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NASA CONTRA REPORT
.- CRYOGENICMAGNETOMETER -x. DEVELOPMENT
by WeS. Goree, R. S. Deauer, Jy., V. W. Hestermmz, and T. W. Rarbee, Jr. 1 .I/>.
c
.. Prepared by STANFORD RESEARCH INSTITUTE Mcnlo Park, Calif. for Anzes Research Center
NATIONALAERONAUTICS AND SPACE ADMINISTRATION WASHINGTON,D. C. JUNE 1968
g# .. - TECH LIBRARY KAFB, NY
006038b F_ NASA CR- 10'73
/' CRYOGENIC MAGNETOMETER DEVELOPMENT
.. - BY w. s. Goree, B. S. Deaver, Jr., V. W. Hesterman, ' and T-.-W; Barbee, Jr.
Distribution of this report is provided in the interest of informationexchange. Responsibility for the contents resides in the author or organization that prepared it.
Prepared under Contract No. NAS 2-2088 by Y" STANFORD RESELUCH INST- Menlo 'Park, Calif.
for Ames Research Center
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield,Virginia 22151 - CFSTI price $3.00
". " \ ABSTRACT
A low field euperconducting shield has been developedand used to provide otable magnetic fieldsof lees than lod G, maintained stable for ao long as 6 days, The shield is a superconducting cylinder 91.5 cm long by 16.5 cm ID, The measured attenuation of externally applied axial field changes is a factor of 31 per shield radius.
The Meissner-effect and zero resistance propertyof superconductors has been used inthe development of a magnetometer for measuring the ab- solute value of magnetic fields, This device has been usedto measure fields as small as 2 x 10" G.
A magnetometer utilizing the unique zero resistanceand quantized flux properties of superconductors has been developedand used to measure magnetic field changes as small as 5 x lo4 G.
The dc Josephson tunneling effect has been usedto construct (1) magnetometers with field sensitivity as goodas lo4 G, (2) magnetic grad- iometers with which field gradients oflo4 G cm have beenmeasured, (3) linear displacement detectors with which displacementsof less than 1500 8 have been measured, and (4) a system for measuring static magnetic susceptibility, which was usedto study the time dependenceof the Meissner effect in hollow tin cylinders.
iii
FOREWORD
This is thefinal report on Contract NAS 2-2088 betweenStanford ResearchInstitute and the NASA-Ames ResearchCenter (SRI Project PHU- 5093).The research period covered 32 months,from 1 July1964 to 7 March 1967. Theprincipal investigator was Bascom S. Deaver , Jr. until Septem- ber 1965. William S. Goreethen was appointedprincipal investigator for theremaining 18 months of theproject. Other participants in the research program were T. W. Barbee, Jr., H. J. Bradley,F. Chilton, V. W. Hesterman, and J. Swedlund.
V
CONTENTS
I INTRODUCTION AND SUMMARY 1 I1 UNIQUE PROPERTIESOF SUPERCONDUCTORS 3 A. Zero Resistance 3 B. Meissner Effect 3 C. Fluxoid Quantization 4 D. Supercurrent Tunneling 5 I11 SUPERCONDUCTING MAGNETICSHIELD 8 IV THERMALLY-FLUSHED JXAD SUPERCONDUCTING SHIELD 1.3 v MEISSNER-EFFECT MAGNETOMETER 16 A.Construction 18 B. Experiments and Results 19 VI QUANTIZED-FLUX MAGNETOMETER 28 VI I OPTICAL HEATING EXPERIMENTS WITH A QUANTIZED-FLUX MODULATOR32 VI1 I APPLICATIONS OF THE dc JOSEPHSON EFFECT 35 IX CONCLUSIONS AND RECOMMENDATIONS 42 A. Magnetic Shield 42 B. Meissner-Effect and Quantized-Flux Magnetometers 42 C. Josephson Junction Devices 46
AppendixA - MAGNETOMETER CIRCUIT ANALYSIS 47 Appendix B - CALCULATIONS OF SKIN DEPTH AND THERMAL RELAXATION FOR SUPERCONDUCTINGTIME FORMODULATORS 58 References 61
vii ILLUSTRATIONS
1 Idealized Critical Tunneling Current versus Magnetic Field for a Double Josephson Junction Interferometer 7 2 Superconducting Magnetic Shield Assembly 9 3 Attenuation of Axial Magnetic Fieldby Superconducting Field 12
4 Thermally-Flushed Superconducting Shield 14 5 Basic Superconducting Magnetometer Circuit 16 6 Meissner-Eff'ect Modulator Construction 18 7 Fixture for Casting Mcissner-Effect Modulators 20 a Noise in Output from Meissner-Effect Magnetometer Mounted in Liquid Helium Bath 22 9 Noise in Output from Meissner-Effect Magnetometer Mounted in Helium Exchange Gas 22
10 Meissner-Effect Modulator Mounted in the 16.5-cm-Diameter Superconducting Shield 24 11 Magnetometer Sensitivity versus Transverse Magnetic Field 25 12 Modulation Efficiency versus Operating Frequencyfor a Meissner-Effect Modulator 26 13 Output Signal from Meissner-Effect Magnetometerfor Square- Wave Heating 27 14 Response of Superconducting Circuit 29 15 Quantized-Flux Magnetometer Circuit 30 16 Quantized-Flux Magnetometer Response 31 17 Optical Modulation Apparatusfor a Quantized-Flux Modulator 33 18 Construction of a Slug Type Josephson Junction 36
19 Josephson Junction Magnetometer 37 20 Josephson Junction Magnetic Gradiometer 38 21 Josephson Junction Displacement Indicator 39 22 Superconducting Transition of a Meissner Modulator 41
viii ILLUSTRATIONS
23 Proposed Design for a SuperconductingMagnetic Shield 43 24 Cooling of the Melssner-Effect Magnetometer from the Inside Out 45
A-l Equivalent Circuit of the Modulated Inductance Superconducting Magnetometer 48 A-2 Reduction of EquivalentCircuit for Analysis 48 A-3 Transformer Primary Inductance versus Coupling Cocfficient for Maximum Output 54
ix I INTRODUCTION AND SUMMARY
The general objectiveof the researchprogram described in this report was to investigate the application of unique the properties of superconductors to instruments. The program had three specific objec- tives: (1) the construction of a superconducting magnetic shield with room temperature access. and the useof this shield for long term stabil- ity tests of theAmes flux gate magnetometer, (2) the investigation of the use of superconducting Meissner-effect circuitsas absolute reading magnetometers for measuring magnetic fields as low as G, (3) the investigation of the use of superconducting quantized-flux circuits to measure magnetic fields or field changes as small as G. These objectives were met as follows:
1. A cylindrical superconducting shieldwas constructed that was 16.5 cm ID by 91.5 cm long with an 8-em-diameter room temperature access coaxial with the shield. Magnetic fields transverseand parallel to the shield axis could be reduced to less than G at the center of the shield and maintained stable as long as the shield was superconducting. The longest test ofthe shield lasted about six days.During this experi- ment,twoAmes flux gatewere tested for long term stability.
2. The linear field-versus-output voltage of Meissner-type modula- tors was used asan absolute magnetometer with sensitivitiesas good as 2 x G. Studies were made of the signal-to-noise ratio as a function of applied magnetic field parallel and perpendicular to the modulator axis; operating frequency; ambient temperature at the modulator; and thermal environment, i.e., the effect of dif’ferentthermal contact between the modulator and the liquidhelium bath.
3. Numerous quantized-flux circuits were constructed and tested. The best of these was usedto detect magnetic field changes assmall as 5 x G. This work was reported in detail in Midterm Report - October 1965 and in a published paper.4
We also studied Josephson tunneling junctions of the type described by Clarke,’ and constructed magnetometersand magnetic gradiometers using the direct current characteristics of thesedevices. A cylindrical cavity was built to study the alternating current characteristicsof the Clarke- type Josephson junction, although time did not permit completionof this stud y .
*References are listed at the end of this report.
1 Progress on this research contract was reportedin informal reports to WSA-Ames:
0 August 23, 1965: an interim report covering the long term stability test of two NASA-Ames flux gate magnetometers.6
0 October 1965: a smary of progress madeduring the first lk months of the contractperi~d.~ This report is very detailed and may be considered to supersedeall previous reports except the August 1965 interim report discussedabove.
Further results of research performed under this contract were reported in a paper published in The Review of Scientific Instruments.* This paper describesall of the work performed on the rotating supercon- ducting shield and thequantized-flux magnetometers except for the optical heating experiments, which are presentedin Section VI1 of this report.
The research effort duringthe last 14 months of the contract has been devoted primarilyto the study of Meissner-effect magnetometers. However, other very interesting programs have received significantatten- tion. The research program during this14-month period can be categorized as fol.lows:
1. Meissner-effect magnetometer.
2. Optical heating experiments with a quantized-flux modulator.
3. Josephson junctions, Clarke slug type.
4. Thermally-flushed lead superconducting shield.
These four topics, plus the magnetic shield and quantized-fluxthe magnetometer, are discussed in separate sections of this report. A des- cription of the Meissner-effect magnetometer and our applications theof dc Josephson effectis given also in Reference 8.
The next section of this report presents the unique propertiesof superconductors that are applicableto this research program. The order of presentation in the following sections(I11 through VIII) is the chron- ological order ofthe discovery of the property most directly relatedto the application. Thus we describe the superconducting magnetic shields in Sections I11 and IV (zero resistance- 1911), the Meissner magnetometer in Section V (Meissner effect- 1933), the quantized-flux magnetometer in Sections VI and VI1 (quantized magnetic flux - 1961), and finally, the supercurrent tunneling devicesin Section VI11 (Josephson effect - 1963). Section IX presents a summary of conclusions and recommendations basedon the overall research program described in this report.
2 If UNIQUE PROPERTIES OF SUPERCONDUCTORS
Severalunique properties of superconductors makethem useful for the measurement and control of magnetic fields.The techniques described here dependprimarily on thefollowing: zero electrical resistance,the Meis- sner effect,fluxoid quantization, and supercurrenttunneling.
A. Zero Resistance
Themost evident property of the superconducting state is thatof zeroresistance, which was noticed by KamerlinghOnnes in1911 when he discoveredsuperconductivity, The resistance to electrical currentflow drops to zero in a fairly narrowregion around the transition temperature, T . Thenarrowness of the region of temperature is typicalof phase changes, C and in a pureType I superconductor,the transition is narrowerthan a millidegree.
Insuperconductors that are carryingcurrents, zero resistance results inbehavior for all frequenciesthat is analogousto the high frequency behaviorof normal good conductors. The currents are confinedto the sur- faceof the sample. Further, zero resistancewith Maxwell’s equations impliesthe exclusion of changesof magnetic flux
”aB 0 at -
withinthe body of a superconductor.
B. MeissnerEffect
An even more generalmagnetic field exclusion is observedin super- conductors.The Meissner effect pertains to
4 B= 0
3 insidethe superconductor. Equations (1) and(2) apply deep within the body of a superconductor. Near thesurface, an exponential decay
is observed.In Eq. (3), z measuresthe distance from the surface into thesuperconducting sample, and )I is the London penetrationdepth, which is typically of order 500 8. Theflux exclusion represented by Eqs.(1 to 3) is theprinciple behind superconducting magnetic shields. By switch- ing a superconductingsample back and forth from superconductor to normal, theflux exclusion of Eqs. (1 to 3) canbe used to measure magnetic field strengths.
C. FluxoidQuantization
.Thesuperconducting state is a macroscopicquantum state. Thus, classical quantitiessuch as thevelocity of the current carriers, the electrons, are definedin the sense of anexpectation value using the wave functionfor the superconducting state. Just as inthe quantumbehavior ofatomic systems, theexistence of the wave functionimplies various interferenceeffects. One ofthese interference effects is that of fluxoid quantization.Quite analogous to the Bohr-Sommerfeld quantization condi- tion, a superconductorobeys
4 e‘ -+ f(2mvs-2; A) dx = nh (4)
4 -4 InEq. (4), v is thesuperconducting electron velocity, and A is the electromagnetlc5 vector potential. The electron charge and mass are e and m, respectively.They appear as 2eand 2m dueto the pairing that causes superconductivity.
In a widevariety of circumstances, one can consider a contourfor this line integral that is deepwithin the bodyof a superconductingsample where v = 0. Thesecond term ofthe integral is proportionalto the mag- neticfaux,
4 linkingthe circuit. Inthese circumstances then,the magnetic flux is quantized(flux quantum unit = 0 = hc/2e a 2 x lo+ G cma ) . 0
Fluxquantization means thatthe only possible values of magnetic flux trappedinside a thicksuperconducting ring are integral multiples of hc/Ze = 2 x lo4 G cma. It is interestingthat flux quantization makes it possible to produce a regionin which there is zero magneticfield. If a hollowsuperconducting cylinder is cooledbelow its transitiontempera- ture in a magneticfield that produces less thanhalf a quantizedSlux unit through it, a current is inducedin the superconductor to cancelexactly thisflux and produce the lowest quantized state, i.e., zero fluxinside thecylinder. Further, the current Slowing in the cylinder is a direct measure ofthe flux that initially existed in thecylinder, and the mag- netic fieldcan be measured without access to the volumeoccupied by the field andwithout motion of thesuperconductor.
D. SupercurrentTunneling
Othermanifestations of the macroscopic quantum nature of thesuper- conducting state, withweakly coupled superconductors, have been used for a number of ingeniousdevices for magnetic measurements .6 1'
Tunnelingcharacteristics unique to thesuperconducting state result when two superconductors are separatedby a verythin dielectric layer, approximakely 20 8,or by thinsuperconducting links. Direct current up to some critical value will tunnelthrough this junction without producing a voltagedrop. This supercurrent tunneling is usuallyreferred to as the dcJosephson effect. For currents somewhat largerthan this critical value, a finitevoltage appears, and high frequency current oscillations occur throughthe junction. This is the ac Josephsoneffect. The Josephson equationhv = 2 eV givesthe frequency, v, ofthese current oscillations versusthe voltage drop, V, across thejunction. In this equation, e is thecharge of a singleelectron and h is Planck'sconstant. Excellent reviewsof these effects are givenin References 10 and 11.
Thedc Josephson effect has received considerable experimental and theoreticalstudy over the past few years and shows promise of being useful as a verysensitive instrument for measuring changes in applied magnetic field, small currents,and very small voltages.The usefulness of these junctionscan best be understood by consideringthe equation that deter- minesthe maximum zero voltagecurrent that can be developed across the tunneljunction. sin(nrr @ ./@) I =I JO C o nn @ ./Go J
5 From thisequation we see thatthe critical current, I (i.e., thecurrent c forwhich a voltagefirst appears) is a periodicfunctlon of the magnetic flux, Q., linkingthe junction between the two superconductingplanes with period$roportional to theflux quantum, ip . Further, we noticethat this 0 equationfor the critical current is analogous to theequation for the amplitudesof the Fraunhofer diffraction pattern of a single slit optical diffractiongrating. This pattern has a maximum at zeroapplied field and successive lower order maxima at integral quantumvalues of the flux throughthe junction.
Inprinciple, a singleJosephson junction exhibiting these diffraction effectscan be used as anabsolute magnetometer, since the critical current is a maximum forzero applied field linking the junction.
In junctions of rather large cross section area or wherehigh tunneling currentsexist, the tunnel current itself is largeenough to influencethe magneticfield within the junction, This effect is analogous to the Meissnereffect and tends to shieldpart of the junction from external fieldchanges, Because of this,junctions cannot be made arbitrarilylarge to gainenhanced sensitivity.
Severalinvestigators have shown thatenhanced sensitivity can be achievedby connecting two or more Josephsonjunctions in parallel.’ For a circuitof two identicaljunctions connected in parallel, the equation forthe critical currentversus magnetic field is
where @ is theflux through each junction and @ is the total fluxlinking the areaj betweenthe junctions. From thisequatlon A we see thediffraction patterngiven in the previous equation for a singlejunction multiplied by a term that is analogous t.o theinterference term of a multiple slit op- tical interferometer.This interference term modulatesthe diffraction effect in a periodicmanner where the period is now proportionalto the magneticflux, @ linkingthe area, A, defined by the leads connecting A’ the two junctions.Since; this area betweenthe junctions can be many times larger(even orders of magnitudelarger) than the junction area, the in- terferenceperiod can be much smaller thanthe diffraction period. Fig- ure 1 showsan idealized current versus field plot for a doublejunction interferometer. We see boththe diffraction envelope of a singlejunction andthe high frequency oscillations due to the interference effect.
6 I .o 0.9 0.8 0.7 0.6 F (x) 0.5
0.4 03 02
01
0 0 I .o 2.0 3.0 4.0 5.0 6.0 x- TB - 5093 - 73
FIG. 1 IDEALIZEDCRITICAL TUNNELING CURRENT VERSUS MAGNETICFIELD FOR ADOUBLE JOSEPHSON JUNCTIONINTERFEROMETER
Themagnitude of theflux quantum is 2 x lod7 G cm2. Thus if the area betweenthe parallel junctions is1 cm2 , we see thatthe interference period may be as small as 2 x lo4 G. If instrumentation allows resolution withinan interference period, fields considerably smaller than 2 x loq G canbe measured. Forgacs and Warnickla reported sensitivities as good as 2 x lo+ G with a doublejunction magnetometer.
7 I11 SUPERCONDUCTINGMAGNETIC SHIELD
Thesuperconducting magnetic shield has been described in detail in the MidtermReport of October 19657 and in a publishedpaper;4 thus only a discussionof the construction and final performance will begiven here.
Sensitivedevices for measuring low magneticfields require a test -8 regionin which the magnetic field can be reducedto less than 10 G and maintainedstable for many hours. For thisreason, a superconducting mag- netic shield was constructed andused with a combinationof several tech- niques to achievethe low fieldenvironment. The shield structure is diagramedin Figwe 2. A pairof ferromagnetic shielding cylinders fab- ricatedof Mu-metal were usedto reduce the ambient field by a factorof approximately100. A coil wound aroundthe inner Mu-metal shield was used toapply an alternating field to this shield to reduce fields due to per- manentmagnetization.
The superconducling shield was thermallyisolated from theliquid he- lium bath SO that its tcmpc,rature could bevaried slowly through the super- conductingtransition temperature. Provision also was made forrotating theshield at approximately 1 revolution/secin order to make useof the shielding.oftransverse fields by theeddy-currents induced in the super- conductingcylinder as described by Vant-Hulland Mercereau. l3 In this way,the transverse fields were reduced by a factorof loa to lo3. Finally, thepredominantly axial field insjde the superconducting cylinder was nullified with a superconductingsolenoid, which was thenswitched to the persistentcurrent mode tomaintain time stabilityof the resulting low field. A superconductingtransformer, connected in series withthe per- sistentcurrent solenoid, was usedfor applying precise small increments ofmagnetic field.
Bothsuperconducting and room temperaturedevices were to beused in the low field region; therefore, a Dewarwas placedinside the supercon- ductingsolenoid to provide isolation from the liquid helium bath. This inner Dewar couldbe filled with liquid helium or maintained at room tem- per ature .
Special care was usedin the selection of nonmagnetic materials for theconstruction of the apparatus. The dewars were primarily aluminum
a andfiberglass and required no liquid nitrogen shields.* The vacuum jacket andsupport structure for the superconducting shield and solenoid were also primarilyaluminum with beryllium-copper tubing used for the vacuum linesfrom the low temperatureregion to the room. Nonsuperconducting cadmj.wn-zincsolder was used,and ,joints between beryllium-copper tubing andaluminum were scaledwith indium gaskets, which were notsuperconducting at theshield operal.i~~g temperature.
Thesuperconducting cylinder was a 0.013-cm-thicklead coating on the surface of a coppcrcylinder 91.5 c:m long IJY 16.5 cm OD with 0.075-cm- t,hjc:lc walls. TIw supercondiicti~~gsolenoid, 13 cm ID and 60 cm long, was wound of 0.025-cm 111 obJ um wire. The large Dewar, containingthe super- conduct-ingshield, was 20 cm 1u by 210 cm long;the inner Dewar provided an 8-cm-diamet.er access insidethe shield, which w'a's maintained at either room temperature or liquidhelium temperature.
The perf.ormanc.v oI' thc ma~nc~ticshield was evaluatedusing a flux
Eat(! magnelomct Thetransition of the lead cylinder into the superconducting state was found to occurover a temperatureinterval of O.Ol°K as determinedby observingthe change in pickup on a sensing coil inside the shield as a small ac field was appliedwith a solenoidexternal to theshield. The superconductingshield was heatedapproximately O.Ol°K abovethe transi- tioninterval and then cooled throughabout 0.04'K over a periodof 1 hour whilerotating at the rate of 1 revolution/sec. When thetransverse field measuredon the shield axis was G initially, a finalfield of approxi- mately lo4 G resulted,indicating an attenuation of lo3. Similaratten- uations may haveresulted for lower initial fields, but we couldnot measure fields less than lo4 G duringthe experiments. The axial magnetic field was found to beunaltered by thetransition of the lead cylinder into the superconducting state. * LindeModel CD-217 liquidhelium hot-cold wellDewar, non-nitrogen shielded. 10 The Ames flux gate magnetometer was usedas a null detectorby first reading along onedirection, flipping the probe180 degrees, and averaging the two readings to determine thezero field; the field at the center of the shield was reduced to less than G by a current flowing in the nio- bium solenoid, which was then switched to its persistent mode. Using these procedures, fields less than G could be achieved over the ten- ter 1-cm lengthof the shield with gradients of approximatelylo-' G/cm over regions upto 30-cm long. The field at the center of the shield was measured continuously fora period of 150 hours and found not to vary by an amount detectable with the flux gateprobe, i .e. , 10" G. During these measurements, a small temperature sensitivityof the flux gate probewas diacovered; however, when corrections were made for temperature variations, or when the probewas operated at precisely constant temperature, duplicate readings were obtained. The field at the end of the 150-hour periodwas measured under identical temperature conditionsand found to be the same as that mappedat the beginningof the test. The attenuation of axial magnetic fields was measured by applyinga uniform axial fieldof 7.0 G with a large solenoid enclosing the outer helium Dewar. The measurements were made with the niobiun solenoid heat switch on, because if the superconducting wireof the solenoid formsa persistent circuit, it couples to the externalfield near its endsand reduces the effective shield attenuation near the shield center.Fig- ure 3 shows the measured field differences along the shield axis.A fit of the data indicates that the field inside the shield is fallingas exp(-3.43Z/R), i.e., a factor of about31 per shield radius, where Z is measured Prom one end of the shield andR is the shield radius. The at- tenuation for transverse fieldswas not measured quantitatively;however, it was checked qualitativelyby applying a transverse field witha small solenoid across theend of the shield and foundto be much smaller than for the axial case. 11 .. I l0,000 IO00 I 00 IO I .o 0.I j END OF G OF SH I ELD SHIELD 0.01' ' I ' I ' I I I -20 -10 0 , IO 20 30 40 50 AXIALDISPLACEMENT FROM END OF SUPERCONDUCTING SHIELD-cm 18-5093.59 FIG. 3 ATTENUATION OF AXIALMAGNETIC FIELD BY SUPERCONDUCTINGSHIELD 12 IV THERMALLY-FLUSHEDLEAD SUPERCONDUCTING SHIELD Many of our experimentswith both the quantized-flux and Meissner- effect magnetometers didnot require the large low fieldsuperconducting systemdescribed in Section 111, which was built to test the Ames magne- tometers. Instead, a considerably smaller system thatwould use much less heliumand be more conveniel~t to workwith in our experimental studies of magnetometerperformance characteristics was built. It was still necessary to have a low field,stable environment for the studies, so we constructed a system suggested by ProfessorHildebrandt of the University of Houston. 14 This system is essentially a closedend cylinder fitting inside a glass helium Dewar as shown inFigure 4. Thecylinder is made ofvery pure lead weldedalong one seam with a sphericalcap welded on one end. The outside diameter is approximatelythe same as theinside diameter of the helium Dewar, withsufficient clearance to allow an easy fit. To produce a low magneticfield environment., it is necessary to cool thelead cylinder through its critical temperaturein a very slow anduniform fashion starting at thevery bottom of the closed end. Once a small portionof the closed endbecomes superconducting, we have a superconducting-normalinterface propagatingfrom this region upward to thetop open end of the cylinder. If this interface is verynarrow and moves slowly and uniformly, the mag- neticflux within the interface will becontinually pushed along and flushed out ofthe volume confined by thesuperconducting cylinder. For thissystem to workeffectively, the interface dimensions, i.e., thedistance from the pointwhere the lead is totally normal to thepoint where it is completely superconducting, must benarrow enough so thatlarge numbers of flux units are nottrapped and thus locked in the volume of the cylinder. Hildebrandthas reported field reductions of the order of lo3 by a thermalcycle as describedabove.15 In his experiments he normally mounted thelead cylinder inside a Mu-metal magneticshield so thatthe ambient field was approximately G andthe resultant field after the thermal flush-processwas G. Inour experiments with a thermal-flushedshield, we were able to get fieldreductions of approximately a factorof 10 starting in fields of G ; several times we obtained a factorof 100 but never any better. We havesince talked with Hildebrandt and learned that the lead used in hisexperiment was considerably more pure(99.9999%) than the lead we used (99.995%),which probably explains the difference in the experimental 13 1- \ r-t \Ha DEWAR--31-'/~' OVERALL 3"UPPERFLANGE 2 vi'l D, 3" OD LIP TO SUPPORT Np DEWAR I N2 DEWAR1 30" OVERALL 1 4 '/2" ID, 5" OD 3 INNERMU-METAL 5"lD I 21"To $ of shields from top flange LEADSHIELD I8"OVERALL LENGTH. 2.530 OD. I CLOSEDAT BOTTOM DEWARPADS-STYROFOAM TB - 5093- 64 FIG. 4 THERMALLY-FLUSHEDSUPERCONDUCTING SHIELD 14 results. The magnetic shielding characteristics of the system were not affected by this lack of adequate field reduction, and we were still able to carry out experiments inside the Mu-metal and superconducting shield. 15 V MEISSNER-EFFECT MAGNETOMETER One of the major objectives of the research program described in this report was to develop an absolute reading magnetometer that does not re- quire any preliminary calibration suchas cool down in a zerofield or ro- tating a pickup coil. Since the magnetic flux excludedby the Meissner effect is a linear functionof the applied magneticfield, we undertook a detailed investigation of this unique superconducting propertyand its application to magnetic field measurement. Several Meissner-effect magnetometershad already been used in some of our preliminary re~earch.~The circuit used in these earlier investi- gations was developedat Stanford University during experimentsto measure quantized flux in superconductors.’“ In this circuit, shown in Figure 5, coils A and B constitute a closed superconductingcircuit; therefore the total magnetic flux linking this circuit must be constant. If the flux linking coil A is changed by A@ (for example, by removing a magnetized sample which was initially enclosedby coil A), a current is induced in the circuit, producing flux changesin A and B whose sum exactly equals -A@, thus leaving the total flux linking the circuit unchanged. The in- duced current will persist and is a permanent record of the flux change A@ in coil A. HEATER J lo d u TI-SO93-I FIG. 5 BASICSUPERCONDUCTING MAGNETOMETER CIRCUIT 16 Operation of the circuit to measure the persistentcurrent, and con- sequently A#, is as follows: Prior to the flux change to bemeasured, any persistent current already presentin the circuitAB is eliminated bymo- mentarily heating a small regionof the circuit with heaterS, producing a normal resistance in thatpart of the circuit and causing the currentto decay to zero. After the heat is removed and AB is again superconducting, a subsequent flux change, A@, produces a persistent current proportional to A#. A solid superconducting modulator,P, inside the pair of concentric coils, B and C, is cooled below its transition temperature through contact with a heat sink, To, and can be raised above its transition temperature with a heater. When the modulator isin the normal state, the current flowing in B causes fluxto link B and C; when the modulator becomes super- conducting, part of this flux is expelled from the modulator volume, thus changing the total flux linkingB and C. When the modulator is heated and cooled periodically, the variation of fluxin C produces an alternating voltage across C linearly proportional to the currentin B and thus pro- portional to the attempted fluxchange, nip. Detailed circuit analysis ap- plicable to the Meissner-effectand quantized-flux magnetometersis pre- sented in Appendix A. (See Figure 15 in Section VI for a Slock diagramof the 6lectronics generally used with these magnetometers.) The difficulty with thv solid post magnetometer circuit proved tobe that the frequency response wasvery low, i.e., limited to about 1kHz. This is presumably because of eddy-current damping of the flux motion over the length of the modulator and, possibly, slow thermal response. The sig- nal power availablefrom a circuit of this type is proportional to the op- erating frequency. Thus it is clear that increased output power may be ob- tained by increasing the operating frequency. To achieve this additional signal power, we have constructed several Meissner-type modulators that are heated internally where the thermal path is now the radial thickness of the modulator rather than its length.The modulator was cast or electroplated on a coaxial resistive heater as shownin Figure 6 and could be thermally switched at frequencies as high as30 kHz. 17 EL INSULATION -Au ALLOY FILM INSULATION 1.25 mm OD) -PICKUP COIL O ASSEMBLY uhu T4 - 5093 - 60 LI FIG. 6 MEISSNER-EFFECTMODULATOR CONSTRUCTION A. Construction Construction of the internally hcatcd modulators was difficult. From the circuit analysisprosc'nted in Appendix A, we see that the signal power is directly proportional to the volume of superconductor that is switched, i.e., the amount of magnetic flux that is expelled per cycle. This, plus the fact that the Meissner effect is not nearly100% complete, implies that a large volume of superconductor must be switched at rather high frequen- cies to obtain adequate signal powerat very low fields, i.e.,fields of the order of G. In our circuits we generally have used modulators 1.25 mm OD by 0.5 mm ID by 1.7 cm long. These dimensions were arrivedat to facilitate construction by calculating the electrical skin depthof the modulator material while it is still in the normal state. These calcula- tions are presented in Appendix B. Evaporation techniques are not suit- able for depositing heavy metallayers, so casting or electroplating tech- niques were used to form the superconducting coating. We used 99.995% pure tin for mostof the Miessner-effect modulators. Construction of the modulator heaterwas very similar (except for size) to that of the heaters used with the quantized-flux circuits described in Section VI. We started with an insulated copperwire, approximately 0.5 mm OD, then evaporated a copper-gold alloy heating film over the insulation that made contact to the wire at one end. It was then necessary to cover this copper- gold film with high temperature insulationso that the thick-walled super- conducting modulator could be caseor electroplated about the cylindrical heater. After considerable investigation we found a duPont high temperature varnishcalled Pyre-ML that was suitable for dipcoating, could be cured at 3OO0C, andwould withstand temperatures as high as 300°C withoutdete- riorating.* To insulatc?the henting layer, the assembly was immersed into thevarnish and then extracted, using a motor drivc,at about 0.1 in./sec. Theassembly was cured at 150°C for 30 minutesand then baked at 3OO0C in anargon atmosphere for 10 minutes. Theinsulatcd heater assemblies were thenready for the superconduct- ingcoating. If anelectroplated modulator was to beused, the heater assembly was mounted in a vacuum cvaporatingsystem on a rotatingfixture, and a thinlaycr or the mctnl to beplated was evaporatedover the varnish. Thismetal lRyer wns used as thecathode in the plating process. To ensure uniformplating thickncss, the heaterassembly was rotatedslowly inside a cylindricalanode during thc plating. The plating bath was stannousfluo- roborate [Sn(BF4).] solution as describedin Reference 17. A current re- versalplating proccdurc wasuscd to producemore uniform platings. Cur- rent wason 18 sec nncl thcn rcvcrsctl for 5 sec, ctc. Using 6-ma current, about 5 hours wc'rc' required to obtain a 0.35-mm wallthickncss cylinclcr. Thecasting Tixturc is shown inFigure 7. It is simply a quartztube whose ID is thc samc as thcdcsirccl modulator OD. Themodulator was in- serted in thistubr, and ccntercd,using small standol'rs made of masking tape. A rubbersuction bulb was fitted to theupper end of the tubeand thelower end was dipped into the molten tin bath. Tin was thcndrawn up intothe tube with the suction bulb to the desiredheight andallowed to cool.Generally thc slight contraction of the tin on cooling was suffi- cientto allow casy rcmoval of themodulator from thequartz tube. Modulatorconstruction was notvery reproducible. It was difficult tocontrol the precise length of the superconducting Cylinder and also to keepthe heater wire centeredin the castingtube. We Were ableto getone symmetric modulator of thc correct lengthhowever, and this mod- ulator wasused in most of ourexperimental studies of the Mcissner- effectmagnetomctc>r. B. Experiments and Results Thepurpose of thesestudies of the Meissner-eEfectmagnetometer was to determine how themagnetic field sensitivity, frequency response, or * Informationon duPont "Pyre-M.L." is availablefrom E. I. duPontde Nemoursand Co., Fabrics and Finishes Department, Insulation Sales, 7250 N. Cicero Ave.,Lincolnwood, Chicago, Ill. 60646 19 I .RUBBERSUCTION BULB HEATERLEADS LCENTERING SPACERS CASTTIN CYLINDER / /-OUARTZ TUBE /” HEATERASSEMBLY ,’ TA-5093-63 FIG. 7 FIXTURE FOR CASTING MEISSNER - EFFECTMODULATORS 20 II I II signal-to-noise is affected by the magneticand thermal environment of the modulator and thereby maximize the sensitivityto magnetic fields, The thermal environments studied were:(1) the modulator mounteddi- rectly in the liquid heliumbath, (2) the modulator mounted ina vacuum container filled with helium exchange gasand immersed in the liquid helium bath, (3) the modulatorand pickup coil assembly coated witha 0.3-mm layer of eilicone vacuum grease, and (4) the modulator and pickup coil assembly mounted in a 3-mm-ID by 4-m-OD quartz tube filled with silicone vacuum grease. The output signal for the modulator mounted directlyin the liquid helium bath had a random low frequency amplitude fluctuation as shownon Figure 8. This fluctuation was similar in appearance to cryotron noise observed by Johnson and Chirlian," which they associated with boiling liquid helium at the surface of the cryotron. Maximum field resolution with this modulatorwas about 8 x lo-" G. -The modulator was next mounted ina helium exchange gas environment to eliminate the possibility of boiling at the modulator. Figure 9 shows a typical response trace. The low frequency noise was greatlyreduced, but the frequency response alsowas reduced so increased field resolution was not obtained. Next, the modulator was uniformly coated witha 0.3-mm layer of sili- cone vacuum greaseand mounted directly in the liquidhelium, Case 3. This uniform coating over the modulatorand pickup coil certainly would prevent gas bubbles from formingin direct contact with the modulatorand should reduce temperature gradients along the lengthof the modulator. The cir- cuit response, field resolution, and noise were identicalto Case 1 where the modulator was mounted directly in the liquid helium bath.This indi- cates that the silicone vacuum grease is an excellent thermal conductor and that the low frequency noise probably is due to temperature gradients at the modulator. The modulator assembly was mounted in a 3-mm-ID by 4-mm-OD by 4-cm- long quartz tube thatwas sealed at both endsto provide further isolation from the liquid heliumbath, Case 4. The circuit response for this case was almost identical to that forCase 2. The heavy wall quartz tube plus the space between the modulatorand the tube account for this similarity. These experiments indicate that the magnetometer was sensitiveto ther- mal environment and that a low frequency noise contribution was dueto helium boiling in contact with the modulator. Reducing this low frequencynoise by altering the thermal environmentdid not measurably improve the magnetic 21 FIG. 8 NOISEIN OUTPUT FROMMEISSNER EFFECT MAGNETOMETERMOUNTED IN -LIQUID HELIUM BATH FIG. 9 NOISE INOUTPUT FROMMEISSNER-EFFECT MAGNETOMETERMOUNTED IN HELIUM EXCHANGE GAS 22 field sensitivity. As will be discussed later in this section, transverse field at the modulator and eddy-current noise appear to limit the sensitiv- ity much more than does helium boiling. All of the above thermal environment experiments were conducted in the Dewar assembly discussed in SectionIV. The modulatpr was mounted with its. axis parallel to the Dewar and shield axis. The ambient magnetic field in this axial (vertical) direction was measuredby determining the applied field required to null the output signal from the magnetometer.This field varied from aboutto G for differentexperiments. During these experiments we observed that the signal-to-noiseratio, measured at the null signal point, seemed to be related to the initial axial field. The next series of experiments was designed to study the effectof mag- netic fields on magnetometer sensitivity. The fields, axial and transverse to the Mu-metal shield, were measured and foundbe to of the same order of magnitude for different demagnetization procedures. Further, if we assume that the thermal-flushing process would'reduce these initial fieldsby ap- proximately equal amounts, then the transverse fieldat the modulator should be of the same order as the initial axial field.Thus, it appeared that transverse fieldsmay be a significant source of modulator noiseor extraneous signal. A conclusive experimental test of this assumption was difficult in the small cryostat due to limited space for coils to control all three field components*. Therefore, the large rotatable superconducting shield was used. The modulator was mounted as shownin Figure 10. The initial magnetic field components at the modulator were measured to an accuracy of f 2 x G using the Ames flux gate magnetometerand were zero parallel to shield axis. The maximum field perpendicular to the shield axis was 1.2 x G. The perpendicular field also was uniform over the magnetometer dimensions.The modulator was mounted with its axis along this maximum perpendicular field and on a fixture that couldbe rotated by f 150 degrees in a plane at right angles to the shield axis. The field transverse to the modulator (i.e., along the shield axis) was controlled with the persistent current niobium solenoid described in Section 111. The field parallel to the modulator was controlled with a copper wire solenoid wound around the fixture holding the modulator. The third orthogonal field component was setat approximately zero by rota- ting the modulator until it pointed in the maximum field direction. The results of these studiesof the effect offields applied trans- verse to the modulator axis are shownin Figure 11. It is clear that the noise is essentially a linear functionof transverse field except at very low fields, i.e., fields low enough to produce only a few flux quanta through the transverse projected area of the modulator. The scatter of BERYLLIUM-COPPER - SUPPORTTUBE - COPPERSOLENOID MEISSNER-EFFECT- MAGNETOMETER _c QUARTZ TUBE FRAME TO SUPPORT MAGNETOMETER "- SUPERCONDUCTING SHIELD Ij ASSEMBLY (See Figure2) n FIG. 10 MEISSNER-EFFECTMODULATOR MOUNTED IN THE 16.5-cm-DIAMETER SUPERCONDUCTINGSHIELD 24 "~"" I I so IO0 50 0 0 0.5 I .o 1.5 2.0 2.5 TRANSVERSEMAGNETIC FIELD - G rB - 5093- 74 FIG. 11 MAGNETOMETERSENSITIVITY VERSUS TRANSVERSE MAGNETIC FIELD points at very low fields probably indicates that the field was not com- pletely uniform at themodulator, possibly due to magnetic moments of the magnetometer fixture. Also signals at these low fields were of the same order as the inherent noise in the detection circuit. A series of measurements was madeof the modulation efficiency versus heating frequency. For dc heating, the modulation efficiency is directly proportional to the change in self-inductance of the pickup coil when the modulator becomes superconducting. If the modulator is perfectly coupled to the pickup coil, the self-inductance willgo to zero when the modulator becomes superconducting. To measure this couplingor modulation efficiency at higher frequencies, 10-kHza field was applied to the modulator-pickup coil assembly with an external solenoid. The modulator was then switched with the resistive heaterat a lower frequency. The output from the pickup coil was displayed on an oscilloscope.The signal from the applied field was amplitude modulated by the superconducting modulator at twice the heat- ing frequency. The modulation efficiency is then given by (e -e )/e maxmin max' 25 0.5 I I I 1 0.4 * 0.3 V z w E 0.2 W U 0 3 0 0 I 0 500 IO00 I500 2000 MODULATORFREQUENCY - Hz (2 f heater) TA- 5093-75 FIG. 12 MODULATIONEFFICIENCY VERSUS OPERATINGFREQUENCY FORAMEISSNER-EFFECT MODULATOR It is very important to note that the modulator efficiency measured in the manner described above is not the same as the efficiency with which fl-lx is excluded and admitted to the modulator volume by switching in dc fields. In the measurements as described, we were measuring the changein inductance of the pickup coil as a functionof modulation frequency, and this depends only on the shape and extentof the outer superconducting sheath during the switching process, since material inside this sheath is almost perfectly shielded from the coil.It does not matter how efficiently magnetic flux has been expelled from the volume inside this sheath. These data do provide an upper limit on the modulation efficiency expected for switching in steady fields. During all of the experimental studies on the Meissner-effect magne- tometer, we made checks of the dependence of the magnetometer sensitivity versus bath temperature (down to about 1.5'K) and heating pulse shape. The bath temperature did not significantly affect modulator performance except that additional heater power was required as the bath temperature was re- duced. The heating pulse shapes used were generally sine wave. We tried 26 I " equare wave heating on several experimentsand, while magnetic field sen- Bitivity was not improved, this method of heatingdid provide more control Over the heating and cooling cycles.It also provided a measure of the rise time of the heating and cooling pulses.A scope photograph of the heating pulseand the magnetometer response using an untuned detection circuit is shown in Figure13. The pulse width of the output due to heat- ing the modulator above its critical temperature is about0.075 msec, while the coolingpul.se width is about0.5 msec. Further, the heating output pulse can be controlled to some extentby changing the amplitude of the heating signal. The cooling pulse width, on the otherhand, is basically fixed by the modulator geometry (eddy-currentpaths) and the thermal environment. From the above studies of the Meissner-effect magnetometer, we can conclude that: (1) fields as small as lo-" G can be measured; (2) the major noise source is the eddy-currents in the modulator that Impede flux motion during the transition between the normal to the superconducting states; (3) additional noise is caused by helium boiling in contact with the modulator; and (4) signal-to-noise ratio is a functionof the trans- ver~lemagnetic field at the modulator. Sensitivity to axial field changes Ulually is not better than several ordersof magnitude less than the total transverse field at the modulator. OUTPUTSIGNAL HEATERPULSE yfx x = 0.5 msec/cm TA- 5093 - ao FIG. 13 OUTPUTSIGNAL FROM MEISSNER-EFFECT MAGNETOMETER FOR SQUARE-WAVE HEATING 27 VI QUANTIZED-FLUX MAGNETOMETER Thequantized-flux magnetometer has been described in detail in the MidtermReport - October 19'657and in a publishedpaper14thus only a brief discussion of theoperating principles and final performance will begiven here. Quantizedflux modulators (which are hollow, thin-walled superconduct- ingcylinders) have been found to switchin and out of the superconducting stateat frequencies as high as several megahert~.~~~"~With this type of modulator,the voltage across coil C (Figure 5) is a periodicfunction of theflux change, nip, as shown incurve (b), Figure 14. When themagnetic fieldin coil B, dueto the persistent current in the circuit AB, produces exactlyonp flux unit (or anyintegral multiple of oneflux unit) through thehollow superconducting cylinder, no fluxchange occurs when thecylin- der is cooledthrough its superconductingtransition. This condition gives thepoints of zerooutput shown onthe response curve; however, for other values ofthe field, current is inducedin the walls of the cylinder as it becomessuperconducting to changethe enclosed flux to thenearest quan- tizedvalue. When thecylinder is cooled in a fieldproducing less than one-halfflux unit within it, a current is inducedto oppose the applied field andproduce zero flux inside the cylinder. If thecylinder is cooled in a fieldproducing slightly more thanone-half flux unit, the inducedcurrent produces a fieldin the same direction as thatof the ap- pliedfield to changethe total flux to oneunit inside the loop. This changegives an output voltage through coil C, oppositein sign to that ofthe previous case. The pattern repeats as the applied field is in- creased,giving an output voltage that is a periodicfunction of thefield applied to thecylinder and thus of A@, theflux change in coil A. Theidealized response, shown in Figure 14, ignoresthe Meissner effectof the walls of the cylinder. In general, the response of the hollowmodulator will be theperiodic effect shown inFigure 14, super- imposedon thelinear output due to theMeissner effect of the walls. An estimateof the signal power, availablefrom the circuit, if L, is pS a solenoidof length A andarea A, is givenby 28 MEISSNER-EFFECT RESPONSE OUANTIZEDFLUX RESPONSE W 0 aI- /r > J /I /I b) O > + FLUX CHANGE 3 TA-5093-ZR FIG. 14 RESPONSE OF SUPERCONDUCTINGCIRCUIT where @ is theflux in h, and v is thefrequency at which the modulator is operated. The sensitivity of themeasurement can be enhanced by using thecircuit of Figure 5 withcoil A replaced by a singleloop pickup coil oflarge area (Figure 15). This device can be used in two ways: if the fieldpenetrating the single loop produces less thanone-half a fluxunit throughthe loop (assuming zero field at coil B), then when thesupercon- ducting circuit is completed, a current will flowto expel all the magnetic flux. A measurementof this current thus constitutes a measurementof the totalmagnetic field. If the field produces many fluxunits through the loop,there is an uncertaintyby the first method,since the current flow- ing will beproportional to the amountby which the total flux differs fromthe nearest integral numberof fluxunits. In principle, one could use a series of loops of varioussizes to determine the absolute field; inpractice, it is simplerto move thepickup loop in the field as with a standardflip coil. Thus, by rotatingthe coil 180 degrees, a fluxchange in theloop, corresponding to twice thetotal field along the initial di- rection, causes a persistentcurrent proportional to that field; a measure- ment ofthis current measuresthe field. Sincethe field at the modulator enclosed by coil B (Figure15) canbe increased from that through the pickup loop byabout a factor (I.C1/n2)(A, /A2) (where I.Cland xz arethe numbers of turns onthe pickup coil and coil B, respectively, and A, and A, are theirareas), a sensi- tivity of G perperiod can be readily obtained. Furthermore, it is possibleto resolve a smallfraction of a fluxunit; thus very small fieldscan be measured. 29 OSCILLATOR 1 3 ISOLATION 3 TRANSFORMER " J L" """-1 ._I"."._. I--"-GRAMPGENERATOR 1 ".. ...-...-I I L COIL c MODULATOR NULL COIL. N TA-5093-IR FIG. 15 QUANTIZED-FLUXMAGNETOMETER CIRCUIT Several magnetometer circuitsof this quantized-flux type have been constructed. The superconducting modulator wasan indium cylinder 1 cm long with 40 p ID and walls about 1 p thick. It was formed by evaporation onto a coaxia1,heater unit fabricated by evaporating a copper-gold alloy film onto an insulated copper wire. The film contacted the copper wire at: one end so that current could be passed through the wire and back through the film, thus producing heatin the resistive film. These modu- lators normally were switchedin and out of the superconducting stateat 30 to 40 kHz. The pickup coil (Figure 15) consisted of a 1-cm-diameter single turn of 0.005-cm-diameter niobium wire connected to a ofcoil the same wire wound about the indium cylinder. The modulator was mounted with its axis parallel to the plane of the pickup coil and along the rotationof axis this coil whenit was used as a flip coil. The trim coilwas used to pro- duce zero net flux through the modulator whenno persistent current was flowing in the circuit. A superconducting transformer with an externally tuned secondary was used to match the low impedance outputcoil (coil C, Figure 15) to a low noise preamplifier and then toJB-5 a Princeton Ap- plied Research lock-in detector. A coil N, closely coupled to the pickup 30 coil, was used to produce an opposing field chargeso that the devicewas used as a null detector where the current flowingin coil N was a measure of the field. The response of the magnetometerto a slowly increasing magnetic field is shown in Figure16, where both the quantized-flux periodicityand the average linear variation dueto the Meissner effect of thecylinder walls fi are evident. The data in Figure 16 indicatea noise limitation of approxi- mately 5 x lo" G. The operating characteristicsand magnetic field sensitivity of the quantized-flux magnetometer usually become worse after several cyclesto room temperature. We feel that more refined evaporation techniques would -. . 0 20 40 60 80 100 t - stc 0 IO0 200 300 H - 10-5 G rn-509)-n, FIG. 16 QUANTIZED-FLUXMAGNETOMETER RESPONSE 31 I VI1 OPTICAL HEATING EXPERIMENTS WITHA QUANTIZED-FLUX MODULATOR Thequantized-flux magnetometer has been described in the previous section and in References 7 and 4. The superconductor was heatedabove andcooled below its transitiontemperature by passingan alternating current through a resistivefilm coaxial with the modulator. The output signal waa at twicethe heater frequency since a heatingpulse anda coolingpulse occur twice forevery cycle, This minimizeselectrical pickupbetween the heater and the outputsignal at the signal frequency, although any secondharmonic content in the heatersignal can still cause noiseor background on themodulator output, We designedan experimental system to test opticalheating of the superconductingfilm in an attempt to eliminate this sourceof extraneous signal.This system, shown schematicallyin Figure 17, consistsessen- tially of a modulatoror superconducting cylinder evaporated onto a quartz fiber.Light is pipedinto the cryostatthrough a quartz light pipeand impingeson one end of thisquartz fiber. The fiber is constructedin theshape of a collimatorto collect more lightfrom the light pipe. The lightsource is a highintensity arc lampmounted in the roomand focused by variouslenses on the mirrorof aHoneywell microgalvanometer.* Thegal- vanometer is of the typeused in optical strip-chart recorders. Its rated frequencyresponse can be as high as 15 kHz and possibly higher forvery low amplitudegscillations. The complete system consistsof a choppedlight beam passingthrough the light pipe into a quartztube onto which the modulator is evaporated. The light is absorbed by the modulator, which heats the superconductor above its transitiontemperature. In this system, direct couplingof the heatersupply current to the modulator outputcircuit is avoidedcompletely. We constructedseveral superconducting modulators evaporated on quartz and tried this opticalmodulation experiment numerous times. All of the experiments were unsuccessfulbecause the evaporated film on the quartz fiber wouldnot become superconducting. Careful inspection of the modulator under a microscopeshowed numerous hairline cracks runningaxially * Honeywell,Denver Division, 4800 E. Dry Creek Road,Denver, Colorado 80217. 32 HONEYWELL GALVANOMETER QUARTZ LIGHT PIPE - MAGNETOMETER ASSEMBLY TA-5093-76 FIG. 17 OPTICALMODULATION APPARATUS FOR AQUANTIZED-FLUX MODULATOR 33 I andcircwnferentially through the modulator material. We sincehave learned thatthese cracks are formed by thermaletching.21 This process occurs when a material is depositedonto a hotsurface. The etching effectively openedthe modulator along the generator in numerous places; thus the only ' effectof switching was theMeissner effect due to fluxbeing expelled from the walls. The walls were extremelythin, and we didnot have sufficient sensitivity in our circuit to see thisMeissner-effect signal. Our hypothesis of thermaletching has beenconfirmed recently by fur- therexperiments at StanfordUniversity, where superconducting modulators havebeen made successfully on quartzfibers. 22 In this case , the deposi- tionprocedure was designedvery carefully to preventoverheating of the quartzduring evaporation. The boat that contained the metal beingevap- orated was opticallyshielded, with room temperatureshields placed between theboat and the modulator except for a small holethrough which the evap- orated metal couldpass. Further , themodulator was mountedon a movable fixture so that it could be rotated overthe evaporation boat for a few seconds, moved away andallowed to cool,then returned--with this process continuinguntil a sufficientsuperconductor thickness was builtup. The modulatorsconstructed at Stanford University still were electrically heated,having an electrical resistive film deposited before the supercon- ductingfilm. Duringour attempts to constructan optically heated modulator circuit, we testedseveral dry tantalum capacitors (Sprague type 150D*) at liquid heliumtemperatures. We anticipatedusing these to tunethe output circuit of themodulator at liquidhelium temperatures, thereby increasing the Q ofthe circuit. In general,the capacitance dropped to aboutone-sixth its room temperaturevalue, and the power dissipation increased by anorder ofmagnitude when the capacitor was cooled to liquidhelium temperatures. We triedthese capacitors because of thevery large capacitance available in a small physicalsize. We now understandthat other types of capacitors, such as thetantalum-mylar capacitor, work very well at heliumtemperatures withno significant change in capacitance or dielectricloss. These were notstudied in our experiments. * SpragueProducts Company, 99 MarshallStreet, North Adams, Mass. 34 VI11 APPLICATIONS OF THE dc JOSEPHSONEFFECT* A briefdiscussion of the theory of Josephson junctions was given in Section 11. We now considerseveral techniques for constructing junctions anddescribe five device applications of thesejunctions. The firstJosephson junctions were built by evaporating a supercon- ductingground plane, covering this with an evaporated dielectric layer, andevaporating another superconductor onto the dielectric. These circuits were very difficult to build 'because the dielectric layer betweensuper- conductorshad to be 10 or 20 % thickwith few or nopinholes that would allowthe two superconducting layers to make directcontact. Due tothe construction difficulties with circuits of this nature, we initiallycon- sideredthe Josephson effect to be an impractical method for constructing a usefulmagnetometer for field application. Recently, several develop- mentsin construction technique have changed considerably the complexity of buildingreproducible, stable Josephson junctions. The first was a techniquedeveloped at theFord Scientific Laboratory called the point contactJosephson junction.a3 This consists essentially of a superconduc- tingground plane that is allowedto oxidize slightly; a sharppointed superconductorthen is pressedinto this ground plane at helium tempera- tures untilthe proper tunneling characteristics are observed.This junction is probably a weak linktunnel where there is physicalcontact betweensuperconductors but over a very small crosssection area. Anotherand even simpler Josephson junction can be built by a tech- niquedescribed by Clarke.6This technique consists of taking a small diametersuperconducting wire, such as tantalum or niobium,allowing the surface to oxidize to a depthof approximately 20 8, and thencasting a "glob"of radio solder about the wire. Thesolder is superconducting as is the core of the wire, and theoxide layer onthe surface of the wire formsthe junction dielectric. Figure 18 is a schematicdiagram of a typicaltunneling junction built in this manner. The characteristics of * Theapplications of the dc Josephson effect described in this section were given in a paperpresented at theInternational Conference on CryogenicEngineering in Kyoto, Japan, during April 1967. 8 35 the junction are measured by passing a currentthrough the niobium wire, across the dielectricbarrier, and then through the solder. The voltage is then measured across the dielectricbarrier. This junction has several distinctadvantages over planar evaporated junctions of the type discussed earlier. NIOBIUM 01 ELECTRIC WIRE 50p LAYER Pb - Sn EUTECTIC (20- 100 8 ) SOLDER BALL (5mm dio) FIG. 18 CONSTRUCTION OF A SLUG TYPE JOSEPHSON JUNCTION The firstadvantage of theClarke junction is thatthe magnetic field linkingthe dielectric barrier is controlled by varyingthe current that passesdirectly through the superconducting center wire. Thiscurrent produces a circumferentialfield that links the area betweenthe two super- conductors. A secondadvantage is thatthe solder glob tends to shield thedielectric barrier from external field changes. Clarke6has given a very completedescription of the use of this cir- cuit to measurevoltages of theorder of Vdc andmagnetic fields of approximately lo-' G. We repeatedthe experiments that Clarke reported andfound that it is quiteeasy to build circuits that would give the same results. Thede-ailed characteristics of jmctionsof this type are not yet well understoodbecause the nature of thejunction is verycomplicated, possiblyconsisting of numerous weak links through the dielectric barrier. In many ofour experiments, we didobserve interference effects that seem to indicatethat the junction actually divided into two junctions separatedby a lengthapproximately equal to the length of the wire covered by thesolder glob, thus giving fairly high resolution interference pat- terns. By resolving a small fractionof one of theseinterference patterns, we were ableto measure currents of less than amp throughthe lo-'- henryinductance of the center wire. 36 We have used this Clarke slug tunneling junction in the following five experimental systems: 1. A low Impedance ammeter as discussed above. 2. A magnetometer for measuring changes in magnetic field (Figure19). Field changes of less than 5 x G were easily resolved with . this devioe. HEWLETT-PACKARD I OSCILLATOR LLhRECORDER ISOLATION TRANSFORMER -KEITHLEY103A I PREAMPLIFIER RAMPGENERATOR Lir?"AC AC VOLTAGE-' "CURRENT CLOSEDSINGLE TURN LOOP OF 2mil ODNIOBIUM WIRE. THE "SLUG" IS CASTAROUND ASEC- TION OF THEWIRE WHERE THE INSULATIONHAS BEEN REMOVED. NIOBIUMOXIDE FORMS THE TUN- NELINGDIELECTRIC. THE SLUG IS MADEOF TIN-LEAD RADIO SOLDER. FIELDCOIL T A- 5093 - 65 FIG. 19 JOSEPHSON JUNCTIONMAGNETOMETER 3. A magnetic field gradiometer (Figure20), which consists of two one-turn circular loops approximately5 cm in diameter, wound in opposite directions ona form. The loops are in parallel planes and separated by about 20 cm. Theytare connected with 0.05-mm-diameter niobiumwire, and a tunneling junction is cast on one of these connecting wires. A field :change common to both loops does not produceany net flux change through the closed superconducting circuit since the loops are counterwound.A field gradient, on the other hand, does produce a net flux change through the circuit, which causes a persistent current to flow. A measure of thiscurrent, using the slugdetector, is then a 37 measure of the field difference betweenthe two loops. This cir- cuit only measures the changes in field gradient that occur after the circuit becomes superconducting. Field gradients of less than lo-’ G cm have been measuredwith this system. 1 / ) TA-5093-61 FIG. 20 JOSEPHSON JUNCTION MAGNETICGRADIOMETER 4. A displacement measuring instrument (Figure21), which is simply a magnetic piston (a superconductingtin bar in our experiment) that is inserted into a closed superconducting loop connectedin series with a slug-type Josephsonjunction. Movement of the mag- netic piston producesan attempted flux change through the closed loop, which causes a persistent current to flow. This current is a function of the piston displacement andthe applied magnetic field. The slug is used to measure this current, calibrated in terms of the linear displacement ofthe magnetic piston. Pre- liminary experiments have proved thatthe technique is feasible 38 andthat displacements of less than 1,500 1 canbe measured easily. Inthese experiments, the sensitivity was limitedonly by the resolution of themethod used to move the magnetic piston, and we expectthat much better sensitivity can be realized. DISPLACEMENT AND CLOSED LOOP TI- 5093 - 60D FIG. 21 JOSEPHSON JUNCTION DISPLACEMENTINDICATOR 5. A verysensitive system for measuring the static magneticsus- ceptibilityof samples at liquidhelium temperatures. This system is very similar to thedisplacement measuring system describedabove. The one-turn coil of thedisplacement measuring system is replacedby a longsolenoid that will coupleefficiently to theentire sample. The sample is insertedin the coil while a heatswitch keeps part of the coil above its critical tempera- tureand the desired external field is applied.The coil then is returned to thesuperconducting state, andthe sample is removed completelyfrom the coil so thatno flux from the sample can couple to the coil. The total currentinduced in the coil, measuredwith the Josephson junction, is directly proportional to themagnetic susceptibility of the sample. Theabove circuit (item 5) hasbeen used in preliminary experiments to studyboth the Meissner effect and the time dependence of theflux motionin the heavy wall Meissner modulators used in our magnetometer experiments.In these experiments, the modulator was mounted inside a snuglyfitting pickup coil and,instead of moving the modulator physically into andout of the coil, we cycled it aboveand below its transition tem- peraturewith direct currentpassing through the resistive film heater. One objectiveof these experiments was to determineif the Meissner effect was exactlyreproducible from cycle to cycle,but the system was notsensi- tive enough to measurethe Meissner effect at very low fieldlevels where fluctuationsare most likely to occur. 39 We were also interested in determining thetime dependence of this flux exclusion process. 'rho sensitivity of our systemwas not adequate to detect, individual i'lusql1nn(;a, although minor refinements (both in the coupling to the F;;unple and t.he electronic readout equipment) should make Ihi~possi.ble. l'lte 1 irnc! rc:sponsc of the system was limited to ahout 0.1 second by thc del ('(:IOI., alld a pen recorder was used to record the signal 1'ruln the t~u~neling.junction. We observed that the superconducting- lu--normaltr:uisition 01 1.1~modulator occurred considerably fasLer than Lhis Lime c:or~lanl, while 11112 normal-to-superconducting transition occurred in Limes var~,ingfrom 1 to 10 seconds depending on the field at the modu- 1 il 1 0)'. Figure %% sliows R l!*pic:al normal-to-superconducting superconducting- lo-norrllal 1.ransition plot. I alcen with this system, These time measurements 01' Lhe ~lormal-lo-superco~ld~~ctingtransition are in verygood agreement with 1 hc work of 1)eSorl)r)J24 wl~t.t.t: the normal-to-superconducting transit-ion was st.utlic~rl 115i11~( mngtleto-optic tcchniques. 40 u)- C 3 sf SUPERCONDUCTING (SUPERCONDUCTIHG TUR N ED ON TURNEDI ONTURNED OFF (L'I 01 t- 0 W t- W 0 z 0 v, I a LNORMAL II W v, 2 z 0 (L LL I- 3 a I- 2 seconds 1.1 3 0 1 TIME - seconds TI- 5093- 62 FIG. 22 SUPERCONDUCTING TRANSITIONS OF AMEISSNER MODULATOR I IX CONCLUSIONS AND RECOMMENDATIONS During our research program, we discovered better, easier,or more logical ways to achieve the stated objectives. Thus this chapter is de- voted to the results of our research and recommendationsfor experimental investigations that would increase understandingof the superconducting devices studied. A. Magnetic Shield The superconducting magnetic shield describedin Section I11 was studied extensively during the many experiments in whichit was used. In gcncral, the shield was completely satisfactory for its designed purpose, i.e., providing a stable low magnetic field environment for magnetometer tests. During these tests, we conceived several ideas for a newshie.ld that would reduce the helium boil-off rateof the shield assembly and make construction easier. We recommend the latter design over the onewe built in this research (see Section 111). The new shield design is shown in Figure23. Helium boil-off rate could be reduced from 1 liter/hour to less than 1 liter/day. The signif- icant features of this design are: (1) all components areplaced in the same vacuum spzceso that heat leaks are minimized,(2) all low tempera- ture demountable vacuum seals are eliminated,and (3) the'room temperature access can pass completely through the shield Dewar. The detailed place- ment of components shown in Figure23 is for illustrative purposes only. Such features as efficient useof the cold helium boil-off vapor, radia- tion shielding, transfer lines, possible omissionof the liquid nitrogen shield, etc., were not considered in this preliminary design suggestion. B. Meissner-Effect and Quantized-Flux Magnetometers The quantized-fluxand Meissner-effect magnetometers could be used to resolve magnetic field changes of the order of G. The resolution was limited by noise from the superconducting modulator that wasdue, as indicated by the experiments discussedin Sections V and VI, primarily to the thermal and magnetic environment at the modulator. From our studies of the Meissner-effect modulator, we can conclude(for cylindrical modu- lators at least) that the resolution of axial magnetic fields is limited by the transverse field at the modulator. 42 LIQUID NITROGEN SUPERCONDUCTING SHIELD-OPEN RADIATION ,/ OR CLOSED AT THE BOTTOM / COPPER TEMPERATURE LINER / SUPERCONDUCTING SOLENOID / CONTROLLED TEMPERATURE ACCESS ,/ INNER VACUUM WALL "- "- /"--- OUTER VACUUM WALL CONTROLLEDHEAT LEAKS 'r ROOM TEMPERATURE "0" RING SEALS AT EACH END FOR 4 ASSEMBLY AND MAINTENANCE TI-5093-19 FIG. 23 PROPOSEDDESIGN FOR A SUPERCONDUCTINGMAGNETIC SHIELD 43 Our studicsalso indicated that all of the noise observed was related to switching the. nlodula1.ctrbetween thenormal and superconducting state. Therclforp, w(' rvc.ommc--nd thal. furtherresclarch on Meissner-effect or quant.i~c~d-flllxtlc.vi(:(:+; shou1.d have LIS oneof its ma.jor objectives a de- tailwl study 01' no is^' i~lhc*~.c~~I.to the intermediate state of superconduc- tors. It is difl'ic.ul1 i.o evaluatethe applications of thesedevices wlth- o~t:addl tional infomationabout this intrinsic noise. Thefollowing discussion describes several techniquesthat ma> im- provemodula101- pc~rlormanc~~:and that would be useful in studying the noise probltwls di scr~ssc~tl;IIJOV(\ '1'hc:se stutlicss were not made duringthis research pw.jc~c*t1)cc.nuso of' 1110 (,xL~*cw~clii'ficulty in obtaining reproducible results with the‘ cyli11d1-ic:almwlrrL:ltors investigated. We now feelthat enough has br.c.11 lcnrncd ;tlmut. 1.11~tlcspc!ndcnce of themodulator output on thethermal andmagnetic cnvironmcnt Lhat thesesuggested extensions of the research would lw I)oth pt-act ical ant1 informative. The. map1c~1ornc.I(\J. r.i I.I*LI~Ls (Meissncr effect and quantized flux) exhib- ilcd wry similar cl~a~.~~~~L~~~'islicsandcan be dealt with together. Magne- lon~c!t.c~~-~c~l~f'o~.n~:~l~(~(~ proIx1bly could be improved ifthe operating frequency c.oultl INS illcl.c:as(d wiLhou1. dccrcasingthe modulation efficiency or in- (~t~~:lsin~tllc: ur.)iscs. (~~11c~111:1l.ionsand ourexperiments have indicated that LIIc? modulation effic:j.cmc:y is most seriouslyreduced by thermal considera- t ions and eddy-currcw 1 f lux-motion phenomena. The thermal problems are (1) opt imjzing 1.h~~Ihc:~-rnal relaxation time ofthe modulator material, (2) rccluc:ing thc: 1;hc;rrnal impedancebetween the modulator and the temper- aturcsink (usually the liquid helium bath), and (3) eliminatingtemper- aturegradients or rluctuations at themodulator. This particularly ap- plies to bubhlcformation at the surface of the modulator. Thethc?rmal relaxat.ion time is relatedclosely to theeddy-current damping, i.c., most. materialswith high thermal conductivity leading to short thermal rclaxations times also havehigh normal state electrical concluctivity,which rcsults in reduced modulation efficiency. A studyof alloysand modulator geometries, other than cylindrical ones, may result inoverall improvement of these two effects. A techniquethat may improvethe modulation efficiency and reduce temperaturefluctuations due to boiling, etc., is shown in Figure 24. Themodulator i's cooled from theinside out bycon.duction along the cen- ter copper wire, therebymaximizing the amount of flux excluded per cycle. Theprobable dirIiculty with this method of cooling is thateddy-current damping inthe center copper wire plusthermal response would limit the operatingfrequency as discussedbelow. 44 I- HELIUM COPPERCYLINDRICAL ENCLOSURE EXCHANGE ,/ GAS I WITH CLOSEDENDS SUPERCONDUCTIhGMODULATOR k / I ,zo MIL(COPPER WIRE I t HE:ATER LEADS E POX Y PICKUP EPOXY SEALS'\PICKUP COIL COIL LEADS 1A - $093 - 71 FIG. 24 COOLINGOF THE MEISSNER-EFFECT MAGNETOMETER FROM THEINSIDE OUT It should be renlixc~tl that thecopper wire that forms the center heatcr conductor01' our modulators also introduces cddy-currcnt damping. Thc skin tl~~pl,hfc>r cop1)c'r. :I 1 ~1.2'K and 10 kHz is only about0.06 nun, so t.his cTfcc.1 is not nc~gligiblc. Thc copper wire may bc replaced with a tliclertric such as quartz; thv heater would then be cvaporatcd on the quariz, insulntcd, and th<. modulator constructed as before. In future work, this tecllniqllcb shoultl bc> investigated. The eddy-currcwl J'lrrx-motion problem scems to set the most serious limitations on modulator pc~rformancc. This is especially true for the Mcissncr-typc: modulators. As discussc~lin Section VIII, the transition from normal to supcrconductiug for a tin cylindrical modulatormay take as long as sevcral seconds. The best way to solvc the thermal impedance problem may be to usea modulator material whose critical temperature is less than the lambda point of liquid helium. Thus no boiling would occur, the uniform tem- pvraturcs would bc much easier to achieve. The quantized-flux modulator could hc constructed of a very thin aluminum film whose critical temper- ature can be controlled in Ihc range from about 1.2 to2OK. The critical tcmpcraturc of bulk aluminum is 1.2'K; it is a difficult material to usein the Mcissncr-effect modulators due to the problemof maintaining this low temperature. In fact, there is no obvious choice of Meissner modulator material witha critical temperature less than2.17'K (lambda point of He4) that also exhibits an appreciable Meissner effect. From the workof DeSorbo,24 we conclude that the normal-state eddy- currents providc the major impedence to flux motion. We have considered several modulator geometries thatshould reduce 'the eddy-currents. The simplest geometry is a cylinder with several axial slits through its 45 walls. We attempted to cast one modulator with these axial slit^ but were unable to get the individual superconductingetrip~ to bond to the modu- lator heater. Another, end probably better, geometry would be multiple plane layers of superconductors, insulators, etc., built up to give a sufficient volume of superconducting material. A modulator of! this type also would have a larger surface-to-volume rutio, possibly giving faster thermal response, C. JoaeDhson Junction Devices In our opinion, thc point contact andClarke slug Josephson junctions are the most promising superconducting elementsfor general device develop- ment. These junctions work even after repeated cycling to room temperature in contrast to evaporated junctions, which generally do not survivea sin- glc temperature cycle. The junction characteristics often change after the junction has been cycledto room temperature, and this lack of stabil- ity is one oi the major problems to be solved before tunnel junctions can bo used in instrument development. The superconducting tunnel junction operates without thermal cycling and therefore does not suffer from the intermedi-ate state noise like that observed with the Meissner-effect and quantized-flux modulators. This is not to say that Josephson junctions are noise free.The tunnel junction is analogous in many ways to a TypeI1 superconductor and would probably exhibit noise due to flux motion and temperature fl.uctuations. Several theoretical studies of shot noise in tunnel junctions have been reported recently,a6 but so far one cannot predict the magnitudeof the noise spectrum. We recommend a serious research effort to understand the noise in Josephson junctionsand to understand how to make junctions with stable, reproducible, and predictable characteristics. These studies could have profound impact on the applications of superconductivity to instruments such as magnetometers with sensitivities good as as lo-'" G and volt- meters as sensitive as10-l' Vdc. 46 Appendix A MAGNETOMETER CIRCUIT ANALYSIS The equivalent circuit diagramof the superconducting magnetometer is shewn In Figure A-1. Themodulator is represented by a time varying inductance, L(t), of thBpickup winding, an emf generator, e1 , and the inductance, L andresistance, R experienced by theeddy currents in e, e' the modulator core when it is normal. (When themodulator core is super- conducting,these eddy currents are replaced by superconductingshielding currents, whichare taken into account by thebulk susceptibility, x, of themodulator core,) The emf , el , is equalto NIP, where IP is the time derivativeof the flux switched in and out of themodulator by theheating andcooling of the core, The flu generatedin the pickup winding by the current, i, is not includedin IP but is takeninto account by theinduc- tance, L. Theresistance, R1, is introducedinto the magnetometer to preventpersistent currents in the primary. It is typically much smaller thanw(L+k ) , e.g. , around lo-' R. Thetransformer, which is entirely superconducting,provides impedance matching between the lowimpedance modulatorand the high impedance of the preamplifier that amplifies eo prior to thelock-in detector. (The preamplifier and lock-in detector are not shown in Figure A-1 .) The resistance, & (typicallyof the order of 0.05 n) is theresistance of the leads comingout of the cryostat. The capacitor, C, was at room temperaturebut could be placed in the liquid heliumbath so that RQ couldbe reduced to zero if desired.The resistance, is theinput resistance of the preamplifier. RL 1 The circuitanalysis to be given contains two major approximations forthe sake of simplification; first, the eddycurrents in the modulator core are notincluded; and second, the inductance, L(t) , is assumedcon- stant. The quality of theseapproximations has not yet beendetermined. It is importantthat this be done inthe future. The second approximation eliminatesan emf term, dL/dt,and holds constant the coefficient, L, inthe inductive voltage drop, L di/dt.These terms, which come fromthe time derivativeof (Lt), would greatly complicate the analysis because of theirnonlinear character, Most ofthe experimental data of this report were takenfor modulation frequencies in excess of 1 kHz, forwhich the amplitudeof modulation was less than 1%. Under thiscondition, the per- centagevariation in L would also be small, and L in the term L dt/dt will bevery nearly constant. The other term, dL/dt,also decreases withthe percentmodulation; however, the desired signal, N@, decreasesfor the 47 +-MODULATOR -1 I I EDDY CURRENT IN ! MODULATOR CORE I RI I. I PICKUPWINDING I 7). - 8013- ?O FIG. A-1 EQUIVALENT CIRCUIT OF THEMODULATED INDUCTANCE SUPERCONDUCTINGMAGNETOMETER (a) FIRST STEP I (b) SECOND STEP R (c) THIRDSTEP TA - 5013 - 7s FIG. A-2REDUCTION OF EQUIVALENT CIRCUIT FOR ANALYSIS 48 ome reamon.Therefore, thir linearanalysio io only a crudeapproxima- tionbut ir uredfor determining the valuer of the circuit quantitieo for look of ,anything better. Thegeneral method of optimization will be to compute eo in terms of all the cirouit quantitierr , determine the value of ca for proper tuning andthen maximize eo as a functionof 4 and b. It will be assumed that Rl , b,and 5, are fixed by otherconeiderations although their effect on 00 oan be examinedfrom the equations to be derived. The voltagegen- erator, 01 , is normed to be known and its valuecomputed later as a functionof the B field to be measured by the magnetometer. The waveform of el (t) is notnecessarily sinusoidal ; however, the high-Q output circuit will amplify only the fundamentalFourier component. Therefore, the funda- mentalFourier Coefficient will be introduced when el is computed.For the purpose of analysis, the rms valuesof q and eo, El and Eo, will be ueed, The circuitcan now be redrawn as shown inFigure A-2(a). The primary is next reflected into the secondarycircuit to obtain the circuit of Fig- ure A-2(b), The reflected quantities are given by :as Since Rl "E1 E{ = L+kL c: = y$+ 49 The values of C: and R' are given by L a 1 + Q, ~3' = ca Q; RL R; = 1 .t Q; where Q = GaRL. Since Q >> 1 for the case beingconsidered, we can L L write R ' L RL = "2- (A-10) QL The circuit can now bereduced to that of FigureA-2(c), where (A-11) (A-12) (A-13) Thecurrent, Ia , is given by (A-14) which is a maximum when thetuning condition 1 WLQ = - (A-15) WC is satisfied. 50 The value of Ca requiredto maintain tuning can be obtained from Eqr. (A-15) and (A-13) to obtain (A-16) where M ha8 been replaced by k ; k beingthe coupling coefficient of thetranrformer (0 k 5 1). For Ca tuned, 10 canbe writ ten as (A- 17) EO is then given by (A-18) or (A-19) where j = m,'i .e. , EO is 90 degrees out of phase with E1 . The total circuit Q canbe defined as 1 - - roLg (1-[:k2L1/L+L1]) (A-20) ' = URCa R so that Eo becomes (A-21) Notethat Eo varieslinearly with Q. If thecircuit is nottuned (i.e., thecapacity is eliminated),then Q in Eq. (A-21) canbe replaced by 1. The effect of tuning is to amplifythe output by a factor Q as might be expected . 51 I . . ". , .._. ". -. "" Thepower output, &/RL can be maximized by maximizing & , since R L hasbeen included in the derivation of Eo and is treated as constant. We now maximize Eo with respect to by writing Q of Eq. (A-21) in terms of by using Eq. (A-201, usingthe relation M = k (A-22) where h=(l- AL+Ll ) (A-2 3) Thus Eo becomes (A-24) This is of the form (A-2 5) The maximum found by setting aEo/ab = 0 is (A-26) This optimum value for LQ results in a Q given by (A-27) an R given by R = 4R2, and an output voltage given by 52 We can now optimize Eo withrespect to by:,using Eq. (A-23) forh, setting aEo/alQ equal to zero,and solving for L.1. ' We obtain (A-29) which is plottedin Figure A-3. Usingthis optimum value for L1, we obtain h=m and (A- 30) If thevalue of Q given by Eq. (A-27) is toohigh from a circuit stability viewpoint, & canbe increased to hold Q fixedat the maximum tolerable value.The optimization of Eo withrespect to lQ, using Eq. (A-21)and M = k , thenbecomes =L (A-31) N Equation(A-29) gives nearly this same valuefor L1 if k < 0.5 as shown inFigure A-3. Forthis type of optimum LQ , we obtain Theinput voltage, el , canbe written as \ el = ~8 = NBA, (A-33) where A is the effective normal area of themodulator core and B is the magneticfield being measured by themagnetometer. This assumes thatthe modulatorlength to diameter ratio is largeenough to make thedemagneti- zationfactor nearly zero. The area, A, is given by 53 5 4 3 2 I 0 FIG.A-3 TRANSFORMER PRIMARYINDUCTANCE VERSUS COUPLINGCOEFFICIENT FOR MAXIMUM OUTPUT 54 I_- A = Aa[ l+ma’)((t) ] (A-34) where A IPthe area of the pickupwinding, a = A /A , where A is the 0 m area of the modulator aore, m ie a factor (0 5 m 2 19, whichaccounts for the Meis8ner ratio and the hole of the core if there is one, and X(t) is the averageeffeetive susceptibility of themodulator core, Thethermal modulation eaumer x to vary between 0 and -1 as the core goes fromthe normal to theruperoonducting state, The voltage, e1 , thenbecomes @=NRMAj( (A- 35) m The fundamental of j( can be written as j, = wq cos wt, (A- 36) where bl Is thefundamental Fourier coefficient. E1 thenbecomes (A- 37) Theinductance b in MKS units is givenapproximately as FONaA C (A- 38) R where is the length of the pickupwinding. The approximation here assumes that L is the inductance of the pickupwinding when it is normal. Actually,an average value somewhat less than this could be used. Using these equations for El and L and Eq. (A-30) for Eo, we obtain (A- 39) 55 The outputpower, g/R is then given by L' E? f VQK p.: (A-40) PQ where (A-27) V = A k = volumeof modulator core m f = w/2n 27ma a$ ka K= - (A-41) 4(1+ dl-ka) Notethat N hasbeen canceled. This means that N is arbitrary andcan be chosen on thebasis of practicalconsiderations such as the size andshape of the wire cross section for maximum coupling to themodulator core. Equation (A-40) states thatthe maximum powerobtainable from the circuit of Figure A-2 is proportionalto the field energy in the volume of the modulator core times Q times thefrequency with which this field is switched in and out of thecore. The power is proportional to thecircuit Q because the resistance associatedwith the source of el is verynearly zero. This means that we have a voltagegenerator, el, withan unlimited source of power.Therefore, as Q is increased,the output power increases,and more power is removedfrom the source of el. This powercomes from theheater currentsupply that switches the superconducting modulator. The numerical value of K in Eq.(A-41) is notto be trusted because of the approximation thatL(t) is constant. Theactual design of thecircuit can now be made as follows: 1. Choose a preamplifierwith high input resistance because Eo in Eq. (A-30) increaseswith R . L 2. Make R1 << &(L+Ll)"/$ so that it contributes little tocircuit loss [see Eq.(A-11) 1. 56 3. Make & as small as possible,except do not allow Q from Eq. (A-27) to become too large forgood circuit stability. If necessary, C canbe placed in the liquid helium bath and & made very small, 4. Choose N convenientfor obtaining good coupling to theflux in the modulator core. 5. Choose a modulator size. This is notstraightforward since the maximum frequencyof modulation is related to the size of the modulator.This then fixes L. 6. Make L.1 L [see Eqs. (A-29) and (A-3111. 7. Choose u) as high as possible to obtain a sigFificantpercentage modulation. Note that Eq. (A-39) contains da inthe numerator. 8. Choose k = 0.9, aneasily obtainable value for a transformer made of close fittingsolenoidal windings. Note that as k approaches unity,both and L.1 (for maximum outputvoltage) go to infinity, Therefore, it is notadvantageous to make k greaterthan about 0.9. 9. Compute LQ from Eq. (A-26) . 10. Compute Ca from Eq. (A-16). It mustbe reiterated that this analysis makes two crudeapproxima- tionsthat have,not yet been evaluated, i.e., theeddy-currents in the modulator core are notincluded, and the inductance, L(t) , is assumed const ant. 57 Appendix B CALCULATIONS OF SKIN DEPTH AND THERMAL RELAXATION TIME FOR SUPERCONDUCTINGMODULATORS The electrical ekindepth,a7 6, In millimeters Is given by where po = 4rr x lom7 henrydm Q = electrical conductivity = l/p p = electrical resistivity w = 2rrf f = frequency in He Thecalculations were donefor f = 10,000 Hz fortin, indium, mercury, lead,and copper. The electrical resistivityjust above the critical temperature was usedin all cases. Theresistivity at 4.2"K was used forcopper. Table B-1 givesthe results of theskin depth calculation. Table B-1 ELECTRICAL SKIN DEPTH AT A FREQUENCY OF 10,000 Hz Electrical Electrical Resistivity, p Skin Depth , 6 Mater i a1 (h> (mm) Tin 11.5 x 10-l' 0.169 Indium 1.7 x 10-l' 0.026 Mer cury 5.3 x 10-lo 0.115 Le ad 1.6 x 10-l' 0.063 Copper 1.7 x 10-l' 0.065 58 Thethermal relaxation time forthe superconducting modulators has beennpprexlmated by oolculatingthe time conetantin the heat diffusion oquat ion for tha moclulrttor material inthe normal state justabove the critical tgmperrture. fn thisequation A R eonstunt K = thermaleenductivlty in w/cm°K C = heatcapacity in jeules/gm°K p = densityin gm/cm3 a = length of thermalpath In cm T = temperaturein OK. Thevalue8 for K and C usedin these calculations were takenfrom Refer- ence 28. Therelaxation time is then lcpaa '=TK For a tin rod 1 cm longthat is heated at oneend and cooled at the other, we find (2,0x10'4j/gm0K)(7.3gm/cma)(l cmIa T=- ria (25 w/cmo K) 7 = 5.91 x lo-' sec The modulatorgeometry used in our experiments was a hollowcylinder of wall thickness A. Assuming that the thermal pulsepropagates from the inner wall of the cylinder (the heat source) to the outer wall (theheat sink)along a radialdirection, the lengthused in calculating the relax- ation time is the wall thickness.Thus 1 cpAa (B-6) '=TK 59 Calculationo were done for a cylinder with 0.5 mm ID by 1.25 mm OD for various modulator materials. The reeults are shown inTable B-2. Table B-2 THERMAL RELAXATION TIMES FOR FIVE: POSSIBLE MODULATOR MATERIALS Relaxation Time, 7 Mater ia1 Tin 8.0 x lo-' Indium 7.6 x Mercury 9.3 x Lead 1.9 x lo-" C op per 1.5 Copper x 10- From.these estimates of thethermal relaxation time, it is clear that modulatorsoperating at frequencies as low as 10to 20 kHz shouldnot be limited by thethermal response. 60 1. Kerwin, W.J., R,M. Munoz, and J.M. Prucha, Proceedings of the IEEE 17th Annual National Aerospace Electronics Conference, Dayton, Ohio (1965) P* 73 2. Munoz, Ro, "The Ames Magnetometer," 1966 National Telemetering Conference Proceedings 3. Sonett, C.P., "Modulation and Sampling of HydromagneticWaves," COSPAR-URSI Meeting, Buenos Aires,May 1965 4. Deaver, Jr., B.S. and W.S. Goree, "Some Techniques for Sensitive Magnetic Measurements Using Superconducting Circuitsand Magnetic Shields," Rev. Sci. Tnstr. 38, 311(1967) 5. Clarke, J., "A Superconducting Galvanometer Bnploying Josephson Tunneling, Phil. Mag. 13J ll5 (1966) 6. Goree, W.S., Progress Report No. 13 on Contract NAS 2-2088, submitted by SRI to NASA-Ames, August23, 1965, NASA CR 73156, 1965 7. Goree, W.S., Cryogenic Magnetometer Development, Midterm Report- October 1965 on Contract NAS 2-2088, submitted by SRI to NASA-Ames, NASA CR 731-57, 1965 8. Goree, W.S. and Troy W. Barbee, Jr., "Sensitive Instruments Using Superconducting Properties," paper presentedat the International Cryogenic Engineering Conference, Kyoto, Japan,April 10-14, 1967. Conference proceedingsto be published 9. Jaklevic, R.C., J. Lambe, A.H. Silver, and J.E. Mercereau, "Quantum Interference Effectsin Josephson Tunneling," Phys. Rev. Letters 12, 159(1964) and "Quantum Interferencefrom a Static Vector Poten- tial in a Field-Free Region," ibid. g,274 (1964); J.E. Zimmerman and J.E. Mercereau, "Quantized Flux Pinning in Superconducting Niobium," ibid. Q,125 (1964) 10. Langenberg, D.N., D.J. Scalapino, and B.N. Taylor, "Josephson Effects," sei. her. 214, 30 (1966) 61 It 11 I Anderson, P.W., The Josephson Effect and Quantum Coherence Measure- ments in Superconductorsand Super Fluids," to be published in Progress in Low Temperature Physics, ed. , C.J. Gorter 12 Forgacs, R.L. and A. Warnick, "Lock-on Magnetometer Utilizing Super- conducting Sensors,It IEEE Trans. on Instr. and Measurement IM-5, 113 (1966) Vant-Hull, L.L. and J.E. Mercereau, "Magnetic Shielding by a Super- conducting Cylinder," Rev. Sci. Instr. 34, 1238 (1963) 14. Hildebrandt , A .F., private communication 15. Hildebrandt, A.F., "The Attainment of Zero Magnetic Field ina Super- conducting Lead Shield," paper presented at the Symposium on the Physics of Superconducting Devices, Univ. of Virginia, April 1967, to be published 16. Deaver, Jr., B.S. and William M. Fairbank, "Quantized Magnetic Flux in Superconducting Cylinders," Proceedings of the Eighth International Conference on Low TemperaturePhysics, R.D. Davies, ed.(Butterworths Scientific Publications, Washington, 1963) p .116 17. Deaver, Jr., B.S., "Experimental Evidence for Quantized Magnetic Flux in Superconducting Cylinders,If PhD thesis,Stanford University, 1962, p.17 18. Johnson, A.K. and P.M. Chirlian, "The Cryotron as an Ultra-Low-Noise Amplifier, Elimination of Excessive CryotronNoise," IEEE Trans. on Magnetics MAG-2, 390 (1966) 19. Kwiram, A. and B.S. Deaver, Jr., "Observations of the Establishment of the Quantized Flux State in Times as Short as Sec," Phys. Rev. Letters l.3, 189 (1964) 20. Pierce, J.M., "A Persistent-Current Magnetometer with Novel Appli- cations," paper presented at the Symposium on the Physicsof Super- conducting Devices, Univ. of Virginia, April 1967, to be published 21. Kingery, W.D.,Introduction to Ceramics, John Wiley and Sons, Inc., New York, 1960, .213 p 22. Holderman, L., Stanford University, private communication 23. Zimmerman, J.E.and A.H. Silver, "Macroscopic Quantum Interference Effects through Superconducting PointContacts," Phys. Rev. -141, 367 (1966) 62 24, BgSorbo, W, , "Preaemion of Flux in Superconducting Indium,"Phil, Mag, -11, $53 (1065) 28. boalapino, D.J., "Current Fluatuatione in Superconducting Tunnel dunetione ,I' and R,E. burgem , "Quantization and Fluctuations in L3llpe~ootldtlot~r~,'~prerrented at Symposium on the Phyeice of Super- oondueting DeviaciB, Univ. of Virginia, Charlottesville, April 1967, Breaeedingr to be publitlhed 27. Bmefrrky, W. and M. Phillipe, "Claseical Electricity and Magnetism," AddiuOn-WeBley PubLiBhing Co., 1956, p.182 28, A Compendium of the Properties of Materiale at Low Temperatures, Pham I, Part 2: Properties of Solids, October 1960, AD #249786 and Part 11: Properties of Fluids, Solids, and Electrical Resistivity of Metallic Elements at Low Temperatures, December 1961, AD #272769 63