UFDC Home | myUFDC Home | Help |

PAGE 1

1

PAGE 2

2

PAGE 3

3

PAGE 4

IamthankfulforallthehelpIhavereceivedinmyPh.D.program,inwritingthisdissertationandinlearningaboutthisresearchsubject.Firstofall,Iwouldliketothankmymentor,ProfessorGaryG.Ihas,whohasledmetotheamazingeldoflowtemperatureexperimentalphysics.Fromhim,IhavelearnedalotofphysicsandIwasabletocarryoutmyaccomplishments.Ireallyenjoythebeautyofquantumturbulencescience.Second,Iwouldliketothankmyparents,whohavegivenmealotofsupport,emotionally,nancially,andspiritually,andalotofencouragementbeforeandduringthepursuitofmyPh.D.Third,Iwouldliketothankthemembersofourresearchgroup,formerandcurrent,andthepeopleinthemachineandelectronicshops.Becauseofthem,Iwasabletostandonthosegiants'shouldersandlookhigherandfurther.Fourth,IwouldliketothankthewholeGainesvillecommunity,whichhasgivenmemuch. 4

PAGE 5

page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 12 CHAPTER 1INTRODUCTIONTOQUANTUMTURBULENCE ............... 14 1.1Introduction ................................... 14 1.1.1BasicPropertiesofHeII ........................ 14 1.1.2Two-FluidModel,andLandau'sTwo-FluidEquations ........ 16 1.1.3QuantizationofVorticesandtheCriticalVelocities ......... 18 1.1.4KelvinWaves .............................. 20 1.2IntroductionofTowed-GridTurbulenceExperiments ............ 20 1.3ProposedTowed-GridSuperuidTurbulenceExperiment .......... 21 1.4HighResolution,FastRespondingMilikelvinThermometers ........ 25 1.4.1NeutronTransmutationDopedGermaniumBolometers ....... 25 1.4.2MiniatureGeFilmResistanceThermometers ............. 27 2SHIELDEDSUPERCONDUCTINGLINEARMOTOR .............. 34 2.1Introduction ................................... 34 2.2ModelsoftheShieldedandUnshieldedSuperconductingMotor ...... 35 2.3SimulationResultsandDiscussions ...................... 39 2.3.1SimulationAnalysis ........................... 39 2.3.2CriticalMagneticFieldsforNiobium ................. 41 2.3.3RequiredVoltageInputfortheSolenoid ................ 43 2.4UnshieldedMotorTestingExperiments .................... 45 2.4.1CapacitanceBridgeandLock-inAmplierforMonitoringArmatureMotion .................................. 46 2.4.2The555OscillatorforMonitoringArmatureMotion ......... 47 2.4.3TheQ-meterforMonitoringArmatureMotion ............ 49 2.4.4TheACBridgeCircuitsforMonitoringtheMotionoftheArmature 50 2.5ImprovedDesignoftheArmatureandtheTestCell ............. 57 2.6Conclusion .................................... 59 3CONSTRUCTIONOFSUPERCONDUCTINGSHIELDEDLINEARMOTORANDEXPERIMENTALCELL ........................... 84 3.1ConstructionofSuperconductingShield .................... 84 3.1.1ElectroplatingTheoryandElectrolyteRecipe ............. 84 5

PAGE 6

......................... 85 3.1.2.1Lead .............................. 85 3.1.2.2Methanesulfonicacid(MSA) ................. 86 3.1.2.3Leadcarbonate ........................ 86 3.1.2.4Labprotectiveequip ..................... 86 3.1.3LeadElectroplatingProceduresandResults ............. 86 3.1.3.1Proceduresteps ........................ 86 3.1.3.2Results ............................ 88 3.1.3.3Troubleshooting ........................ 88 3.2TestingtheExperimentalCellatLiquidHeliumTemperature ....... 90 3.2.1SimulationResults ........................... 90 3.2.2ExperimentalTestingResults ..................... 92 3.2.3ViscousDragandImpedanceForcesDiscussion ............ 92 3.2.4HeatDissipationDiscussion ...................... 93 3.3LeakTightElectricalFeedthroughDesign .................. 94 3.3.1ElectricalFeedthruConstruction .................... 95 3.3.2ThermistorCircuitBoardConstruction ................ 96 3.3.3Conclusion ................................ 97 4THERMISTORSELECTRONICS ......................... 111 4.1Introduction ................................... 111 4.2TheACBridgeCircuitAnalysis ........................ 111 4.3ResolutionMeasurementatRoomTemperature ............... 113 5EXPERIMENTALPROCEDURE,DATA,ANDANALYSIS ........... 118 5.1Introduction ................................... 118 5.2ExperimentalResults .............................. 118 5.2.1ThermistorCalibration ......................... 119 5.2.2BackgroundHeatingCheckat624mK ................ 119 5.2.3PerformingQTExperimentsat520mK ................ 120 5.3ExploringtheKelvinWavesintheEnergySpectra ............. 121 6CONCLUSIONSANDFUTUREWORK ...................... 127 6.1Conclusions ................................... 127 6.2FutureWork ................................... 127 APPENDIX ADERIVATIONANDNUMERICALANALYSISOFMAGNETICFIELDANDFORCE ........................................ 129 BSOMECCODE ................................... 131 CLABVIEWPROGRAMSHOTS .......................... 140 6

PAGE 7

............................... 144 REFERENCES ....................................... 145 BIOGRAPHICALSKETCH ................................ 148 7

PAGE 8

Table page 2-1Optimalparametersforthemotordesign. ..................... 40 2-2Parametersfortheunshieldedtestmotor. ..................... 45 3-1Parametersofsuperconductorshieldedsuperconductinglinearmotorsystem. .. 91 3-2Forcesonthearmaturewhenmovingupat1m/s(Downloadispositive). .... 94 4-1ParametersoftheACbridgeaectingthesensitivityandthepowerdissipation. 114 4-2SensitivitytestoftheACbridge. .......................... 115 8

PAGE 9

Figure page 1-1Viscosityofliquidhelium-4. ............................. 29 1-2Superuidandnormaluiddensitiesasafunctionoftemperature. ....... 29 1-3PhotographsofstablevortexlinesinrotatingHeII. ................ 30 1-4Dampingonasphereoscillatinginliquidhelium. ................. 30 1-5Donnelly-Glabersoninstabilityofaquantizedvortexline. ............. 31 1-6Energyspectrumforhomogeneousandisotropicturbulence. ........... 31 1-7Electricalconductionmechanismsinsemiconductors. ............... 32 1-8Calibrationplotsforthreetestthermistorsdevelopedforcalorimetry. ...... 32 1-9Designforthethermometertestcell. ........................ 33 2-1Gridturbulenceinaclassicaluid. ......................... 60 2-2Superconductingmotormodel. ........................... 60 2-3Armaturemotioninunshieldedandsuperconductingshieldedsolenoid. ..... 61 2-4Armaturemotioninsidesuperconductingshieldedsolenoid(linearacceleration). 61 2-5Armaturemotioninsidesuperconductingshieldedsolenoid(squareacceleration). 62 2-6Uppercriticaleldversustemperatureforniobium. ................ 62 2-7Voltageinputtothesuperconductingshieldedsolenoid. .............. 63 2-8Simulatedarmaturemotionforthesuperconductingshieldedsolenoid. ...... 64 2-9Drivingvoltage. .................................... 65 2-10Circuitoftheswitchbox. .............................. 66 2-11Machinedrawingsandphotosofthemotorsystem. ................ 67 2-12Experimentalapparatusforunshieldedmotor. ................... 68 2-13TheGR1616CapacitanceBridge .......................... 69 2-14Circuitryoftheexperimentalapparatusforunshieldedmotortestingexperimentsusingthe555oscillatorcircuitandLabViewcounterprogramtomonitorthemotionofthearmature. ............................... 69 2-15TestingcircuitofQ-meter. .............................. 70 9

PAGE 10

.............................. 70 2-17MeasuringthecapacitanceofthecapacitivepositionsensorwiththeGR1616capacitancebridgeandthelock-inamplier. .................... 71 2-18Circuitryandsetupfortestingthesuperconductingmotorat4.2K. ....... 72 2-19TheoreticalcalculationofthemagneticforceandRTsensorcalibrationcurve. 73 2-20Motionofthearmatureofthesuperconductingmotor. .............. 74 2-21Simulatedarmaturemotionwiththeinputpulsesenttothesolenoid. ...... 75 2-22Motionofthearmatureofthesuperconductingmotor. .............. 76 2-23Motionofthearmatureofthesuperconductingmotor(I). ............ 77 2-24Motionofthearmatureofthesuperconductingmotor(II). ............ 78 2-25Motionofthearmatureofthesuperconductingmotor(III). ........... 79 2-26Modiedsuperconductingmotorsystem. ...................... 80 2-27MachinedrawingofthegridandthecorrespondingReynoldsnumbers. ..... 80 2-28Calibrationcurveofthepositionsensorat4.2K. ................. 81 2-29Electronicscircuitsforthesuperconductingmotorsystem. ............ 82 2-30Motionofthearmatureofthesuperconductingmotor. .............. 83 3-1Machinerydrawingsforthecellcap. ........................ 98 3-2Machinerydrawingsforthecellbody. ........................ 99 3-3Electrodeforthecellcap. .............................. 100 3-4Electrodeforthecellbody. ............................. 101 3-5Procedurestepsfortheleadplatingforthecellcap. ................ 102 3-6Procedurestepsfortheleadplatingforthecellbody. ............... 103 3-7Masterpieceoftheleadcoatedcellcap. ....................... 104 3-8Masterpieceoftheleadcoatedcellbody. ...................... 105 3-9Towed-Gridexperimentcell. ............................. 106 3-10Simulationforsuperconductorshieldedsuperconductinglinearmotorsystem. .. 107 3-11Motionofthearmatureoftheshieldedsuperconductingmotor. ......... 108 10

PAGE 11

.......................... 109 3-13Leaktightelectricalfeedthrudesignforourcryogeniccell. ............ 110 4-1TheACbridgecircuitsimulation. .......................... 116 4-2ACbridgecircuitforthermistorsresistancemeasurement. ............ 117 4-3Roomtemperaturethermistorresolutioncurve. .................. 117 5-1Thermistorscalibrationcurves. ........................... 123 5-2Motionofarmatureandthermistorresponseatvacuumaround600mK. .... 124 5-3Quantumturbulenceat520mK. .......................... 125 5-4Fittingtheenthalpyofliquidheliumasafunctionoftime. ............ 126 C-1LabViewprogramsforcalculationofcurrent,magneticeld,magneticforceandarmaturemotion. ................................... 141 C-2LabViewprogramstolookforoptimalparameters. ................ 142 C-3LabViewprogramsfordataacquisitionanddataanalysis. ............ 143 11

PAGE 12

Weproducedgridturbulenceinliquidheliumat520mKtocomparewithclassicalexperimentsandtheories.AboveT=1K,withviscositypresent,ithasbeenshownthatgridturbulenceisequivalenttohomogeneousisotropicturbulenceinaclassicaluid.Weseektoinvestigatethenatureofgridturbulencewhenviscosityiszero.Specically,intheabsenceofviscosityinaquantumuid,throughwhatpathdoestheturbulencedecay?Toproducegridturbulence,anactuatorwasdesignedandbuiltthatcanaccelerateanddeceleratethegridrapidlyinashortdistance(1mm),andachieveglidespeedsofupto1m/s.ToavoidJouleandeddycurrentheatingoftheliquidhelium,amagneticallyshieldedsuperconductinglinearmotorwasbuilt.Thegridisattachedtotheendofaverylightinsulatingarmaturerodwhichhastwohollowcylindricalniobiumcansxedtoitabout26mmapart.Thispartoftherodisinsideasuperconductingsolenoidwhich,whendrivenwiththeproperlyshapedcurrentpulse,producesamagneticeldresultingintherequiredmotion. Detailedcomputersimulationsguidedthemotordesign.ThesimulationandmotorcontrolprogramswerewritteninLabViewwithanembeddedCcompiler.Usingthesimulator,variousdesignsofsolenoid(withandwithoutshielding)andarmaturewereinvestigated.Wecomparedthesimulationandtheexperimentalresultsinwhichcomplexcurrentpulseshapeswererequiredtoproducethedesiredmotion. 12

PAGE 13

13

PAGE 14

1 ]anddiscoveredexperimentallybyHallandVinenayearlater[ 2 ]. Superuidquantumturbulenceproducedbytowed-gridexperimentsinliquid4Heatverylowtemperaturesispredictedtodecay,notthroughviscosity,asinaclassicaluid,butbyphononradiationwhentheenergyowsintothesmallerlengthscalesinaKelvin-wavecascade.Weproposeanewcalorimetrictechniquetoprobesuchadecaymechanismofsuperuidgridturbulenceatextremelylowtemperatures,say520mK,whilethenormaluiddensityisonly8.6ppm[ 3 ]. Thesuperuidityofhelium-4wasdiscoveredin1939byAllen,Misener,andKapitza[ 4 5 ]whileOshero,RichardsonandLeedidnotdiscoverthesuperuidityofhelium-3until1971[ 6 ].At2.17K,undersaturatedvaporpressure,thecurveofspecicheatversustemperaturefor4Heshowsadramaticspike,whichlooksliketheGreekletter`'.Thisiscalledalambdatransition,andcorrespondstoasecondorderphasetransition.In3He,thesuperuidtransitionoccursat0.9mKundersaturatedvaporpressure.Below 14

PAGE 15

ThethermaldeBrogliewavelengthofliquidheliumis at2.0K.Thisiscomparabletoorgreaterthanthemeaninterparticledistanceof3:6Aforhelium.SothedeBrogliewavelengthofeachatomislargerenoughtooverlapwithitsneighbor. Thisiswhyliquidheliumiscalledaquantumuid.Becausetherearetwoprotonsandtwoneutronsinthenucleus,thereisanevennumberofnucleons(totalnuclearspin=0),andthequantummechanicalbehaviorsof4HecanbeexplainedbyBose-Einsteinstatistics.Atomsof3HeobeyFermi-Diracstatisticsbecausetheirnucleiicontaintwoprotonsbutonlyoneneutron,totalinganoddnumberofnucleons(totalnuclearspin=1/2).(Thespinsofthetwoelectronscancelout.)Hence,4Heisabosonand3Heisafermion. Thesuperuid4He,alsocalledHeII,hasalmostzeroviscosity,whilethenormaluidof4HeaboveT,HeI,hasmuchhigherviscositywhichcandissipateenergyviainteractionswiththewallsofthecontainer.Theviscosityofliquid4HemeasuredbythemethodofoscillatingdiscviscometerisshowninFig. 1-1 [ 7 ].TwoofthemostfamousexperimentsdemonstratingthesuperuidpropertiesofHeIIarethebeakerexperimentandthefountain(thermo-mechanical)eect.IfyouputthebottomofanemptybeakerintheHeIIbath,a20-30nmthick4Hemobilelmformsonthewallsofthebeaker,andthenliquidHeIIowsalongthelmfromthebathintothebeakeruntilthelevelsareequal.Ifyouthenliftthebeakerabovethebathlevel,theliquidinsidethebeakerwillalsoowalongthelmoutofthewallsofthevesselintothebathuntilthebeakerisempty.NowifyouconnecttwovesselscontainingthesamelevelofHeIIatthesame 15

PAGE 16

8 { 10 ]toexplainthevariousinterestingphenomenathatoccurredinHeII.Inthismodel,theliquidheliumIIisconsideredasamixtureoftwointerpenetratinguids,calledthenormalcomponentandthesuperuidcomponent,withdensities,nands,respectively.Hence,thetotaldensityofliquidHeII[ 11 ]follows: Thesuperuidandnormaluidcomponentdensities,asafunctionoftemperaturebelowTunderthesaturatedvaporpressure,areshowninFig. 1-2 .Thesuperuidhaszeroentropy(Ss=0)andzeroviscosity(=0),whilethenormaluidexhibitsviscosity(n)andentropy(Sn),equaltotheentropyofalltheliquidhelium.Also,thesuperuidisconsideredtobeirrotational: where~vsisthevelocityofthesuperuid. ModifyingEuler'sequationsfortheclassical(Euler)uidsbasedonthecontinuityequation,andusingtherstandsecondlawsofthermodynamics,andhisownpostulatethatthechemicalpotential()isthedrivingforceforthesuperuid,LandauderivedthetwouidequationsforHeII[ 13 ]: @t+~r~v=0(1{5) 16

PAGE 17

@t+~rs~vn=0(1{6)(entropyconservation) andstresstensoris: InLandau'stwo-uidmodel,theelementarythermalexcitations,phononsandrotons,dependingonthewavenumber,ariseintheowofheliumIIthroughatubeorcapillaryatT6=0Kwhenthenormaluidcomponenthastheinteractionswiththewallscausingenergydissipationandviscousloss.Supposeanexcitationiscreatedwithenergy"andmomentumpduetothelossofenergyfromthetube(E=").ThenLandau'srelation(v"=p)givestheminimumvelocityofow requiredtoproduceanexcitation.However,actualcriticalowvelocitiesinexperimentsaremuchsmaller(mm/s)thanLandau'sprediction(60m/satthevaporpressureand46m/sathigherpressure[ 7 ]),duetothequantizedvortices. 17

PAGE 18

13 ]: Inaddition,theKelvincirculationtheorem, (byStokes'law)impliesthatthesuperuidcirculation staysconstant,andifatt=0thesuperuidvorticity!!s=!r!vsiszeroeverywhereitwillstayzero.If!r!vsdisappearseverywhere,thenthesuperuidcirculationis: Assumingthereissomecirculation,theremustbea\singular"regionwhereeither!r!vs6=0orthereisnosuperuid.Soweconsiderthesingularregionasaverythincylinder,calledasuperuidvortexlineorvortexcore.AccordingtoGauss'theorem:Rv(!r!v)d=Hs!vd!S,and!r!r!v0forany!v,wehaveRv(!r!r!vs)d=HS!r!vsd!S=H!vsd!`=0=.Soavortexlinecannotterminateintheuid,butmustendataboundaryorcloseinonitself(avortexring).Sincethevortexlineistheonlysourceofvorticityintheuidfor!r!vs=0everywhereexceptattheline,allpathintegralsencirclingthevortexlinehaveidenticalcirculations. AssoonasliquidheliumIIrotatesormovesbeyondacriticalvelocity,superuidvortexlinesappearanddemonstrateeitheranorderedarrayofvortexlinesbysteadyrotationordisorderedvortextanglesforcounterow(duetoheatow).ThatthesuperuidcirculationisquantizedwaspostulatedseparatelybyOnsagerandFeynman 18

PAGE 19

m9:97104ncm2=s,wherenisaninteger.Theradiusofthevortexcoreisabouta01A(atomicdimensions).ThestablequantizedvortexarraysinrotatingHeIIcanbevisualizedasshowninFig. 1-3 [ 14 ]:stablevortexlinesinrotatingHeIIinacylindricalbucketof2mmdiametertodepth25mmplacedattherotationaxisofarotatingdilutionrefrigeratorat100mK.8%3Hewasaddedtoprovidedampingwhichmaintainedstability.Thenegativeionsaretrappedonvortexcoresandareimagedonaphosphorscreenandrecordedoncinelm.Allsuperuidvortexlinesalignparalleltotherotationaxiswithorderedarraysofarealdensity(orlengthofquantizedvortexlineperunitvolume)asgivenbythefollowingequation: 2 (inlines=cm2),whereistheconstantangularvelocityfortherotation.Thiscanderivedasfollows:thecirculationaroundanycircularpathofradiusrconcentricwiththeaxisofrotation=H!vsd!`=H(!r!vs)d!S=2r2.Andthetotalcirculation=r2n0h=m,wheren0isthenumberoflinesperunitarea.Therefore,n0=2m=h=2=[ 7 ]. Theturbulentstate,describedasamassofvortexlines,usuallyhastwocriticalvelocitiessignalingtheonsetofturbulenceinsuperuidandinthenormaluidseparately,increasingthetotallengthofvorticitywiththeincreasingrelativevelocityofthetwouids.IntheexperimentonthedampingoftherotationofasphereoscillatinginliquidheliumIIasafunctionofthemaximumamplitude(orvelocity)oftheoscillation,theresultisshowninFig. 1-4 [ 7 ].AtregionA,thedampingisconstant,relatingtotheconstantnormalviscosityn.ThetwocriticalvelocitiesoccurredatthetransitionfromregionAtoB(whichistheonsetofturbulenceinthesuperuidcomponent),andCtoDcorrespondingtotheonsetofturbulenceinanordinaryclassicalliquid,wherethedampingincreasesdramatically.InregionsB,C,andD,bothsuperuidandnormaluidarecoupledandmovetogetherduetotheirmutualfriction.Thecriticalvelocityofthesuperuidriseswithreductionindiameterofthechannel. 19

PAGE 20

11 ](seeFig. 1-5 ).Theplaneofthesevibrations(calledKelvinwaves)precessaboutthecentercore,growingexponentiallyalongquantizedvortexlines.Thelengthsofthevortexlinesincrease,eventuallyresultinginavortextangleastheenergyistransferredfromthenormaluidtothesuperuid. Feynmansuggestedin1955thatvorticesapproachingeachotherverycloselyundergoreconnections.TheKelvinwavescanbegeneratedbyvortexreconnections,leavingkinksonthevortexlines,regardedassuperpositionsofKelvinwaves,leadingtothecontinuousgenerationofKelvinwaveswithawiderangeofwavenumbers. 1(whereUisthecharacteristicvelocityandisthekinematicviscosity)andenergydissipationbecauseofviscosityoccurs.However,iftheReynoldsnumberRe=inertialforce viscosityforce1(inan\inertialregime")sothattheviscositycanbeignored,thentheenergywillowinacascadefromlargescalestosmallerscales,asdescribedbytheKolmogorovspectrum[ 11 ]: whereE(k)dkistheenergyperunitmassforspatialwavenumbersintherangedk.ThefunctionE(k)hasdimensions[L3=T2](L:length,T:time).C1:5(theKolmogorovconstant,whichisdimensionless),and"=dE dtdk(thatistheaveragerateofkineticenergytransferperunitmassowingdownthecascade,dissipatedbyviscosityathighwavenumber,k>`1).Thedimensionsof"are[(L=T)2=T]=[L2=T3];thedimensions 20

PAGE 21

1-6 [ 11 ],thelargesteddieshavethemostturbulentenergy,anddecaymostslowly,whichdeterminestheenergydissipationrate(").Inthesteadystate,energyowsfromtheselargesteddiestothesmallesteddies. ThesuperuidgridturbulenceexperimentsinheliumIIabove1K[ 12 ]canalsobedescribedbytheKolmogorovspectrumintheinertialregimeonlengthscaleslargerthanthespacingbetweenvortexlines(`).Inthiscase,theenergydissipationbyviscosityoccursonthelengthscaleoforder`(thespacingbetweenvortexlines)duetothesignicantamountofnormaluidandthemutualfrictionbetweenthesuperuidandthenormaluid. 12 ]showthathomogeneousisotropicturbulenceisproducedbehindatowedgridmovingattheorder1m/s.Computersimulations[ 15 ]predictatzerotemperaturetheKelvinwavesonintersectingvortexlinesproducetheequivalentoftheviscousregimeinaclassicaluid.Thishasyettobeconrmedbyexperiments. Itissuggested[ 16 25 ]thatenergyowstothesmallestscalebyaKelvinwavecascadeonthevortices,leadingtoaKelvin-waveenergyspectrumforthewavenumber~kofKelvinwavesgreaterthantheinversevortexspacing`1.Kelvinwavesdonothaveanydampingatverylowtemperaturesuntilthewavenumbers~k(~k2=2108m1)[ 16 25 ]becomemuchgreaterthan`1.Ithasbeenpredicted[ 16 ]thatat0.46K,energydissipatesbyphononradiation;howeverthishasnotbeenconrmedexperimentally.TheresultsofthesimulationsdemonstratethecontinuousenergyowwithintheKelvinwavestowards 21

PAGE 22

ThecorrespondingKelvinwavespectrum,cutobydissipationat~k~k2,isproposedtobe:[ 25 26 ] ~E(~k)=A2~k1;(1{18) whereE(~k)d~kistheenergyperunitmassandunitlengthofvortexassociatedwithKelvinwaveswithwavenumbersintheranged~k,isthedensityofthehelium,andA2.TherateatwhichenergyowsintotheKelvinwavecascadeperunitmassofheliumisgivenby[ 26 ] ~"(2=2)3L20;(1{19) whereL0=`2isthelengthofthesmoothedvortexlineperunitvolume,and20:3.Theenergycontainedinthe\Kelvinwavecascade"perunitmassofheliumisgivenby[ 26 ] ~E=1 0)2L;(1{20) whereL=AL0ln(~k2`),Evistheenergyperunitlengthofvortexline,and0isthevortexcoreparameter.Thecut-owavenumber~k2isgivenbytheformula[ 16 ] ~k2`=(c` A1=3)3=4;(1{21) wherecisthespeedofsoundinhelium. Bymeasuringtheriseintemperatureoftheheliumaftercreatingturbulencewithahighresolutionthermometer,wecanprobetheturbulencedecayasafunctionoftimesincethetemperaturechangecorrespondingtothedecayofarandomvortextangleisproportionaltothechangeinthevortexlinedensity.Therefore,itispossibletoexploretheexistenceofaKolmogorovspectrumonlargelengthscales,aKelvinwavecascadeonsmalllengthscales,andthedissipationmechanism.Theenthalpyoftheheliumisgivenby 22

PAGE 23

3 ] (inJ=m3).Ifasmallamountofturbulenceenergy(E)isreleasedasthermalenergyinheliumattemperatureT0,theenthalpyvaluesofthetemperaturechangewouldbe (inK4),whichcanbemonitoredasafunctionoftime.Thegridturbulenceiscreatedbydrawingagridthroughtheheliumbyasuperconductinglinearmotorataconstantspeedasfastas1m/sfor10mmforapproximately10ms,whichisfasterthanthedecayspeedoftheturbulence(afewhundredmilliseconds).Anyenergydissipationintheheliumfrommovingthegridmustbemuchsmallerthanthereleasedthermalenergyfromthedecayofthesuperuidturbulence.Supposethesquarecrosssectionofthechannelisddandaverydensevortextangleaswellasquasi-classicalturbulence(onalargerscalethanthemeanvortexlinespacing`)areproducedbythetowed-grid.Theenergycantransfertoeitherlargerlengthscales(onthescaleofd)untilbecomingsaturated,ortosmallerlengthscales(lessthan`)whereenergydissipationoccurs,leadingtotheKolmogorovenergyspectrum.Thetimerequiredtobuildthisspectrumshouldbelessthantheturnovertime: u(d);(1{24) whered=eddysize,andu(d)=characteristicvelocityrelatingtothiseddysize,denedby[ 26 ] Fromthecluesinthepreviousexperimentsabove1K,itissurmisedthataKolmogorovspectrumjoinssmoothlytothe\quantumvelocity", `:(1{26) 23

PAGE 24

26 ] `)(d where0:25.Thetotalturbulentenergyperunitmass,mostofwhichcomesfromthelargesteddiesofsized,isgivenby 2u2(d)=3 2( `)2(d As`increases,turbulencedecaysandenergydissipatesviatheclassicalKolmogorovcascadeasdescribedbytheaboveequation.Attimetd,totalenergydecaywithtimeasdescribedbytheKolmogorovspectrumcanbethoughtofastheenergyowratewithtime[ 26 ], wheret0d,whichvarieswiththetowed-gridspeedsorinitialturbulentintensities.So: 2C3d2(tt0)2:(1{30) ComparingEquations 1{28 and 1{30 ,thetimedependenceof`isgivenby AnothercharacteristictimefortheKelvin-wavespectrum(Equation 1{18 )whichdescribesthefullydevelopedKelvin-wavecascadeisgivenby ~=~E 2)`2 EnergyowsintotheKelvin-wavecascadeattherate"=~",andeventuallydissipatesbyphononradiation.TheenergyperunitmasscontainedintheKelvin-wavecascadeisgivenas ~E=A2`2ln(~k2`):(1{33) 24

PAGE 25

2C3d2(tt0)2+A2`2ln(~k2`):(1{34) Since`increaseswithtime,thedecayofEwillbedominatedbythedecayofEclassforsmall`,butbythedecayof~Eforlarge`.Fortt0,Eclassisproportionaltot2,while~Eisproportionaltot3=2,whichwillbeexpressedbytheobservedrate-of-changeoftemperature. 1.Operatingtemperature:20mK-to1K(dilutionrefrigeratortemperatures). 2.Sensitivetotemperaturechange:T103K,orT=T0:05103. 3.Shortresponsetime:t103s.Theturbulenceenergydecayswithinafewhundredmilliseconds.Inordertohavegoodtimeresolutioninthedata,itisnecessarythatthethermistorsrespondwithin1ms. 4.Smallmass,smallheatcapacity,andgoodthermalconductivity. Sofarwehavefoundtwoexcellentcandidatestofullltheaboverequirementswhichcanbeusedinourcalorimetrictechnique:NeutronTransmutationDopedGermaniumBolometersandMiniatureGeFilmResistanceThermometers.Wehaveusedthelaterinourwork. 1-7 [ 18 ]) 1.Thermalgenerationofelectronsandholesacrossthebandgap,whichisnegligibleatlowtemperaturesincekTEgap. 2.Generationoffreechargecarriersbyionizationofshallowdonors,whichisnegligibleatlowtemperaturesincekTECED. 25

PAGE 26

4.Inheavilydopedandcompensatedsemiconductors,thecompensatingorminorityimpuritiescreatealotofmajorityimpuritieswhichremainionizeddowntoabsolutezero.Thechargecarrierhopsfromanoccupiedmajorityimpuritysitetoanemptysite,whichistheworkingprincipleforthelowtemperaturebolometer.Itisalsocalledhoppingmechanism. Thematerialweuseforourhigh-resolutiondilutionrefrigeratorthermometerisneutrontransmutationdoped(NTD)germanium[ 18 19 ],whichappliesthefourthelectricalconductionmechanismasdiscussedabove. ANTDGehasNAmajorityshallowacceptorimpuritiesandNDminorityshallowdonorimpurities(NA>ND).Atverylowtemperatures(kTEAwhereEAisthebindingenergyoftheelectronstotheacceptors),andinthedark,(NAND)acceptorshaveanelectronvacancyandareneutralwhileNDacceptorscaptureelectronsfromcompensatingdonors. Thetransmutationofstablegermaniumisotopesviathecaptureofthermalneutronsisaccomplishedbythefollowingprocedure: 1.Asingleultra-puregermaniumcrystalisgrowninahydrogenatmosphere(1atm)fromameltcontainedinapyrolyticcarbon-coatedquartzcrucibleusingtheCzochralskitechnique. 2.Six2mmthickslicesof36mmdiameterarecut,lappedandchemicallyetched. 3.Irradiatedwiththermalneutrons;doses7:510161:881018cm2. 4.Aftertenhalflivesof7132Ge(T1=2=11:2d),thesamplesareannealedat400Cfor6hoursinapureargonatmosphere(1atm)toremoveirradiationdamage. Somepapersdemonstratethat,evenatdilutionrefrigeratortemperatures,theNTDGethermometersstillhavesucientsensitivity.Forexample:at25mK,T=T4:8106,andresponsetime<20msforthermometersassmallas1mm1mm0:25mm[ 20 ].SomeverygoodcircuitryfortheNTDGebolometershasbeendeveloped[ 20 21 ]. 26

PAGE 27

22 { 24 ]havealreadybeendevelopedandtestedinourgroup.Thetypicalsizeforthesensitiveelementis300mindiameter,andthemountedgoldleadsare50mindiameter.Theconductionmechanismisvariablerangehopping.Fig. 1-8 showstheabsoluteresistancevaluesandthesensitivity(dR dT)overthetemperaturerangeofinterest,forthreetestthermistorsagainstarutheniumoxidecalibratedthermometer.WeusedtheLR-110picowattACresistancebridgeasthedetectioncircuit,andcalibratedthreeofouravailablethermometers.TheLR-110bridgecanmeasureresistancesbetween10and1.2Mwithhighresolution(betterthan0.1%)andgoodaccuracy(0.05%0:25%).Thecalibrationcurvesdemonstratingtheperformanceandthecharacteristicsofthethreetestthermometersarequitedierentduetothevariationsindopingandheattreatmentduringmanufacturing.Sensingpowerswerelessthan1013watts.Twoofthethermometersarenotidealaswecanseefromthecurves.Forthermistor1,theresistance7or8kunder100mKandwasnearlyconstantbelow38mKwithprettystablesensitivitywithinthemeasuredtemperaturerange.Forthermistor2,theresistancegoestoinnityatlowtemperaturesandonlybecomesmeasurableaboveabout49mK.Thermistor2demonstratesdramaticsensitivitychangeoverawiderangeoftemperatures.Forthermistor3,theresistanceis16kat88.7mKand526kat24.8mK.Thesensitivityrangesfrom1.7Meg=Kto140.3Meg=Kbetween50mKand20mK.Itsresponsetimeislessthan0.001s.Thismakesthermistor3agoodcandidate.Duringturbulencedecay,theresistanceofthermometer3isexpectedtochangefrom4kto1.75k,andthechangefrom3ktoapproximately2krepresentingtheKelvinwavedecayat520mK,whichappearsinournalexperimentalresults. ThemachinerydrawingforthethermometertestcellisshowninFig. 1-9 .Thethermometertestcellisusedtosimultaneouslytestthesensitivityandtheresolutionoftwothermometers(miniatureGelmresistancethermometers)separatedbyasmall 27

PAGE 28

28

PAGE 29

Viscosityofliquid4Hemeasuredinanoscillatingdiscviscometer[ 7 ]. Figure1-2: Superuidandnormaluiddensities(nands)asafunctionoftemperaturebelowlambdatransitionunderthesaturatedvaporpressure. 29

PAGE 30

PhotographsofstablevortexlinesinrotatingHeIIinacylindricalbucketof2mmdiametertodepth25mmplacedattherotationaxisofarotatingdilutionrefrigeratorat100mK. Figure1-4: Dampingonasphereoscillatinginliquidheliumat2.149Kwithaperiodof18.5s[ 7 ]. 30

PAGE 31

Donnelly-Glabersoninstabilityofaquantizedvortexlineoccursifthecomponentofthenormaluidvelocityparalleltothevortexlineexceedsacriticalvalue[ 11 ]. Figure1-6: Energyspectrumforhomogeneousandisotropicturbulence[ 11 ].(k:Kolmogorovwavenumber,whereviscousdissipationbecomessignicant;kC=2 d,d:thesizeofthecontainer;ke(t)=2 `e(t),`e(t):eddylengthscale)[ 11 ]. 31

PAGE 32

Electricalconductionmechanismsinsemiconductors[ 18 ]. Figure1-8: Calibrationplotsforthreetestthermistorsdevelopedforcalorimetry.(a)Resistanceversustemperature.(b)Sensitivityversustemperature. 32

PAGE 33

Designforthethermometertestcell.(a)Overview.(b)Topviewofcap. 33

PAGE 34

2-1 [ 27 ]),whichisthesimplestcaseamongthecomplexnonlineardynamicssystems.Inordertocomparewiththisclassicalcase,weintendtoproducehomogeneousisotropicquantumturbulence(HIQT)inliquidheliumIIbelow1K. InordertoproduceHIQT,wehavedesignedandbuilttheshieldedsuperconductinglinearmotorforourtowed-gridturbulenceexperiments.Firstofall,webuildamodel,showninFig. 2-2 [ 28 29 ]:asinglesuperconductingsolenoidmotorwithanarmaturemovingthroughitscenter.Thislightandhollowinsulatingarmatureisconstructedof3phenolictubesseparatedbytwohollowcylindricalniobiumcansplacedsomedistanceapart,withtheturbulence-producinggridattachedtooneend.Therequirementsandadvantagesofourmotorsystemareasfollows: 1.Thesuperconductingshieldcanavoideddycurrentheatinginthecellwalls. 2.ThesuperconductingsolenoidcanavoidJouleheatingfromthesolenoid. 3.Withanappropriatecurrentpulse,thegridcanbeecientlyacceleratedanddeceleratedfrom0to1.0m/swithin1mm.Andthegridcanbedrivenatanearlyconstantspeed1m/sfor10mm,producinghomogeneousisotropicturbulencewithin20ms. Intheresultinggridmotioninoursimulator,thegridwouldbeacceleratedfrom0to1m/sin1mm.Thenittravelsatalmostconstantspeed,1m/s,for10mm.Thenthegridwouldrapidlydeceleratetoceasewithin1mmwhenthethirdpulseisapplied.Thenweputoursimulationresultsintopractice.Webuildourtestcellguidedbythesimulation.Inourtestcell,wehaveonesuperconductingsolenoiddrivingthearmaturetomovethroughitscenter,withagridattachedattheend.Thislightinsulatingarmatureisconstructedof3phenolictubesseparatedbytwohollowcylindricalniobiumcansplacedexactly26mmapart,withthegridattachedtooneend.Aconductingsection 34

PAGE 35

Ourunshieldedtestmotorsystemhasbeentestedverysuccessfully.Weapplythepulsestothesuperconductingmotortodrivethearmatureinsidethesolenoid:twosinepulseswithDClevelinbetween,followedbysmallDClevelfor250ms.Intheresultingvelocityversustimecurve,wealreadycanacceleratethearmatureto1.1m/s.Thevelocityremainszeroforabout250mswhenthearmatureisheldonthetop.Inthevelocityversuspositioncurve,wecanseethatthearmaturemovesatalmostconstantvelocity1m/s0.1m/sforatleast8mm. Wealsoimprovethisdesigninoursuperconductorshieldedsuperconductingmotorsystem,discussedinthenextchapter.Oneoftheimportanttaskistobuildthesuperconductorshieldontheinteriorofthecell.Thedetailswillalsobediscussedinthenextchapter. Inchapterfour,wewouldliketodiscussabouttheaccomplishmentofthefollowings: 2-2 ,madeofthreecoaxialparts:onesuperconductingshieldwiththeradiusbandlengthh,onesuperconductingsolenoidwiththeinnerradiusrandlengthl,andalightinsulatingrodwithtwoniobiumcylindersattachedandseparatedbydistanceS.Thegridisattachedtotheendoftherodandhenceispushedbyit. Supposethediameterofthesuperconductingwireforthesolenoidisd,andthetotalnumberofturns,N.Wecanestimateapproximatelytheself-inductanceofsucha 35

PAGE 36

IN(0NI)r2 (inHenry,andallthelengthsareinmm),whereisthetotalmagneticuxowingacrossthesolenoid,Iisthecurrentowingthroughthesuperconductingwireofthesolenoid,Bistheapproximatemagneticeldatthecenterofthesolenoid,Aistheaveragecrosssectionareaofthesolenoid,andristheaverageradiusofthesolenoid: r=r+Nd2 Thezcomponentofthemagneticeldattheposition(,,z)nearthesolenoidisderivedasthefollowingbygeneralizingtheprobleminGriths[ 30 ]: where 2)d;z0=l 2)d:(2{5) Forthemagneticelddistributioninsidethesolenoidenclosedbythesuperconductingshield,weciteEq.12inSumner[ 31 ]: hlXkS1(krb)I0(k) where h(2{8) 36

PAGE 37

Supposetheniobiumisaperfectdiamagnet,thenthemagneticforceexperiencedbytheniobiumcylinder#1withthecenterofmassatz=zialongtheaxisofthesolenoid(thecenterofthesolenoidisdenedasz=0position): SinceM=Bz 32 ],themagneticforceisproportionaltothegradientofthemagneticeldsquare: wherem,M,0,ro1,l1arethemagneticmoment,themagnetization,thepermeabilityatvacuum,theouterradiusandthelengthofNbcylinder#1,respectively.Forthepurposeofcomputersimulations,thepracticalformulaforthenumericalanalysisandthecorrespondingCcodeareintheAppendixAandB,respectively. Inadditiontothemagneticforce,thegravityforce~Fgavisalsoconsidered;therefore,accordingtothesecondNewton'slaw,thenetforceexperiencedbythewholesystemwithmassMsystemproducetheacceleration,a:~Fmag+~Fgav=Msystem~a,or Thesystemincludestheinsulatingrod,thetwoniobiumcylindercansandthegrid.BecauseFmag(zi)/I2,wecanwriteFmag(zi)=fmag(zi)I2.Supposethesecondniobiumcylinderissomedistance,S,belowtherstone,thenthecurrentrequiredtoreachtheobjectiveaccelerationwouldbe: (unitinAmpere). 37

PAGE 38

Inaddition,wehaveseveraloptionsforthemathematicalformoftherelationshipbetweenthedestinedterminalvelocityv(inm/s)andthetravelingdistanceS1(inmm)duringtheperiodoftimeoftheaccelerationa(inm=s2),suchaslinear,squareandsinefunction.Foreachsmalltravelingdistance,dz(mm),theaccumulatedvelocity,accelerationandtimeattheithincrement,vi(m/s),ai(m=s2),andti(ms): S1dz(m=s)(2{13) 2)(v S1)2dz103(m=s2)(2{14) aS1)103(ms)(2{15) S21(idz)2(m=s)(2{16) 2)(v2 S1)(m=s)(2{19) 38

PAGE 39

S1)sin2[(i1) S1]g103(m=s2)(2{20) afsin(i S1)sin[(i1) S1]g103(ms)(2{21) Forthedeceleration,wesimplyhavethelinearmathematicalform.SupposethetravelingdistancewouldbeS3(inmm).Foreachsmalltravelingdistance,dz(mm),theresultantvelocity,accelerationandtimeatthejthdisplacementinterval,vj(m/s),aj(m=s2),andtj(ms): S3dz(m=s)(2{22) 2)(v S3)2dz103v2 aS3)103(ms)(2{24) 2.3.1SimulationAnalysis 2-1 (unitsoflengthsinmm). Fig. 2-3 (a)showstherequiredcurrentversustimecurvesfortheunshieldedandsuperconductingshieldedsolenoidwithasinefunctionacceleration(velocityisthesinefunctionoftheniobiumposition).Thecurvesshowthreepeaks:therstandthethirdpeaksaretoaccelerateanddeceleratetheniobiumcylinders.Themiddlepeakisduetothealmostbalancedmagneticforcesonthetwoniobiumcylindersatthatpositionsince 39

PAGE 40

2-3 (a),andseethatthevelocityversuspositioncurveinFig. 2-3 (b)(again-symbols)isvirtuallyunaected.Thedroopinvelocityafterz=10mmisunavoidablesinceallforces,includinggravity,aredirecteddownwardfortherestofthestroke. Table2-1: Optimalparametersforthemotordesign. ParameterDescriptionValue Notethatthesuperconductingshieldrequiresaslightlyhighercurrent(0.14Agreater)toproducethesamemotion.Theeectissmallbecausetheshieldissignicantlylargerthanthesolenoid. InthevelocityversuspositioncurvesinFig. 2-3 (b),weseethatthemotionisasexpected.Theniobiumcylinderstravelatalmostconstantspeed,1m/s,for10mm,butstarttoslowdownwhenthemiddlecurrentpeakoccurs,whichisquitereasonable.Aftertherstniobiumpassesz=10mm,thesecondniobiumisclosertothesolenoidandexperiencesastrongermagneticforceintheoppositedirection,resultingintheslightdeceleration.Therefore,applyingthethirdpulseproducesthedesireddecelerationtorapidlystopthegrid.Theevaluationresultsprovethatoursuperconductinglinearmotorisaveryfeasibledesign. 40

PAGE 41

2-4 ,Fig. 2-5 .Itrequiresaslightlyhighercurrent,0.149Aand0.8Agreater,forthesuperconductingshieldedsolenoidtoproducethelinearandsquareaccelerationmotion.Therefore,sinefunctionaccelerationisamoreecientwaythattakestheleastcurrentamongthethreeoptions. TheshotsofallthesimulationprogramsareinAppendixC. ThetheoreticalestimatesoftheloweranduppercriticalmagneticeldsforthetypeIIsuperconductorsare[ 32 ]: where0isthesuperconductinguxquantum,calledauxoidoruxon: 0=2~c=2e=2:0678107(2{27) (inGausscm2).andarethepenetrationdepthandthecoherencelength,respectively.Forexample,theniobiumhasthepenetrationdepthatabsolutezeroestimatedfromthemeasurementstobe470A[ 33 ],andthesuperconductingcoherencelengthis11nm 41

PAGE 42

34 ].SoHc12980Gauss,Hc254397Gauss.Thepenetrationdepthandthecoherencelengthareactuallytemperaturedependent. Experimentally,Hc1andHc2valueshavebeenmeasuredtobedependentonthepurityandtheresidualresistivityratios[RRR=R300=RN4:2]ofniobium[ 35 36 ],theeldorientation[ 37 ],andthetemperature[ 35 { 38 ].R300istheresistancemeasuredatroomtemperature.RN4:2isthenormalstateelectricalresistivitymeasuredat4.2Kinaeldof0.6Torhigherafterthemagnetizationdatameasurement.Thehigherpuritytheniobium,thehighertheRRRvalues,andthelowertheHc2values.Forexample,inFig. 2-6 [ 35 ],atthetemperatureT1.5K,theuppercriticaleldHc212.8KGauss,7.3KGaussand3.5KGaussforRRRoftheniobiumsamples=3.1,8.8and505.Forthetemperaturedependence,thedatahasshownthethermodynamiccriticaleld,Hc,withtheformHc(T)=1993[1(T Tc)2](inGauss)forRRR1600[ 36 ],thelowercriticaleld,Hc1(T)=1735[1(T Tc)2:13](inGauss)forRRR1400[ 36 ],andtheuppercriticaleldHc2=41001(T=Tc)2 38 ]. Inaddition,thecriticalsurfaceeld,Hc3(T)=1:695Hc2(T),hasbeenpredictedbySaint-JamesanddeGennes[ 39 ]andmeasured[ 36 38 ]fromtheonsetofzeroresistivityandtheACsusceptibility,whichisalsotemperature,purity,RRRvalueandsurfaceofthesamplesdependent.BetweenHc2andHc3,superconductivityandsurfacesupercurrentappearintheformofasurfacesheathwithathicknessabout(T)onsurfacesparalleltotheappliedmagneticeld. Experimentallywhatwewoulddoistomakethinhollowniobiumcylinderswithendcaps.Belowthesurfacecriticaleld,theenhanced\surfacesheath"magnetizationmakesthethinsurfacesheathstillsuperconductingwhilethebulkisinnormalstate.Bymakingthecylinderhollowwewouldenlargethetotalvolumeofniobiumtoexcludemoremagneticuxwithmuchsmallermassandreducingthetotalmassofthewholesystemmaketherequireddrivingmagneticforcemuchless.Evenwhentheeldisbeyondthe 42

PAGE 43

Innumericalanalysis,weuse: (involts),wheredtistheinnitesimaltimeintervalbetweenthetime(t-dt)andtwhenthecurrentowingthroughthesolenoidareI(t-dt)andI(t),respectively.TheLabViewsimulationprogramcalculatestherequiredvoltageinputtothesuperconductingshieldedsolenoidwithsine,linear,andsquarefunctionaccelerationasshowninFig. 2-7 .Sincethecurrentforthesinefunctionaccelerationhassmoothtransitionwithrespecttotime,ithasthebetterperformancethantheothertwo,i.e.lowerrequiredvoltage.Stillthevoltageistoohugetohavethepracticalapplicationinthelaboratory. Inordertosolvethisproblem,weneedanadditionalcapacitorwithcapacitanceC(F)inthecircuittoformanLRCcircuit.InanLRCcircuitunderthesinusoidallydrivenvoltage,V=V0ei!t,theKirchhorulerequiresthatthesumofthechangesinpotentialaroundthecircuitmustbezero,so dt+IR+Q C=LdI dt+IR+1 whereQ(Coulomb)isthetotalchargeonthecapacitor.Thesolutionforthecurrentwouldbe: 43

PAGE 44

and R)(2{33) Atresonance,for!=1 40 ]. Wecancalculatetherequiredvoltageinputtothesolenoidfromthecalculatedcurrentcurve: Inthewayofnumericalanalysis: NCNXi=1I(ti);(2{35) where N(i1 2)(2{36) Anotheralternativewayofsendingthepulsestothesolenoidistoinputtheperfectsinusoidalshapecurrentpulsemodiedaccordingtothepreviouscalculatedcurrentprole,whichwouldstillgivetheexpectedmotionforthearmatureofthemotor,asshowninFig. 2-8 SupposewesupplythecurrentI(t)=I0sin!t.Ifweonlyconsiderthesolenoidwithinductance,L,andtheresistanceforthewholecircuit,R,thentherequiredinputvoltagewouldbe ForI0=2.2A,R=0.1,!=1200rad/s,L=0.056H,thesameparametersasthoseinFig. 2-8 ,thentherequiredvoltageinputtothesolenoidversustimewouldbelikeFig. 2-9 .Somevoltagepulsesaslargeas150Vseemtobetoolargetobeapplicable. Experimentally,wemightneedC=11.2Ftotunethecircuitonresonance.Atresonance,i.e.!=1 R.Duringtheconstantcurrentperiod 44

PAGE 45

2-10 .Thedetailedcircuitryforthewholeexperimentalsetupwillbeintroducedveryshortly. 2-2 .Withthoseparameters,weruntheLabViewsimulationprogramstondouttherequiredcurrentproleforthesinefunctionacceleration,andthenwemodifythiscurrentproleintotwoperfectsinusoidalpulsesalongwiththeconstantDCcurrentinbetween.Fig. 2-11 showsthemachinedrawingsandthephotosforourunshieldedmotortestcell.Aswecanseefromthedrawingsthatwebuildthecapacitivepositionsensorinordertomonitorthemotionofthearmature. Table2-2: Parametersfortheunshieldedtestmotor.RefertoTable 2-1 ParameterValue 45

PAGE 46

2-12 .Wesendthenegativepulsefromthecomputer(analogoutput1:DAC0)throughourcurrentamplier.Thecurrentamplierampliesandinvertsthepulse.Thenthepulseisfedintotheswitchbox,wheretheswitchescanbecontrolledbytheTTLsignalsfromthecomputer(analogoutput2:DAC1).Eventuallythepulseissenttothesolenoidinthecryostatatheliumtemperature,4.2K.Wealsousethecomputertomonitorthepulsesenttothesolenoid(analoginput2:ACH2),andsimultaneouslythecapacitivepositionsensorismeasuringthepositionofthearmature(analoginput1:ACH1). Thesensorisconnectedtothelock-inamplierandcapacitancebridge(GR1616).Wesetthedrivingrmsvoltage1V,frequency1.01kHzfromthereferencesinewaveformoutputofthelock-inamplier,andthetimeconstant100ms.Atroomtemperaturethecapacitancebridgereadsthecapacitanceofthecapacitivepositionsensor3.32pF(themagnitude,R,oftheoutputonthedisplayofthelock-inamplierreadsminimum39V)whenthearmatureisatrestand3.00pF(themagnitude,R,oftheoutputonthedisplayofthelock-inamplierreadsminimum108V)whenthearmaturemovesallthewayuphittingthebrassplate12mmaboveintheair.Bysettingthesensitivityofthelock-inamplier1mVandthestandardcapacitanceofthecapacitancebridge3.32pF,thechannel1outputofthelock-inamplierreads0.44V(R=44.7V)asthearmaturesittingatrest,whileasthearmaturemovesup12mmthechannel1outputreads2.54V(R=255V).Withsuchsignicantvoltagechange,2.10V,whichcanbeeasilyrecordedbytheLabViewdataacquisitionprogram,wecanconvertthevoltageshiftintotheposition,oreventhevelocityofthearmaturemotion.Whencoolingdowntoliquidheliumtemperature,4.2K,someconditionsmightchange.Weneedtochangesomeofthesettingsofthelock-inampliertorecordthevoltageshiftfromchannel1 46

PAGE 47

Itturnsoutthatwedonotneedthecomputercontrolledswitchbox,asthegrayregionintheschematic,becausecurrentamplierltersoutthebackemfsfromsolenoid.Thedistortedpulsewithspikessenttothesolenoidwillbeproducedwithoutbothcurrentamplierandtheswitchbox,asmentionedpreviously.Weturnedupthecurrentsenttothesolenoidlittlebylittlebyturningupthegainofthecurrentampliergradually.Eventually,whenthepeakcurrentreachedtheexpected2.86A,weheardthesoundfromthedewarlikethearmaturehittingthebrassplate12mmaboveit.Whatasuccess!Verydisappointedly,thecapacitancebridgecannotrespondfastenoughtohaveanyobservablechange.Lateronwerealizedfromsomeexperimentalteststhatthecapacitancebridgetakesatleast100mstorespond.Itcouldbetheinductanceoftheratiotransformerslowingdowntheresponsetime.Abettermethodtomeasurequantitativelythepositionofthearmatureofthesuperconductingmotorsystemisnecessary.Sowehave555oscillatorcircuitbuiltandconnecttothesensorinparallelandtheLabViewprogramwiththecounterfunctioncountingthefrequencychangewithtimeisdevelopedasthesecondattemptforthealternativemeasurementtechnique. 2-14 .Nowinsteadofusingthecapacitancebridgeandthelock-inamplier,wehavethe555oscillatorcircuitbox,whichcanoscillateandoutputTTLpulseswith 47

PAGE 48

48

PAGE 49

2-15 (a).Ourtheoreticalsimulationprogramspredictthismethodfeasible,forthecapacitancechangeaccompanyingwithnoticeablecurrentchange,whichgivessomenoticeablevoltagechangeacrosstheresistor,capacitorortheinductor,especiallyforhigherQ(qualityfactor).SincethecurrentinanRLCcircuitinseriesis where R;(2{39) themaximumofthecurrentversusfrequencygraphisat!=!0=1=p ThetestingcircuitisshowninFig. 2-15 (b).Wetriedtotunethefrequencyofthereferenceoutput(sinewave)fromlock-inampliertogetthemaximumvoltageacrossanyoneelementofthecircuit,whichshouldfallatresonanceoftheRLCcircuit.Therefore,withalittlecapacitancechangefromthecapacitivepositionsensor,thecircuitwillbeoresonance,thenwearesupposedtoseethedramaticcurrentdecrease,therefore,dramaticvoltagechange.Unfortunately,wedidn'tobserveanynoticeablevoltagechange(alllessthan2%)eitheracrosstheresistor,capacitorortheinductor.Wealsoexchangedthepositionoftheresistorandinductor,orrearrangethecircuittomakethecapacitorsandinductorinparallel.Butnoneoftheaboveworkedwelltoshowanylargeenoughvoltageshift.Hence,weneedtogiveupthisapproach. 49

PAGE 50

Wehaveusedthecapacitancebridgealongwiththelock-inampliertomonitorthemotionofthearmaturebeforebymeasuringthecapacitancechangeofthecapacitivepositionsensor.Theoutputvoltageshiftfromlock-inamplierwhenmovingthearmatureupanddowncouldbeaslargeas2Vormore,whichgivesenoughsensitivity.Theonlyproblemistoovercometheslowresponsetime,100ms,oftheratiotransformer.Fig. 2-16 showsoneofthesimpleACbridgecircuitswebuilt.Aswhatwehadexpected,theACbridgecircuitcanrespondasfastaslessthanafewmicrosecondswithoutanydelay.Thefollowingsarethedetaileddescriptionsabouttheexperimentalapparatusandsetups. Thecapacitivepositionsensoriscomposedoftwocoppersemi-cylindricalsheetsalongwiththesecondniobiumcan.Inthemagneticeld,theslitsofthecoppercylindricalsensorcouldpreventtheeddycurrentandthereforetheheatdissipationfrombeingproduced.Weusethestrongersuperconductingwirefortheleadsofthesensorandthemoreexibleinsulatedbertubetoprotecttheleads.Epoxyisusedtogluethecoppersensortothecapacitorframemadeofphenolic.Fig. 2-17 showsthecircuitconnectiontomeasurethecapacitanceofthecapacitivesensorwiththecapacitancebridge.Atroomtemperaturethecapacitancebridgereadsthecapacitanceofthecapacitivepositionsensor2.11pF(themagnitude,R,oftheoutputonthedisplayofthelock-inamplierreadsminimum138.9V)whenthearmatureissittingallthewaydown,and1.59pF(themagnitude,R,oftheoutputonthedisplayofthelock-inamplierreadsminimum153.4V)whenthearmaturemovesallthewayuphittingthebrassplate12mmaboveintheair.Thecapacitancedierenceisassmallas0.52pF. NowweconnectthepositionsensortotheACbridgecircuitbox.ThecircuitdiagramisshowninFig. 2-18 (a).Insteadofusingthenewdigitallock-inamplier(SR830),weusetheantiqueanaloglock-inamplier(PAR119)togetridofthedigitizedproblem 50

PAGE 51

Wealsocarefullycalibrateandzerotheosetofthecurrentampliertowithinafewnano-amperes.Afteradjustingthebrassplateabovethetopofarmaturetobe21.8mm,thearmatureisexpectedtohaveenoughspacetomoveupandpassthesecondnetzeromagneticforcepositiontobeheldtherewithsomeDClevel.Fig. 2-19 (a)demonstratesthetheoreticalcalculationofthemagneticforceperunitofcurrentsquareexperiencedbythearmatureinsidethesuperconductingsolenoidasafunctionoftheposition,z,denedastheverticaldistancebetweenthecenteroftherstniobiumcanandthemiddleofthesolenoid.Ourplanistostartapplyingtheaccelerationpulseatz0=6.43mm,aroundthepeakpositionofthepositivemagneticforcezone,thenthevelocityofthearmaturecarriesthroughtherstnetzeromagneticforcepositionataboutz=12.5mm;afterwardsitwouldexperiencesomenegativemagneticforceuntilweapplythesecondpulsefordecelerationatthepeak,z=18.5mm.Ifoursecondbrakepulsedidn'ttotallystopthearmature,thentheresidualvelocitywouldbeabletobringthearmaturefurtherupuntilitpassthesecondnetzeromagneticforceposition,z=26mm.Afterthispoint,thearmaturewouldexperiencepositivemagneticforceagainandsomesmallDClevelpulsewouldbeenoughtocanceloutthedownwardgravityforceandthearmaturewouldbeabletooattherestillforhoweverlongweneed. Theroomtemperaturecalibrationcurvefortheconversionofthevoltageoutputfromchannel1ofthelock-inamplierintotheposition,z,ofthearmature,preciselymeasuredbythedepthmicrometergauge,isdemonstratedinFig. 2-19 (b).Theprobewassettobeverticaltobeasclosetothesituationsoftheactualexperimentsaspossibleandthevariablecapacitorwastunedtoabout3.8pFwhencalibrated.Thedipfortherst

PAGE 52

ln(b=a);(2{40) whereaninnercylindricalconductoroflengthLandradiusaissurroundedbyanoutercylindricalconductorofthesamelengthandradiusb,and"0isthepermittivityoffreespace.Hence,thecapacitivepositionsensorisexpectedtohavethecapacitanceproportionaltotheoverlappinglengthbetweenthesecondniobiumcanandthecoppersensor.Duringz=0and2mm,theoverlappinglengthisaboutthesame,15mm,sothecapacitanceissupposedtohavenochange.However,duetotheedgeorboundaryeect,weseethedipoccursatz=03mminthecalibrationcurveandinthedatawetookforthearmaturemotion.Inthedataanalysistheconversionofsignalsintopositionswillbemodiedaccordingly. Inordertomonitortheactualpulsessenttothesuperconductingsolenoid,wemeasurethevoltagedropacrossthe0.1resistorinserieswiththesolenoid.The0.1resistorboxisconnectedtotheoutputofthecurrentamplier(BOP)directlyviabananaconnectorsandtheothersideisconnectedtothesuperconductingsolenoidviathe12pinconnectoronthetopoftheprobedirectly.ThecircuitdiagramisshowninFig. 2-18 (b).Duetothealmostpurelyinductive(zeroresistance)motorcircuit,thepulsesfedtothesolenoidaresomewhatdistortedandasthegainofthecurrentamplierturnsuptoexceed3Aofcurrentoutput,thespikeswiththeoppositepolarityappear,resultingfromthebackemfduetothefastchangingcurrent.Therefore,weputcrossdiodesacrossthesolenoidinparalleltopreventthisoccurred. 52

PAGE 53

2-20 themotionofthearmatureofthesuperconductingmotorisclearlyexamined.Thepulseprolesenttothesolenoidisdistortedduetotheinductivebehaviorofthesuperconductorsolenoid.Asthegainofthecurrentamplieristurnedup,thehigherthegainthemorethecurrentwouldbefedtothesolenoid.Heretherstcurrentpulsepeakheightreachesaround-1.8A,thendecaysalittlebit,followedbythesecondpeakasmuchas-2.369Athendecayingtozerogradually.Thecurrentampliernotonlyampliesthepulses,butalsoinvertsthepulsesoutput;therefore,wehavethepulseprolewithnegativepolarity.Thecapacitivepositionsensorrespondstothemotionofthearmatureasthearmaturemovesupuntiloutofthereachofthesensor,thendropsbackdownbygravityforceasafunctionoftime.Thearmatureacceleratesto0.6m/satz=5mmwithinabout15ms(averageestimateacceleration40m=s2),thendeceleratestozeroatz=15mmin40ms(averageestimatedeceleration-15m=s2).Afterwards,duetothegravityforceitdropsbackdownandreachesthevelocityasfastas0.4m/satz=4mmwithin70ms(averageestimatedeceleration-5.7m=s2).Thearmatureprobablymovesfurtherupduringthetime60msand100ms,butoursensorcouldnotmeasureanychangesbecausethearmatureatthatmomentisalreadyoutofthedetectablerange.Fig. 2-20 (d)istheoriginalcurrentprolesendingtothecurrentamplierfromtheanalogoutputDAC0ofourLabViewdataacquisitionprogram. IfwecomparewiththetheoreticalpredictionfromoursimulatorwiththesamedistortedcurrentproleasinFig. 2-20 (a),thenthepredictedarmaturemotionislikeinFig. 2-21 .Thearmatureissupposedtoreachthevelocityasfastasmorethan1.0m/s,butitisalsopredictedtomoveasfarasapproximately10.5mmonly.Thedierencebetweenthetheoreticalpredictionandtheactualmotionisstillunderexploration. NowifwegetridofthesecondbrakepulseandincreasetheDClevelfollowingtherstaccelerationpulse,howwoulditaectthearmaturemotion? 53

PAGE 54

2-22 (d),thenthecurrentpulseproleinthesolenoidactuallylookslikeasmoothtransitionfromzerotosomesaturatedDClevelandthecapacitivepositionsensorrespondscorrespondinglybyoscillatingaroundtheequilibriumpositionabout0.9Vanddampingwithtime,Fig. 2-22 (a).FromFig. 2-22 (a)and(b),thearmatureseemstobeacceleratedtoalmost1.0m/swithin10msand4.5mm,thenitslowsdownuntilstopsatthehighestpoint,about6.8mm,anddropsbackdowntoasfastasabout-0.47m/s,asfarasthepositionabout4.3mm.Afterwards,itoscillatesbackandfortharoundtheequilibriumpositionabout5.2mm,likeaharmonicoscillator.Duetotheviscosityandimpedanceoftheliquidheliumandthefrictiononthebearingscontactingwiththearmature,theoscillationmotionalsodampsin80ms,thenthearmaturestaysstationary.AssoonastheDClevelisturnedo,thearmaturedropsbackdowntotheoriginalposition. IfwecomparewiththemagneticforceversuspositiongraphinFig. 2-19 (a),thiskindofoscillationmotionisquiteunderstandable.Weapplytheaccelerationpulseatthemaximumpeakofthemagneticforcezone,z6.5mm.Assoonthearmaturetravelspassingthroughthezeromagneticforceposition,z=12.5mm,itexperiencesnegativemagneticforce,deceleratingandpushingitbackdown.Andthenitexperiencespositivemagneticforceagainbelow12.5mmposition,whichwillpushitup.Suchacyclerepeatsuntilitdamps,thenitwilloatstillatthepositionwherethegravityforceandthemagneticforceallcancelout,resultinginzeronetforces. Ifweapplytheaccelerationpulsefollowedby2.0VDCpulsefor112.5ms,Fig. 2-22 (d),thenthecurrentpulseproleinthesolenoidactuallylookslikearapidtransitionfromzerotothesamesaturatedDClevelandthecapacitivepositionsensorrespondscorrespondinglybyoscillatingaroundtheequilibriumpositionabout0.85Vanddampingquicklywithtime,Fig. 2-22 (a).FromFig. 2-22 (a)and(b),thearmatureseemstobeacceleratedtoalmost0.9m/swithin10msandabout1.3mm,thenitkeepsalmost 54

PAGE 55

WithhigherDClevel,thearmaturecanbeacceleratedtohighervelocityfollowedbymorerapidlydampedoscillationafterwardsbecausetheactualcurrentpulseinthesolenoidisrampedfasteruptothesaturatedcurrentofBOP.Sincewereallyneedtohavethearmaturetravelwithconstantspeedforatleast10mm,thisresultwithourcurrentdesigncannotsatisfyus.Sothearmaturemustbemodied.Withthedistancebetweenthecentersofthetwoniobiumcansabout35mm,wecouldjustsimplyapplyonesinewavepulsefollowedbyaDCpulse,thenweareabletoacceleratethearmatureandholditaround10mmpositionforaslongasweneed.ThedrawbackofthisdesignistheunavoidableoscillationwhichmightmoreorlessaecttheturbulencejustproducedandtheDCpulsetoholdthearmaturemustbeatleastafewamperes. Nowifwereversethepolarityoftheinputpulsegoingtothecurrentamplier,howwoulditaectthearmaturemotion?Weapplytheoriginalcurrentpulsetothesuperconductingsolenoid,Fig. 2-24 (d),thenthemeasuredpulseproleispositiveandtheinductiveeectsarenotsosignicant,Fig. 2-24 (a).Theactualpulsepeakssaturateupto7.5A,morethanwhatwehaveexpected.Thearmatureisacceleratedtoabout0.7m/swithinabout10msand1.5mmandupto0.85m/sat4.2mmpositionandatthetime15ms.Thearmaturegoesupashighas8.7mm,andthendropsbackdownwiththevelocityashighas0.2m/s.Thearmatureseemstogetstumbledforalittlebitwhileatabout4.8mmposition,whereisestimatedtobethezeronetmagneticforcesposition.WegureoutthattheDClevelpulseashighas2Acouldhavedeceleratedthearmature 55

PAGE 56

WelengthentheDClevelto25mswhilekeepingtherestoftheoriginalcurrentprolethesame,Fig. 2-25 (d),thenthemeasuredpulseprolefedtothesuperconductingsolenoidispositiveandtheinductiveeectsarenotsosignicantaswell,Fig. 2-24 (a).Theactualpulsepeakssaturateupto7.5and10.5A,whilewedokeepthegainofthecurrentamplierthesameasinthepreviouscase.Thearmatureisacceleratedtoabout0.72m/swithinabout10msand1.2mmandupto0.9m/sat4mmpositionandatthetime12.5ms.Itseemstogetstumbledandslowdownbetween4and6mmposition,butspeedsupto0.95m/safterwards.Thearmaturegoesupashighas15.2mm,beyondwhichthearmatureisactuallyoutofthedetectablerangeofthecapacitivepositionsensor.Itshowszerovelocityduringthetime30msand110ms,whenthearmatureiseitheroutofthereachofthesensororitisoatingabovethesecondzeronetmagneticposition,z=26mminFig. 2-19 (a),or19.5mmequivalentlyinFig. 2-25 (c).Itthendropsbackdownwiththeprettyconstantvelocity,0.15m/s,allthewaydown.TheDClevelpulseashighas2Aislongenoughnottodeceleratethearmatureintime,soitcanmoveupbeyondthedetectableposition15.2mmorhigherbeforethebrakepulseapplies.Thisprovidesusoneoftheimportantsuccessfulexperiencesofhowwecouldachieveourgoal.Thearmatureisproposedtobeaccelerated,travelforabout10mmwithalmostconstantvelocity,bedeceleratedthenpassthesecondpointofthezeronetmagneticforcepositionandthenbeheldaboveitforhoweverlongweneed.Thedrawbackofthisdesignisthatwedon'tknowifwearegoingtomakethearmaturehitthetopofthecell.TheDCpulselevelshouldbecarefullyadjustedtobejustasmuchaswhatweneedandthewholetrajectoryofthemotionshouldbemonitored.Inordertobeabletomonitorthewholetrajectoryofthemotionofthearmature,thecapacitivepositionsensorneedstobelengthenedtoappropriatelengthwithoutmodifyingourcurrentarmature.Alsoweshouldlowerdownthesensorforafewmm(23mm)toavoidthedipproblem. 56

PAGE 57

2-26 (a)[ 41 ]).Thiscapacitor,coupledtoabridgecircuit,measuresthearmatureposition.Thetotalmassofarmatureisnow2.60g.Thegrid,madeof0.125mmthickspringsteelwith1mmsquareholesand70%transparency,isattachedtothelowerendofthearmature(seeFig. 2-26 (b),(c)andFig. 2-27 (a)).ThecorrespondingReynoldsnumberforthedierentvelocitiesofthegridmotionisshownFig. 2-27 (b).Let'sndouttheReynoldsnumberofourmotorsystemintheliquidhelium-4bathat4.2K.Reynoldsnumberisdenedastheratioofinertialforceandviscosityforce,orthevelocityscalemultipliedbythelengthscale,dividedbythekineticviscosity: =inertialforce viscostyforce:(2{41) Atmotortestingtemperature,4.2Kinliquidhelium,gridReynoldsnumber: (inm/s).Ifweconsiderthesizeofthemeshofthegridasthelengthscale,velocityofthegridmotionasthevelocityscale,thenwehaveReynoldsnumberrangingfrom4000to40,000whenthegridvelocityvariesfrom0.1to1m/s,abovetheonsetofturbulence. Theroomtemperaturecalibrationcurveshowsthemonotonicincreaseinvoltageasmovingupthearmaturewithoutanydip.Theentireassemblyismountedinaheliumtestcellandcooledinatransportdewarcryostat[ 42 ].Thearmaturepositionsensorwas 57

PAGE 58

2-28 [ 41 ]showsthecalibrationcurveatliquidheliumtemperature,4.2K. Intheelectronics,wehavetwoindependentcircuitryforthesuperconductingsolenoidandforthecapacitivepositionsensor(Fig. 2-29 ).Wedrivewiththeproperlyshapedcurrentpulseproledeterminedbysimulation,thenamplifythecurrentviathebipolarpowersupply.Theinputpulsetothesolenoidismonitoredbymeasuringthevoltagedropacrossthe0.1ohmresistorshunt.Twocrossdiodesaretoprotectthesolenoidfromthespikesduetofastchangingcurrent.Forthepositionsensor,weusetheACbridgecircuit.Twoarmsare100ohmresistors,andtheothertwoarevariablecapacitorandthepositionsensor.Whilethearmaturemoves,thecapacitancewouldchange,givingdierentvoltageresponse.Weconvertthevoltageintothepositionofthearmaturewithourcalibrationcurveperformedat4.2K. TheexperimentalresultsareshowninFig. 2-30 [ 41 ].Weapplythepulseprole:twosinusoidalshapepulsesfollowedby-0.1VDClevelfor250ms(Fig. 2-30 (e)).Thesolenoidisprotectedbytwocrossedsilicondiodeswhichhavecut-involtagesof4Vand18Vat4.2K.Therefore,reversingthepolarityofthesolenoidcurrentproducesanasymmetryinresponse(Fig. 2-30 (a)andFig. 2-30 (b)).InFig. 2-30 (c)and(d),withthecurrentpulselikeFig. 2-30 (a)thearmatureisseentoaccelerateto0.8m/swithin40msoveradistanceof9mm(estimatedaverageacceleration20m=s2).Thenitundergoesanearconstantdecelerationtozerovelocitywithin33msinanother12mm(estimatedaveragedeceleration24m=s2).Itwasheldatthepositionof22mmforabout250msuntilthecurrentwasturnedo;itthendroppedundergravity,asfastas0.48m/sin75msover10mmposition(estimatedaverageacceleration6.4m=s2).AsseeninFig. 2-30 (c)and(d),withthecurrentpulseinFig. 2-30 (b)thearmatureacceleratesto1.09m/swithin20msover9mm(estimatedaverageacceleration55m=s2).Thenitslowsdowntozerovelocitywithin38msovertheremaining12mmofstroke(estimatedaveragedeceleration29m=s2).Itwasheldat22mmforabout250msuntilthecurrentwasturnedo,then 58

PAGE 59

59

PAGE 60

Gridturbulenceinaclassicaluid[ 27 ]. Figure2-2: Superconductingmotormodelwithgrid,thermistorsandsuperconductingshield[ 29 ]. 60

PAGE 61

Armaturemotioninunshielded(pinkcurves)andsuperconductingshielded(blackcurves)solenoidunderthesinefunctionacceleration:(a)I(t)curve;(b)v(z)curve.(:modieddatawithoutthecentralpeakinthecurrentprole)[ 29 ] Figure2-4: Armaturemotioninsidethesuperconductingshieldedsolenoidunderthelinearfunctionacceleration:(a)I(t)curve;(b)v(z)curve. 61

PAGE 62

Armaturemotioninsidethesuperconductingshieldedsolenoidunderthesquarefunctionacceleration:(a)I(t)curve;(b)v(z)curve. Figure2-6: UppercriticaleldversustemperatureforniobiumsampleswithdierentRRR.[ 35 ] 62

PAGE 63

Voltageinputtothesuperconductingshieldedsolenoidwith:(a)sine;(b)linear;(c)squarefunctionacceleration. 63

PAGE 64

(a)SinusoidalcurrentinputtothesuperconductingshieldedsolenoidwiththedimensionsasstatedinTable1.;(b)thecorrespondingvelocityversuspositionoftheshaftmotiongraphs;(c)thecorrespondingmagneticeld,andmagneticforceversuspositionoftheshaftmotiongraphs.[ 29 ] 64

PAGE 65

Requireddrivingvoltage(inV)inputtothesolenoidversustime(inms)ifthesolenoidandtheresistoraretheonlyelementsinthecircuit. 65

PAGE 66

Schematicdrawing(a)andthephoto(b)forthespeciallydesignedswitchbox.(c)Detailedcircuitdrawingfortheswitchbox. 66

PAGE 67

Machinedrawingsandphotosofthemotorsystem:(a)machinedrawing[ 29 ];(b)photoofthetestcell;(c)photoofthetestcellinstalledattheendofthesuck-stickprobe. 67

PAGE 68

Experimentalapparatusforunshieldedmotortestingexperimentsusingthecapacitancebridgetomonitorthemotionofthearmature. 68

PAGE 69

TheGR1616CapacitanceBridge:(a)Theapparatusappearanceandrelatedcircuits.(b)Theschematiccircuits. Figure2-14: Circuitryoftheexperimentalapparatusforunshieldedmotortestingexperimentsusingthe555oscillatorcircuitandLabViewcounterprogramtomonitorthemotionofthearmature. 69

PAGE 70

TestingcircuitofQ-meter. Figure2-16: SimpleACbridgecircuit. 70

PAGE 71

MeasuringthecapacitanceofthecapacitivepositionsensorwiththeGR1616capacitancebridgeandthelock-inamplier. 71

PAGE 72

Circuitryandsetupfortestingthesuperconductingmotoratliquidheliumtemperature,4.2K.(a)Monitoringthemotionofthearmaturewiththecapacitancepositionsensor;(b)monitoringthepulsesenttothesuperconductingsolenoid. 72

PAGE 73

(a)Theoreticalcalculationofthemagneticforceperunitofcurrentsquareexperiencedbythearmatureinsidethesuperconductingsolenoidasafunctionoftheposition,z.(b)Roomtemperaturecalibrationcurveofthevoltageoutputfromchannel1ofthelock-inamplierversustheposition,z. 73

PAGE 74

Motionofthearmatureofthesuperconductingmotor.(a)Pulseprolesenttothesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0ofLabView.[ 29 ] 74

PAGE 75

(a)Distortedcurrentproleduetothealmostpurelyinductivebehaviorofthesolenoid(smallresistance1)inthesuperconductingshieldedsolenoidwiththedimensionsasstatedinTable2.;(b)correspondingvelocityversuspositionoftheshaftmotiongraphs;(c)correspondingmagneticeld,andmagneticforceversuspositionoftheshaftmotiongraphs;(d)correspondingmagneticeld,andmagneticforceversustimegraphs.[ 29 ] 75

PAGE 76

Motionofthearmatureofthesuperconductingmotor.(a)Pulseprolesenttothesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0ofLabView. 76

PAGE 77

Motionofthearmatureofthesuperconductingmotor.(a)Pulseprolesenttothesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0ofLabView.[ 29 ] 77

PAGE 78

Motionofthearmatureofthesuperconductingmotor.(a)Pulseprolesenttothesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0ofLabView. 78

PAGE 79

Motionofthearmatureofthesuperconductingmotor.(a)Pulseprolesenttothesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0ofLabView.[ 29 ] 79

PAGE 80

(a)Newmachinedrawingsofthemodiedmotorsystem[ 41 ].(b)Pictureofthearmaturewiththegridmountedattheend.(c)Pictureofthetestcellshowingthegridmounted. Figure2-27: (a)Machinedrawingforthegrid.(b)Reynoldsnumberversusgridvelocityat4.2K. 80

PAGE 81

(a)Thecalibrationofthearmaturepositionsensor(4.2K).Positionsensorbridgevoltageoutputfromlock-inamplierversusthepositionofthearmature[ 41 ].(b)Thecapacitanceofthecapacitivepositionsensorversusthepositionofthearmature,measuredbyusingthecapacitancebridge,GR1616. 81

PAGE 82

Electronicscircuitsforthesuperconductingmotorsystem. 82

PAGE 83

Motionofthearmatureofthesuperconductingmotor[ 41 ].(a)Currentthroughthesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Sameas(a)withpolarityreversed.(c)Velocityofthearmatureasafunctionoftime.(d)Velocityversuspositionofthearmature.(e)OriginalcurrentprolefromanalogoutputDAC0ofNationalInstrumentsboardsenttoKepcoBOPcurrentamplierdrivingsolenoidcurrent. 83

PAGE 84

32 ].Leadplatingisalsoapproachableandeconomictobedoneinthelaboratory.Wehavedecidedtoelectroplate,ratherthanchemicallydepositthelead,becausechemicalvapordeposition(CVD)requireshightemperaturesandisdiculttoperforminthelaboratory.Forreference,leadmetalhasveryhighboilingpoint,about2022K,andmeltingpoint,ashighas600K,usingphysicalvapordepositionmethodrequiringvaporizationofthemetalelementatveryhightemperatures,whichisalsonotapplicableforourlab.Anothersuperconductingmetal,niobium,withcriticaltemperature9.5K[ 32 ]hasmuchhighermeltingpoint,2740K,andevenhigherboilingpoint,about5017K.Therefore,consideringtheoptionswedecidetoelectroplatealeadmagneticshieldingenclosingthemotoratverylowtemperature. 84

PAGE 85

WegotanicerecipefortheelectrolytesolutionmakeupfromTechnicInc.: Sincethecoherencelengthofleadis0.083m[ 32 ],wewouldliketodeposit25moflead,whichismorethanenough.Forourpurposes,ourcellismadeofpurecopperfreeofoxygen,Fig. 3-1 andFig. 3-2 .Forthecellcapandcellbody,theinteriorsurfaceareasareabout68.3cm2and78.9cm2.Weneed1.469Aand1.695Aofcurrenttodeposit1mofleadperminuteonthem,respectively. 3.1.2.1Lead 85

PAGE 86

44 ]. 45 ]. 46 ]. 3.1.3.1Proceduresteps 86

PAGE 87

Thefollowingsaretheactualprocedurestepsofleadelectroplatingperformedinthelaboratory. 1.CleaningthecellwiththeElectronicshop'shelp.Theyusethecommercialcoppercleanerandultrasonicvibrationequipmentforcleaningthecell.Fig. 3-3 (b)andFig. 3-4 (b)showthecopperinteriorofthecellcapandcellbody,andthewell-builtsiliconewall,readyfortheleadplating. 2.Sealingtheholeswithsilicone[?]andbuildingaboutoneinchhighofsiliconewallleaningagainstthepaperwallaboutafewmmextendedoutwardalongtheedgesofthetoprimofthecellcaporcellbody(Fig. 3-3 (b)andFig. 3-4 (b)). 3.Makingtheleadelectrodeforleadplatingofthecellcapandcellbody(thedrawingoftheexactsizeshowninFig. 3-3 (a)andFig. 3-4 (a)).Theleadelectrodeiswelltrimmedandcarefullyadjustedtobeabout2mmclearanceawayfromeverycellwall.Withtheaidofamagnifyingmirror,anohmmeter,andaroundrubberpadattachedtothecenteroftheturntable,wecandoanalmostperfectjob,asshowninFig. 3-3 (c),(d)and(e)andFig. 3-4 (c),(d)and(e).Thecellcapissupportedbyarubberpistonunderneathtostandmorestably.Thecellbodyhasgoldplatedatthebottom.Whilerotatingtheturntable,wemakesuretheresistancebetweentheelectrodeanodeandcellcathodeisinnity. 4.Theelectrolyteisinjectedtothecellcaporcellbodyabouthalftooneinchhigherthantherimenclosedbythesiliconewall(seeFig. 3-5 (a)andFig. 3-6 (a)).Theresistancebetweenthetwoelectrodes(theleadelectrodeastheanodeandthecellasthecathode)nowisonlyafewohms.Thecellisrotatedsteadilyandslowlyontheturntableofabrokenmicrowaveoven.Therefore,theleadanodecanalsoagitatetheelectrolytetomaketheleadionsinthesolutiondistributeveryuniformlywhileleadplatingisperformed.Westarttosupplythecurrentofabout1.47A(Fig. 3-5 (b))forthecellcapandabout1.70A(Fig. 3-6 (b))forthecellbody.Theleadelectrode(anode)connectstothepositiveterminalofpowersupply,whilethecell(cathode)isincontactwiththethinstainlesssteelpiececonnectingtothenegativeterminalofthepowersupply.Nowhitebubblesoccurwithhighconcentrationoflead,30grams/literofleadintheelectrolyte.Theexteriorpartofthecellwallincontactwiththethinstainlesssteelpiece,reducestoshinypurecopperfromtheoxidizedcopper(Fig. 3-5 (c)).Undertheliquidsurface,itiscleartoseethattheleadelectrodeiswell 87

PAGE 88

3-5 (d)andFig. 3-6 (d)).Thedissolvedleadprecipitatesatthebottomofthecell. 5.Thepowersupplyisturnedontosupplythecurrentforapproximately25minutes.Thecurrentuctuatesslightly,butoverallverystable.Thevoltageoutputfromthepowersupplyis8.2Vwhenleadplatingthecellbody.Note:Donottouchtheelectrodesduringtheelectroplating;otherwise,youwillgetburnbecausetheyareveryveryhotduetohighcurrentowingthroughthem.Thewholeleadplatingprocessisdoneintheventhood. 6.RinsewithampleDIwater(aboutonegallon).Drythecellwithcleantissueandushwithahighowofnitrogengasorcoolwindfromtheheatgunimmediatelyandquickly. 7.Theelectrochemicalequivalentforthereaction:Pb2++2e!Pbis3.86g=(Amperehour)[ 47 ].Byleadplatingonthecellbodywithcurrent1:70Afor27minutes,thedepositedleadmassis2:95g.Sincethedensityofleadis11:34g=cm3,thesurfaceareaofthecellbodyis78:85cm2,thethinknessofthedepositedleadwouldbe33.0m. 3-7 andFig. 3-8 showthemasterpiecesafterleadelectroplatingwithshinyleadofsilverwhitecolorintheinteriors,exceptthatcoveredbythesilicone.Acloseviewofthesilverwhiteinteriorofthecellcapshowstherims,thewallsandtheedgesofthewelldowntothecellbottomfullycoveredbythelead.Fig. 3-7 (c)andFig. 3-8 (c)showstheresidueleadelectrodeswhilethepartsimmersedundertheliquidsurfacebecomedarker,dissolvedtoalmostonlyhalfleft. 88

PAGE 89

3.Whiteanddelicatebubblesshowuponthesurfaceoftheelectrolytewithleadconcentrationonly15gperliterofelectrolytewhenturninguptotheoperatingcurrentduringleadelectroplating.Thewhitebubblesonthesurfaceofthesolutionoccurredathighcurrentdensityisne 4.\ModernElectroplating"bySchlesingerandPaunovic(2000)onpage366[ 47 ]:\Insolubleanodescannotbeusedinleadplatingelectrolytesasleaddioxide,PbO2,willformonthesurfaceoftheanodes.Thepurityofthesolubleleadanodesuseddeterminestheextenttowhichalmformsonthesurfaceoftheanodes."Onpage369[ 47 ]:\Duringthedepositionofthickleadcoatings(upto200m)formationofnodulesor\growths"canoccur.Thisfailuredoesnotgenerallyoccurwithafreshlymade-upsolution,andwhenitdoesoccur,itcaninmostcasesberectiedbyapuricationoftheelectrolytewithactivatedcarbon.contaminationoftheelectrolytebybreakdownproductsoftheorganicadditives.togetherwitharapiddecreaseoftheleadconcentrationintheelectrolyte.Theanodiccurrenteciencywasreduced,whichcausedthedropoftheleadcontentinthebath.Bythepassivationoftheanode,leaddioxidewasformedontheanodesurface,whichcausedapartialoxidationoftheorganicadditives." Therefore,weshoulduse100%pureleadastheanodetopreventtheleaddioxidefromformingonthesurfaceoftheelectrode,causinganodicoxidationoftheorganicadditivesontheanodesurface,ortheoxidationoftheorganicadditivesbytheleaddioxide,resultingintheroughnessofleaddeposition.Alsoiftheelectrolytesolution 89

PAGE 90

5.\ModernElectroplating"bySchlesingerandPaunovic(2000)onpage373[ 47 ]:\Discolorationoftheleaddeposittoabrownorblackcoloroccursduetodepositionofcopperontotheleadsurfacebyadisplacementreactionthatcanhappenintheelectrolyteifthecurrentisleftswitchedowhilethepartsarestillimmersed,orintherinsesiftheyareheavilycontaminatedwithcopper." Therefore,afternishingtheleadplating,weshoulddumpouttheelectrolyteimmediatelyafterthepowersupplyisswitchedo.AndrinsethepartswithplentyofDIwaterimmediately. 3-9 showsthemachinedrawingwiththedimensionsandthepicturesofourexperimentalcell.Wehaveonesuperconductingsolenoiddrivingthearmaturetomovethroughitscenter,withagridattachedattheend.Thislightinsulatingarmatureisconstructedof3phenolictubesseparatedbytwohollowcylindricalniobiumcansplaced26mmapart,withtheturbulence-producinggridattachedtooneend.Aconductingsectiononthearmature,composedofoneoftheNbcylindersandsilverpaintcoatingpartofthephenolicrod,isinsideacloselyttingcapacitormadeoftwosemi-cylindricalcoppersheets.Thiscapacitor,coupledtoabridgecircuit,measuresthearmatureposition.ThedimensionparametersofoursuperconductorshieldedsuperconductinglinearmotorsystemarelistedinTable 3-1 .Theelectronicscircuitsarethesameasdescribedinchapter2,e.g.Fig.2-29,excepttheleadresistance0.7.Theexperimentcellismountedtothe0.25inchdiameterprobeandtestedinatransportdewarcryostat[ 42 ]atliquidheliumtemperature. 3-10 (a)),thenthemagneticforcedistributionalongthez-axisofthesolenoidarecalculated,asinFig. 3-10 (b).Tobemoreecient,wewouldapplytheaccelerationpulsewhenthecenterofmassoftheniobiumcan#1islocatedatz=6.5mmposition,anddecelerationpulseatz 90

PAGE 91

Parametersofsuperconductorshieldedsuperconductinglinearmotorsystem. ParameterValue =18.5mmposition.Afterthearmaturepassesthez=26mmposition,wewouldapplytheholdingpulse,justenoughtobalanceoutthegravity. Inthecurrentprolefromoursimulationprogram(Fig. 3-10 (c)),therstpulseproducessinefunctionacceleration,andthethirdpulsedealswithlinearfunctiondeceleration.Thecentralpeakisduetothealmostbalancedmagneticforcesonthetwoniobiumcansatthatposition,whereeachisalmostequidistantfromtheendsofthesolenoid.Wecanremovethecentralpeakandtheinertiawillservetocarrythroughit.Ittakesslightlymorecurrent,0.147Amore,forthesuperconductingshieldedmotorsystemthantheunshieldedone.Intheresultinggridmotion(Fig. 3-10 (d)),thegridwouldhavesinefunctionaccelerationfrom0to1m/sin1mm.Thenittravelsatalmostconstantspeed,1m/s,for10mm.Inthemid-way,thegridstartstoslowdownat12.5mmpositionaftertheniobiumcan#2becomesclosertothesolenoid,meaningstrongermagneticforceintheoppositedirection.Thenthegridwouldrapidlydeceleratetoceasewithin1mmwhenthethirdpulseisapplied.Theemptycirclesrepresentthegridmotionwithoutthecentralpeakinthecurrentprole.Withoutthecentralpeakinthecurrentprole,thegridmotionisnotsignicantlydierent. 91

PAGE 92

3-11 showstheexperimentalresults.Consideringtheinductivebehaviorofthesolenoid,aninductor,thetimeconstantofanLRcircuitisL=R=16:34mH=0:723:3milliseconds.Evenifweapplyasquarepulse,say1V,ittakesvetimesthetimeconstant(116.5ms)tosaturateto1V.Therefore,weneedtotakethisintoaccountwhenweapplythepulsestothesuperconductingsolenoid.Weapplytheappropriatepulseprole:DC2.89Vfor14ms,followedbyDC-0.3Vfor10ms,then2.5msdelay,eventuallytheholdingpulse-0.02Vfor100ms(Fig. 3-11 (d)).Thesolenoidisagainprotectedbythesametwocrossedsilicondiodesasdescribedinchapter2.InFig. 3-11 (b)and(c),thearmatureisseentoaccelerateto0.7m/swithin6.5msoveradistanceof2.5mm(estimatedaverageacceleration98m=s2).Thenitundergoesanearconstantdecelerationtozerovelocitywithin66msinanother14mm(estimatedaveragedeceleration17.5m=s2).Itwasheldabovetheposition28mmforabout100msuntilthecurrentwasturnedo;itthendroppedundergravity,asfastas0.4m/sin60msover12mmposition(estimatedaverageacceleration6.7m=s2).Atthepositionbetween8and17mm,thevelocityofthearmaturewasabove0.6m/sandbetween0.6and0.7m/s. 1.At4.0K,dynamicviscosity=36micropoise=36107Pascalsecond= 36107Ns=m2.(Kinematicviscosity:==;1strokes=1cm2s1)[ 48 ]. 2.Atsaturatedvaporpressure,at4.20K,theliquidhelium-4hasdensity, 49 ]. 92

PAGE 93

50 ]. 4.Totallengthofarmature(Fig. 3-12 )=L=3:1875"=8:10cm=8:10102m.Thediameterofthearmature=D=(1=4)"=0:635cm=0:635102m. 5.Re`=UsL==(1m=s)125:4075kg=m38:10102m 2U2sCf=1 2125:4075kg=m3 Viscousdrag=dragsurfacearea=DragDL=0:2326N=m20:635 50 ]. 6.Forceexertedupontheuppersideplatesofthearmature(Fig. 3-12 (a))=Fext:d=0:3"=0:762cm=7:62103m;totalcrosssections=A0=(d 50 ]. 7.Forceexerteduponthebottomsideplatesofthearmature(Fig. 3-12 (b))=F0ext:Bernoulli'sequation:p=1 2U2s=62:70N=m2[ 50 ];F0ext=pA0=4:607103N. 8.Buoyancyforce=gV=125:4075kg=m39:8m=s22:565106m3= 3:1524103N. 9.Gravityforce=2:60g=0:02548N. 10.Ifthegridismountedattheendofthearmature,thetotalnon-transparentsurfaceareaofthegrid,excludingtheareaunderneaththearmature,isA"=1:7765cm2.Forceexertedupontheuppersideofthegrid=A"v2=22:28103N;forceexerteduponthebottomsideofthegrid=pA"=11:14103N.Sothetotalforcesexerteduponthegridis33:42103N. Sothetotalnetforce(downward)whenthearmaturetravelsupwardatthevelocityof1m/s=0.06994N=2.745Gravityforce(Table 3-2 ).Inoursimulationprogram,weonlyconsiderthegravityforceandthemagneticforce.Asthearmaturemovesathighervelocity,theviscousdragforceandimpedanceforcesbecomesignicant,prettycomparabletothegravityforce. 93

PAGE 94

Forcesonthearmaturewhenmovingupat1m/s(Downloadispositive). ParameterValue Viscousdrag3:758104NFext9:214103NF0ext4:607103NBuoyancyforce3:1524103NGravityforce0:02548NExternalforcesonthegrid33:42103N 43 ]areconcerned,weestimatetheresultingheatingduetothevaryingmagneticeld,whichisnotsignicant.Weuseepoxy-resinimpregnationtopreventfrictionaldisplacementwithoutnoticinganydeformationofthecoil.Wedonothaveanysplicelossproblemwithoutusinganyslices,weassumethattheheatingduetotheabovethreefactorscouldbeneglected.Whenwerunthemotorinthedilutionrefrigerator,wewillrunitwithoutanyliquidheliumandmeasurethebackgroundtemperatureuctuation.PossibleAClossesofthesuperconductingsolenoidduetothevaryingcurrentcanbemeasuredbysubstractingfromtheblankbackgroundwithoutanycurrentinthesolenoid.Andthenwewillrunthemotoragainwithgridimmersedintheliquidheliumbath.Wecanthendothesubtractiontogetthenettemperaturechangesimplyduetothequantumturbulenceenergydecay. 3-13 showsthedesignofourexperimentalcellforthetowed-gridstudiesofquantumturbulenceexperiments. 94

PAGE 95

Fig. 3-13 showsthewholeexperimentalcellassemblyforthetowed-gridexperimentsandthecircuitboardforthethermistorswiththeelectricalfeedthrupinsmounted.Theelectricalfeedthrupinsaregoldplatedonallsurfacestobenetthebestelectricalconductivity Beforeputtingeverythingtogetherandapplyingtheepoxyforseal,thedegreaseandcleaningprocessisveryimportant: 95

PAGE 96

2.Cleanthedirtordustwiththesoftironbrush,roughspongeandsandpaperontheexteriorsurfaceofeachfeedthruholeonthecellwall. 3.SpraytheacetonetowettheQ-tipandthenapplytheQ-tiptocleantheinteriorofeachfeedthruholeonthecellwall. 4.SpraytheacetonetowettheKimwipeswipersandthenapplythewiperstocleantheexteriorsurfaceofeachfeedthruhole. Applyingtheepoxytothejointsurfacesbetweenthecoppercellwallandthefeedthruplugneedsenoughsurfaceedgesfortheepoxytoadherewell,sowemakethepolycarbonateplugshigherthanthecellwallsurface,stickingfromoutsideandthenon-connectionpartoftheeveryelectricalfeedthrupinislongerthaneveryplug(Fig. 3-13 (a)).Itusuallytakesadaytodryouttheepoxy;however,wecanilluminatewiththeinfraredlighttoshortenthetimetoaboutahalfday.Shinningthislightalsohelpsstrengthentheepoxy.Weshouldbeverycarefulwhencoolingdownandwarmingupthecellveryslowly,avoidchemicaltouchingoralsoputtinglargeforcesonthejoints.Inthisway,thesealcanbeusedforthermalcyclesformanytimeswithoutanycrack. 51 ].Theyarelessthan300mdiameterandwillbeimmersedintheturbulentheliumallowfastcalorimetricmeasurementstobemade.Therefore,wehavethethermistorcircuitboardspeciallymade(Fig. 3-13 (b)).Thecircuitboardhasradius0.5incharcononesidetomatchtheinteriorarcofthecell;ontheotherside,anextensionpartismadefora0-80slottedatscrewtomounttheboardtothebottomofthecellandalsofortheeaseofourngershandling.Twominiaturegermaniumlmthermometersaremountedtothecircuitboardbyindiumsolderandattached/gluedtotheboardbythecryogenicgrease.Threeelectricalfeedthrupinsaremountedinparalleltothecircuitboardbyindiumsolderandthetwothermistorsare 96

PAGE 97

3-13 (b):electricalfeedthrupin#1)andtoslideinto(e.g.Fig. 3-13 (b):electricalfeedthrupin#1')anotherthreecounterelectricalfeedthrupinsimbeddedinthecellwall(e.g.Fig. 3-13 (b):electricalfeedthrupin#2).Atroomtemperature,theresistancesforthetwothermometersmeasuredfromtheelectricalfeedthrupinsoutsidethecellare60.0and57.5,respectively. Wehaveleakcheckedthecellatroomtemperatureandatliquidnitrogentemperature,77K,withourhomemade\Redeye"instrument.Thisprovesthatourelectricalfeedthrudesignisasuccessfuldesign. Outsidethecell,wewillplugtheelectricalfeedthrupin#2withtheelectricalfeedthrupin#3connectedtoaminiaturecoaxialcable 97

PAGE 98

Machinerydrawingsforthecellcap. 98

PAGE 99

Machinerydrawingsforthecellbody. 99

PAGE 100

(a)Thedrawingoftheleadelectrode.(b)Thecellcapsupportedbyarubberpistonunderneathbeforeleadplating.(c),(d)and(e)Adjustingtheleadelectrodepositiontobe2mmclearanceawayfromeverywallwiththeaidofamagnifyingmirrorandanohmmeterwhenrotatingtheturntable.(Note:Thepicturesof(c),(d)and(e)areforthesecondattempt.) 100

PAGE 101

(a)Thedrawingoftheleadelectrode.(b)Thecellbodybeforeleadplating.(c),(d)and(e)Adjustingtheleadelectrodepositiontobe2mmclearanceawayfromeverywallwiththeaidofamagnifyingmirrorandanohmmeterwhenrotatingtheturntable.(Note:Thepicturesof(c),(d)and(e)areforthesecondattempt.) 101

PAGE 102

Procedurestepsfortheleadplatingforthecellcap.(a)Fillingupthecellcapwithelectrolyteabouthalftooneinchhigherthantherim.(b)1.47Aofcurrentissuppliedduringplating.(c)Closeviewofthecellwhenleadplating.(d)Theleadelectrodeis2mmawayfromeverywallofthecell. 102

PAGE 103

Procedurestepsfortheleadplatingforthecellbody.(a)Fillingupthecellbodywithelectrolyteabouthalftooneinchhigherthantherim.(b)1.70Aofcurrentissuppliedduringplating.(c)Closeviewofthecellwhenleadplating.(d)Theleadelectrodeis2mmawayfromeverywallofthecell. 103

PAGE 104

(a)Themasterpieceshowingshinysilverwhitecolorofleaddepositontheinteriorwalls.(b)Closelookatthecellcap.(c)Electrodeafterleadplating.(d)Cellcapgettingridofthesiliconewall. 104

PAGE 105

(a)Themasterpieceshowingshinysilverwhitecolorofleaddepositontheinteriorwalls.(b)Cellbodygettingridofthesiliconewall.(c)Electrodeafterleadplating.(d)Cellcapandcellbodyhasleaddepositontheinteriorwalls. 105

PAGE 106

(a)Machinedrawingoftheexperimentalcell.(b)Pictureofthesuperconductingmotorsystem,composingthesuperconductingsolenoid,thecapacitivepositionsensor,thegridandthearmature.(c)Pictureoftheexperimentalcellmountedonthe0.25inchdiameterprobefortestingattheliquidheliumtemperature. 106

PAGE 107

(a)Schematicdrawingofthesuperconductingmotorsystem.(a)Calculatedmagneticforceperunitofthecurrentsquareexperiencedbythearmatureversusthepositionoftheniobiumcan#1.(c)Simulatedcurrentprole.(d)Simulatedgridmotion. 107

PAGE 108

Motionofthearmatureoftheshieldedsuperconductingmotor.(a)Currentthroughthesolenoidandcapacitivepositionsensorresponseasafunctionoftime.(b)Velocityofthearmatureasafunctionoftime.(c)Velocityversuspositionofthearmature.(d)OriginalcurrentprolefromanalogoutputDAC0. 108

PAGE 109

(a)Externalforceonthetopsurfacesofthearmaturewhenitmovesupwithvelocity1m/s.(b)Externalforceonthebottomsurfacesofthearmaturewhenitmovesupwithvelocity1m/s. 109

PAGE 110

Themachinedrawingfortheexperimentalcelldesign.(a)Experimentalcellassembly.(b)Circuitboardwiththethreeelectricalfeedthrupinsandtwothermistorssolderedwithindiumandattachedbythecryogenicgrease. 110

PAGE 111

4-1 (a)).Theadvantagesofthecircuitisthatithasenoughresolutionandsensitivitytomeasureslightresistancechange,i.e.,temperaturechange,ofthethermistors,andinthemeantime,withoutputtingtoomuchheatonthethermistors.Our300mindiameterGermaniumlmthermistorswithgoldleads50mindiameterareverydelicate;therefore,wemustbeverycarefulnottohavetoomuchheatdissipationonthem.TheorderofmagnitudeofthepowerdissipationinnWwouldbeappropriate,eitherfornotburningoutthethermistors,orfornotaectingthetimedependenttemperaturerisemeasurementfromtheproducedturbulence.Hence,wecarefullycalculatetheoptimalcongurationsofthesetuptoachieveourgoal. AsshowninFig. 4-1 (a),alock-inamplier(PrincetonAppliedResearch,PAR)istheheartofthethermistormeasurementcircuit.Itsuppliesthe70kHzbridgesignalatVref=0.1VthroughaR=100kOhmresistortomakethebridgedrive1A. InFig. 4-1 (a),Rsistheresistanceoftheresistorconnectedinseries.Rthistheresistanceofthedelicatethermistor.Xistheresistanceoftheadjustablevariableresistor.andRistheresistanceofthetworesistorsonthebottomtwoarms.Sothetotalresistanceforthewholecircuitwouldbe: 111

PAGE 112

Thepotentialaftertheresistor,Rs,becomes: Therefore,thecurrentI1owsthroughthethermistor,Rth,is: whilethecurrentI2owsthroughthevariableresistor,X,is: Theresultingpowerdissipationonthethermistorwouldbe: ThepotentialatpointAis: whilethepotentialatpointBis: Thepotentialdierencedetectedbythenulldetectoris: Rs(X+2R+Rth)+(Rth+R)(X+R) (4{9) 112

PAGE 113

[Rs(X+2R+Rth)+(R+Rth)(R+X)]2:(4{10) ForVref=0:1Vrms,Rs=100k,Rth=100,R=10k,theLabViewprogramforourACbridgecircuitanalysisasshowninFig. 4-1 (b)tellsthattheclosertheXtoRth,theclosertheVABtozeroinVABversusXgraphandjdVAB Table 4-1 listshowthefourparameters,Vref,Rs,RthandR,wouldaectthesensitivity,dVAB=dXjX=Rth,andthepowerdissipation,Pth,onthethermistors.Basically,dVAB=dXjX=Rth/Vref,Pth/V2ref.WehavechosentherstsetofparametersforourACbridgecircuitsettingssinceithasenoughsensitivity,andthepowerdissipationislimitedtotheorderofmagnitudeofnW.Rthrangesfrom100to200k,representingtheresistancechangeofthethermistorsfromroomtemperaturetolowtemperatures,aslowasafewdecadesofmilliKelvins.Thecalculationofthetemperaturesensitivityofthethermistorissimplythethermalresolutiongivenontheresistancebridge,whichwillbeexplainedingreaterdetailinthenextchapter. 4-2 isthecircuitryfortheresistancemeasurementofthethermistors.Thethermistor#1hasresistance133.8,whilethethermistor#2hasresistance130.8.Table 4-2 isthesensitivitytestingresultsatroomtemperature.ThenulldetectorPAR116(PrincetonAppliedResearchanaloglock-inamplier),isadjustedtohavethesensitivityrange50V)astheadjustabledecaderesistorturnsto133.6forthermistor#1.Sotheresolutionisasmuchas2.8mV=(Fig. 4-3 ). 113

PAGE 114

ParametersoftheACbridgeaectingthesensitivityandthepowerdissipation. 0:1100k10010k0:47130:022650:1100k100010k0:43080:22460:1100k10k10k0:22732:0660:1100k50k10k0:064107:3970:1100k100k10k0:0293310:410:1100k200k10k0:0116111:900:1100k1001k0:45210:024730:1100k10001k0:24750:24510:1100k10k1k0:043082:2460:1100k50k1k0:0078127:9360:1100k100k1k0:00328911:040:1100k200k1k0:00124112:440:1100k1001000:24980:024950:1100k10001000:045210:24730:1100k10k1000:0047132:2650:1100k50k1000:00079817:9940:1100k100k1000:000332911:100:1100k200k1000:000124912:490:1010010k9:8039:8030:10100010k8:26482:640:1010k10k2:500250:00:1050k10k0:2778138:90:10100k10k0:0826482:640:10200k10k0:0226845:350:101001k82:64826:450:1010001k25:002500:00:1010k1k0:8264826:40:1050k1k0:03845192:20:10100k1k0:00980398:030:10200k1k0:00247549:500:10100100250:025000:00:1010001008:2648264:50:1010k1000:09803980:30:1050k1000:003984199:20:10100k1000:000998099:800:10200k1000:000249849:95 114

PAGE 115

Table4-2: SensitivitytestoftheACbridgecircuitatroomtemperature. DecadeResistorChannel1Output(mV)Box()Thermistor#1 33.6283283.61452133.632183.61343233.62732283.64132333.65552383.66932433.68352 115

PAGE 116

TheACbridgecircuitsimulation:(a)Schematiccircuitdrawing.(b)LabViewprogramfortheACbridgecircuitanalysis. 116

PAGE 117

ACbridgecircuitforthermistorsresistancemeasurement.PrincetonAppliedResearch(PAR)lock-inamplierisusedtosupplytheACvoltageoutputanddetectthesignal. Figure4-3: Roomtemperatureresolutioncurveforthermistor#1. 117

PAGE 118

Thequantumturbulenceisproducedinliquidhelium4inthebottomoftheexperimentalcellbyagridtowedbythesuperconductinglinearmotorenclosedinthesuperconductingshieldedcell.Theturbulence,producedbythetowedgridinafewmilliseconds,isthenmonitoredwithasensitivethermistorwhichresponsesveryrapidlytomeasureanyheatdissipation.Thesourcesofheathavealreadybeendescribed.OuranalysisidentiestheheatassociatedwiththedecayoftheturbulenceandcomparestheresulttotheKelvinwavetheorythatwehavediscussed. 118

PAGE 119

5-1 (a).TemperatureisttedasafunctionoftheresistanceofathermistorinFig. 5-1 (b)usingasinglepowerlawindicativeofhoppingconductioninanamorphousmaterial Holdingthetemperatureconstant,wechangethedecaderesistorsettingandmeasurethebridgeoutputfromthelock-inamplierforthetwothermistors.TheplotsandquadratictstothesecalibrationsareshowninFig. 5-1 (c).Wefurthertthethermistor#1resistance,Rtherm,asafunctionoftheoutput(V)ofthelock-inamplierPAR124A: Thisallowsustoconvertthechangingbridgesignalintotemperatureastheturbulencedecays. 5-2 (a).Weuseanaccelerationsquarewavepulse(10ms)toacceleratethearmatureup,whilethedecelerationpulselastsonlyfor2.5ms,justenoughtostopthearmature,followedbya-0.1VDCholdingpulsewhichisexpectedtoholdthearmatureonthetopfor250ms.WecanseethethermistorresponseinFig. 5-2 (b).Thebridgeoutputrisesfromabout 119

PAGE 120

5-3 (a)showstherawdataresults.Weseethethermistorandthecalibratedthermometerwarmupafterthegridmotion. Theperformanceofourshieldedsuperconductinglinearmotorat520mKisnearlyasexpected.Weapplyonesquareaccelerationpulse,2.86Vfor10msandonesquaredecelerationpulse,2.86Vfor2.5ms,withsomeDClevel0.32Vfor10msinbetween,followedby-0.1Vholdingpulsefor250ms.Inthevelocityversustimegraph,Fig. 5-3 (b),weseethegridmovesasfastas1m/sandwaszeroforabout40mswhenbeingheldatthetop.Inthevelocityversuspositioncurve,Fig. 5-3 (c),weseethegridwasmovingatalmostconstantspeedabove0.90.1m/sforabout9mm. InFig. 5-3 (b)and(c),thearmatureisseentoaccelerateto1m/swithin20msoveradistanceof7mm(estimatedaverageacceleration50m=s2).Thenitundergoesanearconstantdecelerationfrom0.8m/stozerovelocitywithin32msinanother8.5mm(estimatedaveragedeceleration25m=s2).Itisheldupat28.5mmforabout40msuntilthecurrentwasturnedo;itthendropsundergravity,asfastas0.6m/sin38msat13.5mm(estimatedaverageacceleration15m=s2).Between12and20.5mm,thevelocityofthearmaturewasabove0.8m/sandnearlyconstantat0.9m/swithabout10%uncertainty.Ifweconvertthethermistorandthermometerresponseintothetemperaturesasafunctionoftime,wefoundthedramatictemperatureriseoftheliquidheliuminthecell,from520mKto1.5Kafterthegridmotion,whiletheexperimentalcellonlychangesforafewdecademilliKelvins.Sincetheexperimentalcoppercellhasheatcapacity3.9 120

PAGE 121

5-3 (d),theliquidheliumtemperaturerisesafterthearmaturemotionindicatesthedecayofturbulence.Afterthearmaturedropsbackdowntotheoriginalposition,wecanseethattheliquidheliumtemperaturerisesdramatically,fromabout700mKto1.5Kwithinthenext120ms.Thiscouldbecausedbythedecayofadditionalturbulencecreatedbythefallinggrid.Duringtherst400mswhenthethermistorhasalargetemperaturechange,weseeuctuationswhichmustbeinvestigated. Wethenconvertthetemperatureintotheenthalpyofliquidheliuminthecellasafunctionoftime.TheenthalpyoftheliquidheliumvaryingwithtimeisshowninFig. 5-3 (e),obtainedfromasplineinterpolationfromTable7.6inreference[20].Sinceturbulenceisanonlinearchaosdynamicssystem,thetemperaturechangeduetotheturbulencedissipationuctuatesirregularly.Fortheerraticpart,wesimplyaverageevery400adjacentpointsinourdataanalysistogettheredcurves. Wewilltthiscurveintwodierenttimedomainswiththettingequation: ,tocomparetotheKelvinwavetheoryinthenextsection. 5-4 .WettheredcurveseparatelyintwodierenttimedomainswiththefunctionH(t)=a+btc.InFig. 5-4 (a)and(b),theenthalpyiscalculatedfromthesplineinterpolationoftheTablevaluesinRef.[20]. InFig. 5-4 (a)theenthalpy(H)isttedasafunctionoftime(t)duringtherst230and275ms: 121

PAGE 122

InFig. 5-4 (b)theenthalpy(H)isttedasafunctionoftime(t)duringthelater295and360ms: ,meaningthatthedecayofturbulenceenergypermoleisproportionaltot3:608atlaterstage.Fortheenthalpyduringthesecondtimedomain,wegettheexponentcorderof-3.6,whichmustbestudiedmore. Fromtheexperimentsofthevisualizationofquantizedvorticesinliquidhelium4achievedbyLathrop'sgroupusingsmallsolidhydrogenparticlesandParticleImageVelocimetry(PIV)technique[ 52 ],thequantumturbulenceisproducedattensofmillikelvinbelowthetransitiontemperature(2.172K).Sinceourexperimentsareperformedatmuchlowertemperatures(0.5K)wheretheviscosityisevenlowerandtheReynoldsnumberisevenlarger,itisverypromisingthatthequantizedvorticesinsuperuidhelium4wouldbeproducedwithourtowed-gridmoreeasily. 122

PAGE 123

Thermistorscalibrationcurves:(a)Thermistor#1and2arecalibratedagainstthecalibratedthermometerRuO2848.(b)Temperatureisttedasafunctionoftheresistanceofthermistor#1.(c)Calibrationofthermistor#1and2attheliquidheliumtemperatureabout500mK:varyingtheresistanceofthedecaderesistorasafunctionofthefunctionoutputoftheanaloglock-inamplierPAR124A.(d)Fittedcurveofthermistor#1resistanceasafunctionofthefunctionoutputoftheanaloglock-inamplierPAR124A. 123

PAGE 124

Motionofarmatureandthermistorresponseatvacuumatabout600mK.(a)Pulseprolesenttothesolenoid.(b)Rawdatatakenforthemonitoredpulse,positionsensorandthermistorresponses.(c)Thevelocityofthearmatureasafunctionoftime.(d)Thevelocityofthearmatureasafunctionofthepositionoftheniobiumcan1. 124

PAGE 125

Quantumturbulenceat520mK:(a)Rawdata.(b)Velocityofarmatureasafunctionoftime.(c)VelocityofarmatureasafunctionofpositionofNbcan#1.(d)Zoomintoseethethermistorresponseattherst400ms.Liquidheliumtemperaturerisesafterthearmaturemotionasanindicationofproducedturbulencebeingdissipated.(e)Enthalpyoftheliquidheliumasafunctionoftime. 125

PAGE 126

Fittingtheenthalpyofliquidheliumcalculatedfromsplineinterpolationasafunctionoftime:(a)Fittingenthalpycurveduringtherst230and275ms.(b)Fittingenthalpycurveduringthelater295and360ms. 126

PAGE 127

InclassicalgridturbulenceandsuperuidgridturbulenceaboveoneKelvin,eddieseithergrowaslargeasthechannelordiminishassmallastheviscousdissipationlength(classicaluid)ortothescaleofvortexlinespacing(quantumuid).Classically,theenergywilleventuallydecayviaviscositythroughthesmallestofeddiesfollowingtheKolmogorovspectrum.Thisisnotthecase,however,insuperuidquantumturbulenceclosetozeroKelvinwherethereisnoviscosity. TheonlytheorypredictstheenergywilldecayviaaKelvinwavecascade,ultimatelyresultinginphononradiation.Kelvinwaves,likerotatinghelicalwaves,havetransverseandcircularlypolarizedwavemotionandaresupportedbyquantizedvortices.KelvinwavescanbeproducedbytheDonnelly-Glabersoninstabilityorvortexreconnections.Eddieswillgrowordiminishoncetheturbulenceisproduced.Theenergyoftheturbulenceisinjectedatalowfrequencyanddissipatesbyphononemissionatahighfrequency. Theenergydecayrateofgridturbulenceat520mKisexploredandcomparedwiththeKelvinwavecascadetheory.Ourexperimentalresultsatthisearlystagesupportthistheory. 127

PAGE 128

Turbulenceisaverycomplexsystemandthehomogeneousisotropicturbulenceisjustthesimplestcase.Quantumturbulenceusinglowtemperatureheliumasatestuidhasveryuniquefeaturesandthersttaskistoreproduceourexperimentalresultsattemperaturesdownto20mK. 128

PAGE 129

Thefreeenergyoftherstniobiumcylinderwiththecenterofmassatz=ziinteractingwiththeexternalmagneticeldproducedbythesolenoid: (A{1) Themagneticforceexperiencedbytherstniobiumcylinderwiththecenterofmassatz=zi: z(A{2) zf1 z(Zz=zi+l1=2z=zil1=2Zz=zi+l1=2+zz=zil1=2+z)Z20Z=ro1=0~B2z(;;z)dddz=1 z(Zz=zi+l1=2z=zil1=2Zz=zi+l1=2+zz=zil1=2+z)f(z)dz; where z(Zz=zil1=2+zz=zil1=2Zz=zi+l1=2+zz=zi+l1=2)f(z)dz(A{6) 129

PAGE 130

NNXi=1f(xi);(A{7) 2)(ba N)(A{8) zZz=zil1=2+zz=zil1=2f(z)dz=1 zz NNXi=1f(xi)=1 where 2)(z N)(A{10) 2)(z N);xj=zi+l1 2)(z N0)(A{12) Considertwoniobiumcylinderswithsomedistanceapart,dS: where 2)(z N);(A{14) 2)(z N0);(A{15) 2)(z N00);(A{16) 2)(z N000):(A{17) 130

PAGE 131

53 ]

PAGE 140

Fig. C-1 (a)isoursimulationprograminLabViewtocalculatetherequiredcurrent,voltage,magneticeldandmagneticforcebychangingdierentparameters.Justnoticeherethatthecurrentneedstodrivethemotorarecalculatedforagivencoilandarmaturedesign. Fig. C-1 (b)isanothersimulationprograminLabViewtondoutthevelocityversusthepositionofthearmaturebyinputtingthecalculatedcurrentprole. Inordertondouttheoptimalparametersforourdesign,wehavewrittenanotherLabViewprogram,Fig. C-2 (a).Bychangingoneparameteratonce,youcanndoutwhichdesignneedstheleastcurrent,voltage,ormagneticeld. WehaveimprovedtheLabViewprogram,Fig. C-2 (b),tolookfortheoptimalparameters.Thisprogramcanchangeasmanyparametersatonceaspossible. WehavewrittenthedataacquisitionprograminLabView,Fig. C-3 (a),tooutputspecialpulsestothesuperconductingsolenoid,acquirethedataforthearmatureposition,andtheactualpulsesendingtothesolenoid. WehavehomemadedataanalysisLabViewprogram,Fig. C-3 (b),toconverttherawdatafromthepositionsensorandthelowtemperaturecalibrationcurveintothevelocityversustimeandvelocityversuspositiondiagrams. 140

PAGE 141

LabViewprogramsforcalculating:(a)thecurrent,magneticeldandforce.(b)armaturemotion. 141

PAGE 142

LabViewprogramstolookforoptimalparameters. 142

PAGE 143

LabViewprogramsfordataacquisitionanddataanalysis. 143

PAGE 144

Feynman'sspeculationsaboutthenatureofturbulenceinthesuperuid:"Inordinaryuidsowingrapidlyandwithverylowviscositythephenomenonofturbulencesetsin.Amotioninvolvingvorticityisunstable.Thevortexlinestwistaboutinanevenmorecomplexfashion,increasingtheirlengthattheexpenseofthekineticenergyofthemainstream.Thatis,ifaliquidisowingatauniformvelocityandavortexlineisstartedsomewhereupstream,thislineistwistedintoalongcomplextanglefurtherdownstream.Totheuniformvelocityisaddedacomplexirregularvelocityeld.Theenergyforthisissuppliedbypressurehead.Wemayimaginethatsimilarthingshappeninhelium.Exceptfordistancesofafewangstromsfromthecoreofthevortex,thelawsobeyedarethoseofclassicalhydrodynamics.Asinglelineplayingoutfrompointsinthewallupstream(bothendsofthelineterminateonthewall,ofcourse)cansoonllthetubewithatangleofline.Theenergyneededtoformtheextralengthoflineissuppliedbythepressurehead.(Theforcethatthepressureheadexertsonthelinesactseventuallyonthewallsthroughtheinteractionofthelineswiththewalls).Theresistancetoowsomewhataboveinitialvelocitymustbetheanalogueinsuperuidheliumofturbulence,andacloseanalogueatthat." 144

PAGE 145

[1] R.P.Feynman,inProgressinLowTemperaturePhysics,editedbyC.J.Gorter(North-Holland,Amsterdam,Netherland,1955),Vol.1,p.34. [2] H.E.HallandW.F.Vinen,Proc.R.Soc.LondonA238,204(1956). [3] R.J.DonnellyandC.F.Barenghi,inJ.Phys.Chem.Ref.Data27,1217(1998). [4] J.F.AllenandA.D.Misener,Nature,Lond.,141,75(1938a). [5] P.Kapitza,Nature,Lond.,141,74(1938). [6] D.D.Oshero,R.C.Richardson,andD.M.Lee,Phys.Rev.Lett.,28,885(1972). [7] J.WilksandD.S.Betts,AnIntroductiontoLiquidHelium(OxfordUniversityPress,NewYork,1987). [8] L.Tisza,ComptesRendus207,1035and1186(1938). [9] L.Tisza,J.dephys.etrad.1,165and350(1940). [10] L.Landau,J.Phys.U.S.S.R.5,71(1941). [11] R.J.Donnelly,J.Phys.Condens.Matter11,7783(1999). [12] S.R.Stalp,L.Skrbek,andR.J.Donnelly,Phys.Rev.Lett.82,4831(1999). [13] S.J.Putterman,SuperuidHydrodynamics(North-Holland,Amsterdam,Netherlands,1974). [14] E.J.Yarmchuk,M.J.V.Gordon,andR.E.Packard,Phys.Rev.Lett.43,214(1979). [15] W.F.Vinen,M.Tsubota,andA.Mitani,J.LowTemp.Phys.134,457(2004). [16] W.F.Vinen,Phys.Rev.B64,134520(2001). [17] F.Pobell,MatterandMethodsatLowLemperatures(Springer,Berlin,1992). [18] E.E.Halleretal.,inProceedingsoftheFourthInternationalConferenceonNeutronTransmutationDopingofSemiconductorMaterials,NationalBureauofStandards,Gaithersburg,1982,editedbyR.D.Larrabee(Plenum,NewYork,1984),p.21. [19] E.E.Halleretal.,InfraredPhys.25,257(1985). [20] N.Wang,B.Sadoulet,T.Shutt,J.Beeman,E.E.Haller,A.Lange,I.Park,R.Ross,C.Stanton,andH.Steiner,IEEETrans.Nucl.Sci.35,55(1988). [21] A.Cummings,N.Wang,T.Shutt,P.Barnes,J.Emes,Y.Giraud-Heraud,E.E.Haller,A.Lange,J.Rich,R.Ross,B.Sadoulet,G.Smith,andC.Stubbs,IEEETrans.Nucl.Sci.38,226(1991). 145

PAGE 146

V.F.Mitin,J.McFarland,G.G.Ihas,andV.K.Dugaev,Physica(Amsterdam)B284,1996(2000). [23] C.M.McKenney,V.K.Dugaev,G.G.Ihas,V.V.Kholevchuk,V.F.Mitin,I.Yu.Nemish,E.A.Soloviev,andM.Vierra,inProceedingsofIEEESensors2002(Piscataway,NewJersey,2002),p.1275. [24] N.S.Boltovets,V.K.Dugaev,V.V.Kholevchuk,P.C.McDonald,V.F.Mitin,I.Yu.Nemish,F.Pavese,I.Peroni,P.V.Sorokin,E.A.Soloviev,andE.F.Venger,inProceedingsofEighthInternationalTemperatureSymposium{Temperature:ItsMeasurementandControlinScienceandIndustry,editedbyD.C.Ripple,AIPConf.Proc.No.684(AIP,NewYork,2003),p.399. [25] W.F.Vinen,Phys.Rev.B61,1410(2000). [26] W.F.VinenandJ.J.Niemela,J.LowTemp.Phys.128,167(2002). [27] U.Frisch,Turbulence(CambridgeUniversityPress,Cambridge,1995). [28] S.C.Liu,Y.Zhou,andG.G.Ihas,inProceedingsofthe24thInternationalConfer-enceonLowTemperaturePhysics,Orlando,FL,Aug2005,editedbyY.Takanoetal.,AIPConf.Proc.No.850(AIP,NewYork,2006),p.213. [29] S.C.Liu,G.Labbe,andG.G.Ihas,J.LowTemp.Phys.145,165(2006). [30] D.J.Griths,IntroductiontoElectrodynamics(Prentice-Hall,NewJersey,1989),p.213. [31] T.J.Summer,J.Phys.D20,692(1987). [32] C.Kittel,IntroductiontoSolidStatePhysics(JohnWileySons,NewJersey,1996). [33] B.W.MaxeldandW.L.McLean,Phys.Rev.139,A1515(1965). [34] A.Homann,DoctoralThesis,UniversityofCalifornia,SanDiego(1999). [35] E.S.Rosenblum,S.H.Autler,andK.H.Gooen,Rev.Mod.Phys.36,77(1964). [36] D.K.Finnemore,T.F.Stromberg,andC.A.Swenson,Phys.Rev.149,231(1966). [37] D.E.Farrell,B.S.Chandrasekhar,andS.Huang,Phys.Rev.176,562(1968). [38] S.Casalbuoni,E.A.Knabbe,J.Kotzler,L.Lilje,L.vonSawilski,P.Schmuser,andB.Steen,Nucl.Instr.andMeth.A538,45(2005). [39] D.Saint-James,P.G.deGennes,Phys.Lett.7,306(1963). [40] E.M.Purcell,ElectricityandMagnetism(McGraw-HillBookCompany,NewYork,1965)p.282. 146

PAGE 147

S.C.Liu,G.Labbe,andG.G.Ihas,\ProducingTowedGridQuantumTurbulenceinLiquid4He,"inProceedingsoftheInternationalSymposiumonQuantumFluidsandSolids,Kyoto,Japan,Aug2006,J.LowTemp.Phys.,inpress. [42] B.N.Engel,G.G.Ihas,E.D.Adams,andC.Fombarlet,Rev.Sci.Instrum.55,1489(1984). [43] Y.Iwasa,CaseStudiesinSuperconductingMagnets(DesignandOperationalIssues),(PlenumPress,NewYork,1994),Chap.7. [44] TeckComincoMetalsLtd.,LeadMetalMaterialSafetyDataSheet,2005. [45] Technic,Inc.,MethaneSulfonicAcidMaterialSafetyDataSheet,2003. [46] FisherScienticCompany,LeadCarbonateMaterialSafetyDataSheet,2005. [47] M.SchlesingerandM.Paunovic,ModernElectroplating(JohnWileySons,NewYork,2000). [48] R.D.TaylorandJ.G.DashPhys.Rev.106,398(1957). [49] R.J.DonnellyandC.F.Barenghi,TheObservedPropertiesofLiquidHeliumattheSaturatedVaporPressure(Website:http://darkwing.uoregon.edu/rjd/vapor1.htm).c2004. [50] J.F.Douglas,J.M.Gasiorek,andJ.A.Swaeld,FluidMechanics(LongmanScienticandTechnical,England,1995),Chap.11.9,p.344. [51] Y.Zhou,V.F.Mitin,S.C.Liu,I.Luria,M.Padron,R.Adjimambetov,andG.G.Ihas,inProceedingsofthe24thInternationalConferenceonLowTemperaturePhysics,Orlando,FL,Aug2005,editedbyY.Takanoetal.,AIPConf.Proc.No.850(AIP,NewYork,2006),p.1631. [52] G.P.Bewley,D.P.Lathrop,andK.R.Sreenivasan,Nature441,588(2006). [53] W.H.Press,B.P.Flannery,S.A.Teukolsky,andW.T.Vetterlig,NumericalRecipesinC:TheArtofScienticComputing(CambridgeUniversityPress,Cambridge,England,1992). 147

PAGE 148

Shu-chenLiuwasborninChuang-huaCounty,Taiwan,theRepublicofChina,in1974.ShegraduatedfromthegiftedclassinTaichungGirls'SeniorHighSchoolinTaichungCityinTaiwan,andthengotguaranteedadmissiontoNationalTaiwanNormalUniversityin1993.AfterbeingaphysicsandchemistryteacherintheShin-YijuniorhighschoolinTaipeiinTaiwanfrom1997-1998,shereceivedaB.S.inPhysicsfromNationalTaiwanNormalUniversityin1998.ShebecametheteachingassistantoftheDepartmentofPhysicsattheNationalTaiwanNormalUniversityin1998-2000,andthenwenttoUniversityofFloridaintheUnitedStatestopursueherPh.D.inphysicssince2000.Hercurrentresearcheldislowtemperaturephysicsinthespecialityofquantumturbulenceinsuperuidhelium-4atmillikelvintemperaturesundertheinstructionofProfessorIhas.HerfavoriteproverbisDescartes'"Cogitoergosum." 148