworkissupportedinpartbythefollowinggrantsandcontractstotheUniversityof Florida:DARPAcontractHR0011-09-C-0099,USAirForcegrantFA9453-12-1-00246,ONR grant#N000141010909,DARPAgrantHR0011-10-1-0061,andNSFgrantsAGS-0940248and ANT-0944639. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS....................................4 LISTOFTABLES.......................................7 LISTOFFIGURES.......................................8 ABSTRACT...........................................10 CHAPTER 1INTRODUCTION....................................12 1.1ConventionalELF/VLFWaveGeneration.....................12 1.2PreviousMeasurementsofIonosphericELF/VLFWaveGeneration........14 1.2.1LocalIonosphericandGeomagneticConditions..............15 1.2.2HFTransmissionParameters........................17 1.2.2.1HFpower............................17 1.2.2.2ObliqueHFheating.......................18 1.2.2.3Rapidheaterbeamscanning...................18 1.2.2.4OtherHFtransmissionproperties................21 1.3AnalysisTechniques................................22 1.3.1NeutralizationofWaveguidePropagationEffects.............23 1.3.2PulsedHFHeating.............................23 1.3.3PhaseversusFrequency...........................24 1.3.4TimeofArrivalAnalysis..........................25 1.4ScienticContributions...............................25 2ELF/VLFWAVEGENERATIONMECHANISMANDTHETOAMETHOD.....27 2.1ELF/VLFWaveGenerationMechanism......................27 2.1.1TheIonosphere...............................27 2.1.2RefractiveIndex...............................29 2.1.3IonosphericConductivityModication...................31 2.1.4ELF/VLFSourceCurrents.........................32 2.1.5ELF/VLFReectioninthe D -regionIonosphere..............36 2.2ELF/VLFTime-of-ArrivalTOAAnalysisMethod................37 2.3TOAProperties...................................42 2.3.1TimingAccuracy..............................42 2.3.2TimingResolution..............................44 3EXPERIMENTALVALIDATIONOFTHETOAMETHOD..............49 3.1TOAObservationsversusModelPredictions....................49 3.2SourcePolarization.................................51 3.3TOAversusHFFrequency&Power........................53 5

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3.4TOAasaFunctionofModulationFrequency...................54 3.5BroadBeamConstructionfromMultipleNarrowBeams.............55 3.5.1NarrowBeam/BroadBeamExperimentDescription............56 3.5.2ResultsandAnalysis............................57 4OBSERVATIONSOFELF/VLFSOURCEPHASING.................59 4.1BeamPainting/GeometricModulationBP/GM..................59 4.1.1BP/GMExperimentDescription......................59 4.1.2BP/GMExperimentalObservations.....................62 4.1.2.1Frequencyandtimeresponseobservations...........62 4.1.2.2Amplitudeasafunctionofarclength..............66 4.1.3BP/GMAnalysis..............................72 4.2OptimizedHeatingOrderforBP/GMConstantDuration............75 5OPTIMIZATIONOFELF/VLFANPHASEDARRAY.................78 5.1OptimizationExperimentDescription.......................78 5.2ExperimentalObservations.............................78 5.2.1ELF/VLFObservationsvs.Azimuth....................79 5.2.2ELF/VLFAmplitudevs.DutyCycle....................80 5.3OptimizationofBeamPainting...........................82 5.3.1DutyCycleDependencevs.Azimuth....................84 5.3.2GradientDescentMethod..........................85 5.3.3DeterminationofInitialValues.......................87 5.3.4OptimizationResultandAnalysis......................90 6SUMMARYANDFUTUREWORK...........................93 6.1SummaryofContributions.............................93 6.2SuggestionsforFutureResearch..........................94 6.2.1ImplementationofOptimalHeatingPattern................94 6.2.2HighFrequencyResolutionTOA......................94 6.2.3SeparationofHallandPedersenCurrents.................95 REFERENCES.........................................96 BIOGRAPHICALSKETCH..................................102 6

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LISTOFTABLES Table page 5-1OptimizedamplitudecomparedtoAMandGM.....................92 7

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LISTOFFIGURES Figure page 2-1CartoondiagramofELF/VLFwavegenerationatHAARP...............28 2-2Structureoftheionosphere................................29 2-3Refractiveindex......................................31 2-4North-SouthandEast-Westcoordinates.........................34 2-5Plasmaparameterat3kHz................................37 2-6TOAobservationsandsincfunctionswithpositiveandnegativefrequency.......41 2-7CRLBofthestandarddeviationofthetimedelayforthepeakamplitude........43 2-8LOSsignaldeconvolvedbyleastsquareerrorsearchalgotrithm.............45 2-9TOAobservationsanddeconvolutionsuccessrates...................46 2-10Variancesofdeconvolvedpulses.............................47 3-1MapoftheELF/VLFreceiversites............................50 3-2TOAobservationswithnoiseapproximation.......................51 3-3Comparisonbetweenmodelpredictionsandobservations................52 3-4TOAwithantennarotation................................53 3-5TOAasafunctionofHFfrequencyandpower......................54 3-6TOAwithdifferentmodulationfrequency........................55 3-7HFbeampattern:narrowandbroadbeams........................56 3-8TOAobservationsofnarrowandbroadbeams......................57 4-1Cartoondiagramofmodiedgeometricmodulation...................60 4-2SpectrogramandfrequencyresponseofGMcirclewithobliqueAM..........62 4-3TOAobservationsofGMcircleandobliqueAM....................63 4-4GMvs.verticalandobliqueAM.............................64 4-5AmplitudeofsymmetriccirclesweepwithverticalAMatParadise...........65 4-6AmplitudeofasymmetriccirclesweepwithobliqueAMatParadise..........66 4-7AsymmetriccirclesweepwithobliqueAMatOasis...................67 8

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4-8AverageasymmetriccirclesweepwithobliqueAMatParadise.............68 4-9BP/GMvs.GM......................................69 4-10AmplitudestructureofGM................................70 4-11PhasestructureofGM..................................71 4-12Campaign-AveragedResults...............................74 4-13Optimizedheatingorderandamplitude..........................76 5-1Azimuthalresponse....................................79 5-2Dutycycleresponse....................................81 5-3DiagramofHFheatingpattern..............................82 5-4Dutycycledependenceonazimuth............................84 5-5Convergenceofparameters................................86 5-6Off-timeagainsttotaldutycycle.............................89 5-7Optimizedamplitudeandefciency...........................90 5-8Optimalsteeringpatternandorder............................91 9

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy OPTIMIZATIONOFBEAMPAINTINGFORELF/VLFWAVEGENERATIONATHAARP USINGTIME-OF-ARRIVALANALYSIS By ShujiFujimaru May2014 Chair:RobertC.Moore Major:ElectricalandComputerEngineering Thisdissertationexperimentallyandtheoreticallyinvestigatesthegenerationofradiowaves intheextremelylowfrequencyELF,3HzandverylowfrequencyVLF,3kHzbands byhighfrequencyHF,3MHzheatingofthelowerionosphere.ELFandVLFwavescan propagatetolargedistancesaroundtheglobewithlittleattenuation,makingthemideallysuitedfor longdistancecommunicationsandionosphericremotesensing.Thesewavesmayalsopropagate intonear-Earthspace,wheretheycancontrolthepopulationofenergeticradiationbeltparticles. ImprovingtheefciencyofthisunconventionalmechanismforELF/VLFwavegenerationisthe primaryemphasisofthiswork. Fortheexperimentalobservationspresentedherein,theELF/VLFsignaldetectedatthereceiverisconsideredtobethesumofseveralmulti-pathcomponents.Thesemulti-pathcomponents areproducedbyreectionsfromthegroundandthelowerionosphere.Anoveltime-of-arrival TOAanalysistechniqueisappliedtoobservationstodistinguishbetweenline-of-sightLOS andionospherically-reectedIRcomponents.ThisdecompositionenablestheexperimentaldifferentiationofHFheatingi.e.,sourceeffectsandEarth-ionospherewaveguidei.e.,propagation effects.TOAanalysisofexperimentalobservationsforvariousHFheatingschemesarecompared againstatheoreticalmodeltodemonstratethevalidityofthetechnique. TOAanalysisisappliedtoevaluatetheELF/VLFsourcepropertiesproducedbyrapidly scanningtheHFbeamacrosstheionosphere,averyefcientmodulationtechniqueknownas beam-painting.BypreciselycontrollingthedurationoftheHFpulseduringthebeam-painting 10

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experiments,theamplitudeandphaseofindividualELF/VLFarrayelementsareexperimentally measured.Theinuenceofthesourcearea,phasingdistribution,heatingandcoolingtimescales, andobliquenessoftheHFbeamonthereceivedELF/VLFamplitudeareexperimentallyquantiedforthersttime.Basedontheseobservations,asimplechangetothemodulationformatis proposedtosignicantlyincreasethereceivedELF/VLFamplitudeby > 4dBandtheHF-to-ELF conversionefciencyby > 7dB. Lastly,arigorousoptimizationmethodisappliedtomaximizethereceivedELF/VLFwave amplitude.Theoptimizationisbasedonexperimentalobservations,andutilizestheobserved amplitudes,phases,andpropagationdelaysassociatedwith8differentHFheatinglocations.The optimalheatingpatternispredictedtoincreasethereceivedELF/VLFamplitudeby 7dBand theHF-to-ELFconversionefciencyby 11dB,constitutingatremendousimprovementoverthe currentstate-of-the-artmodulationformats. 11

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CHAPTER1 INTRODUCTION Thisdissertationinvestigatesthegenerationofradiowavesintheextremelylowfrequency ELF,3HzandverylowfrequencyVLF,3kHzbandsbyhighfrequencyHF,3 30MHzheatingofthelowerionosphereinthepresenceoftheauroralelecrojetcurrentsystem. AllexperimentspresentedhereinwereperformedattheHighFrequencyActiveAuroralResearch ProgramHAARPobservatoryinGakona,Alaska.Anovelmethodisemployedtoisolatethe detectedELF/VLFsignalfromEarth-ionospherewaveguidepropagationeffects.Asadirectresultofthisanalysis,newHFmodulationtechniquesareproposedtooptimizetheamplitudeofthe ELF/VLFsignalreceivedatasinglesite.Thischapterintroducesthedifcultiesassociatedwith conventionalELF/VLFwavegeneration,providesaliteraturereviewfocusedELF/VLFwavegenerationbyHFheating,andconcludesbyidentifyingthescienticcontributionsofthisdissertation. 1.1ConventionalELF/VLFWaveGeneration ELF/VLFwavesreectbetweentheEarth'sionosphereandgroundandpropagatetoglobalscaledistanceswithrelativelylowattenuationintheEarth-ionospherewaveguide.Theyalsopenetratetensofmetersintoseawater.Forthesereasons,theyareideallysuitedforlong-distance communications.NaviesinseveralcountriesuseELFandVLFwavestocommunicatewithsubmergedvehicles[e.g., Bernsteinetal. ,1974; Merrill ,1974].BeforetheadventoftheglobalpositionsystemGPS,ELF/VLFwaveswereusedforglobalnavigationandtimetransfer[e.g., Frank 1983; Swanson ,1983],andtheyhavesubsequentlyprovidedavalid,althoughcoarser,failsafefor GPS.Furthermore,ELF/VLFwavesareeffectivetoolsforremotelysensingthepropertiesofthe ionosphere[e.g., Cummeretal. ,1998; AgrawalandMoore ,2012]andmagnetosphere[e.g., Inan andCarpenter ,1987; Gokowskietal. ,2011].Forinstance,particularattentionhasbeenpaidto theionosphericandmagnetosphericeffectsoflightning[e.g., Laubenetal. ,2001; Dowdenetal. 2002; Mooreetal. ,2003; Saidetal. ,2010]andnuclearexplosions[e.g., FieldandEngel ,1965; Helliwell ,1965]. 12

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Despitethenumerouscommunications-orientedandscienticapplications,conventionalmethodsforthegenerationofELF/VLFwavesarecostly.AlthoughanumberofVLFtransmitters currentlyoperateinthe 15kHzbandwithreasonableefciency > 20%,therequiredantenna sizeisontheorderofhundredsofmeters[ Watt ,1967].OneofthemostpowerfulVLFtransmitters isoperatedatCutler,MainebytheUSNavy.Thistransmitterconsistsoftwostarantennas:each antennaisaverticalmonopolewithleadsconnectingthecentermasttosixsurroundingmasts.The averageheightofthemastsis 200mandthetotalareaenclosedbytheantennasis 2 10 6 m 2 500acres.Thecentermastthatradiatesthesignalis 300mhigh,anditisstillelectronically smallforthe10kmwavelengthintheupperVLFrange.Tuningtotheresonantfrequency makesitpossibletomaintain > 70%radiationefciencyat14kHz[ Watt ,1967],butthebandwidth ofoperationissignicantlylimited'sofHz.ItshouldbenotedthattheCutlertransmitter presentlyoperatesatadifferentfrequency.0kHz. AtthelowerendoftheELF/VLFfrequencyrange < 5kHz,alonghorizontalwireisamore practicalimplementationthatcanachievelengthscomparabletoawavelength > 60km.Because thelonghorizontalwireliesclosetotheground,however,imagesourcestendtocancelmostof theradiatedelds.Evenonthickicesheets,ELF/VLFantennasradiatewithlowefciency.For instanceatSipleStation,Antarctica,a21.4kmhorizontalantennatransmittedwavesatafew kHzwithatmost 2%efciency[ Raghurametal. ,1974].Forlow-ELFfrequencies < 100Hz, theantennaprojectattheWisconsinTestFacilityusedamultitudeof 22.5kmwirestoachieve efcienciesontheorderof 0.01%[ Papadopoulosetal. ,1990].Inthiscase,onceagain,the bandwidthofthetransmissionisseverelylimited. Forallofthesetransmitters,operationandmaintenancecostsarehighandtheavailablebandwidthisasmallfractionofthecenterfrequency.Fromthisperspective,modulatedHFheating oftheionosphereinthepresenceofnaturallyoccurringelectriccurrentsisanimportantalternativemethodtogenerateELF/VLFwaves,andsimultaneouslyprovidesameanstostudylong distanceELF/VLFpropagationinacontrolledenvironment.Whilethisunconventionalmethod forELF/VLFwavegenerationsuffersfromevenlowerefciency 0.0001.001%[ Barretal. 13

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1985; Mooreetal. ,2007; CohenandGokowski ,2013],itisnotsignicantlylimitedinbandwidth.Recenteffortstoimprovetheefciencyhaveachieveda10-foldenhancementinradiated ELF/VLFpowerbyrapidlyscanningtheHFbeamacrosstheionosphere[ Cohenetal. ,2008, 2010a,b].Whiletheimprovementinefciencyhasbeendocumented,thephysicalreasonsforthe improvementhavenotbeenexperimentallyquantied.Asaresult,itisnotyetpossibletooptimizetheELF/VLFsourceregionforcontrolledinjectionintotheEarth-ionospherewaveguideor intonear-Earthspace.Asarststeptowardprovidingsuchcapabilities,thisdissertationexperimentallyquantiestheeffectsproducedbyindividualHFbeamsteeringparametersonELF/VLF wavegenerationandinvestigatestheoptimalcombinationofthoseparameterstomaximizethe ELF/VLFwaveamplitudereceivedatanindividualground-basedreceiver. 1.2PreviousMeasurementsofIonosphericELF/VLFWaveGeneration Since Getmantsevetal. [1974]rstsucceededinELF/VLFwavegenerationbyheatingthe ionosphere,anumberofeffortshavebeenconductedinordertoincreasetheefciencyofELF/VLF wavegeneration,whichisontheorderof 0.0001.001%.Typically,theradiatedpowerofthe ELF/VLFwavesourceisestimatedbycomparingtheobservedELF/VLFamplitudewithanHF heatingandELF/VLFwavepropagationmodel.AtTroms,Norway,using1MWofHFpower, Barretal. [1985]estimated1to2WofradiatedELF/VLFpower,dependingontheionospheric condition.AtHAARPinAlaska,using960kWofHFpower, Moore [2007]estimated4W anddetectedthesignalmorethan4,500kmawayfromHAARP.Morerecently,afteranupgrade oftheHAARPHFtransmitterto3.6MW, CohenandGokowski [2013]estimatedamaximum radiatedELF/VLFpowerof 265W.Fortheseestimations,thetransmissionformatswerelimited toavertical,narrowbeamwithamplitudemodulation,andthecarrierandmodulationfrequencies were2.75.25MHzand0.53.5kHzrespectively.Ofcourse,ELF/VLFwavegenerationdepends onthestrengthoftheauroralelectrojetcurrents,onthepropertiesoftheionosphere,andonthe HFtransmissionparametersemployed.Althoughwecanonlycontrolthelastoftheseitems,itis worthexplainingtheimportanceofthegeomagneticconditionslocaltoHAARPpriortodelving intotheHFtransmissionparameters. 14

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1.2.1LocalIonosphericandGeomagneticConditions LocalionosphericandgeomagneticconditionsplayanimportantroledeterminingtheELF/ VLFsignalstrengthandgenerationefciency.Thepropertiesoftheionospherevarysignicantly withtimeevenminutebyminute.StrongorweakELF/VLFsignalscanbegenerated,dependingonhowtheelectrondensityandelectrontemperaturevarywithaltitudewithinthe D -region ionosphere,evenforthesameHFbeamconguration.Inessence,theionosphericparametersaffecttheefciencyofionosphericconductivitymodulationproducedbyHFheating. Cohenand Gokowski [2013]statisticallyanalyzedELF/VLFsignalgenerationatHAARPforoveracourse of91days.TheiranalysisrevealedthattheaverageELF/VLFsignalstrengthwashighestduring thedaytime,butthestrongestsignallevelsforshorterperiodsoftimeweregeneratedduring thenighttime.Thisstatisticalobservationisconsistentwiththetheoreticalmodelof Milikhand Papadopoulos [2007]thatpredictslargerELF/VLFsignallevelsforhigher D -regionionospheric electrondensities. FurtherstudiescorrelateobservedELF/VLFsignalstrengthswithmagnetometerobservations[ Rietveldetal. ,1987; Jinetal. ,2009,2011].Themagnetometermeasuresnear-DCmagnetic elductuationsthatarerelatedtothestrengthoftheauroralelectrojetcurrentsat 150km altitude. Jinetal. [2011]integratedmagnetometermeasurementswithriometerabsorptionand ionosondeelectrondensitymeasurementsanddemonstratedcorrelationbetweenELF/VLFsignal strengthsandmagnetometermeasurementsinmostcases. Rietveldetal. [1983]observedadirect correlationbetweentheELF/VLFsignalamplitudeandpolarizationandtheauroralelectriceld strengthanddirectionmeasuredusingtheSTAREradarsystem. Rietveldetal. [1984]observed aspatialcorrelationwithSTAREobservationsbytiltingtheHFbeamindifferentdirections,and Rietveldetal. [1987]reportedatemporalcorrelationusing32hoursofELF/VLF,STARE,magnetometer,andriometerobservations. MostoftheELF/VLFgenerationexperimentshavebeenperformedathighlatitudes > 60 N becauseofthestrongauroralelectrojetelectriceld.However,atequatoriallatitudes,theequatorialdynamocurrentnaturallyowsinthelowerionosphere.AttheAreciboObservatory N, 15

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66 WinPuertoRicoandattheJicamerca S,76 WinPeru,successfulELF/VLFsignals generationexperimentshavebeenperformed.TheELF/VLFamplitudesgeneratedattheArecibo andJicamercawere10timessmallerthanthosegeneratedathighlatitudes[ Ferraroetal. 1982,1984; Lunnenetal. ,1984]. WhilenaturallyoccurringelectriccurrentsareanimportantpartoftheELF/VLFwavegenerationprocess,theyarenotabsolutelynecessarytogenerateELF/VLFsignals.Severalrecent experimentshavefocusedongeneratingELF/VLFwavesintheabsenceofastrongauroralelectrojet. Papadopoulosetal. [2011a,b]showedtheoreticalandexperimentalresultsoftheionospheric currentdriveICDmechanism,inwhich F -regionpressurewasmodulatedbyHFheating.The generatedELFsignal < 70Hzwas 10dBweakerthanELF/VLFwavesgeneratedbyelectrojetmodulation. Eliassonetal. [2012]'sobservationsupportedthemodelresultbydetecting theELFsignalsatthefurthersitekmwhentherewasnosignaldetectiondirectlyat theHAARPsite.WavegenerationwithICDislimitedto < 100Hz,however.AnotherelectrojetindependentELF/VLFwavegenerationmechanismworksmoderatelywellathigherfrequencies. ThecubicmodulationformatwasinitiallythoughttobeatoneHFsignalwiththesecondharmonicofasecondHFsignal.Thistransmissionformatwasrstperformedby KotikandErmakova [1998]broadcastingonebeamat 9MHzandtheotherbeamat 4.5MHzinwhichthe 9MHz beamandthesecondharmonicofthe 4.5MHzbeamdifferbyafrequencyintheELF/VLFrange. Mooreetal. [2013]performedasimilarexperiment,butusedTOAanalysistodeterminethatthe sourceheightresidedinthe D -regionionosphere. Mooreetal. [2013]furtherprovidednumerical modelingtodeterminethatthedominantcubicgenerationmechanismathighlatitudesconsists ofthebeatingofoneHFsignalwiththeinnerproductoftherstandsecondHFsignal.Observed signalamplitudeswerelowerthanAMelectrojetmodulationby 30dBinthe5kHzrangebut onlyby 10dBinthe20kHzrange. AlthoughmechanismsexisttogenerateELF/VLFwaveswithoutuseoftheauroralelectrojet currents,atthepresenttime,ELF/VLFwavegenerationismuchmoreefcientwhentheelectrojet isemployed.Fortheremainderofthisdissertation,Ifocusontechniquestomodulatetheauroral 16

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electrojetcurrentsforELF/VLFwavegeneration.InowconsidertherolethatHFtransmission parametersplayinELF/VLFwavegenerationprocesses. 1.2.2HFTransmissionParameters TheHFtransmissionparametersaretheonlycontrollableknobsintheELF/VLFwavegenerationsystem.AtHAARP,theHFpower,frequency,polarization,modulationfrequency,and modulationwaveformareallpreciselycontrollable.TheHAARPHFtransmitterisalsocapable ofrapidlyscanningtheionosphere.Itcanre-positionthebeamwith5 m -secondaccuracy,aslong asthepositionsarewithin15 ofonecentralizedpoint.Inowdiscusstheeffectstheseparameters haveonELF/VLFwavegeneration. 1.2.2.1HFpower IncreasingthepoweroftheHFbeamincreasesthegeneratedELF/VLFsignalstrength,althoughthespecicrelationshipbetweenELF/VLFamplitudeandHFpowerisnon-linear.For instance, Stubbeetal. [1982]comparedtheamplitudeproducedbyAMat0%and50% modulationpowerdepth.TheamplitudeswouldbethesameiftheELF/VLFsignalstrengthvaried linearlywithHFpower.Theamplitudeproducedby0%powerdepthwas 1.5timeslarger thantheamplitudeproducedby50%powerdepth,however. Moore [2007]measuredthe amplitudewithdifferentaverageHFpowerchangingmodulationpowerdepth%andidentiedtheoptimalaverageHFpower.AtlowHFpowerlevels,researchersgenerallycharacterized therelationshipwithasimplepower-law:theELF/VLFsignalamplitudeisproportionaltotheHF powerraisedtosomeexponent. Ferraroetal. [1984], Barretal. [1987]and Barretal. [1988] used0.5fortheexponenttomodeltheirreceivedsignals. Papadopoulosetal. [1990]theoretically determinedtheexponentas < 0.5forlowaltitudes 70kmandas 2forhigheraltitudes > 90km. BarrandStubbe [1991a]observedtheELF/VLFsignalwithchangingHFeffective radiatedpowerfrom50MWto1GWandtthepower-lawequationtotheobservations.The exponentvariedbetween0.7and0.97dependingonthemodulationfrequency. BarrandStubbe [1993]appliedthepower-lawtotheharmonicsoftheradiationanddeterminedtheexponentas 0.95. 17

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Despitetheexcellentmatchoftheobservationstothesimplepowerlaw,athighHFpower levels,thepowerlawrequiresmodicationtoaccountforobservationsofsaturationeffects[ Moore etal. ,2006]. 1.2.2.2ObliqueHFheating ObliqueHFheatingoftheionospherewasintroducedby Rietveldetal. [1984]. Barretal. [1987]and Barretal. [1988]tiltedtheHFbeamfrom + 37 to )]TJ/F22 11.9552 Tf 9.289 0 Td [(37 towardandawayfromthe receiver.Theyobserved 1kHzsignalsat 550kmdistantsiteandshowedthattiltingthe HFbeamtowardthereceiverproduced8dBlargeramplitudethantiltingthebeamawayfrom thereceiver.Theamplitudechangesbyalargerdegreeathighermodulationfrequencies. Barr etal. [1988]concludedthattheamplitudeincreasedordecreasedduetothedistributedphasingof theELF/VLFsourcewithintheheatedregion.WhentiltingtheHFbeamtowardthereceiver,the relativephasingoftheelementalsourcecomponentswithintheheatedregionproduceconstructive interferenceatthereceiver.Ontheotherhand,whentiltingtheHFbeamawayfromthereceiver, therelativephasingoftheelementalsourcecomponentsproducedestructiveinterferenceatthe receiver. Cohenetal. [2010a]presentedsimilarexperimentalresults. 1.2.2.3Rapidheaterbeamscanning ByrapidlyandrepeatedlydirectingtheHFbeamtowarddifferentpositionswithintheionosphere,HFtransmitterscangeneratemultipleELF/VLFsources.Dueinlargeparttotherelative timingofthetransmissions,thesourceswillhavesignicantlydifferentphasesandconstitutean ELF/VLFphasedarray.Thesimplestphasedarrayisatwo-elementphasedarraycreatedbyalternativelyheatingtwolocationswithaCWbeam[ Barretal. ,1987].Inthiscase,onelocationwas aimedtowardthereceiver 550kmawayfromTroms,whereasthesecondlocationwasinthe oppositedirection.Theoff-zenithanglesweresymmetricallychangedtoobservetheinterference patterncreatedbythetwosources.Thereceivedamplitudewasapproximatelydoubledwhenthe locationswereseparatedbyhalfoftheELF/VLFwavelength. Undercertaincircumstances,eachsourcewithintheELF/VLFphasedarraycanbetreated independently,andthetotalreceivedELF/VLFsignalcanbeestimatedasthelinearsumofthe 18

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eldgeneratedbythesesources. Gokowskietal. [2013]comparedobservationsagainstasimple model,whichindicatedthatindependenttreatmentofELF/VLFsourceswasvalidatleastupuntil theHFbeamsoverlappedatthe3-dBpoint. Increasingthenumberofsourceelements,orequivalentlyincreasingtheareaofthesource hasalsobeenshowntobeaneffectivemethodtoincreasetheELF/VLFamplitudeandefciency. [ BarrandStubbe ,1991a]experimentallyshowedthattheELF/VLFsignalamplitudeisproportionaltothesourcearea. CohenandGokowski [2013]transmitteddifferentHFbeampatternsand thebroaderbeampatterngenerallyproducedlargerELF/VLFamplitudes.TwonovelHFmodulationschemesdesignedtoeffectivelyincreasethesourceareaandformthephasedarrayhave beensuggestedandimplemented:beampaintingandgeometricmodulation.BothofthetechniquesinvolverapidlyscanningtheHFbeamoveravastarea,effectivelyincreasingtheareaofthe ELF/VLFsourceregion. ThebeampaintingBPtechniquedescribedby Papadopoulosetal. [1989]providesameans toincreasetheareaoftheionosphericELF/VLFsourceregionwithoutsignicantlyaffectingthe localizedconductivitymodulation.ThemodulationtechniqueisimplementedbyrapidlyandrepeatedlyscanningavastareaoftheionospherewiththeHFbeam.Therapidheaterbeamscanning isfollowedbyacoolingperiodduringwhichtheHFtransmitterisoff,suchthattheontimeplus theofftimecorrespondstothedesiredperiodoftheELF/VLFwavetobegenerated.Inorder forthismodulationtechniquetoworkasdesigned,itisnecessarythatthecharacteristictimeconstantforelectronheatingissignicantlyshorterthanthatforelectroncoolingsothatthebenet ofalargerheatingareamorethancompensatesforthelossassociatedwithashorterHFheating duration[ Papadopoulosetal. ,1989,1990]. Papadopoulosetal. [1989]theoreticallysimulatedthebeampaintingat200Hzmodulation frequency.TheyclaimedtodetermineanoptimalratioofheaterontoofftimethatwouldincreasetheHF-to-ELFconversionefciencyby 500timescomparedtosquare-waveAM.This powerconversionefciencywashopefultooutperformthelongwireELFtransmitter[ Papadopoulosetal. ,1990].However, BarrandStubbe [1991a]and Barretal. [1999]experimentallytested 19

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theheating-coolingresponseoftheionosphereandshowedthattheminimumratiooftheheating andcoolingresponsewas 0.3whiletheBPmechanismrequiredaratioof0.05toachievethe citedefciencyimprovement. GeometricmodulationGM,asimplementedby Cohenetal. [2008],isaspecialcaseof beampainting.DuringGM,theHFbeamscanstheionosphereinageometricpatterne.g.,acircle oraline,cyclingthroughthepatternatadesiredELF/VLFfrequency. Cohenetal. [2008]differentiatedGMfromBPbynotingthatGMdoesnothaveanyofftimetheHFbeamisalwaysat fullpowerandthatGMcyclesthroughthegivenpatternonlyonceperELF/VLFperiod.Similar toBP,GMproducesalargedistributedELF/VLFsourceregion,andithasbeendemonstratedthat theresultingsourcecanbetreatedasanELF/VLFphasedarray[ Cohenetal. ,2010a].GMis effectiveatincreasingthereceivedELF/VLFsignalamplitudeforhighermodulationfrequencies > 3kHzandproducesagainof7dBoververticalAMsquare-waveheatingwith50%duty cycle[ Cohenetal. ,2008,2010a]. Cohenetal. [2010a]alsoimplementedBP,andobservedonly afewdBenhancementoftheamplitudeoverAMatanearbysite 34km,butnoenhancement atfarthersites 700km. Cohenetal. [2010b]'smodelresultshowedthatBPwasnoteffective becauseevenHAARP'sachievableHFpowerwasnotsufcienttoincreasetheelectrontemperaturequicklyenoughtotakeadvantageofBP.Nevertheless,differentiationbetweentheBPand GMtechniquesismerenomenclature:thebasicphysicalconceptsguidingthetwomethodsarethe same. TheBPandGMexperimentshighlighttheprimaryfactorsthatcontributetotheELF/VLF signalamplitudesgeneratedusingaphasedarray,whichare:theHFheatedarea,thedutycycle, thespatialdistributionofphase,andtheobliquenessoftheHFbeam.Thesefourfactorshavenot beentreatedsystematicallyinthepaststudies,andtheireffectscompetewitheachother.ThisdissertationoptimizesthereceivedELF/VLFamplitudebyproperlyaccountingforthesecompeting effects. 20

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1.2.2.4OtherHFtransmissionproperties ThissectionsummarizeseffectsofotherimportantHFtransmissionproperties.First,HF frequencyisdiscussed.TheHAARPHFtransmittercanbroadcastbetween2.7and9.5MHz. Withinthatrange,lowerHFfrequenciesexperiencealargerrateofabsorptionwithinthe D -region ionosphere[ James ,1985].Forinstance, Cohenetal. [2012a]comparedthereceivedELF/VLF amplitudesproducedbyanarrowbeamat3.25MHzandabroadbeamat9.50MHz,bothof whichhadroughlythesameHFpowerdensity.Theobservationshowedthenarrow3.25MHz beamproduced5dBlargeramplitudethanthebroad9.50MHzbeam. HFbeampolarity,X-orO-mode,alsoproducesadifferenceinthereceivedELF/VLFsignal amplitude.ItisgenerallyconsistentthatX-modegenerates4dBlargerreceivedELF/VLFamplitudethanO-mode[ Stubbeetal. ,1982; Ferraroetal. ,1984; Jamesetal. ,1984; Villascoretal. 1996; Barretal. ,1999]becausetheX-modewavecounteractsthenaturaldirectionofelectron motionaroundtheEarth'smagneticeld,andinturn,experiencesalargerrateofabsorption. Themodulationwaveformisalsoanimportantfactortoconsider.Themostcommonwaveformisthesquare-wavewaveformforwhichthedutycyclecanbecontrolledprecisely.The ELF/VLFamplitudeincreaseswithincreasingdutycycleupto20%anddecreasesathigher dutycycles[ BarrandStubbe ,1991b; Cohenetal. ,2010a; Jinetal. ,2012].Thistrendisdue tothefactthattheionosphericheatingtimeconstanttendstobelargerthanthecoolingtimeconstant[ BarrandStubbe ,1991b]. Jinetal. [2012]experimentallycomparedtheamplitudegenerated by2125Hzmodulationforsquarewave,sinewave,andsine-likeoptimalwaveformaninverted waveformdesignedtominimizethegenerationofharmonics.Theexperimentalresultsindicated thatthesquarewavemodulationat40%dutycyclegeneratedthelargestamplitudeandthatthe squarewaveat20%dutycyclewasthemostefcient. BarrandStubbe [1991b]foundthatthe efciencyofsquarewavemodulationwasslightlydifferent,however.While20%dutycyclewas themostefcientat510Hz,at2010Hzand6010Hztheefciencymonotonicallydecreasedwith 21

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increasingdutycycle.TherehavebeenotherwaveformstransmittedfortheELF/VLFwavegenerationsuchasthesquare-root-sinusoidandtrianglewaveforms.Thesewaveformshavenotbeen analyzedfromtheaspectofefciencyimprovement[ Cohen ,2009; AgrawalandMoore ,2012]. Havingsummarizedtheeffectsofionosphericandgeomagneticconditions,aswellasthe effectsofvariousHFtransmissionparametersonthereceivedELF/VLFsignalamplitude,Inow progresstodiscussanalysistechniques. 1.3AnalysisTechniques TwoprimaryeffectsmustbeconsideredinordertoproperlyanalyzeELF/VLFsignalsobservedontheground:1theformationoftheionosphericELF/VLFcurrentsourcebyHFheating, and2thepropagationoftheradiatedELF/VLFsignalwithintheEarth-Ionospherewaveguide. Conventionally,twoseparatemodelsareemployedtopredicttheELF/VLFsourceformationand theEarth-ionospherewaveguidepropagationtotesttheunderstandingofsourceandwaveguide effects[e.g., Barretal. ,1987; Rietveldetal. ,1987; Mooreetal. ,2007; Cohenetal. ,2012b; Gokowskietal. ,2013].AlthoughpropagationpropertieswithintheEarth-ionospherewaveguidearehighlyvariableandfrequencydependent,theycannotbedirectlycontrolled;asaresult, ELF/VLFwavegenerationefciencystudiesfocusoncontrollingthepropertiesoftheionospheric ELF/VLFcurrentsource.Carefullydesignedexperimentsarerequiredtodistinguishbetween propagationeffectsandsourceeffects. AmultitudeofworkssuccessfullycompareELF/VLFobservationstomodelpredictions.Due tothecomplexityofthemodelsandtheirdependenceoftheionosphericparameterswhichcan varywidely,andarelargelyunknown,however,itismoredesirabletoexperimentallyisolatethe twocontributionsinordertosimplifythemodelingandtomaketheexperimentalmeasurement morephysicallymeaningful.ThisdissertationintroducesandrigorouslyappliesELF/VLFtimeof-arriveTOAanalysistoseparateELF/VLFsourceeffectsfromwaveguidepropagationeffects. Inthefollowingsections,Ireviewpastexperimentalandanalyticaleffortsrelatedtothistopic. 22

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1.3.1NeutralizationofWaveguidePropagationEffects BecauseELF/VLFpropagationwithintheEarth-ionospherewaveguideishighlydependent onfrequency,itisdifculttoderiveELF/VLFsourcepropertiesbasedonobservationsatdifferentfrequencies.Forinstance,dependingontheELF/VLFfrequencyemployed,theamplitudeof thesecondharmonicmaybeobservedtobelargerthanthatofthefundamental.Undernormal circumstances,thisisawaveguidepropagationeffect,withthefrequencyofthesecondharmonic approachingoneofthewaveguideresonances.Onepossiblewaytoneutralizetheeffectofthe waveguideistonormalizethereceivedeldortocompareitagainstareferencesignal.Forexample, BarrandStubbe [1993]investigatedtheharmonicsgeneratedduringELF/VLFwavegenerationexperiments.Theynormalizedtheamplitudeofthethirdharmonicat3kHz,generated usinga1kHzfundamentalfrequency,forinstancetotheamplitudeofthefundamentalfrequency at3kHz,generatedusinga3kHzfundamentalfrequency.Thetwotransmissionswereclosely spacedintimeinordertoavoidcomplicationsarisingfromatemporallychangingionosphereor thetemporallychangingstrengthoftheelectrojetcurrent.Thenormalizedfrequencycontentof theradiatedELF/VLFwavenearlyexactlymatchedthenormalizedfrequencycontentofthetransmittedmodulationwaveform BarrandStubbe [1993].Theharmonicratiowasusedtocalculate heatingandcoolingtimeconstantsaswellasthepowerlawindexofHF-to-ELF/VLFconversion. MooreandAgrawal [2011]and AgrawalandMoore [2012]alsonormalizedtheirobservationby supplyingareferencesignalatthesamefrequency.Thesecasessuccessfullyinvestigatedmulti-HF beamheatingunderdifferentpowersettings.Thenormalizationwasusedtocancelwaveguideand electrojetstrengthvariationswithtime.ItwasdeterminedthatcontinuousHFheatinginaddition tomodulatedheatingsuppressesthereceivedELF/VLFamplitudeandthedegreeofsuppression asafunctionofpowerwasusedtoestimateelectrondensitiesinthe D -regionionosphere. 1.3.2PulsedHFHeating PulsedHFheatingexperimentsprovideanothermeanstoisolatetheELF/VLFsourceeffects fromwaveguideeffects. Stubbeetal. [1982]transmittedsquarepulsesandobservedtherst ionosphereresponseat0.7.8msfollowedbyweaksignalsfor 2ms.Therstsignalwas 23

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interpretedasline-of-sightLOSpropagationfromtheionospheretothereceiver,whereasthe followingsignalswereinterpretedasionosphericallyreectedIRsignals.Theobservationof thepulseinthetimedomainseparatestheLOSsignalfromtheIRsignalsandisadvantageous tosimplifythemodelwithouttheEarth-Ionospherereections.Usingthisadvantage, Rietveld etal. [1986]characterizedtheheatingandcoolingtimeconstantswithanexponentialheating model.Similarly, Papadopoulosetal. [2005]comparedtheLOScomponentofpulsedheating observationsagainstaconductivitymodulationmodelanduseda3-DGreen'sfunctiontocalculate thetemporalevolutionofmagneticelds. WhilethereiscertainlyutilityinpulsedHFheatingexperiments,theexperimentalobservationsrepresentonlytheinitialreactionoftheionospheretoHFheating.ForELF/VLFwave generation,thesinusoidalsteady-statesolutionisthedesiredobservation.TheELF/VLFTOA analysispresentedinthisdissertationprovidesthedesiredsinusoidalsteady-statesolution. 1.3.3PhaseversusFrequency AsimpliedversionoftheTOAanalysismethoddiscussedinChapter2consistsofestimatingthegroupdelayofthereceivedELF/VLFsignalbydifferentiatingthereceivedsignalphase withfrequency. Stubbeetal. [1981]and Rietveldetal. [1989]appliedthismethodtodetermine thegroupdelayasafunctionofmodulationfrequencyoftheELF/VLFsignalgeneratedusing alinearfrequency-timemodulationformat.Usingthecalculatedgroupdelays,theyestimated ELF/VLFsourceheightsthatvariedrapidlyasafunctionoffrequencybetween60and130km. ThelargestuctuationsoccurrednearEarth-ionospherewaveguideresonances.Itislikelythat theseuctuationsoccurredbecausesimplydifferentiatingthephasewithfrequencydoesnotisolatetheLOSandionospherically-reectedsignalcomponents. Riddolls [2003]appliedessentially thesamemethodtotheELF/VLFharmonicsgeneratedduringtheHFheatingprocess,andfound similarresults.Inthecontextofthisdissertation,theeffectivesourcealtitudesdeterminedby Stubbeetal. [1981], Rietveldetal. [1989],and Riddolls [2003]arecontaminatedbyionosphericallyreectedsignalcomponents. 24

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1.3.4TimeofArrivalAnalysis ThetimeofarrivalanalysispresentedhereinprovidesameanstoisolateLOSandIRsignalcomponents.Theanalysisproducesbandwidth-averagedamplitude,phase,andpropagation delaymeasurements.InChapter2,wedemonstratethatthisdecompositionprovidesanaccurate measurementoftheELF/VLFsourcephase,andinChapters3,4,and5,wedemonstratehow thisknowledgecanbeusedtooptimizetheELF/VLFsignalamplitudereceivedatanindividual receiversite.SimilaranalysistechniquescanbeusedtooptimizeELF/VLFexcitationoftheEarthionospherewaveguideortooptimizeELF/VLFinjectionintospace,assuminghighfrequencyresolutionTOAanalysiscanbeprovided.ThecombinationofhighfrequencyresolutionandTOA analysisisbeyondthescopeofthisdissertation.Nevertheless,theabilitytoderiveinformation regardingELF/VLFsourcephasedistributionandtheabilitytomanipulatethatdistributionisof criticalimportancetoallthreegoals.ThroughtheapplicationofTOAanalysis,thisdissertation demonstratesbothcapabilities. 1.4ScienticContributions Thescienticcontributionsofthisdissertationareasfollows: 1. TheELF/VLFtime-of-arrivalTOAanalysismethodisintroducedasaneffectivemeans toseparateline-of-sightLOSsignalcomponentsfromionospherically-reectedIRsignal componentsreceivedatanindividualELF/VLFreceiver.ItisdemonstratedthatTOAanalysis identiesthemaximumaltitudeofthedominantELF/VLFsourcegeneratedbymodulatedHF heating.Byseparatingthethemulti-pathsignalcomponents,theELF/VLFsourceeffectsare successfullyseparatedfromEarth-Ionospherewaveguidepropagationeffects. 2. UsingTOAanalysis,theparametersthataffectELF/VLFwavesgeneratedusingbeampainting BPandgeometricmodulationGMareexperimentallyquantiedforthersttime.By decomposingthespatialdistributionoftheELF/VLFsource,theHFheatingareaisidentied asthemostimportanteffectonreceivedELF/VLFamplitude.Conversely,thedistributionof sourcephasingisidentiedastheeffectmostdetrimentaltotheELF/VLFamplitude.Basedon 25

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theexperimentalobservations,simplemodicationstothespatialheatingpatternaresuggested toincreasethereceivedELF/VLFamplitudes. 3. TheeffectofmodulationdutycycleonELF/VLFwavegenerationisquantiedasafunction ofsourcelocation.Itisdeterminedthatperceivedheatingandcoolingratesderivedfromthese measurementsaredependentuponthesourcelocationrelativetothereceiverlocation. 4. AmethodtooptimizetheHFbeampaintingpattern,maximizingtheELF/VLFsignalamplitudeatagivenreceiverlocation,isdemonstrated.Theoptimizationincorporatesexperimental observationsmadefor8heatinglocationsandaccountsfortheeffectivedutycycle,source area,andsourcephasing. 26

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CHAPTER2 ELF/VLFWAVEGENERATIONMECHANISMANDTHETOAMETHOD ThischapterreviewsthebasicphysicalmechanismforELF/VLFwavegenerationbymodulatedHFheatingoftheionosphereanddescribeshowitisadaptedtotheTOAtechniquethatwill beusedthroughoutthisdissertation.TheimportantphysicalprocessesandHFheatingparameters arediscussedtoprovideacontextwithinwhichinterprettheTOAmeasurements.Inaddition, theTOAtimingaccuracyandresolutionarediscussedtogetherwithphysicalandmathematical limitations. 2.1ELF/VLFWaveGenerationMechanism ThecartoondiagramshowninFigure2-1depictstheprocessofELF/VLFwavegeneration byHFheatingofthelowerionosphere.AtHAARP,usingthe12 15elementarraywith3.6MW inputpower,anHFbroadcastforELF/VLFwavegenerationtypicallyhasacenterfrequencyof 3MHz,anERPof0.1GW,andilluminatesanareaof 25kmby 20kmat 80km altitude.AstheHFwavepropagatesupward,itinteractswiththeionosphere,andthewaveenergyisabsorbedbetween 60kmaltitude,theso-called D -region.Thewaveabsorptionis signicantinthe D -regionduetothehighcollisionfrequency 1MHz.Thephysicalprocess ofELF/VLFwavegenerationisbrokenupintoseveralparts:HFwavepropagationandabsorptioninthe D -regionionosphere,themodulationofionosphericconductivities,themodulationof theauroralelectrojetcurrentsatELF/VLFfrequencies,andtheresultingradiationofELF/VLF waves. 2.1.1TheIonosphere Theionosphereisaplasmamediumcontainingelectrons,ions,andneutralparticleswhichare ionizedbytheradiatedenergyfromthesun.Thestructureoftheionospherefrom80kmto400km isshowninFigure2-2.Thedistributionsofionosphericconstituentsareprovidedbyionospheric models:theInternationalReferenceIonosphereIRIandMSIS-E-90AtmosphereModelforthe ionizedandneutralparticles.Thesedataareavailableonline[ Bilitza ,2012].Theionospheric structurevariesasafunctionoftimee.g,dayornight,seasone.g,summerorwinter,and 27

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Figure2-1.AcartoondiagramoftheELF/VLFwavegenerationmechanism. locatione.g,latitudeandlongitude.ThestructureshownintheFigure2-2isfor8October2002at 12:00UTatcoordinates62 Northand145 West.ThislocationcorrespondstoHAARP'slocation atalocaltimeof3:00am.Figure2-2aincludesthedensitiesofelectrons,neutralmolecules,and neutralatoms.Theelectron,neutral,andiontemperaturesareshownintheFigure2-2b. Theregionsoftheionospherearetypicallyclassiedasthe D -regionkm,the E -region km,andthe F -regionabove150km[ Davies ,1990],althoughthesedenitionsarenot strict.Generallyspeaking,the F -regionhasthehighestelectronconcentrationandtemperature becauseitisaffectedmostbythesun'sradiation.Atloweraltitudes,theelectrondensitydecreases. Ontheotherhand,densitiesofneutralmoleculesandneutralatomsincreaseattheloweraltitudes resultinginthe D -regionbeingahighcollisionalregion. Theelectron-neutralandelectron-ioncollisionfrequenciesareshowninFigure2-2ctogetherwiththetotalofthetwocollisionfrequencies.Thesevaluesarecalculatedfromthedata showninFigure2-2aandbusingasimplemodel[ Ratcliffe ,1959].Electronscollidewithheavy particlessuchasions,molecules,andatoms;becauseofthesecollisions,thewaveisabsorbed asitpropagatesthroughthecollisionalplasmamedium.Athigheraltitudes,thetotalcollision 28

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Figure2-2.aDensityofelectronsandneutralparticles,bElectronandneutraltemperature,c Electron-neutral,electron-ion,andtotalcollisionfrequencies. frequencyisdominatedbyelectron-ioncollisions,whereasinthe D -regionionosphere,electronneutralcollisionsdominate. 2.1.2RefractiveIndex Therefractiveindex, n ,determinestherateofabsorptionwithinthe D -regionionosphere. Withtherefractiveindex,ageneralsolutionofthewaveequationtakesthephasorformofinthe caseofE-eldpropagatinginthepositivezdirection, E = E 0 e )]TJ/F55 8.9664 Tf 8.311 0 Td [(jn b 0 z e j w t where E 0 istheamplitudeoftheelectriceld, b 0 isthefree-spacewavenumber,and w isthe angularfrequencyofthewave.Therefractiveindexcantakeacomplexform,denedas n = m )]TJ/F55 11.9552 Tf 12.742 0 Td [(j c .BysubstitutingthecomplexformoftherefractiveindexintoEquation2,itbecomes, E = E 0 e )]TJ/F56 8.9664 Tf 7.191 0 Td [(cb 0 z e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j mb 0 z e j w t 29

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Theeldsarethusattenuatedalongthedirectionofpropagationduetotheimaginarypartofthe refractiveindex.Inturn,thewavepowerisabsorbedbythemediumthatthewavepropagates through.TherefractiveindexisdeterminedbytheAppleton-Hartreeequation[ Ratcliffe ,1959], n 2 = 1 )]TJ/F55 11.9552 Tf 120.995 8.093 Td [(X 1 )]TJ/F55 11.9552 Tf 12.742 0 Td [(jZ )]TJ/F55 8.9664 Tf 18.161 4.71 Td [(Y 2 sin 2 Q 2 1 )]TJ/F55 8.9664 Tf 6.967 0 Td [(X )]TJ/F55 8.9664 Tf 8.312 0 Td [(jZ r Y 4 sin 4 Q 4 1 )]TJ/F55 8.9664 Tf 6.967 0 Td [(X )]TJ/F55 8.9664 Tf 8.312 0 Td [(jZ 2 + Y 2 cos 2 Q wherethesignoftheradicalinthedenominatordeterminesthemodeofpropagation: + isforthe ordinarymodeO-mode,and )]TJ/F22 11.9552 Tf 12.515 0 Td [(isfortheextraordinarymodeX-mode. Q istheanglebetween thewave k -vectorandtheEarth'smagneticeld,and X = w 2 N w 2 ; Y = w ce w ; Z = n w where w N istheplasmafrequency, w ce isthegyrofrequency, w istheangularfrequencyofthe wave,and n isthecollisionfrequency.Individually, w N and w ce aredened: w 2 N = N e q 2 e e 0 m e and w ce = B j q e j m e where N e istheelectrondensity, q e istheelectroncharge, e 0 isthepermittivityinfreespace, m e is theelectronmass,and B isthemagnitudeoftheEarth'smagneticeld.Usingtheelectrondensity showninFigure2-3, w N isontheorderof5 10 6 rad/s.8MHzforthe D and E region,and 5 10 7 rad/sMHzforthe F region.Meanwhile, w ce isontheorderof9 : 5 10 6 rad/s.5MHz wheretheEarthmagneticeldis 50 m T TherefractiveindexiscalculatedusingEquation2fora3MHzX-modeHFwave.The resultsareshownonlogscaleinFigure2-3,wheretherealpartoftherefractiveindexremains closeto1inthe D and E -regions,implyingthattheHFwavepropagatesthroughwithoutsignicant reection.Inthiselectrondensityprole,therefractiveindexgoesto0andreectstheHFwave at 245kmnotshown.Meanwhile,theimaginarypartof n islargestat 90kmaltitudeand decreasesathigheraltitudes,indicatingthatmostoftheabsorptionoccursinthe D -region. 30

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Figure2-3.Realandimaginarycomponentsoftherefractiveindex, n TheabsorbedHFwavesenergizetheelectronsandcanincreasetheirtemperatureswellbeyond 1000K.Itisthisheatingprocesswhichenablesthemodulationofionosphericconductivities. 2.1.3IonosphericConductivityModication TheionosphereisananisotropicmediumduetothepresenceoftheEarth'smagneticeld, andtheconductivityisrepresentedasatensor.Theconductivitytensorcanbeexpressedas: s = 2 6 6 6 6 4 s P )]TJ/F56 11.9552 Tf 9.289 0 Td [(s H 0 s H s P 0 00 s jj 3 7 7 7 7 5 wherewhenthecollisionfrequency, n ,isconstant: s P = N e q 2 e m e n n 2 + w 2 H s H = N e q 2 e m e w H n 2 + w 2 H 31

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s jj = N e q 2 e m e n s P s H ,and s jj denotethePedersen,Hall,andparallelconductivities,respectively.Usingthe electrondensityproleinFigure2-2, s P isontheorderof1 10 )]TJ/F22 8.9664 Tf 6.967 0 Td [(7 S/m,and s H and s jj areon theorderof1 10 )]TJ/F22 8.9664 Tf 6.967 0 Td [(6 S/m. Theconductivitiesaredependentonthecollisionfrequency, n ,andweassume n energy. Theionosphericconductivitiesarethusmodiedbychangesinelectrontemperature.Equations2 72arederivedassumingaconstant n ,however.Accountingforanenergy-dependent n ,the ionosphericconductivitiesare,asexpressedby Tomko [1981]: s P = 4 p 3 j q 2 e m e w Z 0 U U 2 )]TJ/F55 11.9552 Tf 10.352 0 Td [(Y 2 v 3 e f e ; 0 v e dv e s H = )]TJ/F22 11.9552 Tf 9.289 0 Td [(4 p 3 j q 2 e m e w Z 0 U U 2 )]TJ/F55 11.9552 Tf 10.352 0 Td [(Y 2 v 3 e f e ; 0 v e dv e s jj = 4 p 3 j q 2 e m e w Z 0 1 U v 3 e f e ; 0 v e dv e where U is1 )]TJ/F55 11.9552 Tf 13.124 0 Td [(jZ v e istheelectronthermalvelocitywhere n isproportionalto v 2 e ,and f e ; 0 is theelectronenergydistributionfunction,whichweassumeremainsMaxwellianthroughoutthe heatingprocess.Theionosphericconductivitiesaremodiedbyheatingthe D -regionionosphere withHFwaves.IftheHFsignalismodulatedatanELF/VLFrate,theionosphericconductivities aremodulatedaccordingtothatrate.Inthenextsection,IdiscusstheELF/VLFsourcecreatedby themodulatedionosphericconductivity. 2.1.4ELF/VLFSourceCurrents Inthepresenceofanexternalelectriceld,theconductivitiesthataremodiedbyHFheating formanELF/VLFcurrentsource.TherelationshipisexpressedbyOhm'slaw: J = s E 32

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where J isthecurrentdensity, s istheconductivitytensor,and E istheexternalelectriceld. ThemodulatedconductivitiesthuscreateanoscillatingELF/VLFcurrentdensity, J .Inthe polarregions,whereELF/VLFexperimentsaretypicallyperformed,theelectriceldexistsin theionosphereastheso-calledauroralelectrojetelectriceld.Thetypicalstrengthoftheelectriceldisontheorderof5-100mV/m[ Baumjohann ,1982; Payneetal. ,2007].Theresulting ELF/VLFcurrentdensityservesasanELF/VLFsourcethatradiatesanelectromagneticwave[ Balanis ,1989].ThisdissertationisprimarilyconcernedwiththegeneratedELF/VLFmagneticux density B .Tondtheexpressionofthemagneticuxdensity,IstartwithformingtheELF/VLF currentsource, J ,showninEquation2.Equation2isexpandedinamatrixform, 2 6 6 6 6 4 J x J y J z 3 7 7 7 7 5 = 2 6 6 6 6 4 D s P )]TJ/F63 11.9552 Tf 9.289 0 Td [(D s H 0 D s H D s P 0 00 D s jj 3 7 7 7 7 5 2 6 6 6 6 4 E x E y E z 3 7 7 7 7 5 where D s H isthemodulatedHallconductivity, D s P isthemodulatedPedersenconductivity,and D s jj isthemodulatedparallelconductivity.FromFigure2-4, E x and E y aredescribedbythe magnitudeanddirection,thatis E x = j E j sin q E y = j E j cos q Thus,themodulatedelecrojetcurrentbecomes 2 6 6 6 6 4 J x J y J z 3 7 7 7 7 5 = 2 6 6 6 6 4 D s P j E j sin q )]TJ/F63 11.9552 Tf 10.949 0 Td [(D s H j E j cos q D s H j E j sin q + D s P j E j cos q D s jj E z 3 7 7 7 7 5 Thecurrentsource, J ,isahorizontaldipoleduetothelackofcontributionof J z because E z =0. IfweaccountonlyfortheLOSsignalswithanimagesourceovertheEarth'sgroundandassume thattheEarth'sgroundisaperfectconductor,theimagesource, J imag ,is 33

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Figure2-4.North-SouthandEast-Westcoordinatesmappedontoxandycoordinates. j E j isthe electrojetelectriceldmagnitude,and q istheelecrojetelectricelddirectionrelative toNorth.The + z directionoutofthepagecoincideswithincreasingaltitude. J imag = )]TJ/F55 11.9552 Tf 9.289 0 Td [(J J imag islocatedattheoppositesidetotherealsourceoverthegroundplaneandisequallydistanced. Theradiatedmagneticeldincludingtheimagesourceisexpressedas,[ Balanis ,1989,p.283] B x = m 4 p Z V )]TJ/F55 11.9552 Tf 10.448 -9.69 Td [(z )]TJ/F55 11.9552 Tf 10.95 0 Td [(z 0 J y )]TJ/F74 11.9552 Tf 10.95 9.69 Td [()]TJ/F55 11.9552 Tf 5.475 -9.69 Td [(z + z 0 J y ; imag 1 + j b 0 R R 3 e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R dv 0 B y = m 4 p Z V )]TJ/F74 11.9552 Tf 10.618 9.689 Td [()]TJ/F55 11.9552 Tf 5.475 -9.689 Td [(z )]TJ/F55 11.9552 Tf 10.949 0 Td [(z 0 J x + )]TJ/F55 11.9552 Tf 5.476 -9.689 Td [(z + z 0 J x ; imag 1 + j b 0 R R 3 e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R dv 0 B z = m 4 p Z V )]TJ/F55 11.9552 Tf 10.449 -9.69 Td [(y )]TJ/F55 11.9552 Tf 10.95 0 Td [(y 0 J x + J x ; imag )]TJ/F74 11.9552 Tf 10.95 9.69 Td [()]TJ/F55 11.9552 Tf 5.475 -9.69 Td [(x )]TJ/F55 11.9552 Tf 10.95 0 Td [(x 0 J y + J y ; imag 1 + j b 0 R R 3 e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R dv 0 = 0 34

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where J x ; imag and J y ; imag aretheimagecurrentdensitiesforxandydirection, b 0 isthewavenumber, z isthelocationoftheobservation, z 0 isthelocationofthesource, R isthedistancebetweenthe sourceandanobservationpoint,and v 0 isthevolumeofthesourcetointegrate.Ifthesourceis locatedattheheight, h ,withtheeffectivevolumeof D V ,thehorizontalmagneticeldobservedat thegroundisexpressedas,byexpandingEquation2withEquation2, B x = )]TJ/F56 11.9552 Tf 13.45 8.093 Td [(m 2 p hJ y 1 + j b 0 R R 3 e )]TJ/F55 8.9664 Tf 8.311 0 Td [(j b 0 R D V B y = )]TJ/F56 11.9552 Tf 13.45 8.093 Td [(m 2 p hJ x 1 + j b 0 R R 3 e )]TJ/F55 8.9664 Tf 8.311 0 Td [(j b 0 R D V B z = 0 InsertingEquation2toEquation2and2yields, B x = )]TJ/F56 11.9552 Tf 10.783 8.093 Td [(m h H 2 p D s H j E j sin q 1 + j b 0 R H R 3 H e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R H D V )]TJ/F56 11.9552 Tf 11.992 8.093 Td [(m h P 2 p D s P j E j cos q 1 + j b 0 R P R 3 P e )]TJ/F55 8.9664 Tf 8.311 0 Td [(j b 0 R P D V and B y = m h P 2 p D s P j E j sin q 1 + j b R P R 3 P e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R P D V )]TJ/F56 11.9552 Tf 12.444 8.093 Td [(m h H 2 p D s H j E j cos q 1 + j b R H R 3 H e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j b 0 R H D V where h H and h P arethesourceheightsofthemodulatedHallandPedersenconductivities, R H and R P arethedistancebetweenthesourceoftheconductivitymodulationandtheobservationpoint forHallandPedersen.UsingthecoordinateinFigure2-4, B x and B y aremeasuredbyNorth-South NSandEast-WestEWantennarespectively.Duetothetwodifferentsourcesofthemodulated HallandPedersenconductivities,andthedirectionoftheelectrojetelectriceld,NSandEW observationsareexpectedtobesomewhatdifferent. TheTOAmeasurementisnotabletodiscernthesourcesofthemodulatedHallandPedersen conductivitiesduetothelimitedtimeresolution,althoughitisaninterestingproblemthatmaybe 35

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resolvedinthefuture.TheTOAmeasurementindicatesthecombinedeffectsofthetwosources, however,itislikelydominatedbythemodulatedHallconductivitymodulation.ThepastliteratureshaveshownthattheHallconductivitymodulationdominatesthePedersenmodulationin ground-basedobservations[ Rietveldetal. ,1986; Moore ,2007].Throughouttheobservationsof thisdissertation,theTOAmeasurementassumesoneeffectiveELF/VLFsource. Theequationsabovedescribeamagneticeldoverangroundplanethatpropagatesdirectly fromthesource,theso-calledline-of-sightLOSpath.ThissignalistypicallythelargestcomponentoftheTOAmeasurementforreceiverswithin 200kmofHAARP.Othercomponentsnot expressedabovearecalledionosphericallyreectedsignals,whichreectattheEarth'sgroundand the D -regionionosphereandreachestheVLFantennaontheground.TheTOAmethodseparates thesesignalsbytheirdifferenceinarrivaltime,allowingustosimplymodeltheLOSsignaland focusonELF/VLFsourceexcitation.Whilethesumofallionosphericallyreectedcomponents representstheeffectsoftheEarth-Ionospherewaveguide,theLOSsignalcomponentisconsidered tobeindependentoftheEarth-ionospherewaveguide.Althoughthisdissertationfocusesonthe LOSsignalcomponent,itisimportanttoreviewtheionosphericwavereectionprocessforbetter understandingoftheTOAmeasurement. 2.1.5ELF/VLFReectioninthe D -regionIonosphere ItiswellknownthatELF/VLFwavesreectatanaltitudeof 60kminthe D -region ionosphereandpropagatebetweentheionosphereandtheground[e.g, Lewisetal. ,1973; Rietveld etal. ,1986].ThereectionprocessiscomplicatedgiventhelargeELF/VLFwavelengthandthe slowlyvaryingionosphericmedium.Inthissection,Iroughlyestimatethereectionheightusing therefractiveindexgiveninEquation2asintroducedin[ Ratcliffe ,1959]. Oneofconditionswherethereectionofaverticallyincidentwaveoccursisthattherefractive index, n ,isequaltozero.Whentherefractiveindexisequaltozero,thewaveeldcannot propagatebecauseitbecomesanevanescentwaveEquation2.At10kHz,therefractiveindex iszeroatanaltitudeof 120km.However,when Z 1Equation2,thereectionoccursdue toarapidchangeoftheimaginarypartoftherefractiveindex, c ,belowthealtitudewhere m = 0. 36

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Figure2-5.Plasmaparametersat3kHz. Therapidchangeoccursatanaltitudewhere X Z .Theionosphereactslikeadielectricbelow thatthealtitudeandaconductorabovethataltitude.At10kHz, X Z atanaltitudeof 82km, asshowninFigure2-5. 2.2ELF/VLFTime-of-ArrivalTOAAnalysisMethod ThegoaloftheTOAmethodistoestimatetheamplitudeandphaseofELF/VLFwaves arrivingatthereceiverasafunctionoftimeinsuchawayastorevealcharacteristicsofthe ELF/VLFwavesourceregion.As Payneetal. [2007]demonstrated,thisisnotpossibleusinga single-tonemodulationfrequency.Instead,weutilizeafrequency-timerampmodulationformat, typically,from1kHzto5kHzover4seconds.ThistypeofsignalisbroadlyknownasFrequency ModulatedContinuousWaveFMCWinradarapplications[e.g., Barrick ,1973; Schusteretal. 2006]andiscommonlyreferredtoaschirpmodulation. Thisparticularmodulationformatisselectedduetotherelativelysimpleanalysisthatresults. Thelinearfrequency-timeramphasanapproximatelyatresponseinthefrequencydomain.Also, becausethereceivedsignalisbetween 1kHz,thecombinedeffectsofconductivitymodulation andLOSpropagationisexpectedtohaveanapproximatelyatfrequencyresponse.Theconductivitymodulationdecreaseswiththereciprocalofthemodulationfrequencyafter 1.5Hz[ Stubbe 37

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etal. ,1985],andLOSpropagationEquation2increasesasthemodulationfrequencyincreases.Thesetwoeffectsessentiallycanceltoprovidetheatresponse.Thebandwidthofthe rampischosentobebroadenoughtoextracttheLOSsignalinthepresenceofionospherically reectedsignals. Thebandwdithofthefrequencyrampischosentobearoundorbroaderthan4kHzinorder toseparatethemultipathcomponents.Thetimeresolutionasafunctionofbandwidthisdiscussed inSection2.3.2.TheFMCWwaveformcanbereplacedbyFrequencySteppedContinuousWave FSCWaslongasthereciprocalofthefrequencyintervalismuchgreaterthanthepropagation delays.Thegreaterthenumberoffrequencystepstaken,themorerobustthesystemistonoise. Tomaximizethenoiseperformance,thisdissertationfocusesontheFMCWchirp. Thetime-dependenceofthemodulationfrequencyprovidesameanstodifferentiatebetween signalsarrivingatdifferenttimes:theimpulseresponseofthesystemmaybedirectlycalculated fromtheobservations,providingatime-domainestimateofthemulti-pathpropagationdelaysand othersignalproperties.ItshouldbenotedatthispointthattheELF/VLFwavegenerationprocessis inherentlynonlinear,whereastheTOAanalysismethodpresentedislinear.Forinstance,ELF/VLF harmonicsatmodulationfrequenciesthatarenottransmittedareregularlyobservedinELF/VLF recordings.TheimplementationoftheTOAanalysisrstseparatesthereceivedELF/VLFharmonicsandconsidersthemindividually.Additionally,becauseELF/VLFwavegenerationisnonlinear withHFpowerandsignicantlyvarieswithHFfrequenciesandpolarizations,itisexpectedthat thecalculatedimpulseresponseappliesonlyforagivenHFpower,frequency,andpolarization. Lastly,becausedifferentmodulationwaveformsproducedifferentharmoniccontentwhendriving theionosphericconductivitymodulation,wedonotexpectthecalculatedimpulsetoapplytoall modulationwaveforms.Instead,theintentistointerpretagivenTOAimpulseresponsetoyield informationabouttheELF/VLFsourceregionforagivensetoftransmissionparameters. Ibeginbyexpressingthetime-averagedPoyntinguxoftheHFtransmissionasthesumof harmoniccomponents: 38

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h P t i = n h P n t i = n A n cos 2 p n f 0 t + D f 2 t 2 + f 0 n where h P n t i representsthetime-averagedPoyntinguxofthe n th harmonic, f 0 istheinitialfrequencyoftheramp,and D f istheslopeofthefrequency-timeramp. A n and f 0 n aretheamplitude andphaseofthe n th harmonic,bothofwhichareassumedtobeconstantwithfrequencyinthis work. Foragivenharmonic,thereceivedsignalmaybeexpressedas: 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 istheeffectiveimpulseresponseconvertingHFpowertoionosphericcurrentmodulationforthe n th harmonic, p t istheimpulseresponsecharacterizingELF/VLFwavepropagation tothereceiver,and denotesconvolution.TOAanalysisnds h n t ,theeffectiveimpulseresponse combiningtheeffectsofcurrentgenerationandwavepropagationforagivenharmonic. ThetotalreceivedELF/VLFsignal, R t ,maythusbeexpressedas: R t = n A n cos 2 p n f 0 t + D f 2 t 2 + f 0 n u t = T )]TJ/F22 11.9552 Tf 10.95 0 Td [(1 = 2 h n t u t = T )]TJ/F22 11.9552 Tf 10.949 0 Td [(1 = 2 X F s t where T isthedurationofthefrequency-timeramp, F s isthesamplefrequencyofthedataacquisitionsystem,and u and X aredenedas: u t = 8 > < > : 1 j t j < 1 2 0 j t j > 1 2 X t = n = )]TJ/F63 8.9664 Tf 6.966 0 Td [( d t )]TJ/F55 11.9552 Tf 10.949 0 Td [(n Theprocessingofthe n th harmonicbeginsbymixing-downandlteringthereceivedsignal. Themixingkernelforthe n th harmonicmaybeexpressedas: m n t = e )]TJ/F55 8.9664 Tf 8.311 0 Td [(j 2 p n f 0 t + D f 2 t 2 u t = T )]TJ/F22 11.9552 Tf 10.95 0 Td [(1 = 2 39

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b t is,typically,the100-Hzbandwidthlow-passlter,implementedusinga2000-tap,8 th -order Kaiserwindow.Afterapplyingthelowpasslter, b t ,thebase-bandsignalismixed-uptoits originalfrequencyrangeusingthecomplexconjugateof m n t ,andtherealcomponentofthe resultingcomplex-valuedsignalrepresentstheisolated n th harmonic. Theisolated n th harmonicofthefrequency-timeramp, y n t ,maythenbedescribed: y n t = f [ R t m n t b t ] m n t g Theimpulseresponse, h n t complexformof h n t ,iscalculatedbyFourieranalysis,using y n t astheoutputsignaland x n t astheinputsignal: x n t = cos 2 p n f 0 t + D f 2 t 2 u t = T )]TJ/F22 11.9552 Tf 10.949 0 Td [(1 = 2 X F s t h n t = F )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 F y n t F x n t u f )]TJ/F55 11.9552 Tf 10.95 0 Td [(nf 0 nT D f )]TJ/F22 11.9552 Tf 12.145 8.094 Td [(1 2 where F denotestheFouriertransformand F )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 denotestheinverseFouriertransform.Note that D fT representsthefullbandwidthtraversedbythefrequency-timeramps.Therectangular windowisappliedhereforonlyapositivecomponentforasimplerinterpretationexplainedin detailslater.Then, h n t reducesto: h n t = A n t e j f n t n e j 2 p f c t sinc nT D ft nT D f o where A n t and f n t representthebandwidth-averagedamplitudeandphaseofthereceivedsignal asafunctionoftime,and f c isthecenterfrequencyofthefrequency-timeramp.Assumingfareldpropagation, f n t isequaltothephaseofthedominantELF/VLFcurrentsource,whereas A n t dependsonboththeamplitudeofthedominantELF/VLFcurrentsourceandthedistance fromtheionosphericsourcetothereceiver.Here, h n t iscomplex-valuedinordertodirectly assessthephase f n t .Thisresultisachievedbyeliminatingthenegativefrequencycomponents inEquation2[ Gabor ,1946]. 40

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Figure2-6.AcomparisonbetweenTOAobservationsleftandconvolvedsincfunctionsright. Thebluelinesuseonlypositivefrequencycomponentswhereastheredlinesuseboth positiveandnegativefrequencycomponents. Anexampleofcomplex-valued h n t andreal-valued h n t isshowninFigure2-6.As seeninEquation2,theTOAresultconsistsofthecomplex-weightedsumofsincfunctions. Eachsignalarrivingatthereceiveratdifferenttimesisconvolvedwithasincfunctionandforms theTOAresult.Figure2-6alsocomparesTOAresultsforcalculationsperformedusingonly positivefrequencycomponentsandthoseperformedusingbothpositiveandnegativefrequency components.Whilethecombinedfrequencyformproducesanarrowermainlobe,itdoesnotdirectlyprovidephasinginformationitisentirelyreal-valued.Additionally,thepositive-frequency complex-valued h n t representsthesameinformationasthecombined-frequencyreal-valued h n t ,duetoconjugateHermitiansymmetry[ Boashash ,2003].Thecomplex-valuedformof h n t isusedthroughoutthiswork. AscanbeseenintheEquation2,Iapplyarectangularwindowinthefrequencydomain andtransformittothesincfunctioninthetimedomain.Adifferentwindowcanbeused,suchasa HammingorKaiserwindow,whosesidelobesaresuppressedtoagreaterextentthanthoseofthe rectangularwindow.However,themainlobeoftherectangularwindowisthenarrowestofall.In thisdissertation,therectangularwindowisusedtomaximizethecapabilityofseparatingmultipath 41

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signalsintime.Thewidthofthesincfunctionisdeterminedbythebandwidthofthefrequency ramps, D fT ,anditdictatestheTOApropertiessuchasthetimingaccuracyandresolution. 2.3TOAProperties 2.3.1TimingAccuracy OnemainconcernregardingtheTOAmethodisthetimingaccuracyofthedetectedpeak amplitude.Theeffectiveimpulseresponseisasampledversionofthecontinuousimpulseresponse convolvedwithasincfunctionwhosewidthisdeterminedbythebandwidthofthetransmission. WhilethedetectedpeakamplitudemaybeinterpolatedintimeusingstandardFouriertechniques, thedetectedpeakamplitudemaynotexactlycoincidewiththetimingoftheactualpeakamplitude incidentuponthereceiver,duetoconvolutionwiththesincfunction.Toassessthisaccuracy, wecalculatetheCramr-RaoLowerBoundCRLB[ Schusteretal. ,2006,andreferenceherein] usingtheoutputofamodulatedHFheatingmodelthatpredictsthetimedistributionofamplitude andphasegeneratedbymodulatedHFheatingofthelowerionosphere.WenowdescribetheHF heatingmodelandhowitisusedtocalculatetheCRLB. TheHFheatingmodelemployedwasdevelopedby Moore [2007],anditrequiresasinput theHFfrequency,modulationfrequency,andHFpower.Electrontemperatureanddensityproles,togetherwithmolecularnitrogenandmolecularoxygendensityproles,arealsoprovided asinput.WeapplytheelectrondensityprolesusedinpreviousELF/VLFstudies[e.g., Lev-Tov etal. ,1995; Moore ,2007; AgrawalandMoore ,2012]andtherestoftheionosphericparameters areavailableintheMSISE-90Modelonthewebsiteathttp://ccmc.gsfc.nasa.gov/modelweb/.Usingthisinput,themodelcomputesthemodulatedconductivitiesPerdersen,HallandParallelat each1kmgridin3-Drectangularcoordinates.Themodelassumesaconstantelectrojetelectric eldparalleltogroundthroughoutthe D -regionionospheretopredictthemagneticeldincident uponagivenreceiverlocationasafunctionoftimeassumingfree-spacepropagation[ Payneetal. 2007].Forexample,themodelmaybeusedtopredicttheamplitudeandphaseofthemagnetic eldincidentuponareceiverasafunctionoftimeusingamodulationfrequencyof2.5kHz,an 42

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Figure2-7.TheCramr-RaoLowerBoundCRLBofthestandarddeviationofthetimedelayfor thepeakamplitudecomputedbytheHFheatingmodel. HFpowerof85.7dBW,andanHFfrequencyof3.2MHzwithX-modepolarization.ThepropagationmodelemployedneglectsEarth-Ionospherewaveguideeffects,however.Forthereceiver locationsusedinthisworkeachlessthan 100kmawayfromtheHAARPtransmitter,thisassumptionisreasonableashasbeendemonstratedby Payneetal. [2007],whichshowedexcellent agreementbetweensimpleray-tracingandfull-wavemodelingresultsatthesedistances.ApplyingtheTOAtechniquetothepredictedmagneticeldtimeseries,Iwasabletoassessthetiming accuracyofmypeakTOAmeasurement.Eachtimebinhasthreeunknownparameters:amplitude,phase,andtimedelay.WecreatetheFisherinformationmatrix[ Schusteretal. ,2006,and referenceherein]whichmaybeusedtodirectlycomputetheCRLBfordifferentwhiteGaussian Noiselevels.Figure2-7showstheCRLBofthestandarddeviationofthetimedelayforthepeak amplitudeinthemodelasafunctionofthesignal-to-noiseratioSNR.Typically,theSNRofour observationsis5dBorhigher,andFigure2-7indicatesabest-caseaccuracyof 1 m secat5dB SNR.Whilemodelpredictionsusingotherionosphericprolesmayyieldslightlydifferentresults thanpresentedhere,weexpectthe 1m secaccuracyguretobegenerallyrepresentativeofthe 43

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accuracyoftheTOAmeasurement.AlthoughELF/VLFdataisalsosensitivetoimpulsivenoise fromlightning,forexampleandtopowerlineradiationintheELF/VLFrange,theCRLBisstill areasonablebenchmarkfortimingaccuracy,sincewecanincreaseintegrationperiodtoreduce thenoise,orIcanjustavoidaparticularimpulsivenoiseorfrequencybandwidth.Inadditionto theerrorfactorsdiscussedabove,thereisa27.5 2.5 m sectransmissiondelayduetotheHAARP transmissionand 30 n secGPStimingaccuracy,whichhavebeenaccountedforinouranalysis. ToexperimentallyevaluatetheSNRofthemeasurement,IperformthesameTOAanalysis onthedatasetstartingwithanoffsetofahalfperiodofthefrequency-timeramp.Idonotexpect HAARP-generatedELF/VLFwavestocontaminatethismeasurement,yieldinganeffectivemeasurementofthenoiseoor.Fromamongthemanynoise-oormeasurementsthattheTOAanalysis produces,Ipickthepeaknoisemeasurementasthenoiseoor.Asanexample,Figure3-2inthe nextchapterexhibitsanapproximateSNRof 12dBmarkedwithahorizontallineforthepeak amplitudeatSinonaCreekandanapproximateSNRof 25dBmarkedwithahorizontallinefor thepeakamplitudeatMilepost71,bothevaluatedusing2.5minutesofdata.Thenullsinthenoise linemaybecausedbyhumnoiseinterference.InotethattheSNRofthemeasurementincreases signicantlybyrepeatingthefrequency-timerampsforafewminutes. 2.3.2TimingResolution Althoughthetimingaccuracyisnotsignicantlylimiting,thetimeresolutionoftheTOA methodismoresignicant.ThetimeresolutionoftheTOAmethodisdeterminedbythereciprocalofthemodulationbandwidth,whichis,forexample, 333 m secwith3kHzbandwidthof frequencyanalysis.ThepropagationtimedifferencebetweentheLOSandtherstionospherically reectedIRpathisapproximatedto 450 m secwith D -regionELF/VLFwavesourceandreectionheight,ifweassumeaspeed-of-lightpropagation.Thistimedifferenceisfarapartenoughto resolvethetwosignals,however,themeasuredresultsmaybedistortedbyconvolutionwitha sinc functionwhichisintroducedbyarectangularwindowinFourieranalysis. Topreciselyextractthesignals,Iapplytwodifferentdeconvolutionmethods:1theCLEAN method,and2anexhaustiveleastsquareerrorsearchalgorithm.TheCLEANmethoditeratively 44

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Figure2-8.aExampleoftheTOAobservationatParadise'sEWantennafor1-6.5kHzwith5 pulses.bTimedelay,amplitude,andphaseofLOSsignalasafunctionofthenumber ofsignals N subtractsaportionofthelargestamplitudesignalfromtheTOAobservationsuntilthenoiseooris reached[ SegalovitzandFrieden ,1978].TheCLEANmethodthusdecomposestheobservedTOA intoaseriesofcomplex-valued d functions. FujimaruandMoore [2011]reportedanexcellent matchwithamodelresultshowninFigure3-3inthenextchapter.However,theCLEANmethod cannotestimateeachsignalaccuratelyifthelargestamplitudesignalhasbeendistortedbyother signalsspacedcloselyintime.ThisdistortionoccurswhentheLOSandIRsignalsarriveclose intimerelativetothetimeresolutiondeterminedbythebandwidthofthetransmission.Thetime separationbecomessmallerasareceiversiteisfurtherawayfromthesourceregion.Tosolvethis issue,theleastsquareerrorsearchalgorithmistypicallyapplied. Theexhaustiveleastsquareerrorsearchalgorithmisappliedtodeconvolve N pulsesamplitude,phase,andarrivaltimefor N differentpathsthatbestmatchobservations.Thealgorithm scanscombinationsof N pulsearrivaltimes,andcalculatesamplitudesandphasesateachtime combinationinaleastsquaresense.Thepulsesareconvolvedbackwiththe sinc functionand 45

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Figure2-9.aTOAobservationsanalyzedusingdifferentbandwidths.bPercentageofsuccessfulanalysesusingtheleastsquareerrorsearchalgorithmasafunctionofbandwidth. ColorindicatesSNR. comparedwiththeoriginalTOAobservationsusingL-2norms.Thedeconvolvedpulsesarethe onesthatgivetheleasterror.Choiceof N isdependonauser'sinterest. Therelationshipsbetween N andtheextractedpulsesareplottedinFigure2-8.Figure2-8a isaTOAobservationatParadise'sEWantennawith1-6.5kHzramp.ThebluetraceistheTOA observation,andtheredcirclesaretheextractedsignalin5differentpaths N = 5.Startingfrom theearliestarrivingsignals,theyindicateLOS,the1stIR,2ndIR,andsoforth.Figure2-8bisthe propagationdelay,amplitude,andphaseoftheLOSsignalasafunctionof N ,where N isanumber ofsignalstoextract.Eachquantityconvergesas N increases.Thelarger N providesmoreaccurate solution,however,atthecostofsignicantlymorecomputationtime.Typically, N = m + 1yields asatisfactoryresultwhere m indicatesthedesiredsignalcomponenttobeanalyzed. Itisworthnotingthattheresultofthisleastsquaremethoddependsonthebandwidthand SNR.InordertoinvestigatethedistributionoftheresultswithdifferentbandwidthsandSNRs,the leastsquaremethodisperformedwiththeobservationsofthefrequencyrampbetween1kHz. Toseetheeffectsofthebandwidth,Iusethefrequencywindowsof1kHz,2kHz,3kHz andsoon,sothatthefrequencybandwidthchangesbutthecenterfrequencystaysthesameto 46

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Figure2-10.Variancesofpulsesaamplitude,bphaseandcpropagationdelaysdeconvolved usingtheleastsquareerrorsearchalgorithmasafunctionofSNR.Colorindicates bandwidth. compareapproximatelythesameaveragesignal.ToseetheeffectofSNR,Iaddednoisetothe observationstofalselysettheSNRtoacertainvalueinpost-processing.Thenoiseistakenduring ambienttimeswhentherampsarenottransmitted.Therawobservationhas40dBSNRwhichwill bethemaximumSNRconsideredhere.ForagivenfrequencywindowsandSNR,theleastsquare methodwasappliedfor100trialswhereateachtrialnoiseisaddedtakenfromdifferentambient times.TheresultsofthisanalysisareshowninFigure2-9and2-10. Figure2-9aplotstheTOAobservationsofthedifferentbandwidthswith 40dBSNR.The widthofthemainandsidelobesiswideratnarrowbandwidth.With1kHzbandwidth,theLOS andthe1stIRsignalsarenotresolvedastwoseparatepeaks.Figure2-9bshowsthesuccessrate oftheleastsquarealgorithmwith100trialsatdifferentSNRandbandwidths.Theleastsquare algorithmdoesnotprovideareasonablesolutionwhenthecombinationofthearrivaltimesisnot sensitiveenoughtottotheobservation.ThisoccursmoreoftenwithlowerSNRandnarrower bandwidth.1kHzbandwidthisimpracticalfortheleastsquaremethod. Figure2-10showsthevarianceoftheleastsquarealgorithmforLOSamplitude,phaseand arrivaltimeasafunctionofbandwidthsandSNR.WithhigherSNRandbroaderbandwidth,the varianceissmaller.For40dBSNR,thestandarddeviationsoftheamplitude,phase,andarrival 47

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timesfor3kHzbandwidthvaryonlyfrom 0.012.039pT, 0.5 ,and 0.35.0 m s respectively.With30dBSNR,thestandarddeviationsoftheamplitude,phaseandarrivaltimesfor 3kHzbandwidthvaryonlyby 0.03.1pT, 1.5.0 ,and 1.0.5 m s respectively.Most oftheTOAobservationspresentedinthisdissertationhaseitherhighenoughSNR > 40dBfor anarrowerbandwidthkHzorbroadenoughbandwidth > 4kHzforalowerSNR 30dB, whoseerrormarginsarelessthan6%fortheamplitude,lessthan3 forthephase,andlessthan2 m s forthearrivaltimes.Thissmallerrorwouldnotaffecttheanalysispresentedinthisdissertation. 48

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CHAPTER3 EXPERIMENTALVALIDATIONOFTHETOAMETHOD Inthischapter,IwilldemonstratethattheTOAtechniqueisavalidmeasurementbycomparingtheexperimentalTOAobservationswiththeamplitudespredictedbytheHFheatingmodel. Furthermore,TOAanalysisisappliedtoobservationsperformedduringsimpleexperiments:the resultsdemonstratethattheTOAELF/VLFsourcepolarizationandtheTOAELF/VLFsource amplitudeasafunctionofmodulationfrequencybehaveasexpectedforsimpleexperimentgeometries.Additionally,TOAanalysisisappliedtogetherwithadifferentialspatialanalysisto experimentallydetectthespatialdistributionofELF/VLFsourcephasing. Someofthematerialspresentedinthischapterhavebeenpublished[ FujimaruandMoore 2011]. 3.1TOAObservationsversusModelPredictions HAARPexperimentsdesignedtovalidateTOAanalysiswereperformedon29July2008 UniversalTimeUT.Duringtheexperiment,a7 7elementsub-arrayradiateda3.2MHzXmodeHFbeammodulatedwithalinearchirpedfrequencyformatbetween1and5kHzover aperiodof4seconds.Thefrequency-timerampswererepeatedsequentiallyfor150seconds. ObservationswereperformedattheELF/VLFreceiversystemsthatconsistoftwoorthogonal air-coremagneticloopantennasorientedtodetectthehorizontalmagneticeldatgroundlevel, apreamplier,alinereceiver,andadigitizingcomputerthatsamplesat100kHzwith16-bit resolution.Thereceiversaresensitivetomagneticeldswithfrequenciesbetween 300Hzand 45kHz.ThelocationsoftheELF/VLFreceiversusedthroughoutthisdissertationaremappedin Figure3-1. Figure3-2showstheTOAobservationsatSinonaCreekSCandMilepost71MP71on theNorth-SouthNSantennatogetherwiththeapproximatednoiseoor,demonstratingthatthe transmissionsequencemaybeusedtoproduceobservationswithsignicantSNR 12dBatSC and 25dBatMP71.Figure3-3comparesthesesameobservationswithmodelpredictions.The solidbluelinesareexperimentalobservations,thesolidredtracesarethepredictedamplitudes 49

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Figure3-1.MapshowingthelocationsofELF/VLFreceiversitesdeployedbetween2009and 2013forexperimentsrelatingtoHAARP. asafunctionoftimewithoutprocessing,butincludingionosphericreectionwiththereection heightsetat65kmandtheeffectivereectioncoefcientsetat0.3 150 ,andthedashedred linesrepresentthepredictedamplitudesasafunctionoftimefollowingTOAprocessing.The solidgreenspikesinFigure3-3arederivedusingtheCLEANmethod.Iinterpretearlierarrival timese.g., 573 m secondsatSCand 673 m secondsatMP71astheresultofline-of-sight LOSpropagation,whereasIinterpretlaterarrivaltimese.g., 900 m secondsatSCand 1.04 millisecondsatMP71astheresultoftheionosphericallyreectedIRpropagation. Figure3-3showsthatthemodeledLOSsignalsreasonablymatchestheobservedTOAat bothSCandMP71.TheTOAoftheIRcomponentsatMP71alsocloselymatchthetimingof themodelresults,althoughatSC,themodelandobserveddataarenotalignedintime.Thisis possiblyduetothelowSNRoftheIRcomponentinSCdataFigure3-2.Itmayalsobepossible thattheIRcomponentsobservedatSCandMP71havedifferentreectionheightsand/orreection coefcientsduetothedifferentanglesofincidenceattheionosphericboundary.Thisexample,and particularlytheMP71observation,demonstratestheabilityoftheTOAtechniquetodiscernLOS andIRpathcomponentsoftheELF/VLFwavesobservedatthereceiver.Italsodemonstratesthe abilitytoassignamplitudevaluesasafunctionoftime.Bothexperimentalobservationsandthe 50

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Figure3-2.TheTOAamplitudesandphasesofthereceivedELF/VLFsignalversustime.Sinona CreekNSantennaleftandMilepost71NSantennaright.Thedashedlineineach caseshowstheapproximatenoiselevelforeachsite.Thehorizontalwidedashedline isournoisereferenceleveldeterminedbythepeakapproximatednoiselevel. HFheatingmodelindicatethatthetimedifferencebetweenthedirectandIRsignalpathsisgreater than 400 m sec,implyingabandwidthof 2.5kHzissuitabletoresolvethetwopeaks. 3.2SourcePolarization Sourcepolarizationsaredeterminedbytwoorthogonalsourcecurrents,theHallandPedersencurrents.Thestrengthanddominantaltitudeofthesesourcecurrentsisdifferent.Although Figure3-3showstheTOAanalysisforonlytheNorth-SouthNSantenna,duetotheinterference inamplitudeandphaseproducedbyHallandPedersencurrents,Iexpectobservationsonthe NSandEWantennatobesomewhatdifferent.Furthermore,becausethedirectionoftheHalland 51

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Figure3-3.AComparisonbetweenmodelpredictionandobservationsatSinonaCreekleftand Milepost71right.Onthisplot,theCLEANmethodisemployedusingagainloop of0.4. Pedersencurrentsdependonthedirectionoftheauroralelectrojetcurrents,Iexpecttheperceived timeofarrivaltodependonthedirectionoftheauroralelectrojetSection2.1.4. Figure3-4showstheexperimentalobservationoftheinterferenceofthetwosources.The antennahasbeenarticiallyrotatedinpost-processingtosimulatetheTOAvariationwithauroral electrojetdirection.Fromtheleftpanel,itisclearthattheTOAanalysisisdependentuponthe electrojetdirectionandantennaorientation.Expandingthetimeaxisintherightpanel,itisclear thatthepeakarrivaltimedependsontheelectrojetdirection,varyingby30 m sec.Hence,theTOAs observedontheNSandEWantennasaredeterminedbyacombinationofthemagneticeldsradiatedbytheHallandPedersencurrentswhichinturndependonthedirectionofelectrojetelectric eld.AlsoshownintherighthandpanelinblackisthemagnitudeoftheTOAobservation. Themagnitudedistributionvarieswithtime,butdoesnotdependonthedirectionoftheauroral electrojet. 52

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Figure3-4.TOAatSinonaCreekasafunctionofthedirectionofelectrojetcurrentcalculatedby rotatingtheNSandEWantennaorientationsinpost-processing. 3.3TOAversusHFFrequency&Power ThesourceheightsasafunctionofHFfrequencyandHFpowerareinvestigated.The frequency-timerampsinthiscaserangedfrom1to5kHzoveraperiodof4seconds.Every 4secondsperiod,theHFpoweralternatedbetween25%,50%and100%power,andeachperiod repeatedfor5minutes.Every5minutes,theHFfrequencyswitchedbetweeen3.2MHzX-mode and5.8MHzX-mode.ObservationswereperformedatSinonaCreekandatMilepost71,but theintroductionofcommercialpowerlinesnearMilepost71sitehassignicantlyreducedthedata qualityatthatsite.Inthissection,onlyobservationsfromSinonaCreekwillbediscussed. Figure3-5showstheTOAanalysisresultsforthemaximumpeakmagnitudeasafunctionof HFpowerat3.2MHzandat5.8MHz.ThevariationsinTOAaresmall,lessthan10 m seconds, whetherintermsofHFfrequencyorintermsofHFpower.Theexperimentalresultspresented inFigure3-5donotdenitivelyexhibitamonotonicincreaseintheTOAintermsoftheHF power,andneitherdotheydenitivelyshowanincreaseintheTOAfrom3.2MHzto5.8MHz. Nevertheless,itisclearthattheeffectsofHFfrequencyandpowerarerelativelysmallcomparedto otherparameters,suchastheHFbeamdirection.Itwillbenecessarytocompleteafullstatistical 53

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Figure3-5.TOAasafunctionofHFfrequencyandpoweratSinonaCreek. analysisofHFpowerandHFfrequencyTOAobservationstodeterminewhetheraconsistent dependencemaybederivedfromthisdataset. 3.4TOAasaFunctionofModulationFrequency TheELF/VLFwavegenerationasafunctionofmodulationfrequencyhasbeenofgreatinterestduetothefrequencydependentnatureoftheEarth-ionospherewaveguide.However,analysis ofthedatarequirestheuseofacomplicatedEarth-IonosphereEIwaveguidemodelwithan approximatedionosphericcondition.Here,theTOAmethodisusedtoexperimentallydiscount Earth-ionospherewaveguideeffectsanddeterminetheeffectivesourcealtitudeasafunctionof modulationfrequency. ForthedatashowninFigure3-6,TOAanalysiswasperformedusinga3kHzbandwidth centeredondifferentfrequencieswithinthe1-5kHzfrequency-timeramp.Theeffectivesource altitudetendstodecreasewithincreasingmodulationfrequencyfromacenterfrequencyof2.5kHz to3.5kHz.ModelpredictionsshownintherightpanelfromtheHFheatingcodeintroducedin Section2.3.1demonstratethatthesourcealtitudetendstodecreasewithmodulationfrequency: theconductivitymodulationdirectlyabovetheHAARPtransmitterfor1kHzmodulationcontains 54

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Figure3-6.aTOAasafunctionofmodulationfrequencyatSinonaCreekandParadise.b AmplitudeofHallconductivitymodulationasafunctionofheightat1and5kHz usinggenericelectrondensityandtemperatureproles. largerconductivitymodulationcomponentsathigheraltitudesthanfor5kHz.Thevariationin thetwotracesisalmostexactlythesamebelowanaltitudeof85km.Above85km,the1kHz modulationisrelativelystrongerthanthe5kHzmodulation.ThemodulationofthePedersen conductivitynotshownexhibitssimilareffects. 3.5BroadBeamConstructionfromMultipleNarrowBeams Inthissection,wedemonstratethattheELF/VLFwavesgeneratedusinganarrowHFbeam patterndirectedatmultiplespeciclocationsintheskycanbelinearlysummedtoaccuratelyapproximatetheELF/VLFradiationproducedbyabroadenedHFbeampattern.Recently,asimilar effecthasbeendiscussed: Gokowskietal. [2013]interpretedobservationsofELF/VLFwaveamplitudesgeneratedbysimultaneouslymodulatingtheionosphereusingtwoHFbeamsatdifferent HFfrequenciesasthesumoftheELF/VLFsignalsgeneratedusingtheindividualHFbeams.The theoreticalpredictionswereprovidedbyasimplemodelandheuristicallymatchedobservations. Theanalysisprovidedby Gokowskietal. [2013]isnotsubstantiallydifferentfrompastworkthat analyzedELF/VLFphasedarrays[ Barretal. ,1987; Papadopoulosetal. ,1989; Cohenetal. ,2008, 2010b,a],inthatthephasedarraystructureofthesourcewasmodeledandcomparedtoobservationstoshowconsistency.TheexperimentdescribedinthissectionusesHAARP'sbroadbeam 55

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Figure3-7.topThreenarrowHFbeampatterns:15 off-zenithwith104 azimuth,verticaland 284 azimuth.bottomAcomparisonofthesumofthethreenarrowbeampatterns leftwiththeverticalBBEWpatternright. patterntogeneratewaves,andthenapproximatestheresultbysummingthewavesgeneratedseparatelybythreenarrowbeampatterns.Inthiscase,theHFbeamsareallatthesameHFfrequency, andnotheoreticalmodelingisrequired.Theseexperimentalresultsarethustherstexperimental conrmationthatalinearsumoftheELF/VLFwavesgeneratedbymultiplenarrowHFbeams suitablyapproximatestheELF/VLFeldsgeneratedbythebroaderHFbeampattern. 3.5.1NarrowBeam/BroadBeamExperimentDescription HAARPiscapableofbroadcastingaBroadEWHFbeampatternBBEW,whichspoils thenarrowHFbeampatternintheEast-Westdirection,asshowninFigure3-7.TheBBEWbeam patterncanbeapproximatelydecomposedintoappropriatelyscaledinERPnarrowHFbeam patternsdirectedtoward:284 Azwith15 off-zenithOZ,Vertical,and104 Azwith15 OZ. Thethreenarrowbeampatternsandthesumofthethreenarrowbeampatternsareshownalongside theBBEWpatterninFigure3-7.TheBBEWpatternisgrosslyequivalenttothesumofthethree appropriatelyscalednarrowbeams. 56

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Figure3-8.leftTOAobservationsforthethreenarrowbeampatterns.rightTOAobservations forthesumofthethreenarrowbeampatternsandtheBBEWpattern. On8October2010,HAARPbroadcasteachbeampatterndescribedaboveat3.2MHzXmode.EachbeamwasmodulatedusingAMsinemodulationwithalinearfrequency-timechirp from0.5kHzto6.5kHzover6seconds. 3.5.2ResultsandAnalysis TOAobservationsfromParadiseareshowninFigure3-8.TheTOAobservationsareprocessedusingabandwidthof1kHzandproduceadecentSNRdB.Figure3-8includes TOAobservationsforBBEW,thethreeindividualnarrowbeams,andthesumofthethreenarrow beams.ComparingtheBBEWandthesumofthenarrowbeams,theamplitude,phasenotshown, andtimingoftheTOAanalysesareallextremelysimilar.Hence,ELF/VLFwavegenerationusing theBBEWpatterncanbecloselyapproximatedbysummingtheELF/VLFeldsgeneratedbythe threenarrowbeampatterns.Thisapproximationextendstoamoregeneralconclusion:anarbitrarilyshapedHFbeampatterncanbesuccessfullyapproximatedusingthelinearsummationof narrowbeamsthatproducethearbitrarybeampattern.Thisconceptwillbeusedtoanalyzethe phasedarraystructureoftheELF/VLFsourcegeneratedbyBP/GMformatsdiscussedinthenext twochapters. 57

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Together,thecalculationsandobservationspresentedinthischapterdemonstratethevalidity andutilityoftheELF/VLFTOAanalysismethod.Insubsequentchapters,TOAanalysisisappliedtoexperimentalobservationsinordertoquantifyphysicalpropertiesproducedbyspecic modulationformats. 58

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CHAPTER4 OBSERVATIONSOFELF/VLFSOURCEPHASING Intheprevioustwochapters,theELF/VLFTOAanalysismethodhasbeendescribedindetail andappliedtoexampleexperimentalobservationstodemonstrateitsutility.Inthischapter,TOA analysisisappliedtopredictmethodstoincreasetheamplitudeofgeneratedELF/VLFwaves. BasedonpreviousexperimentalobservationsofELF/VLFwavesgeneratedusingtheGeometric ModulationGMformat,whichincreasestheELF/VLFamplitudeby7dBoververticalAM heatingatfrequenciesabove 3kHz[ Cohenetal. ,2008,2010b,a],theformationofanoptimized ELF/VLFphasedarrayisthemostpromisingtechniquetofurtherimprovetheamplitudeELF/VLF wavegeneration.Theanalysispresentedinthischapterisusedtoprovidealimitedoptimizationof thesignalradiatedbyaphasedELF/VLFsourceandtoidentifytheadditionalparametersrequired tocompleteafulloptimization. NewexperimentalobservationsarepresentedofELF/VLFwavesgeneratedusingamodied GMformat:GMiscombinedwithpulsemodulationineffectproducingbeampainting,orBP, modulationtocontrolthephysicalareaoftheionosphericELF/VLFsourceregion.Asaresult, fourcompetingphysicaleffectsthatcontributetothereceivedELF/VLFamplitudeareclosely investigated:theareaoftheELF/VLFsourceregion,theobliqueangleofHFheating,theeffective dutycycleofGM,andthephasedistributionwithintheELF/VLFsourceregion.Basedonthese observations,newmodulationformatsarepredictedtoincreasethereceivedELF/VLFmagnitude bymorethan4dBandtheHF-to-ELFconversionefciencybymorethan7dB. 4.1BeamPainting/GeometricModulationBP/GM 4.1.1BP/GMExperimentDescription 20daysofsuccessfulELF/VLFobservationswereperformedoverthecourseoffourexperimentalHAARPcampaignsbetween19Jul2011and12May2012.Duringthesecampaigns,the HAARPHFtransmitterbroadcastavariablepulselengthgeometricmodulationformat.Twotypes oftransmissionformatswereemployed,andbotharedepictedschematicallyinFigure4-1.Both transmissionformatsarebasedonthecirclesweepGMformat,whichtracesoutacircleinthe 59

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Figure4-1.Cartoondiagramsformodiedcirclesweepgeometricmodulationformats.aSide view.bTopview:twosymmetricarcs.cTopview:threeasymmetricarcs.The orangeandblueregionsindicatewhentheHFbeamisONorOFF,respectively. ionosphere,asdepictedinFigure4-1a.Theseformatsadditionallyemployedavariablepulse lengthmodulationformatsuchthattheHFtransmitterwasONonlyforaportionofeachcircle sweep.TheendresultisacirclesweepGMformatthatproducesanELF/VLFsourcewitha certainknownarclength. Fortherstformat,depictedinFigure4-1b,thetimingofthevariablepulselengthmodulationproducesarclengthsvaryingfrom20 to360 in20 steps.Thearcswereproducedsuch thattheywereallcenteredonthesameazimuthaldirection:81 eastofnorthEoNwhichis thedirectiontowardtheELF/VLFreceiverlocatedatParadise.Forthesecondformat,theresultingarclengthsvaryfrom10 to360 in10 steps,butthearcsareincrementedasymmetrically asindicatedinFigure4-1c.Strictlyspeaking,onlythe360 arclengthtransmissionsareGM formats,whereastheremainderofthetransmissionswouldbeclassiedasBPformatsbecause theyincludeofftimeduringthemodulationperiod.Accordingly,wewillrefertotheseformatsas BP/GMtransmissionformats. ForbothoftheseBP/GMtransmissionformats,HAARPbroadcastanHFwaveat3.2MHz X-modewith15 off-zenithangleand85.7dBWeffectiveradiatedpowerERP.Thetransmissionforeacharclengthhadadurationof3seconds.Duringthe3-secondduration,thespeedofthe 60

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circle-sweeplinearlyincreased,sothattheexpectedELF/VLFmodulationfrequencylinearlyincreasedfrom1.5to4.5kHzoverthecourseofthe3seconds.Theresultingfrequency-timeramp, orlinearchirp,isusedinpost-processingtodeterminethepropagationdelaybetweenHAARP transmissionandELF/VLFwavereceptionbyemployingtime-of-arrivalTOAanalysis.After each3-secondperiod,thearclengthincreasedinthestepsdescribedabove. InordertoprovideacomparisonwithamplitudemodulationAMformats,theBP/GM transmissionswereboundedbyAMtransmissions.The25symmetricformattransmissionswere boundedbyAMtransmissionsthatwereaimedvertically,whereasthe77symmetricand69asymmetricformattransmissionsemployedobliqueAMheatingtransmissionsthatwereaimedata15 ofoff-zenithangleand81 EoNazimuth.BothverticalandobliqueAMtransmissionsbroadcast at3.2MHzX-modewiththesameERPandthesamefrequency-timerampasGMusing50% dutycyclesquare-wavemodulation. AdirectcomparisoncanbemadebetweenELF/VLFsignalsgeneratedusingobliqueAM heatingformatsandthosegeneratedusingBP/GMformatswitharclengthsof20 .The360 GMformatsareimplementedusinganaverageof12HFbeampositions.Atlowermodulation frequencies,moreHFbeampositionsareusedtoimplementthecirclesweep,whereasathigher frequencies,fewerHFbeampositionsareused.At3kHz,however,exactly12HFbeampositionsareused.THeBP/GMarclengthof20 exactlycorrespondtoanobliqueAMheating transmissionswith5.6%dutycycle.Asaresult,weareabletousetheELF/VLFamplitudesobservedat3kHzforAM50%dutycycleheatingandBP/GMwith20 arclengthasameasureof ELF/VLFamplitudedependenceondutycycle.Thismeasurementenablesthecharacterizationof ionosphericheatingandcoolingratesaswellasthecharacterizationoftheeffectivedutycyclefor GMformats. Inthissection,Ipresentastatisticalsummaryofobservationsperformedoverthecourseofthe fourcampaignsandforwhichthegeomagneticandionosphericconditionsvariedsignicantly, butwehighlightobservationswithparticularlyhighsignal-to-noiseratioSNRperformedon20 July2011and19February2012.On20July2011,theHAARPux-gatemagnetometerregistered 61

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Figure4-2.AsymmetricGMCirclesweepwithobliqueAM:SpectrogramaandfrequencyresponsebfordifferentarclengthscolorofthecirclesweepandobliqueAM.The AM+15 labelidentiesamplitudemodulationwithabeamtilted15 towardParadise az. uctuations < 75nT,ionosphericabsorptionasmeasuredbytheHAARPriometerwas 0.2dB, andthe K p indexwas4.On19February2012,theHAARPux-gatemagnetometerregistered uctuations < 50nT,ionosphericabsorptionasmeasuredbytheHAARPriometerwas 0.3dB, andthe K p indexwas3 )]TJ/F22 11.9552 Tf 9.289 0 Td [(. 4.1.2BP/GMExperimentalObservations 4.1.2.1Frequencyandtimeresponseobservations AspectrogramandassociatedfrequencyresponsesfortheBP/GMformatsarecomparedto obliqueAMheatinginFigure4-2.Therstrampinthespectrogramisgeneratedbyoblique AMheatingandtheremainderoftherampsaregeneratedbyBP/GMwhosearclengthincreases from10 to90 .Forbothtypesoftransmissions,thesecondandthirdharmonicsaresuccessfully detected.ThefrequencyresponsepanelcontainsobliqueAMandBP/GMforevery60 arclength. Overthisfrequencyrange,theamplitudeincreasesupto 180 arclengthanddecreasesafterward, withdetailsdependingonfrequency. Figure4-3presentsTOAobservationscomparingGMfullcirclesweepandobliqueAM heating.EachtraceexhibitsadominantLOSpeakat 0.7millisecondsandasecondarypeakat 1.1milliseconds,whichisinterpretedastherstionosphericallyreectedIRsignal.Usingthe leastsquaredeconvolutionprocedurediscussedinChapter2,weidentifytheamplitude,phase,and 62

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Figure4-3.TOAobservationsforGM360 circlesweepandobliqueAMheating%dutycycle atParadiseforathenorth-southantennaandbtheeast-westantenna.Errorbars indicatetheuncertaintyinamplitudefortheLOSandIRsignalcomponents. propagationdelayassociatedwiththeLOSandIRsignalcomponents,allofwhichareidentied inFigure4-3.WhilethepropagationdelayidentiesthemaximumpossibleELF/VLFsource altitude,wecanassumeaspecicgeometryandapproximatethesourcealtitudeforthatgeometry. Forexample,thesourcealtitudeforobliqueAMheatingcanbeapproximatedas 90kmaltitude ifweassumeELF/VLFwavespropagateatthespeed-of-lightandthatthesourceislocatedatthe centeroftheHFbeam. ForthecaseshowninFigure4-3,GMenhancestheLOSamplitudeonlyfortheEWchannelascomparedtoobliqueAM.ThetotalELF/VLFsignalmagnitudeforGMisonly 2dB strongerthanforobliqueAM,andthisistypicallythecase.Figure4-4aplotstheratioofthe ELF/VLFsignalmagnitudeindependentofsignalpolarizationforGMtothatforobliqueAM averagedoverthedurationofthefourcampaignswiththeaverageweightedbysignal-to-noise ratioSNR.GMistypicallyweakerthanobliqueAMby 1dBnear2kHz,butstrongerthan obliqueAMby 1-3dBathigherfrequencies.UsingTOAanalysis,GMistypicallystrongerthan obliqueAMby0.6.6dB.Forcomparison,Figure4-4bplotstheratiooftheELF/VLFsignal magnitudeforGMtothatforverticalAMheatingsimilarlyaveragedoverthedurationofthefour 63

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Figure4-4.aTheSNR-weightedratiooftheELF/VLFsignalmagnitudeforGMtothatfor obliqueAMaveragedoverthedurationofthefourcampaigns.bSameplot,butfor verticalAM. campaigns.TheratioofGMtoverticalAMheatingisconsistentwithpastobservationsandpredictions[ MooreandRietveld ,2009; Cohenetal. ,2010a].ComparedtoverticalAMheating,GM produceslargerELF/VLFsignalmagnitudesbyatleast2dBacrossthefrequencyrange,andat highermodulationfrequenciestheeffectismorepronouncedupto9dB.TOAanalysisindicates thatGMistypicallystrongerthanverticalAMby5.9.1dB.Similarobservationled Cohenetal. [2008]toimplythatELF/VLFwavegenerationusingGMmightproduceunprecedentedHF-toELFconversionefcienciesathighermodulationfrequencies.ComparedtoobliqueAMheating, however,GMproduceslowerELF/VLFsignalmagnitudesatfrequenciesof2kHzandbelow.At 3and4kHz,GMproduces1dBlargersignalmagnitudes,butthedifferenceappearstostop increasinginthatfrequencyrange.Inthiscase,itappearsthatthenatureofobliqueAMheatingat highermodulationfrequenciesproducesasubstantialportiondBoutof7dBofthegain previouslyreportedandattributedtotheGMheatingformatathigherfrequencies. Theseobservationsareactuallyconsistentwiththeobservationsreportedby Cohenetal. [2010a],whoindicateda3dBenhancementinamplitudeforobliqueAMheatingcomparedto verticalAMheatingandalsoidentiedamplitudegainsof 2.5dBforobliqueheatingat5010Hz 64

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Figure4-5.SymmetriccirclesweepamplitudesasafunctionofarclengthcomparedwithAM verticalheatingatParadise. versus1249Hz. Cohenetal. [2010a]concludedthatbasedontheirobservations,obliqueheating contributedonlyasmallfractionofthegainobservedforGMformats.Athigherfrequencies, however,ourobservationsnear4kHzaremoreconsistentwiththesumoftheirobliqueHF 65

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Figure4-6.AsymmetriccirclesweepamplitudesasafunctionofarclengthcomparedwithAM oblique Azimuth,15 off-zenithatParadise. heatingeffects:a5.5.5dBenhancement.Thesegainsattributedtoobliqueheatingare,infact, asignicantportionofthe7dBenhancementoriginallyattributedtotheGMheatingformat athighfrequencies.ItisnoteworthythatobliqueAMheatingismoreefcientaccountingfor shortertransmissiondurationsthanGMheatingby3dBat2kHzandby0.5.0dBat4kHz, observationsthatareperfectlyconsistentwiththetheoreticalpredictionspresentedby Mooreand Rietveld [2009]. Itshouldbenotedatthispoint,however,thatthedirectionalityoftheELF/VLFsourceproducedbyobliqueheatingproducesacompetingeffectoncemultiplebeamsareemployed.If N beamdirectionsareemployed,theheatedareaapproximatelyincreasesbyafactorof N .Dueto thedirectionalityoftheELF/VLFsourceproducedbytheobliqueHFbeam,thisfactorof N isnot realizedinpractice.Thiseffectwillbediscussedingreaterdetaillaterinthischapter. 4.1.2.2Amplitudeasafunctionofarclength Figure4-5showstheELF/VLFsignalamplitudesandmagnitudesreceivedatParadisefor differentfrequencies,3and4kHz,theLOSsignalcomponent,andtherstIRcomponentasa functionofarclengthforthesymmetricBP/GMexperiment.Theamplitudes/magnitudesforspecicfrequenciesareshownintheleftpanelsa,bandc,whiletheamplitudes/magnitudes 66

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Figure4-7.AsymmetriccirclesweepamplitudesasafunctionofarclengthcomparedwithAM oblique Azimuth,15 off-zenithatOasis. fortheLOSandrstIRcomponentsareshownintherightpanelsd,eandf.TheLOS amplitudes,isolatedfromthewaveguideeffects,arecomparedwiththepredictionsofasimpledistributedphasedarraymodel.Asidefromspecicdetails,alloftheplotsareverysimilarinnature. Inallcases,thesignallevelincreasesuntilanarclengthof180 .Atlargerarclengths,the signalleveldecreases.Atlowarclengths,thesignallevelsincreaseapproximatelylinearlywith arclength,whichisnotunexpectedconsideringthatpastworkhasindicatedthattheELF/VLF signalamplitudeisproportionaltotheareaoftheheatedregion[ BarrandStubbe ,1991a].The tracesexhibitslightcurvaturesatlowarclengths,however,andweattributethiscurvaturetothe differentsourcephasingasafunctionofarclength.Thisphasedarraynatureismuchmorepronouncedatlargerarclengths,wherethiseffectisthedominantcauseofthereductioninsignal level > 200 .PlottedtogetherwiththeBP/GMtracesaretheamplitudes/magnitudesobserved forverticalAMheating.Wehaveplottedthesepointsat20 arclengthtoindicatethesimilar natureofthetwotransmissions.VerticalAMheatingproduceslargersignalamplitudesthanthe 20 BP/GMsweepdueinlargeparttothelargerdutycycleemployed.Wehesitatetomakea directcomparisonusingverticalAMtransmissions,however,andreservedetailedcommentfor comparisonswithobliqueAMheating. 67

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Figure4-8.Averageasymmetriccirclesweepamplitudesasafunctionofarclengthcomparedwith obliqueAM Azimuth,15 off-zenithatParadise. Figures4-6and4-7showtheresultsofasymmetricBP/GMcomparedwithobliqueAMobservedatParadiseandOasisrespectively.Becausethetracesaresosimilar,wehaveonlyplotted theresultsforsignalmagnitude.WhilethetracesshownforParadiseareextremelysimilartothose forthesymmetricexperiment,herewehighlightthecomparisonwith oblique AMheating.The signallevelsgeneratedbyobliqueAMareamuchlargerfractionofGMthanthosegeneratedby verticalAMheating.Infact,inmanycases,thesignalgeneratedusingobliqueAMheatingis largerthanthatgeneratedusingthefullsweepGM.TheobliqueAMheatingtransmissionisonly differentfromthe20 BP/GMtransmissionintheirdutycycles:obliqueAMutilizeda50%duty cycle,whereasthe20 BP/GMtransmissionisequivalenttoa5.6%dutycycle.Basedonourobservations,thedutycycledifferencetypicallyproducesa3.9.5dBgaininfavorofthe50%duty cycle.ObservationsatOasisservetohighlightthephasedarraynatureoftheELF/VLFsource.All oftheobservedsignallevelsincreaseupto180 anddecreasetonullamplitudesat360 .For360 eachoftheindividualsourceregionscanbepairedwithout-of-phasecounterparts,sinceOasisis locatedveryclosetoHAARPatthecenterofthecircle,andtheseobservationsareconsistentwith themodelpredictionsprovidedby Cohenetal. [2010b]. 68

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Figure4-9.Thecampaign-averagedratiooftheELF/VLFsignalmagnitudegeneratedusing360 GMtothemaximumBP/GMsignalmagnitude. RefocusingonceagainonobservationsperformedatParadise,Figure4-8presentsweighted averagesignalmagnitudesfortheasymmetricBP/GMexperimentfor20transmissionsperformedduringthe2012FebandMayBRIOCHEcampaigns.FortheTOAanalysis,onlytheruns forwhichtheleastsquareanalysisconvergedtoaresultwereincludedintheaveraging.Forthe frequencyanalysis,aminimumSNRthresholdof3dBwasemployedtoavoidunnecessarynoise content.Plottedtogetherwiththesetracesaretheweightedaveragesignalmagnitudesforoblique AMheatingat2,3,and4kHz,andfortheLOSandIRsignalcomponents.Itcanbeseenthatwhile the360 GMsweeptypicallyproduceslargerELF/VLFsignalmagnitudesthanobliqueAMheating,at180 BP/GMsweeping always produceslargerELF/VLFsignalmagnitudesthanoblique AMheating.Figure4-9showsthecampaign-averagedratiooftheELF/VLFsignalmagnitude generatedusing360 GMtothemaximumBP/GMsignalmagnitudeobservedasafunctionofarc length.BP/GMproduceslargeratleast0.5.5dBsignalmagnitudesatallfrequencies,although itproducesthelargestgainsdBatlowerfrequencies. InordertobetterdisplaythephasedarraynatureoftheBP/GMsourceregion,theamplitude andphasecontributionproducedbyaparticularsourceelementiscalculatedbydifferentiating theTOAobservationsasafunctionofarclength.InordertoachievereasonableSNRlevels,30 69

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Figure4-10.TheamplitudesLeft:3kHz,Right:LOSatParadiseareplottedasafunctionof azimuthcenteredatParadise.0 indicatesazimuthaldirectiontowardParadise.30 arclengthsareintegratedtocalculatetheamplitudeandphase.Theorangelineisthe samemodelresultusedinFigure4-5. 70

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Figure4-11.ThephasesLeft:3kHz,Right:LOSatParadiseareplottedasafunctionofazimuth centeredatParadise.0 indicatesazimuthaldirectiontowardParadise.30 arclengths areintegratedtocalculatetheamplitudeandphase.Theorangelineisthesamemodel resultusedinFigure4-5. arclengthsareused.Similarly,theamplitudeandphaseover30 arclengtharecalculatedinthe frequencydomain.TheLOSand3kHzamplitudeandphaseobservedatParadiseareplottedin Figures4-10and4-11.Weobserve 5dBamplitudedifferences,whichissomewhatlarger thanpastobservations-10dBobservedby Barretal. [1987]and6-8dBobservedby Cohen etal. [2010a].Theportionofthecircledirectedtowardthereceiverupto120 arclength producesbyfarthelargestsignalamplitudes,andtheportionofthecircledirectedawayfromthe receiver>240 arclengthproducesthelowestamplitudes.Theseobservationssupport Moore 71

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andRietveld [2009]'spredictionthattheportionofthecircleclosesttothereceiverdominatesthe receivedamplitude. TheinterpretationofthephasefortheLOScomponentandthe3kHzcomponentissomewhat different.UsingtheTOAmethod,thephaseofthemeasurementrepresentstheELF/VLFsource phase,whereasinthefrequencydomain,thephaserepresentsthephaseofthesourceplusthe propagationphase.ThephaseshowninFigures4-11canddisthesourcephase.Thephase approximatelyfollowsalinearprogressiondashedlineduetothetimingoffsetofheatingby sweeping.Theuctuationalongthelinearphaselineshowsarelativesourcephasedifferencedue totheionosphericresponse,ortodifferencesintheHFbeampatternasafunctionofazimuth.On theotherhand,Figures4-11aandbshowthephasestructureat3kHzwhichincludethephase contributionduetopropagationincludingionosphericreections. 4.1.3BP/GMAnalysis Basedontheobservationsreportedintheprevioussection,itisclearthattheamplitudeof thereceivedELF/VLFsignaldependsontheareaofthesourceregion,therelativephasingofindividualsourceelements,thenatureofobliqueHFheating,andtheeffectivedutycycle.Previous analyseshavetypicallycomparedGMheatingtoverticalAMheating.Weprovidethefollowing expressiontoconvertverticalAMheatingtoGM,andweanalyzeeachofitsindividualcomponents: A v A o A v D GM S GM S o N i = 1 A i N max A i N i = 1 A i e j f i N i = 1 A i = N i = 1 A i e j f i where A v istheamplitudeproducedbyverticalAMheatingwith50%dutycycle, A o istheamplitudeproducedbyobliqueAMheatingwith50%dutycycleaimedtowardthereceiver, D GM accountsfortherelativesignallevelchangeproducedbytheeffectivedutycyclerelativeto50% dutycycle,and S GM and S o arethe3-dBheatedareasforGMandobliqueAM. A i and f i arethe amplitudeandphaseproducedbythe i thsourceelementaroundthecircle,and N isthetotal numberofsourceelementsconsidered. Steppingthrougheachofthetermsfromlefttoright, A o = A v convertstheverticalAM% dutycyclesignaltoanobliqueAMsignal,andwewillrefertothisastheobliqueheatingeffect. 72

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D GM covertstheobliqueAM50%dutycyclesignaltoanobliqueAM X %dutycyclesignal.At thispoint,XisunknownbecausetheeffectivedutycycleoftheGMsweepisunknown.Wewill refertothiseffectasthedutycycleeffect.Thelastremainingeffectistheincreasedareaofthe GMsweep.Inadditiontosimplyincreasingthearea,denotedbytheterm S GM = S o ,theamplitude generatedchangesasafunctionofazimuthduetothedirectionalityofobliqueheating.This effectisaccountedforusingthe N i = 1 A i N max A i term,whichwewillrefertoastheobliquedirectionality effect.Therelativephasingoftheelementalsourcecomponentsisalsoimportantandaccounted forusingthe j N i = 1 A i e j f i j N i = 1 A i term.Wewillrefertothiscomponentasthephasingeffect.Intheend, combiningalloftheseeffectsproducesthenalGMamplitude: N i = 1 A i e j f i .Notethattheoblique directionalityeffectandthephasingeffectareproducedasside-effectsofdirectingtheHFbeam todifferentlocationsinordertoincreasethetotalheatedarea,meaningthatthevalueascribedto eacheffectisonlyvalidwhenalsoaccountingforthe17.9dBenhancementduetotheincreasein area. Allofthetermsdescribedabovecanbecalculatedbasedonourobservations.Theratio A o = A v canbederivedstatistically, S GM = S o isknownforagivenHFtransmissionfrequencyand A i and f i canbeextractedfromthedatashowninFigures4-10and4-11. D GM iscalculatedaftersimplifying theEquation4: D GM = S o S GM N max A i A o DutycyclereferstotheratioofHFheatingtimetotheHFmodulationperiod.Paststudiesshow thattheELF/VLFsignalsaremaximizedaround 40%[ BarrandStubbe ,1991b; Barretal. ,1999; Cohenetal. ,2010a]andthatlowerdutycyclestendtobemoreefcient[ BarrandStubbe ,1991b; Barretal. ,1999; Jinetal. ,2012].EstimatingthedutycycleforGMcanbecomeverycomplex, sincetheheatingtimevarieswithintheheatedregionasafunctionofdistancefromthecenterof thecircletotheheatedregionbytreatingGMasacontinuouscirclesweep.Thedutycyclefor GMrangesfrom5%asafunctionofradiusinthecircle[ Cohen ,2009],forinstance. Cohen [2009]alsoestimatetheaveragedutycycleas 12%bytakingaratioofansingleHFbeamarea -dBbeamwidthtoanentireGMcirclearea. 73

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Figure4-12.QuantiedeffectscontributingtotheamplitudeofELF/VLFwavegeneration,averagedoverthetwocampaigns. TheaveragedanalysisresultsareshowninFigure4-12,notingthatthe17.9dBincreasein area,whichisconstantasafunctionoffrequencyisnotshown.Thedramaticincreaseinthearea oftheGMtransmissionisthemostimportantfactorincreasingthereceivedELF/VLFamplitude. Thesecondmostimportantfactoristhephasingeffect,whichdecreasesthereceivedELF/VLF amplitudesignicantlyby 10dBatlowfrequencies,andtoalesserextentdBathigher frequencies.Theobliqueheatingeffectisthenextmostimportantfactor,producing + 2dBgains atlowerfrequenciesand + 6dBgainsathigherfrequencies.Atlowfrequencies,theoblique 74

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heatingeffectisalmost,butnotquite,canceledbytheobliquedirectionalityeffectthatonlyoccurs togetherwithamassiveincreaseinarea.Theobliquedirectionalityeffectischaracterizedbya 3dBloss.Thelasteffectisthedutycycleeffect:thelowereffectivedutycycleoftheGM transmissioncomparedtothe50%dutycycleAMtransmissionreducesthereceivedELF/VLF amplitudeby 3dB.Asasidenote,the 3dBdutycycleeffectcorrespondstoaneffective dutycycleof16 0.5%atlowerfrequenciesand18 2%athigherfrequenciesfortheGMformat, whichseeminglycorrespondstothe60 beamwidthoftheHFbeamdividedbythe360 fullcircle .7%. Basedonthisanalysis,increasingtheheatedregionareaprovidestheprimarygainfactorfor theGMformat.Combiningtheeffectsofarea,obliquedirectionality,andphasing,increasingthe areahasanoveralleffectof + 7 : 9 : 9dBonthereceivedELF/VLFsignalamplitude.Whilethe dutycycleandobliqueheatingeffectsnearlycancelatlowfrequencies,obliqueheatingproduces largeranadditional3dBgainsathigherfrequenciesthatarenotmatchedbythedutycycleeffect. Foragivensetofionosphericheatingpoints,itisclearthatthephasingeffectistheprimaryeffect tomitigate,particularlyatlowfrequencies,andthatthedutycycleeffectisimportant,although secondary. 4.2OptimizedHeatingOrderforBP/GMConstantDuration Intheprecedingsections,TOAanalysishasprovedtobeuseful,althoughnotentirelynecessary.Inthissection,thepropagationdelaysandsourcephasesderivedusingTOAobservations areleveragedtoprovideanoptimizedheatinglocationorder.Usingthespatialamplitudeand phaseTOAmeasurementsshowninFigures4-10and4-11,wepredicttheELF/VLFamplitude thatwouldresultusingadifferentheatingorder.Thedifferentheatingordercontrolsthephase structureoftheELF/VLFsourceregion.Weconsidertwooptimizations:1simplymaximize thereceivedELF/VLFamplitude,and2maximizetheELF/VLFamplitudesuchthattheheating orderissymmetric. Forthisexercise,thedutycycleorequivalentlyheatingdurationforeachsourcesegmentis thesameasduringtheexperimentweusetheamplitudedirectlyfromFigure4-10andmodifythe 75

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Figure4-13.Theamplitudepost-processedtooptimizeheatingorderofGM.a:Optimalheating orderwithdifferentnumbersofheatinglocations.b:Optimizedamplitudesred arecomparedwiththoseofGMcirclegrayandsymmetricheatinggreen.For symmetricheating,thelocationsareequallyapartinacircle. phasefromFigure4-11accordingtothechangeoforder.Figure4-13showstheoptimalheating orderfor N heatinglocationsintheleftpanelandtheresultingoptimizedamplitudesintheright panel.TheoptimizedandsymmetricresultsarecomparedwiththoseforobliqueAMandGM.The symmetricheatingisconstrainedtoheatthesegmentsinanorderthatproducesanapproximately symmetricELF/VLFbeampattern.Forthesymmetricformat,however,weallowthedutycycle toincreasesothatthe100%ofthemodulationcycleisavailableforheating. Themaximumamplitudeisachievedwhenonly8outof12arcsegmentsareused.The amplitudeisincreasedby4dBcomparedtoGM andtheefciencyisincreasedby7dB. TheoptimalheatingorderstartswiththesegmentsfartherawayfromParadiseandendswith closersegmentsinordertobestmatchthepropagationphase.Atthelowernumberoftheheating segments,theselectionofthesegmentsisprioritizedtotheclosersegmentstoutilizethehigher amplitudes. Forsymmetricheating,theamplituderemainsinthesamerange 0.6.8pTforanypercentagesofthecircleheated.TheoptimaldutycycleisthesameasfortheGMformatno beam-offtime,exceptat2/12%ofthecircle.Tomakesymmetricheatingpattern,eachsegmentis 76

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assignedequallyafractionofthemodulationperiodandwithintheassignedtimethedutycycle andoff-timeareadjustedtomaximizethetotalamplitudes.Forthisreason,themaximumamplitudeisgeneratedbytheGMformatbecausethelargerdutycycleproducesthelargeramplitude upto 40%.At2/12%ofthecircle,eachofthetwochosensegmentsareassigned40%ofthe modulationperiod,andthebeamisturnedofffortheremainingtime. ThediscrepancyofthemagnitudeatGMfullcircleand12/12onSymmetryisfromthe differentdirectionofthesweeprotation.Tondanoptimalsymmetricheating,weestimatethe magnitudesforallpossiblesymmetricpatternthatcanbedoneforonerotationofthecircle.Even thoughtheamplitudeandphasestructuresareasymmetricshowninFigures4-10and4-11,the changeofrotationdirectionmakesslightdifferenceinthetotalamplitudeexperimentallyreported by Cohenetal. [2008]. Inthischapter,wehavedemonstratedamethodtooptimizetheorderofheatinglocations, assumingthatthedurationofheatingateachlocationispre-determined.Inthenextchapter,we considerafulloptimizationoftheELF/VLFsourceregion,allowingthestarttimingandduration foreachheatinglocationtovary. 77

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CHAPTER5 OPTIMIZATIONOFELF/VLFANPHASEDARRAY ThepreviouschapterincreasedtheELF/VLFamplitudegeneratedusingaELF/VLFphased arraybychangingtheorderofheatinglocationswhilekeepingthedurationofheatingateach locationthesame.Inthischapter,weexperimentallyinvestigatetheeffectofdutycycleasa functionofthesourcelocationrelativetothereceiverlocation.Asaresult,weareabletoperform anoptimizationthatconsidersthebestorderingofheatinglocationtogetherwiththebestheating durationsforeachindividualheatinglocations.SolutionsareconstructedusingTOAanalsyisof ELF/VLFamplitudesandphasesobservedwhentheHFbeamisaimedateightdifferentazimuthal directionswith15 off-zenith. 5.1OptimizationExperimentDescription Tomeasuretheamplitude,phase,andpropagationdelayasafunctionofionosphericheatinglocation,theHFbeamisaimed15 off-zenithineightazimuthaldirections.Theazimuthal directionsareseparatedby45 ,from14 to329 eastofnorth.Eachbeamwastransmittedwith amplitudemodulationwith50%dutycycle.Inordertoinvestigatetheeffectofdutycycle,theHF beamwasdirectedattwoheatinglocationsalternatively and261 azimuthat15 off-zenith, andthedutycyclechangedfrom5%to75%in5%steps.Thetransmissionswereperformed closelyintimesothataccuratecomparisonscouldbemade.Alltransmissionswereat3.25MHz X-modeandatfullpower.6MW,84.7dBW.ThebeamwasmodulatedwithanAMsquare waveandthemodulationfrequencylinearlyvariedfrom1kHzto5kHzwitha1kHz/secslope. Forthisanalysis,wefocusonELF/VLFobservationsperformedatParadise. 5.2ExperimentalObservations DuringtheBRIOCHEcampaigninMarch,2013,ELF/VLFwavesweregeneratedwithexcellentSNR>21dBfordifferentazimuthsanddutycycles.TheKpIndexwas4-andtheGakona Magnetometerregisteredmagneticuxvariationsof < 125nT.TheobservedELF/VLFwavesat Paradisearepresentedinthissectionandareusedtooptimizetheheatinglocationandorder. 78

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Figure5-1.aAmplitude,bphaseandcpropagationdelaysasafunctionofazimuthdirection. Thesolidlineistheobservationandthedashlineisasinusoid. 5.2.1ELF/VLFObservationsvs.Azimuth TheobservedELF/VLFsignalsfor8azimuthaldirectionsareshownbysolidlinesinFigure51.TheamplitudesandphasesareshownfortwopropagationpathsLOSand1stIRandforthree differentfrequencies.5,3.0,4.5kHzinadditiontopropagationdelaysforLOSand1stIR.The amplitudesoftheEWsignalsarelargerthantheNSsignalsby 38dB.SinceEWcomponent oftheobservedELF/VLFsignalisdominant,wefocusontheEWcomponentfortherestofthis chapter. TheamplitudesfortheLOSandIRpropagationpathsandforthreefrequencieshaveasimilar shape:theamplitudeislargestwhenthebeamisaimedtowardthereceiverParadiseat81 andsmallestwhenitisaimedawayfromthereceiver.Theamplitudedifferenceasafunctionof azimuthis 5dBwhichisconsistentwithpastobservations[ Barretal. ,1987; Cohenetal. 2010b].Thephasesforthefrequenciesandpropagationpathsareinterpreteddifferently.The phasesforthefrequencyresponseincludetheELF/VLFsourcephaseaswellasthepropagation 79

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phaseincludingeffectsofthewaveguide,whilethephasesfortheLOScomponentrepresentonly theELF/VLFsourcephase. ThepropagationdelayforeachpropagationpathisshowninthemostrightpanelinFigure51.TheLOSpropagationdelayfollowsastraightforwardinterpretation:heatinglocationscloser tothereceiverproduceshorterpropagationdelays.The1stIRpropagationdelaysarenotso simple,however.Thepropagationdelayseemslongerwhentheheatedlocationistothesouth >90 and<270 azandshorterwhenitistothenorth.Theobservationmaybeexplainedby differentionosphericconditionsorincidentangles,oramixofthoseeffects,butitismostlikely duetothefrequency-dependentreectioncoefcientsfortheair-ionosphereinterface.TheIR componentscontainamultitudeofphysicaleffectsthatarenotconsideredinthisdissertation,and itwillhavetosufcetoapproximatetheirpropertiesinordertogetthebestestimateoftheLOS signalcomponent. Allcomponentsamplitude,phase,andpropagationdelayofthereceivedELF/VLFsignals varysinusoidallywithazimuth.ThedashedlineinFigure5-1isasinusoidallineprovidedfor comparison.Insubsequentsections,thisfactwillbeusedtoestimatetheeffectofdutycyclebased onmeasurementsatonlyafewheatedlocations. 5.2.2ELF/VLFAmplitudevs.DutyCycle ThereceivedELF/VLFamplitudeandphaseasafunctionofdutycycleareshowninFigures5-2.Theamplitudesandphasesarenormalizedbythesignalwith50%dutycycle.The amplitudeandphaseplotsarecomparedwithananalyticalexpressionfortheeffectofdutycycle [ BarrandStubbe ,1991b]usingaheatingconstant-to-coolingconstantratioof0.282. ThereceivedELF/VLFamplitudeincreaseswithdutycycleuntilitreachesamaximumnear 30%dutycycle,andatlargerdutycyclesitdecreaseswithincreasingdutycycle.Themaximumamplitudesare30%largerthanat50%dutycycle.Themaximumamplitudeoccursat lowerdutycyclesbecausethetimeconstantforelectronheatingisshorterthanthatforelectron cooling[ BarrandStubbe ,1991b; Cohenetal. ,2010b].Thephasesfordifferentfrequenciesand 80

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Figure5-2.aAmplitude,bphaseandcpropagationdelaysasafunctionofdutycycle.The amplitudesandphasesarenormalizedbythesignalwith50%dutycycle. propagationpathsarealsocomparedwiththeanalyticalcase.Thephaseofallcomponentsin Figure5-2varyalmostlinearlywithdutycycle:theydeviatefromlinearbyonly 10 Mostimportantly,theELF/VLFamplitudedependenceondutycycleadditionallydepends uponthelocationoftheELF/VLFsourcewithrespecttothereceiverlocation.Theresponsesare slightlydifferentwhentheHFbeamisdirectedawayfromthereceiverandtowardthereceiver. Duringtheoptimizationprocess,wewilldesireknowledgeofthedutycycleresponseatalleight heatinglocations.Basedontheobservationspresentedintheprevioussection,weestimatethis responseasafunctionofazimuthbyttingasinusoidtotheamplitudesobservedasafunctionof dutycyclefor81 and261 azimuth. ThepropagationdelayasafunctionofdutycycleisshownintherightpanelofFigure52.ThepropagationdelaysfortheLOScomponentareallwithin 10 m secofeachother.This translatestoamaximumsourceheightdifferenceofonly 2kmassumingthatthesourceislocated atthecenteroftheHFbeam.ThepropagationdelaysfortherstIRcomponentvaryby 25 m sec. Onceagain,weattributethevariationobservedintherstIRcomponenttoionosphericconditions: 81

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Figure5-3.DiagramofHFheatingpattern mostlikelythefrequency-dependentreectioncoefcientsattheair-ionosphereinterfaceaffect thismeasurement. 5.3OptimizationofBeamPainting Giventheobservationspresentedinthetwoprevioussections,weprovideanoptimization fortheELF/VLFamplitudeatParadisethataccountsfordifferentON/OFFtimesateightheating locations,anddifferentheatinglocationordering.Toaccomplishthis,theobservedELF/VLF amplitudesattheeightheatinglocationsshowninFigure5-1aremodiedbythedutycycle,and thephaseismodiedbythepropagationdelay,dutycycle,andtimeoffsetduetothestarttiming oftheheating.AsisshowninSection3.5.1,alinearsummationofthesesignalsapproximatesthe totalreceivedsignalsquitewell.Thetotalreceivedamplitudecanbedescribed: S = S N k = 1 A k e j f k D k d k e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j 2 p k m = 1 d m )]TJ/F22 6.9738 Tf 5.418 0 Td [(1 + D t m )]TJ/F22 6.9738 Tf 5.419 0 Td [(1 where N isthetotalnumberofheatinglocations, A k and f k aretheamplitudeandphaseofthe k thELF/VLFsourcethesubscriptindicatestheheatinglocationat50%dutycycle, D k isthe amplitudeandphaserelativeto50%dutycycleasafunctionofdutycycle, d k ,and D t k isthetime thattheHFbeamisoffbetweenthe k thand k + 1 thheatinglocations.Theseparametersare diagrammedinFigure5-3.Thereisnounitin D t k because D t k isthefractionofthemodulation period.ForTOAanalysis,theaboveequationismodiedto: 82

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S = max n S N k = 1 A k e j f k D k d k sinc [ B t )]TJ/F56 11.9552 Tf 10.949 0 Td [(t d ] e j 2 p f c t )]TJ/F56 8.9664 Tf 6.966 0 Td [(t d e )]TJ/F55 8.9664 Tf 8.312 0 Td [(j 2 p k m = 1 d m )]TJ/F22 6.9738 Tf 5.418 0 Td [(1 + D t m )]TJ/F22 6.9738 Tf 5.419 0 Td [(1 o where B isthebandwidthoftheramp, t d k isthepropagationdelayatthedutycycle d k t isthe timevector t 1 ; t 2 ; t 3 ;::: ,maxndsthemaximumvalueasafunctionof t ,andthesincfunctionis denedas: sinc x = 8 > > < > > : 1if x = 0 sin p x p x otherwise InTOAanalysis,thesincfunctionarisesasaresultofrectangularwindowinginthefrequency domain.Thewidthofthesincfunctionisdeterminedbythebandwidthoftherectangularwindow. Thegoalistomaximizethamplitude S byoptimizingthedutycycleandtheHFheatingoff timewithacombinationoftheheatinglocations.Theoptimizationexpressionis: maximize S subjectto N k = 1 d k + N )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 k = 1 D t k < = 1 ; d k > = 0 ; D t k > = 0 : Theoptimizationisnotstraightforwardduetothetrade-offbetweenphaseinterferenceandduty cycle.Forinstance,with N = 2,wemaychoosetheclosestheatinglocationstothereceiverforthe largestamplitudes.However,forthesignalstointerfereconstructively,eachdutycyclehastobe shortandtheamplitudesgeneratedateachlocationbecomesmaller;thusthetotalamplitudemay becomesmaller. Tosolvetheoptimizationproblem,weapplyagradientdescentmethodwhichiteratively updatestheparametersaccordingtothederivativesof S VLF .Tomakesurethesolutionistheglobal maximum,theresultofthegradientdescentmethodiscomparedtothatofadirectsearchmethod whichscansthroughallpossiblecombinationoftheparameters.Duetotheheavycomputational 83

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Figure5-4.Dutycycledependenceonazimuth. requirements,thedirectsearchcancompute S VLF onlyupto N = 5inareasonabletimeframe.It sufcestoobserveatypicaltrendof S VLF andtomakesure S VLF convergestotheglobalmaximum for N 6. 5.3.1DutyCycleDependencevs.Azimuth TheELF/VLFamplitudedependenceondutycyclealsodependsuponthelocationofthe heatedregionrelativetothereceiverlocationFigure5-2.Inordertooptimizethesignalsgeneratedattheeightazimuthallocations,weestimatetheamplitudesandphasesasafunctionof dutycyclefortheazimuthallocationsusingtheobservationsshowninFigure5-2.Theresult correspondstothefunction, D k d k inEquations5and5. ToestimatetheELF/VLFamplitudedependenceondutycycle,weestimatethatboththe amplitudesandthephasesvarysinusoidallyasafunctionofazimuth.Thepeaksofthesinusoids aredeterminedbytheexperimentaldata.Foreachdutycycle,thesinusoidalcurvesareestimated usingalleightazimuthaldirections.ResultsareshowninFigure5-4.Itisworthnotingthatthe dependenceofELF/VLFamplitudeondutycyclevarieswithtime.Forinstance,whileitwouldbe 84

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idealtomeasurethedutycycledependenceallazimuthalangles,itislikelythationosphericconditionshavechangedbythetimethemeasurementhascompleted.Usingthesinusoidalassumption allowsforrapidaccountingofthedutycycleeffect. 5.3.2GradientDescentMethod Thegradientdescentmethodisusedtoiterativelyoptimizeforthemaximumamplitudeor minimumerrortothemaximumamplitudeinEquation5and5[ Gilletal. ,1981]. S VLF convergestothemaximumamplitudewithagivenheatingorder,andthelargestamplitudeofallthe possibleordersisdetermined.Thevariablestobeoptimizedare d 1 ; d 2 ;::: d N and D t 1 ; D t 2 ;::: D t N )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 whicharetheheatingdurationdividedbythetotaldurationi.e.,dutycycleforeachheating locationandthelengthoftimeforwhichtheHFbeamisoffbeforeheatingatthenextlocation. Theiterativemethodstartswithaninitialguessforeachoftheunknownvariables.Subsequently,thevariablesareupdatedbyusing: b i + 1 = b i + m J where b isasetofvariablesi.e, [ d 1 ;::: d N ] and [ D t 1 ;::: D t N )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 ] ,thesuperscript i istheiteration count, m isthestepsizeand J isasetofthepartialderivativesof S withrespecttoeachvariable. Thestepsizeisadjustedbytheusersothatthevariablesconverge.Thederivativesarecomputed numericallyeveryiteration. ThevariablesmustsatisfytheoptimizationconstraintsinEquation5.Tosimplifythe equation,Equation5isre-writtenwith b : maximize S subjectto 2 N )]TJ/F22 8.9664 Tf 6.966 0 Td [(1 k = 1 b k < = 1 ; b k > = 0 ; k = 1 ; 2 ;::: 2 N )]TJ/F22 11.9552 Tf 10.949 0 Td [(1 Tomeettheconstraints, b k isforcedtobezerowhenitbecomesnegative,and J ismodiedwhen b i + 1 = b i + m J > 1.Themodicationisfairlysimple.When J hasnegativeelementsand 85

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Figure5-5.ConvergenceofparametersontimeandofftimetooptimizeforthemaximumamplitudeusingGradientdescentmethod.Blueandgreentracearetheupdatedparameters withdifferentinitialvalues.Redtraceisthemaximumamplitudefromdirectsearching method. b 'selementsatthesameindicesarepositive, J 'spositiveelementsaremodiedtozeroandthe J 'snegativeelementsremainthesame.Whenthisisnotthecase,wekeepthelargestof J 'selementsasisandreplacethesmallestof J 'selementswiththelargestelementthatisnegated.The otherelementsof J aremodiedtozero.Themodied J hasapositivevaluefortheelementof b whichcontributesthemosttoincrease S andhasanegativevaluefortheelementof b whichcontributestheleasttoincrease S .Bymeetingtheconstraintswiththismodication, S willcontinue convergingtothemaximumvaluewithout b i + 1 exceeding1. TheconvergenceofthegradientdescentmethodisshowninFigure5-5withcomparison totheresultsofthedirectsearchingmethod.Thedirectsearchingmethodscansthroughallthe possiblecombinationsandlocatestheglobalmaximum.Figure5-5showsthatthegradientdescent 86

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methodconvergestotheglobalorlocalmaximumdependingoninitialvalues.InFigure5-5,the heatingdirectionis104 and14 Az.Theredtraceshowsthemaximumamplitudeatalength oftimespentonthatlocation.Theglobalmaximumforthisheatingandlocationsis229dBfor d 1 = 25% ; d 2 = 25% ; D t 1 = 50%.Thereisalsolocalmaximumat D t 1 = 0%.Theblueandgreen tracesareupdatedeachiterationwithdifferentinitialvaluesfor D t 1 ,oneofwhichis0%andthe otherofwhichis50%.Dependingontheseinitialvalues,thetraceconvergestoeitherthelocalor globalmaximum.Sincewecannottellwhichsetofinitialvalueconvergestotheglobalmaximum, theglobalmaximumisdeterminedbycomparingtheconvergedamplitudeswithdifferentsetsof theinitialvalues.Itisimportanttouseallpossibleinitialvaluesthatconvergetothemaxima, otherwisewemaynotbeabletoidentifytheglobalmaximum.Inthenextsection,wediscusshow todeterminetheinitialvalues. 5.3.3DeterminationofInitialValues Theinitialvaluesthatconvergetoanymaximaare 8 > > < > > : d 1 ;:::; N = 0 : 1 D t 1 ;:::; N = 0 Or 8 > > > > > > < > > > > > > : d 1 ;:::; N = 0 : 1 D t k = 0 : 4 k = i D t k = 0 k = 1 ;:::; N ; k 6 = i Theseinitialvaluesindicatethatthedutycycleforheatingisoperatedinanefcientrangei.e.,the lowerdutycycleismoreefcient,andtime-offperiodsbetweentwoheatinglocationsarezeros forthesignalstoconstructivelyaddeachother.Thelargetime-offperiodsuchas40%isequivalent tothezerotime-offperiodbetweentwolocationsif N k = 1 d k + N )]TJ/F22 8.9664 Tf 6.967 0 Td [(1 k = 1 D t k = 1,justlikethecasein Figure5-5.25%ofaperiodforheatingat104 az,50%forturningoffand25%forheatingat14 az,isequivalentto25%forat14 az,25%forat104 azand50%forturningoffjusttheorder hasbeenchanged.Inthissection,wediscusshowthezerotime-offmaximizestheamplitude. 87

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Tosimplifythediscussion,weanalyzeacaseofheatingtwolocationswithalinearphase. Thephaseofthetwosignals F 1 and F 2 indegreesare, F 1 = j 1 + 90 )]TJ/F22 11.9552 Tf 10.949 0 Td [(180 d 1 F 2 = )]TJ/F22 11.9552 Tf 9.289 0 Td [(360 d 1 + D t 1 + j 2 + 90 )]TJ/F22 11.9552 Tf 10.949 0 Td [(180 d 2 where f 1 and f 2 arethephasesofthesignalsateachlocationwith50%dutycycle, d 1 and d 2 isthe dutycycleateachlocation,and D t 1 isthetimeoffbetweenheatingthetwolocations. 90 )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 d k modies j k with d dutycycleEquation5or5,and )]TJ/F22 11.9552 Tf 9.289 0 Td [(360 d 1 + D t accountsforthetime delayofheatingatthe2ndlocation.Therelativephasefor F 1 and F 2 is DF = F 2 )]TJ/F63 11.9552 Tf 10.95 0 Td [(F 1 = j 2 )]TJ/F56 11.9552 Tf 10.95 0 Td [(j 1 )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 d 1 + D t 1 + d 2 )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 D t 1 = D f )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 d 1 + D t 1 + d 2 )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 D t 1 where D f = j 2 )]TJ/F56 11.9552 Tf 10.95 0 Td [(j 1 .Forthesignalstointerfereconstructively, DF iszero.So, 0 = D f )]TJ/F22 11.9552 Tf 10.95 0 Td [(180 d 1 + D t 1 + d 2 )]TJ/F22 11.9552 Tf 10.949 0 Td [(180 D t 1 whichreducesto, D t 1 = D f 360 )]TJ/F22 11.9552 Tf 12.145 8.094 Td [(1 2 d 1 + d 2 Theequationaboveisplottedwithconstraints d 1 > 0 ; d 2 > 0 ; D t 1 > 0 ; d 1 + d 2 + D t 1 1in Figure5-6.Thegrayshadeindicateswheretheconstraintsaresatised.Thecolorlinesshow theEquation5atdifferentrelativephase, D f .Toachieveaconstructiveinterferenceandthe longesttotalheatingtimemaximum d 1 + d 2 isanintersectionofacolorlineandeither D t 1 = 0 or d 1 + d 2 + D t 1 = 1. 88

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Figure5-6.Off-timebetweenthe1stand2ndheatinglocationagainsttotaldutycycleof1stand 2ndheatinglocation.Thegrayshadeindicatestheregionwheretheconstraintmeets. Differentcolorlinesindicatethecombinationof D t 1 and d 1 + d 2 thatmakesin-phase withdifferentrelativephaseofthetwolocation. Althoughthelongesttotalheatingtimedoesnotnecessarilymaximizetheamplitudesdue tothenon-linearrelationofamplitudesoverdutycycle,itislikelytomaximizetheamplitude especiallywhen d 1 + d 2 < 0 : 8.Theamplitudeincreasesmonotonicallyupto 40%dutycycle; thustheoptimaltotalamplitudeofthetwolocationsincreaseuntilbothofthedutycyclereachto 40%whentheyarein-phase.Inourexperimentalobservation,therelativephase, D f ,isfrom0 to120 orfrom240 to360 dependingontheorderofheatinglocations.Thisyieldsthatoptimal d 1 + d 2 islessthan0.72. Ihavediscussedhowtodeterminetheinitialvalueswithtwoheatingsections.Similarly, itgenerallyworkswith N heatinglocations.Anoptimaltime-offperiodbetweenthersttwo heatinglocationsiszerotobein-phase,andanexttime-offperiodbetweenthe2ndand3rdheating 89

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Figure5-7.Optimizedamplitudeaandefciencybasafunctionofnumberofheatinglocations. locationsisalsozerotoproducein-phaseradiation.Then,therstthreelocationsareallin-phase andthissequencecontinuesto N thlocation. Zerotime-offperiodsbetweenheatinglocationsdonotnecessarilymaximizethereceived ELF/VLFamplitude.Nevertheless,suchanapproximationsufcesforaninitialguess.Todeterminetheoptimizedamplitudeatagivenorderofheatinglocations,wecomparetheconverged amplitudesfromallthesetsofinitialvalues. 5.3.4OptimizationResultandAnalysis TheresultsforoptimizedELF/VLFamplitudesareshowninFigure5-7.Comparedtovertical AMheatingwith50%dutycycle,theamplitudeisincreasedby10dBandtheefciencyis increasedby7dB.Comparedtogeometricmodulationcircleshowninthepreviouschapter, theamplitudeisincreasedby 7dBandtheefciencyisincreasedby 11dB.Thecomparisons areshowninTable5-1. ThelargestoptimizedamplitudeforLOSandallfrequencycomponentsareproducedwith eightheatinglocationsoutofeightconsideredlocations.However,theamplitudeconverges asthenumberofheatinglocationsincreases,indicatingthatincreasingthenumberofheating locationsincreasesthereceivedELF/VLFamplitudetoalesserextentasthenumberofheating locationsincreases. 90

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Figure5-8.aOptimalsteeringpatternandborderforvariousnumberofheatinglocations. TheoptimalheatingpatternfortheLOSsignalcomponentisshowninFigure5-8.The optimalheatingordergenerallystartswithheatinglocationsfartherfromthereceiver azand endswithlocationsclosertothereceiver.Thisordermakesupfortheshorterwavepropagation delaysclosertotheheatinglocations. Thedutycycleateachlocationbecomessmallerasthenumberofheatinglocationsincreases. ThesmallerdutycyclegeneratesELF/VLFwavesmoreefciently,decreasesthephasedelaydue totheheatingorder,andmakesthesignalsinterferemoreconstructively.Thesmallerdutycycle isoptimallyselectedoverthelargerdutycyclewhichwouldgeneratelargeramplitudesateach location,butwouldproducelargerdestructiveinterferenceforthetotalsignal. Alloftheoptimaloff-timesbetweenlocationsarezeroexceptfor N = 2,6,and8;eventhe largestoff-timeisonly1.7%at N = 8.Thezerooff-timesarelikelytoproducein-phasedsignals withanoptimaldutycycle,whichisdiscussedinSection5.3.3 HAARPiscapableofsteeringthebeamwith10 m secdwelltime.Thedwelltimecorresponds to3%dutycyclefor3kHzmodulationfrequency.ToimplementthebeampatterninFigure5-8 91

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Table5-1.ReceivedamplitudedBrelativetoverticalAMat50%dutycycle MethodLOS1.5kHz2.0kHz3.0kHz4.0kHz4.5kHz OptimizedBP12.19.812.214.4 GMMaximum7.7.36.4.36.9.89.5.1 GMFullCircle5.9.12.6.85.4.68.4.8 atHAARP,wecansimplyroundthedutycyclesatmultiplesof3%andtheoptimizedamplitudes wouldchangeonlyby 0.5dB.Ifahighermodulationfrequencyisused,thedwelltimebecomes moresignicant.Forinstance,10kHzmodulationfrequencywouldhave10%dutycycleresolutioninbeampainting.Atthishighfrequency,ratherthanroundingoptimaldutycyclesto10% resolution,thegradientmethodcanbemodiedsothattheoptimaldutycycleisupdatedusing 10%resolution. Whenitcomestosymmetricheating,wherethereisnofavorinanyazimuthaldirection,the optimalheatingpatternisverysimilartostandardcircle-sweepgeometricmodulationwherethe beammovesalonginacircleandheatseachspotatthemaximumallowedtime.5%dutycycle ateachofeightlocations.Thepost-processedamplitudefortheLOScomponentis 2dBlarger thanexperimentalobservationsofGMTable5-1.Thediscrepancycomesfromthenumberof heatinglocations:geometricmodulationwasimplementedwith12heatingstepswhichproduce moreoverlappingregionsattheheatinglocations.Theoverlapyieldsdifferenteffectivedutycycles andwaveformsattheheatedspots,andchangesthetotalreceivedamplitude.Whiletheoverlapof thebeamsmaybeengineeredtoincreasethereceivedamplitude,theeffectisnotconsideredhere. 92

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CHAPTER6 SUMMARYANDFUTUREWORK 6.1SummaryofContributions Inthisdissertation,IhaveprovidedtransmissionsequencesthatoptimizethereceivedELF/ VLFamplitudeataparticularreceiverbyengineeringtheELF/VLFphasedarraycreatedinthe D -regionionospherebyrapidheaterbeamsteeringatHAARP.BypaintingavastareaoftheionosphereatthedesiredELF/VLFratewiththeHFbeam,IcreatedanON-OFFpatternatelemental sourcelocations,andIobservedlargerELF/VLFsourceregionswithdistributedamplitudeand phase.Throughouttheexperimentalobservations,theTOAmethodwasusedtomeasuretheamplitude,phase,andpropagationdelaysofthereceivedELF/VLFsignals. InChapters2and3,IprovidethemathematicalframeworkfortheELF/VLFTOAanalysis methodinthecontextofELF/VLFwavegenerationphysics.Ishowedexperimentalobservations andnumericalmodelingresultstodemonstratethattheTOAmethoddistinguishesLOSandIR signalcomponentsandidentiestheELF/VLFsourceheights.TheTOAobservationsindicate thatthesourceheightdecreaseswithincreasingmodulationfrequencyandismostlyinsensitiveto theHFpowerlevelsandHFfrequency. InChapter4,theGeometricModulationGMformatiscombinedwithavariableHFheating pulsetoinvestigatethefourimportanteffectsthatcontributetothegeneratedELF/VLFamplitude. TheresultsarecomparedwithconventionalAMheating.Thosefoureffectsaretheareaofthe sourceregion,theobliquenessoftheHFbeam,theeffectivedutycycleoftheheating,andthe phasedarraystructureofthesource.UsingmeasurementsofthespatialdistributionofELF/VLF amplitudeandphasecreatedbyGM,anoptimalheatingorderisidentied.Theresultsindicatethat theoptimalheatingorderincreasestheELF/VLFamplitudeupto4dBandtheHF-to-ELF/VLF conversionefciencyupto7dB.However,forsymmetricheating,theGMformatHFbeamison continuouslyproducesthelargestamplitude. InChapter5,insteadofoptimizingsweepspeedandheatingorderindividually,Ioptimizethe heatingdurationsandorderstogether.Theobservedamplitudeandphaseatdifferentazimuthsand 93

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dutycyclesarepost-processedtopredictthereceivedamplitudeatParadise.Thegradientdescent algorithmisemployedtoidentifytheglobalmaximumforthereceivedamplitude.Asaresult,the amplitudeisincreasedupto7dBandtheefciencyisincreasedupto11dBcomparedtoGM. 6.2SuggestionsforFutureResearch 6.2.1ImplementationofOptimalHeatingPattern Thisdissertationsuggestsanoptimalheatingpattern,buttheoptimalheatingpatternhasnot yetbeenimplemented.Toconrmtheprediction,observedELF/VLFamplitudesshouldbedirectlycomparedtothosegeneratedusingobliqueAMandGMformats.Theoptimalformatdependsonionosphericconditions.ItisidealtooptimizetheHFbeampatterninreal-timeasthe ELF/VLFsignalsarebeinggenerated.Atpresent,real-timeimplementationisunreasonablefor thecurrentELF/VLFreceiversetupandcalculationtimeforoptimization. TheprovidedoptimizationdoesnotcurrentlyaccountfortheoverlappingofHFbeams.At 3.25MHz,theoverlapofthe3dBbeamwidthismerely10%withitsneighborheatinglocations whentheyare45 azimuthapart.Itisbettertoquantifythiseffectthantoassumeitisnegligible. Toquantifythiseffect,IsuggestalteringtheHFfrequency.TheHFfrequencycontrolsthe3dB beamwidth,withamorefocusedbeamathigherfrequencies.Itisimportanttokeepinmindthat theazimuthaldependenceanddutycycleresponsewouldalsochangefordifferentHFfrequencies. Theoptimalheatingpatternwillbeboundedbytheazimuthalanddutycyclesteptransmissionsat thesameHFfrequency. 6.2.2HighFrequencyResolutionTOA ProbablythemostimportantnextresearchstepisthedevelopmentofahighfrequencyresolutionTOAmethod.TheTOAobservationweretypicallyperformedusinga3kHzbandwidth inordertoaccuratelydiscernLOScomponentsfromIRcomponentsbytheirtimedifferences. Theamplitude,phase,andpropagationdelaysmeasuredbytheTOAmethodareaveragedover thebandwidth,andasaresult,frequencyresolutionislost.Importantphysicalquantitiesdepend onfrequency,however.Forinstance,reectioncoefcientsfortheair-ionosphereboundaryare expectedtobefrequency-dependent.WithahighfrequencyresolutionTOAmethod,itmaybe 94

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possibletoquantifyreectioncoefcientsasafunctionoffrequencyandprovideanapproximationof D -regionproperties. 6.2.3SeparationofHallandPedersenCurrents TheorthogonalELF/VLFantennasmeasuresomewhatdifferentamplitudesandphasesdue todirectionoftheauroralelectrojetcurrents.Inthisdissertation,thetwodirectionalsignalsare modeled,butarenotseparated.Amorein-depthstudyoftheconductivitymodulationwouldfocus onmeasuringandseparatingtheHallandPedersencurrentcontributionstotheELF/VLFsource. WithhighfrequencyresolutionTOAmethod,suchadecompositionoftheELF/VLFsignalmay bepossible. 95

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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,Combinationfrequenciesintheinteraction betweenhigh-powershort-waveradiationandionosphericplasma, JETPLett. 20 ,101. Gill,P.E.,M.W.,andM.H.Wright, Practicaloptimization ,Academicpress. Gokowski,M.,M.B.Cohen,D.L.Carpenter,andU.S.Inan,Ontheoccurrenceofground observationsofELF/VLFmagnetosphericamplicationinducedbytheHAARPfacility, J.Geophys.Res. 116 ,A04208. Gokowski,M.,M.B.Cohen,andR.C.Moore,Modulationofauroralelectrojetcurrents usingdualmodulatedHFbeamswithELFphaseoffset,apotential D -regionionosphericdiagnostic, J.Geophys.Res.SpacePhysics 118 ,2350. Helliwell,R.A., Whistlersandrelatedionosphericphenomena ,DoverPublications,New York. Inan,U.S.,andD.L.Carpenter,Lightning-inducedelectronprecipitationeventsobserved atL 2.4asphaseandamplitudeperturbationsonsubionosphericVLFsignals, J.Geophys. Res. 92 A4,3293. James,H.G.,TheELFspectrumofarticiallymodulated D / E -regionconductivity, J.Atmos.Terr.Phys. 47 ,1129. James,H.G.,R.L.Dowden,M.T.Rietveld,P.Stubbe,andH.Kopka,Simultaneous observationsofelfwavesfromanarticiallymodulatedauroralelectrojetinspaceandonthe ground, J.Geophys.Res. 89 A3,1655. Jin,G.,M.Spasojevic,andU.S.Inan,Relationshipbetweenelectrojetcurrentstrengthand ELFsignalintensityinmodulatedheatingexperiments, J.Geophys.Res. 114 ,A08301. Jin,G.,M.Spasojevic,M.B.Cohen,U.S.Inan,andN.G.Lehtinen,TherelationshipbetweengeophysicalconditionsandELFamplitudeinmodulatedheatingexperimentsatHAARP: Modelingandexperimentalresults, J.Geophys.Res. 116 ,A07310. Jin,G.,M.Spasojevic,M.B.Cohen,andU.S.Inan,Harmonicminimizationwaveforms formodulatedheatingexperimentsatHAARP, J.Geophys.Res. 117 ,A11315. Kotik,D.S.,andE.N.Ermakova,Resonancesinthegenerationofelectromagneticsignals duetothethermalcubicnonlinearityinthelowerionosphere, J.Atmos.Sol.Terr.Phys. 60 1257. Lauben,D.S.,U.S.Inan,andT.F.Bell,Precipitationofradiationbeltelectronsinduced byobliquelypropagatinglightning-generatedwhistlers, J.Geophys.Res. 106 ,29,745,770, doi:10.1029/1999JA000155. Lev-Tov,S.J.,U.S.Inan,andT.F.Bell,Altitudeprolesoflocalized D regiondensitydisturbancesproducedinlightning-inducedelectronprecipitationevents, J.Geophys.Res. 100 A11,21,375,383. 98

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BIOGRAPHICALSKETCH ShujiFujimarureceivedhisbachelor'sdegreeinelectricalandcomputerengineeringfromthe UniversityofFloridain2009.WiththeAlumniFellowshipawardfromtheUniversityofFlorida, heenteredthePh.Dprograminelectricalandcomputerengineering.Hereceivedthemaster's degreein2011withguidancefromDr.RobertMoore,andcontinuedtocompletePh.Din2014. HisresearchfocusesonELF/VLFgenerationusingmodulatedHFheatingofthelowerionosphere. Hisstudiesaremainlyappliedtoelectromagnetics,plasmaphysics,andsignalprocessing. 102