Download - Detection coil design for a high Information rate Earths field nuclear precession magnetometer

8/13/2019 Detection coil design for a high Information rate Earths field nuclear precession magnetometer

1/168

A HIGH INFORMATIONRATE EARTH'S FIELD NUCLEAR

MAGNETOMETER

Richard S. Gardiner


2/168

[E SCHOOL


3/168


4/168


5/168

DETECTION COIL DESIGN FOR A HIGH INFORMATION RATEEARTH'S FIELD NUCLEAR PRECESSION MAGNETOMETER

by

Richard S. GardinerLieutenant, United States Navy-

Submitted in partial fulfillmentof the requirementsfor the degree ofMASTER OF SCIENCEIN

ENGINEERING ELECTRONICS

United States Naval Postgraduate SchoolMonterey, California

1956


6/168

Thesis


7/168

This work is accepted as fulfillingthe thesis requirements for the degree of

MASTER OF SCIENCEIN

ENGINEERING ELECTRONICS

from theUnited States Naval Postgraduate School


8/168


9/168

PREFACE

This paper describes the detection coil design andconstruction involved in making an earth's field magneto-meter which has substantially a continuous informationrate. Background information concerning the protonfree precession magnetometer is supplied and the testresults of the high information rate system are presented

The authur worked on this project in conjunctionwith Lieutenant Grover M. Yowell at Varian Associates,Palo Alto, California, in the early months of 1956.

The author wishes to thank Varian Associates,Dr. Martin Packard, and all the members of the InstrumentDivision whose cooperation made the accomplishment ofthis project possible.

ii


10/168


11/168

TABLE OF CONTENTS

Item Title Page

Chapter IChapter IIChapter IIIChapter IVChapter VChapter VIChapter VIIChapter VIIIBibliography

Introduction 1Nuclear Magnetic Resonance .... 6Free Precession Magnetometer ... 17Coil Design and Construction ... 28Coil Field Measurements 45System Design 58System Test 61Conclusion 69

72

iii


12/168


13/168

LIST OF ILLUSTRATIONS

Figure Page2-1 Proton Alignment in Steady Field 92-2 Proton Precession in Suddenly Applied Field 92-3 Nuclear Magnetic Resonance Apparatus 102-4 v mode Signal 122-5 u mode Signal 122-6 Portion of Ethyl Aloohol Spectrum 123-1 Free Precession Signal 203-2 Station Magnetometer Block Diagram 213-3 Station Magnetometer 223-4 Polarizing Coils and Sample 243-5 Station Magnetometer Record 274-1 Magnetic Field from a Straight Wire 324-2 Magnetic Field from Two Straight Wires 324-3 Components of Double Solenoidal Coil 384-4 Assembled Double Solenoid 394-5 Toroidal Coil 435-1 Field Measurements Using Station Magnetometer 465-2 10,000 Turn Pick Up Coil 475-3 External Magnetic Field Intensity of DoubleSolenoid 1 , 505-4 External Magnetic Field Intensity of DoubleSolenoid 2 515-5 External Magnetic Field Intensity of Double

Solenoid 3 52iv

>


14/168


15/168

LIST OF ILLUSTRATIONSContinued

Figure Page5-6 External Magnetic Field Intensity of Toroidal

Coil 1 535-7 External Magnetic Field Intensity of ToroidalCoil 2 545-8 External Magnetic Field Intensity of ToroidalCoil 3 556-1 Dual Coil System Simplified Block Diagram 597-1 Double Solenoid Arrangement for System Test 627-2 Noise Induced Fluctuations 637-3 Data Presentation 1 667-4 Data Presentation 2 677-5 Data Presentation 3 . 68


16/168


17/168

CHAPTER IINTRODUCTION

The measurement of the earth's magnetic field has beenof interest to scientists and navigators for many years.More recently such data has become useful to geophysicistsand to the military. Field measurements have been madewith compass needles, earth inductors (1), saturable coredevices (2), (3), electron beam deflection tubes (4),electron paramagnetic resonance (5), and by free precessionnuclear magnetometers (6). The type to be discussed inthis paper uses the free precession of protons as describedby Bowen (7) and by Bacon (8).

The free precession magnetometer uses a strong,100 oersted, magnetic field to polarize the nuclear momentsthus creating a large value of magnetization in the samplevolume. This strong field is suddenly turned off.

tAt

this time the nuclear magnetization vector is forced bythe torque of the earth 1 s field and the intrinsic spinangular momentum of the nucleli to precess about the earth'sfield vector. The frequency of precession is directlyproportional to the magnitude of the earth's field. Theseprecessing nuclear moments induce an exponentially decayingsignal in a detection coil surrounding the sample. Thissignal is amplified and its frequency determined in order

to establish the value of the earth's field.1


18/168


19/168

The free precession system has a limitation in therate at which measurements can be made. The sample mustbe polarized with a steady magnetic field of about 100oersteds for a time on the order of one second. Followingthis there is a frequency count time which consumes anothersecond. With careful design the entire cycle can be com-pleted in only one second but with a sacrifice in accuracy.Thus the data, rate is limited to once per second. Foraerial prospecting where the velocity over the terrain iseasily 100 yards per second a more continuous flow ofinformation is desirable for detailed mapping. Another usefor a high information rate would be upper atmospheremeasurements by rockets where the entire time of flightfor several hundred miles may be only a few minutes.

One answer to obtaining a higher data rate is to usetwo systems and time share their outputs in the recordingor display device. To do this two major things must beaccomplished. First, two systems must be married by aproper timing cycle and the dual information presented insuitable form. Second, the polarizing and signal coilof each system must be magnetically isolated from thatof the other. Each system has one coil which serves bothto polarize and to detect the signal. The isolation isessential since the polarizing field of 100 oersteds atone coil must not affect the earth's field of one-halfoersted at the other coil. This is so because one coil will

2


20/168


21/168

be detecting a signal at the same time the other is beingpolarized, A distance of four feet was selected as thecoil separation distance with a view that the system shouldeventually be airborne and probably towed in a bird . Thispaper is primarily concerned with the coil designs and methodsinvestigated for isolating them.

Suoh a dual system was successfully demonstrated usinga double concentric solenoid type coil for each system. Thetiming cycle was obtained from the binary counters in thefrequency determining elements of a standard magnetometer.The system is described in some detail in Chapter VI andmore completely by Yowell (14).

The units of measurement employed for magnetio fieldsare often puzzling even to those working currently in thefield. Therefore, the following comments seem in order. Thegeophysioists and most workers in magnetism have found itconvenient to use the electromagnetic units (emu) the chiefvalue of which is that the permeability of free space is onegauss/oersted. Therefore numerically the magnetic inductionB equals the magnetic field intensity H in free space andfor practical purposes in air. At the International Conferenceon Physios, London meeting of 1934, it was decided to call Hby the name oersted and B by the name gauss. Gauss was formerlyused for the field strength H. The acceptance of oersted


22/168


23/168

has been somewhat less than overwhelming. Consequently, gaussis still used frequently in the literature for H. Geophysi-oists have found it convenient to define a unit of magnetic

field strength called the gamma which is 105

oersteds. Theearth's field is thus nominally one-half oersted or 50,000gamma. The gamma is convenient because the diurnal variationof the earth's field is on the order of a few tens of gammas.

The emu system is based on the idea of a unit magneticpole. H is measured in oersteds where each oersted representsa dyne of force acting on a unit pole placed at the point offield measurement. In the meter kilogram second system H ismeasured in units called ampere turns per meter. This pointsout the fundamental observed fact that a loop of steadycurrent exhibits the same properties as the pole of apermanent magnet. In the mks system the permeability offree space is 4 IT x 10 7 henrys per meter.

In what follows both mks and emu units will be used inequations and suoh will be noted in the margin if ambiguityis possible. The following conversion table should behelpful in accounting for the 4 7T's and powers of ten whichare always cropping up in magnetio problems.


24/168


25/168

TABLE I

For measurements of the same physical quantity thevalue in either the mks or emu system would be as indicatedbelow:

SAME SYMBOL MKS UNIT EMU UNITLENGTH I 1 METER 102 CENTIMETERMASS M 1 KILOGRAM 103 GRAMSTIME t 1 SECOND 1 SEC ONDFORCE F 1 NEWTON 105 DYNESWORK W 1 JOULE 107 ERGSPOWER P 1 WATT 10 7 ERG/ SECONDELECTRIC CHARGE a 1 COULOMB lO 1 ABCOULOMBEMF, POTENTIAL # V 1 VOLT 108 ABVOLTSCURRENT I 1 AMPERE 10 1 ABAMPERESRESISTANCE R 1 OHM 910 ABOHMSCAPACITANCE C 1 FARAD 10~ 9 ABFARADSMAGNETIC CHARGE m 1 WEBER 108'47fUNIT POLEMAGNETIC DIPOLE-MOMENT m 1 WEBER- METER 10 10Mjr POLE-CMMAGNETIZATION M 1 WEBER/ S^, MTR 104 '47T POLE/SQ.CMMAGNETIC FIELD-INTENSITY H 1 aMP. TURNSi/MTR 4TTX10~3 OERSTEDPERMEABILITY /> 47TX10 7 HENRYS/MTR 1 GAUSS/OERSTEDINDUCTION B 1 WEBER/SQ.,MTR 104 GAUSSINDUCTION FLUX ? 1 WEBER 108 MAXWELLSINDUCTANCE L 1 HENRY 10 9 ABHENRYS


26/168


27/168

CHAPTER IINUCLEAR MAGNETIC RESONANCE

1. TheoryNuclear magnetic resonance (NMR) measurements may be

possible for nuoleii which possess a finite magnetic moment^and an angular momentum a. a. is usually expressed as a spinI according to the relation a- = I h/2TT 2-1 emuwhere h is Planck's constant 6.6234 x 10~27 erg-sec.I may have integral or half integral values. The value ofthe proton spin is l/2. For raagnetio field measurementsthe proton is usually ohosen as the nuclear particle touse. It has a comparatively large gyromagnetic ratiofy ~ l yfl/l ap\ 2-2 emu( ju and a. are either parallel or anti-parallel) whichmakes possible a highly accurate measurement of the pre-cession frequency. The precession frequency is given bythe relation CO n tfp H 2-3 emuElectron paramagnetic resonance has been used for earth'sfield measurements but its accuracy is limited by itsbroad line width of approximately 2000 gamma (5).

The national Bureau of Standards has measured Yp to anaoouracy of one part in 40,000 as (2.67528 .00006) x 104seconds * 1 oersteds 1 . Thus, since Yp Is known, a fieldcan be accurately and absolutely measured by making afrequenoy measurement and using the relation of equation2-3: H = 2TTf/*p = 2.3486 x 10-4f(ops) 2-4 emu

6


28/168


29/168

To exhibit proton resonance it is necessary to have asupply of hydrogen to provide the protons. Water is aconvenient source. The sample is placed in a large magnetic

field H Q , say, 10,000 oersteds. As a simple model itcan be assumed that each proton will align its magneticmoment axis either with or against the field. There is afinite energy difference W between the two positions and thisenergy is absorbed or given up during a transition from align-ment with the field to against the field or vice versa. Thisenergy is equal to the torque exerted by the magnetic fieldon the magnetic moment of the proton times the angle throughwhich it is rotated, namely TK It is apparent fromfigure 2-1 that the torque is not constant but varies assin S where Q is the angle between the field H and theaxis of the proton. Consequently:W =. f \\ yjp / Ode = l/ip Wo 2-5 emu

From quantum theory it is known that energy is absorbedor radiated in discrete amounts equal to hf where f is thefrequency of the radiant energy and h is Planck f s constant.Thus W must equal hf = ZlSLyUp or H = ht/Z/fp sl^f^:^, 2-3 emuGeneralized to H = Ihi/u this equation describes NMR for allparticles when I and u are those of the particle Undercons ideration.

As another approach to NMR consider a sample of waterwhich is in no external field. If an external field His suddenly applied consider the motion of one of the randomly


30/168


31/168

distributed protons whioh make an angle Q with H$ Sincethe proton possesses angular momentum a and a magneticmoment/W ; H will exert a torque on the proton as shown infigure 2-2. Torque iB equal to the rate of change of angularmomentum. Therefore:^ /UfHo Si*& The vector * is ^ .Thus |^ =2Tr{c*S.^^/0 |+o S^a Consequently HQ ^2> = /x>ewhich is equation 2-3 again. It must be pointed out thatthe resonance frequency is independent of the angle .

2. Experimental methodsThe techniques for detecting the WMR signal are

historically two. The Harvard group headed by Furcell useda bridge comparison technique to detect the ohange in Q, ofa Gravity containing protons when the resonant frequency wasapplied (10) (11). The Stanford method of nuclear induction,directed by Bloch, used the protons to couple energy froman applied radio frequency field coil to a pick up coilwhich were otherwise essentially decoupled (12).

In the nuclear induction method a 10,000 oerstedfield H is applied to the sample in the Z direction andthen swept a few oersteds by a 60 cycle line voltage (13).As shown in figure 2-3 a radio frequency field 2H_oos6o tat 42.5 megacycles is applied by small coils in the Xdireotion. A pick up coil solenoidal around the sample

8


32/168


33/168

Ho

eX p an\ /ip

/ /Figure 2-1

Proton Alignment i# Steady Field

Figure 2-2Proton Precession in Suddenly applied Field


34/168


35/168

Q9a

04

+3CO

CO8rHOPS5

I

ob

-o

cc


36/168


37/168

with axis in the Y direction is connected to a narrowband preamplifier followed by a homodyne receiver. Theoutput of this receiver is placed on the Y input of anoscilloscope and the 60 cycle modulation on the X input.The local oscillator signal for the homodyne receiver issupplied by a leakage signal from the transmitter coil tothe receiver coil. The phase of the leakage is adjusted bymeans of copper and carbon paddles which steer the leakageflux through the pick up coil.

As the H field is swept through the precise value ofresonance it is possible to have displayed one of two typesof signals. These signals correspond to the proton inducedvoltage which is either in phase or in quadrature with theapplied radio frequency signal. Bloch (12) describes theseas the v and u modes corresponding to the magnetizationcomponents in a rotating coordinate system. Figure 2-4shows a v mode signal and figure 2-5 a u mode signal.The sensitivity associated with detecting either signalis the same. Usually the symetric or TTv mode is displayedin NMR spectroscopy work. Figure 2-6 shows a portion ofthe ethyl alcohol spectrum. The field difference betweenthe major peaks is a few milli-oersteds.

3. Signal VoltageThe NMR signal is not induced by all the protons in

the sample but rather only from the net difference betweenthose turning to the lower energy state and those turning

11


38/168


39/168

'V Mode SignalFigure 2-4

u Mode SignalFigure 2-5

Portion of Ethyl Aloohol SpectrumFigure 2-6

12


40/168


41/168

to the higher energy state. This fractional difference isgiven by the Maxwell-Boltzmann law for the particle distribu-tion according to energy levels. Let n* and nh representthe number of low and high proton energy levels and 2/^Hbe the difference in energy as given by equation 2-5. Thenn nn exp (2/^H/KT) 2-6 emuSince there are 6.686 x 102 ^ protons in one cubic centimeterof water n n + nh * 6.686 x 1022 . Solve these two equationsfor the difference n^ -n^. Assume the following valuesfor the parameters:

yuf -LH-IKIO' ergs/oersted Ho~ /0> oo oersteds/C -/,32x/o ergs/degree Kelvin ' - ^ 00 Kelvin

Therefore: ^f> H*/KT = &-Wo ^


42/168


43/168

time derivative of the Y component of the magnetization.4* ^t: -5^- abvolts 2-9 emu

N * number of turns in the ooil and A is the sampleoross section taken perpendicular to the coil axis.M Alp Si* Hitn*'~ U+S-y* 2-10

2-11

H is the applied steady field modulated by the 60 cyclesweep. Hr tv/ty Hrf = 2^008 OJt: defines theapplied radio frequency field. Bloch (12) shows thissolution for 1^ is valid when 60 and H vary adiabatically fthat is when ||~|


44/168


45/168

4. Signal to noise ratioThe thermal noise voltage from the resistance in the

detection ooil is:

Taking the ratio of the peak voltages gives:cy - LCZ^f/VA^ 2 Ho* *\f* 2 _ 18

5. Relaxation timesAnother .aspect of the NMR picture is the matter of

relaxation times. Before the application of a magneticfield the populations are equal in the two levels but theapplication of HQ must result in a net unbalance in favorof the lower energy level. This unbalance builds up untilan equilibrium is reached between the rate of absorptionof energy by the protons and the rate at which they are ableto transfer their energy to the thermal reservoir. Thereservoir is comprised of the other motional degrees offreedom of the particles comprising the sample. The expon-ential rate at which this equilibrium condition is reachedis characterized by a time constant T.. . The thermalreservoir is often referred to as the lattice and T-, asthe spin-lattice or longitudinal relaxation time. T-^ mayvary from a few hundred micro-seconds to many secondsdepending on the nucleous and its environment.

There is also another relaxation time T2 the spin-spinor transverse relaxation time. This is caused by the effectof local fields at the proton existing beoause of theneighboring protons. The same observed effect is also


46/168


47/168

caused by inhomogenieties of the H field. This is apparentfrom equation 2-3: CO^Yft . If H is not everywhere the samein the sample there will be a frequency distribution about6^0 s *X H . The time for these individual precessionvectors to spread out so the signal has dropped to 37$is Tg. For protons in water T


48/168


49/168

CHAPTER IIIFREE PRECESSION MAGNETOMETER

1# Need for free precession magnetometerThe free preoession magnetometer is necessary for

measuring low fields because an NMR technique as describedabove is not practical. The signal to noise ratio availableis the primary limitation.

Using equation 2-18 and the typical detection coilparameter values given below results in:

S/N s 10 H 2N = 500 turns R = 2 ohmsA 100 square centimeters B 50 cycles

Since H is the earth*s field and is only one-half oerstedthe resulting signal to noise ratio is 2.5. According toYowell (14) for a signal to noise ratio of ten to one therms error for a one second oount time would be one-tenthgamma. For a one- tenth second oount time it would be fivegamma. In order that a system have an accuracy comparablewith other magnetometers the error should be about one-tenthgamma. It is apparent then that a one-tenth gamma accuracyand a one-tenth seoond data rate could not be achieved usingthe NMR technique.

2. Free precession magnetometerRussell Varian (6) oonoeived of a fundamentally simple

means of increasing the signal several hundred fold by17


50/168


51/168

using a large, 100 oersted, polarizing field whioh thencreated a magnetization roughly 200 times as large as theearth's field would do. In equation 2-18 H 2 can be replacedby HpHe representing the polarizing and the earth's fieldsrespectively. Consequently the signal to noise ratio becomes500 to one.

When this D.C. polarizing field is applied the magnet-ization increases in an exponential fashion with a timeconstant T,. The field is usually left on for one or moretime constants and then cut off by a critically dampingRC circuit. When the polarizing field has decayed to aboutten oersteds, roughly one-half ampere, the circuit isopened completely. The fast final turn off is^essential orelse the proton spins oan follow the decaying field and noobservable precession occurs.

At turn off the protons begin a precession about theearth's field and the coil terminals are now connected toa capacitor which tunes the coil to the frequency of theexpected signal. For the two kilocycle signal correspondingroughly to an earth's field of one-half oersted this signalwill build up in the resonant circuit with a time constant =QJu . For the normal Q of 80 this is 6.5 mill i-secondsThe signal itself will decay in an exponential fashion withthe characteristic time constant Tp. For water T^ is abouttwo seconds. Thus if the initial signal to noise ratio was500 to one and a count is made for two time constants thesignal to noise ratio at the end of the count will beS/N = 500C2 = 67


52/168


53/168

This Is well within limits for the prescribed accuracy ofone-tenth gamma. Figure 3-1 shows a free precession signal.

It has been assumed that the earth's field is always atright angles to the polarizing field for this provides themaximum signal. If the two fields were aligned parallelno signal would result. In fact the signal magnitude isproportional to the sine of the angle between the polarizingfield vector and the earth's field veotor.

The free precession magnetometer measures theearth's magnetic field by measuring the proton precessionfrequency. To do this there are basically two functions tobe performed. One is the polarizing of the sample and theother is the frequency determination. The frequency deter-mination could be made directly with a counter or on a beatfrequency basis with a standard oscillator. However, incounting there is always a possible error amounting to onecount. For example, a discrete counter could registereither 2000 cyoles or 2001 cycles but the actual frequencymight lie anywhere between these two numbers. Thus for atwo kilocycle signal there would be a one in 2000 error oran error of 25 gamma in an earth's field of 50,000 gamma.To reduce this error the two kilocycle signal is used togate a high frequency crystal driven counter. If thecrystal frequenoy is 500KC the least count error is reducedby a factor of 250 or to one-tenth gamma.

Figure 3-2 is a block diagram of the Varian V-4900station magnetometer. Figure 3-3 shows the packaging of

19


54/168


55/168

FIGURE 3-1 FREE PRECESSION SIGNAL

20


56/168


57/168

Station Magnetometer Blook DiagramFigure 3-2

21


58/168


59/168

j*V.i . V /

FIGURE 3-3


60/168


61/168

the magnetometer and figure 3-4 shows two of the detectioncoils, a brief description of the station magnetometerfollows.

The coil is wound with five layers of 97 turns eachon a 4.25 inch outside diameter coil form six inches long.The wire is #15 formvar coated. This results in aninductance of 15 millihenries and a Q, of 80 at two kilocyclesThere is a 75 foot twinax cable connecting the coil to thepolarizing relay.

The polarizing relay_ is a double pole double throw D.C.actuated type. Two contacts are necessary since the coilterminals are balanced to ground while one side of the polar-izing supply is grounded. The switch has an RC circuitacross it providing an overdamped current decay. When thepolarizing current has dropped to about one-tenth of itsoriginal value of five amperes the field has decreased toabout ten oersteds and a relay completely opens the circuit.To be effective the final turn off must occur in a time muchless than the period of the two kilocycle precession signal.Consequently the self resonant frequency of the coil shouldbe 20 kilocycles and preferably higher.

The detection coil is series tuned and transformercoupled to the first of four stages of audio amplification.Following amplification the signal is squared and fed tothe first of thirteen flip-flops comprising the signalcounter. When enabled by a signal from the timing cams

23

*


62/168


63/168

i

-J

OjQ

O)ZMa--cO


64/168


65/168

the binaries begin counting from their reset value. Thisreset value is not zero but effectively a negative numbercorresponding to 128 cycles of the signal. This eliminatesthe transient rise of the signal amplitude from the partwhich is counted. When the binaries reach zero the 500 KCgate opens beginning the count of the 500 KC oscillator signal.This gate is closed stopping the 500 KC count when the pre-cession frequency has completed 256, 512, 1024, 2048 or4096 cycles. The count interval is selected by switchingout successively the last five binary stages in the signalcounter.

The crystal oscillator is an electron coupled Pierceoscillat.or running at 100 KC. The output of this is amplifiedand multiplied by five in a second stage. This 500 KC signalactuates a squaring amplifier which is gated to the highspeed binary counters.

There are nine sets of binaries in the 500 KC counterso that a count of 2 9 or 512 is possible. At the end of thecount the bincry number is analogued as a DC voltage levelby varying the current through an analoging resistor. Thecurrent is varied by introducing any of nine differentcurrent paths through relays selected by the state of thebinaries. Only the last 512 cycles or fraction thereof inthe 500 KC count is recorded. If the signal count is madefor 2048 cycles of a 2000 cycle per second signal then thisis (2048/2000) 500,000 * 512,000 cycles. The record thenis made of only a fraction representing the last one thousandth

25


66/168


67/168

part of the count. Using H ZRf/ltp to determine the fieldcorresponding to a 2000 oycle per second signal givesH s 2 x ,23486 - .46792 oersteds. The recording rangerepresents a thousandth part of this or 46.8 gamma. By switch-ing out the last binary stage and doubling the analog resistorthe recorder sensitivity is increased to 23.4 gamma full scale.The most sensitive scale of 11.7 gammas is obtained by droppingthe last two binaries and again doubling the analog resistor.

The recorder is a standard Gr-10 graphic recorder made byVarian Associates. The plot is rectangular, full scale fiveinches, with a chart speed varying from 4 inches per minuteto four inches per hour. The analog voltage is only avail-able from the end of the count until the time of reset;therefore the recorder servo is supplied with power onlyduring this time.

The timing cam unit consists of a 60 rpm timing motorand five disc cams actuating micro-switches . The functionsperformed are actuating the polarize relay, triggering thesignal count gate, resetting both counters and turning onthe servo motors in the recorder.

Figure 3-5 shows a portion of a station magnetometerrecord.

26


68/168


69/168


70/168


71/168

CHAPTER IVCOIL DESIGN AND CONSTRUCTION

1. GeneralThe high information rate magnetometer requires that

the earth's field be measured at two points four feet apartusing essentially two station magnetometers and time sharingtheir outputs in the recorder. This means that to have anaoouracy on the order of one-tenth gamma the polarizingfield of one coil should not contribute more than one-tenthgamma in a vector addition to the earth's field at the othercoil. At first the problem seems easily solved by aligningthe residual field from the coil at right angles to theearth's field. However, this would do only for a stationarysystem or a moving system properly stabilized. To have tostabilize the system would sacrifice the most advantageousfeature of the free precession system. That is that themeasurement is independent of coil angular relation tothe earth's field vector.

The problem involved here has nothing to do with themutual coupling between the coils. The effect which mustbe reduced is the vector addition of the D C magnetic polar-izing field of one coil to the earth's field at the otheroo il. However, if there is a ripple in the polarizing powersupply then the mutual inductance will cause a ripple noisemodulation of the signal. Consequently low mutual isdesirable and is achieved as a natural result of solvingthe prj^ary problem.


72/168


73/168

2. Design Parameters and RestrictionsAny coil designed for this system should attempt to

obtain a high signal to noise ratio. Equation 2-18 givesthe signal to noise ratio and from this the parameterswhich influence coil design may be obtained.%v __ A //ArtK+0*S *M$z 4-1

Where H He has replaced HQ2 as explained before.Eliminating constants and factors which are not affectedby coil design results in:

Where: n (number of nuoleii) oC Volume -JiA


74/168


75/168

A better approach to coil design would be optimizingthe various parameters: wire size, coil length and diameter,and number of turns for maximum S/N ratio. This to be donegiven a prescribed volume, or weight or polarizing power.In airborne or rocket work all three of these restrictionswould be important. Since optimum coil design does notbear directly on producing a low external field coil itwill not be pursued further here.

Because the polarizing current turn off must be rapidthere is a very important restriction on the coil designrequiring that it have low distributed capacity. At leastit must be small enough so that its self resonant frequencyis 20 KC or greater. The exponential decay of the currentshould be rapid - at least a fractional millisecond timeconstant. The decay is more rapid the higher the resistanceof the coil. Consequently the signal to noise and the turnoff requirements are opposite in their demands on coilresistance.

Increasing the Q, of the coil will increase the signalto noise ratio. However, there is a practical limit imposedby the diurnal field fluctuations for a stationary systemor by the field contours traversed by a moving system. Ifthe Q, is 100 then the pass band at two KC is 20 cyclescorresponding to 500 gamma. A nominal value for the North-South gradient of the earth's field is five gammas per mile.Consequently an aircraft could easily fly beyond thetuning range provided by 20 cycles. For aircraft systems

30


76/168


77/168

automatic} frequency tuning by bands is essential. Thedual coil system discussed herein did not incorporatesuch tuning.

In order to reduce the field interaction between thetwo coils there are three adjustable variables. First, theseparation distance which has arbitrarily been taken asfour feet. Second, the polarizing current can be reducedthereby reducing the field. This is possible if the signalto noise ratio can be maintained high enough by other means.Third, by configuring each coil in a particular manner the

fexternal field can be minimized. Coil configuration is theprimary technique considered in the remainder of thischapter.

3. Magnetic Field CalculationsIn order to appreciate the magnitude of the values

in the coil design problem it is necessary to digress andsolve two magnetic field problems. First, the field from awire of finite length carrying a steady current is given by:H = i^rA-2 f ^m9ik From figure 4-1 4-1 mks9-7T J&

t^Jl. &

Therefore H -^=~z j Si*Q


78/168


79/168

Figure 4-1Magnetic field from a Straight Wire

H-ft

Figure 4-2Magnetic field from two Straight Wires

32


80/168


81/168

Thus, a current of one ampere in a single one inch leadoan cause a large field in relation to the one-tenth gammafield desired.

The second problem is to see what field results fromtwo such wires placed side by side but carrying current inopposite directions. Taking #14 wire which is .0641 inchesin diameter and using superposition, a figure eight patternresults which has a maximum in the plane containing thewires. This maximum is given by:H * JL cos ( 1 '22 - 1*22 \ 1.341x10 fn. &zrr oob^ ^1# 22 . .000815 T7ZZ .00081b) ~ ~TrfIn this case the interest is in the effect of the leadin cable to the coil. If its effective length is fourfeet then tan , = 2 and cos 0, * .446 and

-rH m Trr x ,446 x 1#34 x 103 = 9.51 x 10 5 amp- turns /meterr H s .119 I gammas. Consequently it is desirable tomake the leads coaxial as this will reduce the externalfield to zero.

4. Coil ConfigurationsA. Double Solenoid

There are several possible configurations toachieve a coil system which has a low external field. Asconfiguration that would achieve this is two solenoids,one inside the other. If the flux from each coil is thesame in magnitude but opposite in sign then the externalfield will be small. The residual field is due to thefact that the shape of the field is not quite the same

33


82/168


83/168

sinoe the coil sizes are different. The field at the centerof a long solenoid is given by H = NI/1 and thetotal flux by


84/168


85/168

If two flux balls are constructed and made concentricthen the coordinates (^ ;

, can be made equal to H^j. if Ho^z\\ a x 4-3A similiar requirement obtains for H_. Practically inorder to vary I y the number of turns is varied along thesurface of the sphere in accord with sine . If N is hereused for the turns per centimeter at the equator then tosatisfy equation 4-3 it is necessary that A/,


86/168


87/168

5. Double Solenoid Coil ConstructionA. Double Solenoid #1

The first ooil system constructed was a doubleconcentric solenoid. The coils were made so that theirmagnetic moments were equal by making /V,


88/168


89/168

was constructed with six layers on a three inch outsidediameter coil form and two layers on a five and 25/32 inchcoil form. Each layer was six inches long and had 88 turnsof number 14 formvar coated wire. Figures 4-3 and 4-4 showthe construction of this coil. The inductance of the coilwas 7.1 millihenries and the self resonant frequency was40 KC. The field from this coil was .36 gammas per ampereat a distance of four feet at a minimum point in the fieldpattern. Figures 5-3 to 5-5 show plots of the field compon-ents at points about the coil.

G. Source of SignalThe field plots have been given in gammas per

ampere because the polarizing current is a variable thatcan be changed to reduce the external field. Changing thecurrent will change the polarizing magnetization and therebythe signal to noise ratio. The integral of H over thesample volume is the best measure of the effective magnet-ization created by any coil configuration. For the doublesolenoid it is apparent that there are two volumes whichcan contribute to the signal: the inner volume and thevolume between the coils. The field is greatly reducedexternal to the two coils so this volume is neglected. Thecentral volume field is about 100 oersteds as the resultof the two fields bucking. The field between the coilsis the resultant of adding the outer coil field to theportion of the inner coil field that threads the spacebetween the coils. This field value is about 75 oersteds.

37


90/168


91/168

ooQ

8CO

s

E-W3O

3

38


92/168


93/168

.{ . ) (I ;; U |ll

i r > r * .- j r r r i r n : o I k i l \ v i '.i t i i: I : i i i I

Ufti 4-429


94/168


95/168

It is logical now to determine if the two sample volumescontribute signals which are in phase and thus enhancethe signal.

A double subscript notation is convenient to representthe various voltages induced. The first subscript willindicate the sample volume producing the signal and thesecond subsoript which coil it is induced in. Thus VAg isthe voltage induced in the outer coil (2) by the protonsin the inner sample (A). The protons are initially pro-cessing in planes parallel to a plane containing the centerline of the coils. Since the fields in the two volumes arein opposite directions and the coils are connected inseries opposing the following equation for the signalvoltage results: V - VA1 + vB1 + Y^2 - VA2 4_4Using both volumes results in a net signal gain over thesignal from the inner volume alone.

In order to use the outer annular volume it wasnecessary to insulate the windings from the water. Thisproved to be a difficult task. A commercial resin Epon ,was used to cover the coil. This proved unsatisfactoryas after a few days a leakage path of one magohm appearedbetween coil and water. Since the system required twodouble solenoids the second one was insulated with Eponand a liquid latex. This proved satisfactory for the shorttime tested. However, the final system tests were madeusing kerosene as a sample since it is an insulator.

40


96/168


97/168

6. Toroidal Coil ConstructionTo test the toroid idea a toroidal coil form was made

by joining two return U pieces of three inch diameterpyrex glass tubing into a circle. The wire was then rolledon by leaving the wire end free. Each layer was pulleddown tight and cemented with Epon before the next layerwas wound. The wire ends were welded together by thehell-arc process. The layers were wound back and forthrather than continuously around in order to avoid creatingcurrent loops around the torus.

If the radius of a section of the torus is a andthe distance from its center to the torus axis is b thenthe following formulas apply:Volume = Zir%c - 3-06% LitersH center s -~- = 15.1 I oerstedBI /*> A/*B>-(bx-cftS} 9.5 mh.fhAV = TTNo^I s 46 5*00 1 oersted - cm3The numerical values are those of the constructed fourlayer toroid having 856 turns. The integral of the H fieldover the volume is comparable to that of the stationmagnetometer coil nominal value of 40,000 I oersted-cm .The least field at four feet was two gammas per ampere.The Initial signal to noise ratio was 72 to one for a sixampere polarizing current and a 3.3 second polarize time.It is apparent that this coil will not produce the desiredlow field unless a much smaller ourrent is used.

In order to increase the signal to noise ratio two

41


98/168


99/168

more layers were added giving a total of 1270 turns.Figure 4-5 shows this coil. The inductance of this ooilwas 21.4 millihenries. The least field was three gammasper ampere at four feet. The signal to noise ratio was180. Thus there has been some gain since the externalfield has gone up only 50$ while the signal to noiseratio has increased by 150$. Consequently less polarizingcurrent can be used for the same signal to noise ratioand thereby the external field is reduced.

This six layer toroid had one major drawbaok. Itsdistributed capacitance was high. The ring frequency was13 KC and the decay time constant was long - one milli-second. The effect of this was to oause an erratic polar-izing current turn off. This was evidenced by a large(25$) fluctuation in the initial amplitude of the signal.

i

The toroid did not have as low an external fieldas the double solenoid so it was not used in the systemtest. A toroid wound on a form which did not have such alarge torus diameter as three inches would have lesswinding error and more closely approximate an ideal toroid.Sample volume would be sacrificed but for a given ourrentthe external field should be less.

7. Lead in CablesTo minimize the lead in cable field a double coaxial

cable was constructed by sliding a one-half inch braid overa standard RG-58/U coaxial cable. The center wire and theinner coax carry the polarizing ourrent and the outer braidis tied to the Faraday shield around the coil.


100/168


101/168


102/168


103/168

In dealing with cables it can be pointed out thatsome cables available have steel strands in them for strengthand care must be taken not to use these. Even this smallamount of magnetic material near the coil will cause fieldinhoraogenieties that can measurably reduce the observed Tp.

44


104/168


105/168

CHAPTER VCOIL FIELD MEASUREMENTS

1, Measurement MethodsThe magnetic field about the constructed coils had

to be determined. The primary method used was to pass a400 cycle current through the magnetometer coil and thenmeasure the induced voltage in a small 10,000 turn pick upcoil placed at a measurement point, As a check on thismeasurement a standard station magnetometer was used.The magnetometer recorded the change in field occur ingwhen a known DC current was passed through the low fieldcoil placed in proximity to the station magnetometer coil.Figure 5-1 shows an example of one of these measurements.

2. Pick up Coil CalibrationThe 10,000 turn pick up coil was wound on a two inch

diameter split ring brass coil form as shown in figure 5-2.The depth of winding was .625 inches. Using a formulasuggested by Frowe (16)

a (eff)s [ao+a^Wj^the effective radius of the coil was .0337 meters.The voltage induced is then:Vs Hjf =A/FcL-d& -/VircL^cuHcc^Lot 5-1 mksWhere H sinujt is the uniform field threading the coilat right angles to the plane of the coil.V * Nrra^aTr-fH = )o*TT(.o337)\7rto 72nf H - a.32f Hi6 ^ 5.2 mksWhere V is in volts and H is in ampere turns per meter.


106/168


107/168

T^T l- i ' ,l, .L, ili(ittFitii i

Figure 5-1

Fiela Measurements Usin - . t-. tion i ;netorieter

46


108/168


109/168

.

-* -c

o

M

8

CVJI


110/168


111/168

Converting to oersteds results in:V volts = 3. $ H0*iM = -2^^^VHflmteis 5-3H oersteds s iHL-L * Yvoits 5-4TH gamma - t^9. y. Vmillivolts 5. 5

To verify this calibration a pair of Helmholtz coilsof 17 inch radius and 17 inch separation were used toexperimentally calibrate the pick up coil. *McComb (1), page 132, gives the following convenientformula for the field at the center of a Helmholtz pair.

H = 89.9 N I 5 _ 6Where H is in gamma, I is in milliamperes , a is thecoil radius and separation in centimeters and N is thenumber of turns on each coil.

The pick up coil was placed at the center of andparallel to the Helmholtz pair. A 400 cycle current of afew milliamperes was sent through the Helmholtz coils andthe output voltage of the pick up coil measured. The meanof several measurements gave 3.27 millivolts induced in thepick up coil for each milliampere of current in the Helmholtzcoils. Using equation 5-6 and the values of the particularHelmholtz pair results in:H gpmma * 35.4 IM J>^ W * 10.84 W 5-7This is at 400 cycles. The voltage induced is directlyproportional to the frequency consequently:H gamma 10.84 x 400 Vmv 4340 mv_ 5. 8f f-

48


112/168


113/168

This compares within 3$ of the value given by equation 5-5.Experimental error in this calibration was approximately 2$.

3. Field MeasurementsThe field plots of the various coils as shown in

figures 5-3 to 5-8 were made using the 10,000 turn pick upcoil connected by a coaxial oable to a Hewlett Packard 400Dvoltmeter. With this arrangement the normal noise voltagewas ,04 millivolts rms corresponding to .447 rms gamma byequation 5-8. This indicates that a one gamma field couldbe measured and the error due to noise would be 10$.

There are two ways to increase the signal to noiseratio so that measurements of lower fields are possible.The first is to increase the current in the coil. An 110volt 400 cycle power supply was used. For the doublesolenoid this gave a current of 6.2 rms amperes and 2.06rms amperes for the six layer toroid. For most of themeasurements out to four feet this was adequate. A secondmethod to increase sensitivity is to take the output ofthe voltmeter and feed it to a 400 cycle band pass filterand present this on an oscilloscope. By this means a one-tenth gamma measurement was possible. Since the radialfall off of the field was in general of the form H = Kr xit was possible to make measurements at three feet andcalculate the value at four feet.

The field components were measured in cylindricalcoordinate fashion by placing the pick up coil so the -o;f or Z coordinate vector would thread the coil. The

49


114/168


115/168

Scale:1 inch - .23> gamma/ampere

V

*

Components measuredin X-Y plane atradius of k feet

2 70

K

K0-jI-Of --+- I ' V . -fI 4- I | r&- 70/ Vfc. \ (TOmmfl /amnaicgamma/ampere

//

Figure 5-3/SO c

External Magnetic Field Intensity of Double Solenoid 1


116/168


117/168

Scale:1 inch - 1

Xcomponents measuredin X-Y plane atradius of h feet

/ _


118/168


119/168

/Oo

Jfo

10

v H. That such a substance may exist is by nomeans a certainty.

Another possibility of enhancing the signal is tosynchronize the polarizing current turn on so as to catchthe remaining polarization at the end of the count period.This would allow the polarization to build up to a highervalue for a given polarize time. That such a techniquewas feasible was demonstrated but not incorporated inthe system.


156/168


157/168

The coils designed and used demonstrated primarilythat it is possible to operate two detection systems inclose proximity. The gradient of the external field acrossthe signal coil does not appreciably reduce T2 and readingsare therefore possible.

To further reduce the external field effect the coilsoan be separated a greater distance. For example, separatingthe double solenoids by six feet would reduce the externalfield to .1 gammas per ampere.

To improve the low external field coil design thefollowing should be considered, A toroid constructed witha large overall diameter (12 inches or greater) but a smalltorus diameter (one inch) would greatly roduoe windingerrors, A system of field compensation using Helmholtzcoils could be used. A flux ball construction could betried.

71


158/168


159/168


160/168


161/168

BIBLIOGRAPHY (oontd.

11. Bloembergen, N.Puree 11, E. M,Pound, R. V.12. Bloch, F.

13. Bloch, F.Hansen, W. W.Packard, M.14. Yowell, G. M.

15. Blewett, J. P.

16. Frowe, E. W.Aronson, C. J.

RELAXATION EFFECTS IN NUCLEARMAGNETIC RESONANCE ABSORPTIONPHYSICAL REVIEW 73, p 679, April 1948NUCLEAR INDUCTION. PHYSICAL REVIEWVol. 70, p 460, Oct. 1946THE NUCLEAR INDUCTION EXPERIMENTPHYSICAL REVIEW Vol. 70, p 474,Oct. 1946HIGH DATA RATE FREE PRECESSIONMAGNETOMETER, THESIS USNPGS 1956MAGNETIC FIELD CONFIGURATIONSDUE TO AIR CORE COILS. JOURNALAPPLIED PHYSICS Vol. 18, 1947,pp 968-982DOUBLE SOLENOID SYSTEM FORMAGNETIC MEASUREMENTS. JOURNALOF APPLIED PHYSICS Vol. 16,Nov. 1945, pp '667-669

73


162/168


163/168


164/168


165/168


166/168


167/168

FEI958 53 1 2JA2760 5308,i.-_ b4 13 17]

TKesii rto^iG184 GardinerDetection coil design fora high information rateearth's field nuclear pre-cession magnetometer.

F E I 9 : 5 *, \ 2J A 27 60 :5 3 8S 22 64 13 17 1

GF184 GaxrAiner Q.Detection coil design fpr.ahigh xnforma.tion rate^arth'sfield nuclear precession magneto-meter.


168/168

thesG184coil design for a high interna

3 2768 002 01045 6DUDLEY KNOX LIBRARY

Download - Detection coil design for a high Information rate Earths field nuclear precession magnetometer

Top Related