IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-34, NO. 2, JUNE 1985
testing for systematic effects before obtaining final results.Ultimately we hope to obtain a value of Ypy(low)NBS with anuncertainty of 0.05 ppm or less, which should yield a value ofa with an uncertainty of about 0.02 ppm.
ACKNOWLEDGMENT
The authors would like to thank E. Muth and D. Trammellfor their dedication in helping to construct the solenoid; H.Layer who calibrated the laser; G. Barrett who helped analyzedata; K. Maruyama, an NBS Guest Scientist from the TokyoInstitute of Technology, Japan, who designed the injectorprobe, and F. Fickett, of NBS/Boulder, for measuring the sus-ceptibility of the solenoid form material.
REFERENCES
[1] E. R. Williams and P. T. Olsen, "New measurement of the protongyromagnetic ratio and a derived value of the fine-structure con-stant accurate to a part in 107," Phys. Rev. Lett., vol. 42, pp.1575-1579, June 1979.
[21 E. R. Williams, P. T. Olsen, and W. D. Phillips, "The proton gyro-magnetic ratio in H20-a problem in dimensional metrology," inPrecision Measurement and Fundamental Constants II, Natl. Bur.Stand. (U.S.), Spec. Publ. 617 (USGPO, Washington, DC), B. N.Taylor and W. D. Phillips, Eds., 1984, pp. 497-504.
[31 H. L. Curtis, C. Moon, and C. M. Sparks, "A determination of theabsolute Ohm, using an improved self inductor," J. Res. Natl. Bur.Stand., vol. 21, pp. 375-423, Oct. 1938, and private communica-tion with R. L. Driscoll.
[4] E. R. Williams and P. T. Olsen, "A noncontacting magnetic pickupprobe for measuring the pitch of a precision solenoid," IEEEPans. Instrum. Meas., vol. IM-21, pp. 376-379, Nov. 1972.
[5] H. P. Layer, "A portable iodine stabilized helium-neon laser,"IEEE Trans. Instrum. Meas., vol. IM-29, pp. 358-36 1, Dec. 1980.
First Results of the 'y, Experiment at the PTB
KURT WEYAND
Abstract-A zyp,low experiment based on a novel method of deter-mining the coil constant has yielded preliminary results. The coil con-stant is found by measuring the flux profile along the axis of the wind-ings. When the NMR experiment is performed in the free precessionmode, the value of yp amounts to '4 = 2.675 143 X 108 (± 3.4 X 10-6)T-1 * s-1 with a (1 a) uncertainty.
I. INTRODUCTIONT HE MOST important problem in carrying out a yp experi-
ment in low mangetic fields is to determine the value ofthe flux density acting on the NMR probe. Up to now the di-mensions of single-layer coils have been measured by mechani-cal and optical methods [11, [2], sometimes in combinationwith electromagnetic indicator systems [3], and from the re-sults of those measurements the flux density at the center ofthe field coil has been evaluated. Whatever procedure is used,in order to determine the diameter of these coils a comparisonwith an end gauge must be performed, and this may be an im-portant source of error. Added to this, even if the positions ofthe layer are well known, there is another source of error dueto the current distribution in the wire, which is influenced bythe wire's history and chiefly by the winding procedure.For this reason a novel method based on measuring the ef-
fect of current flowing in multilayer coils has been developedin order to find the coil constant of a system of coils, i.e., as it
Manuscript received August 20, 1984.The author is with the Physikalisch-Technische Bundesanstalt,
Bundesallee 100, D-3300 Braunschweig, Federal Republic of Germany.
I 1,(BzBo 7-'
Fig. 1. Method for determining the effective radius of a current loopby relative field measurement.
is understood here, the value of flux density at the center ofthe system as a function of the current through the coils.
II. DETERMINATION OF THE COIL CONSTANTThe principle of this method can be made clear by a simple
example. Assuming a single circular turn with radius 'r' asshown in Fig. 1 the flux density B5 along the z-axis is given by
B=i[1 + (z/r)2]3/2 .2r
(1)
Thus the only unknown geometric dimension 'r' may be evalu-ated by measuring the field Bo at the center and Bz at anyother point P on the axis of the turn at a distance z and byforming the field ratio Vz = Bo /Bz, giving:
ref=Z [V2/3 - 1]-1/2 (2)
where all B values may be measured in arbitrary units. Thus
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-34, NO. 2, JUNE 1985
Coil 4 Coil 2 Coil 1 Coil 3
1 1
0.8 -
6vbh1
6h2bV
-02
-0.4
Fig. 2. Functions of the relative partial derivatives of field ratios in atwo-package coil arrangement.
the flux density at the center can be obtained from the valueof reff, i.e.,
(3)2reff
This means that the somewhat problematic measurements of
the coil geometry may be replaced by measurements of field
ratios and mechanical displacements. As mathematical evalua-tion shows, comparatively large deviations from the ideal cir-
cular current path can be tolerated without producing errors
above 1 ppm.In order to achieve a central field strength high enough for
the yp experiment, a coil system made from discrete elements
should be used instead of a long single-layer solenoid. This is
because the most important information on the geometric di-
mensions is found near the point of inflexion of the relativeflux density profile, as may be seen in Fig. 2. The figure showsthe relative partial derivatives of the field ratio function for a
two-coil arrangement with a base diameter 2a = 31 cm, a mean
distance between coils = A I + A2 = a/2, a coil length 21 .4
cm and a coil height h 1.25 cm. The influence of the geo-
metric dimensions in the region near the point of inflexion on
the flux density function amounts to about twice that on the
coil constant. Thus if the flux profile along the axis of such a
coil system is calculated in terms of its as yet unknown dimen-sions and is measured in arbitrary units at a number of points,the comparison of the magnetometer readings with the calcu-lated profile yields a set of effective dimensions from whichthe coil constant may again be evaluated.As the one-pair winding coil system does not yield sufficient
homogeneity over the NMR sample volume, the new coil sys-
tem consists of two pairs of nominally identical coils, as shownin Fig. 3(a). All the coils are of the same nominal diameter(309.17 mm) and are wound between flanges on a cylinder offused silica. The flanges, which are made of glass fiber, are
2r =309,17
153,9 1 153,9
N4 = 2916 N2 = 1295 Nr 1295 N3- 2916
(a)
(b)Fig. 3. (a) Dimensions of the four-element field coil, and (b) measured
field profiles: 1) field generated by all coils, 2) field generated byboth the inner coils, AB = 2.5 nT.
glued carefully onto the cylinder to ensure coaxiality. Thenumber of turns, the length of the windings, and the mean dis-tances of the coils are so chosen that the coefficients of themagnetic scalar potential expressed in zonal harmonics vanishup to the seventh order. Because of the symmetrical arrange-ment of the coils the even terms vanish in any case; thus theinhomogeneity over a sphere the size of the NMR sample atthe center should theoretically be less than 10'7, while thecoil constant amounts to 17.5 mT/A [4].
Fig. 3(b) shows the measured flux density profiles in thecenter of the system generated by all four coils (curve 1) andgenerated by both inner coils (curve 2). Because of tolerancesin manufacture, the currents through the outer coils must beslightly different from those through the inner ones, given bythe ratios:
m3 = I3/IO = 1.000 393, m4 = I4/IO = 0.99 548
I1 =I2 =Io0
The scatter in plot 1 is due to temporal variation of noncom-pensated extraneous fields.
In order to measure the flux profiles produced by the coils,a pneumatic coil-carrying apparatus has been constructed asshown in Fig. 4. The translating device is made of glass fiberand consists of a piston 600 mm in diameter and 550 mm inlength inside of a cylindrical tube 1200 mm in length. Thesmall airgap of about 0.1 mm between piston and tube makespossible a linear motion with an angular deviation of not morethan 0.05°.Thus the coils carrying a current equal to that which it is in-
tended to use for the measurement of the precession fre-
168
WEYAND: THE P EXPERIMENT AT THE PTB
to data acquisition system
Fig. 4. Pneumatic field coil-displacing apparatus.
quency are moved in an axial direction past a SQUID probe.The magnetometer is a somewhat modified commercial typeusing a one-turn flux transformer coil, 6 mm in diameter, andthus giving a resolution of 0.003 nT. It is mounted inside a
special super-insulated Dewar, also made of glass fiber, whichrests on a triaxially adjustable slab, in order to align the probewith the magnetic axis of the field coils. During the motionthe flux linking the probe and the readings of a laser inter-ferometer are both recorded; this gives the relative displace-ment of coil former and probe.Two different measurements are necessary to determine
the coil constant of the whole system. First, the flux profileof the inner pair is recorded and from that record the set ofdimensional values is found, representing only the coil con-
stant of the inner pair. The total coil constant of the fourelements is then found by energizing the outer pair instead ofthe inner one and by comparing the flux produced at thecenter point with that produced by the inner pair. Fig. 5shows a block diagram of the flux profile measuring circuitand the schedule for one of the field-measuring procedures.The magnetometer readings are split into two parts; one partrepresents, by means of a digital flux counter, a value in termsof an integer multiple of the flux quantum 00, while the otherpart is an analog signal representing values less than 40. Thissignal is observed by a fast-acting sample-and-hold digital volt-meter, from which a command for recording is initiated bycomparing its output voltage with a predetermined value,when a preset number of flux quanta n ¢0 is encountered.Thus a record of correlated magnetometer and interferometerreadings will be obtained in almost constant steps of n 00/. Inthe range close to the center point, this recording mode ismodified; here, correlated readings are recorded in equidistantaxial steps.
data registration controlled by
AO-I(A) AOa¢I(Az) \
Z' ° : ' : ~~~~~z-2rthermal reset
Fig. 5. Block diagram of flux profile recording circuit and lapse of timeof such a procedure.
The current variation at the beginning and the end of a fieldprofile measurement, and the piston velocity during the mea-surement are controlled in such a way that the flux slew rateat the SQUID does not exceed 10 00/s. At the end of a mea-suring cycle the piston is again held in the start position andthe residual flux value acts as a first reliability test for the mea-suring run. If it exceeds 2 X 10-6, the flux value at the centerof the coil system, the measurement is discarded. The mea-sured flux values must be corrected for the size of the fluxtransformer. The correction function depends on the ratioof the radii of the flux transformer loop and of the field coil,and is proportional to the second derivative of the field func-tion; therefore, the correction factors do not exceed 100 ppm[5] .
III. SETUP OF THE NMR EXPERIMENTThe experiment is performed in the free precession mode
using water as a proton source, as is usual. The probe itself isa spherical sample, 4 cm in diameter, filled in an artificial N2atmosphere with tri-distilled water by means of a special dis-tilling apparatus [6].
Fig. 6(a) shows the block diagram of the signal-detecting cir-cuit while Fig. 6(b) displays the observed signal trace. On thestarting pulse, the control unit initiates the polarizing currentsource and after this, the burst oscillator for the RF-900 pulse.To avoid spikes, the polarizing current should not be switchedabruptly, but slowly controlled. Several milliseconds after dis-abling the burst oscillator the signal amplifying path is openedup and the precession signal is fed through a preamplifier act-ing as a line driver to a high-gain tuned amplifier. Its outputvoltage is mixed with the frequency fr from a synthesizer ina phase-sensitive detector PSD. fr is set several hertz lowerthan the expected signal frequency fo; thus the PSD acts as a
169
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-34, NO. 2, JUNE 1985
(a)
I
\I -A-A-AA
ls
(b)
Fig. 6. Block diagram of the precession signalobserved signal.
detecting circuit and
narrow-band filter. Its output signal, consisting of a frequencyfo fr, is fed through a low-frequency bandpass filter to a
transient recorder for observing the signal and to a computingcounter for measuring the difference frequency. As can be
seen in Fig. 6(b) the relaxation time T2 amounts to 2.2 s forthe observed precession signal, which shows a signal-to-noiseratio better than 50 for a bandwidth of 8 Hz.
IV. COMPENSATION OF THE EARTH'S MAGNETIC FIELD
All these experiments must be performed in magneticallyneutral surroundings to avoid errors in determining the actualmagnetic field strength during the measurements of the preces-sion frequency and of the field profile. A nonmagnetic build-
ing has, therefore, been erected about 300 m away from theother laboratories. Before construction was started, the ter-
rain was magnetically surveyed. A site was found where the
spatial gradient in the Earth's magnetic field showed a maxi-
mum value of about 0.25 nT/m. Alternating magnetic fields
at the site were found to be of the order of 4 nT peak-to-peakat 50 Hz and 0.5 nT at 150 Hz [7]. The site plan in Fig. 7
displays the equiflux density of the Earth's field vertical com-ponent (continuous lines) and the curves of equal 50-Hz fluxdensity in peak-to-peak values. The arrows indicate the direc-tion of the highest amplitudes.To compensate the Earth's magnetic field a large three-
dimensional Braunbek coil system has been constructed con-sisting of four octagonal coils in each direction [8], (seeFig. 8). By careful adjustment of the currents through thesecoils the main field in a spherical volume, 100 cm in diameter,at the center of the system, has been reduced to values of notmore than 1 nT. Variations in the Earth's magnetic field areobserved by means of a tri-axial flux gate magnetometer witha sensitivity of 100 mV/nT up to 0.3 Hz. The sensor is placedhalfway between the nonmagnetic building and an observationstation about 80 m away which contains all the electronicequipment. The variations are reduced by a factor of 20, bymeans of additional currents through the coils as shown inFig. 9. This figure shows the Earth's vertical field componentinside (trace b) and outside (trace a) the Braunbek coil system.Because of man-made noise during the day, all yP measure-ments were performed at night. The upper trace c is a recordof the temperature at the field coil.
V. RESULTSIn order to determine the coil constant of the field coil a
total of 12 field profile measurements was taken, five of whichproved to be of no use because of large residual flux values orpoints of inconstancy in the flux density profile. The resultsof the seven relevant measurements and their uncertainties areshown by Fig. 10 in chronological order. The error bars in-clude both the uncertainties of the field profile and of the fieldratio measurements, which are necessary to compare the fieldof the inner pair of coils with that of the outer pair. Thesemeasurements take considerably less time than the profilemeasurements, and are thus less affected by disturbing fields.The deviation from the mean value of a set of 10 ratio mea-surements seldom exceeds the 1-ppm level. The uncertaintiesgiven by Fig. 10 are, therefore, mainly related to the profilemeasurements. The large difference in the. uncertainties forthe different measuring runs is most probably due to two ef-fects: from time to time sporadic variations of the 50 Hz dis-turbing field have been observed, perhaps caused by reversalsof load on a high-voltage line about 800 m away or it may bethat the piston's velocity is not correctly controlled. Both ef-fects may lead to badly correlated magnetometer and inter-ferometer readings.The uncertainty of the profile measurement with the equip-
ment at present available had been estimated at 2 ppm. Ingeneral, values twice as high have been observed in the experi-ment. This may be due to a nonsymmetrical radial field pro-file caused by magnetic impurities in the coil former. Suchimpurity spots have been found experimentally. The temporaltrend in the coil constant is probably related to the aging ofthe winding elements.On the basis of the seven determinations the mean value of
the coil constant amounts to 17.85814 mT/A with a Io un-
170
WEYAND: THE p EXPERIMENT AT THE PTB
I I i
LLA.LLL.4~k
flllU "~
I * 7528
Fig. 7. Site plan of the measuring station, equiflux density curves ofthe Earth's vertical field component (continuous lines), curves ofequal 50-Hz flux density-peak-to-peak value-(dashed lines), the ar-rows indicate the direction of the highest amplitudes.
certainty of 3.3 ppm. As can be seen in Table I, the uncertain- tained to be 1.3 X 10-6/0C. The temperature at the coil wasties due to other error sources affecting the yp determination within 0.2 K (see Fig. 8), thus yielding an additional error ofare comparatively small. The temperature coefficient of the 0.25 ppm. Depending on the transfer standards available atcoil constant in the range between 18°C and 260C was ascer- the time, the unit of current in the NMR experiment is uncer-
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-34, NO. 2, JUNE 1985
Fig. 8. Setup for canceling the Earth's magnetic field with the coil-displacement device in the center.
1K
26i4 b
1O i.A :
2°° 3°° 4°° 5°° 6°° 7°° 8°° 9°° 19g 20° 21 22- 23-Fig. 9. Temporal variation of the Earth's vertical field component. (a)Outside and (b) inside the Braunbek coil system. (c) Variation oftemperature at the field coil.
4 6 7 9 10 11 12
Fig. 10. Results of the coil constant, kp, measurements, showing meanvalue and confidence limits, SkE.
tain to less than 1 ppm for the voltage standard and 0.5 ppmfor the resistance standard.The precession frequency has been measured in eight series
during the sane period in which the coil constant was deter-
TABLE IRELATIVE UNCERTAINTIES IN THE DETERMINATION OF zy
source of error S-10'-coil constant hp 3.2temperature coefficient of kp 0.25voltage transfer 1.0resistance transfer 0.5precession frequency 0.1additionat currents 0.02
ST, 3.4
mined. Each series consists of six measurements with reversedsense of current direction in order to eliminate noncompensatedextraneous fields. The mean value of these measurementsamounts to 38 672.827 Hz with an uncertainty of 0.1 ppm.The uncertainty due to the additional currents in the outer
winding packages is also of negligible order. Thus from these
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-34, NO. 2, JUNE 1985
measurements the gyromagnetic coefficient has been found tobe yp4 2.675 146 X 108 (1 ± 3.4 X 10-6) s' TBI77 Thisvalue is about 5 ppm higher than that recommended by Codatain 1973. In comparison with the determinations carried outat other standard laboratories its present uncertainty is ratherlarge. Nevertheless, it may be of some use, because the coilconstant hasi been determined in a way quite different fromthe usual one. Some modifications in the magnetometer andin the equipment which is used to cancel the Earth's magneticfield, and a new design of field coil give rise to hopes that, inthe near future, the uncertainty can be reduced by a factorof 5.
ACKNOWLEDGMENTThe author would like to thank Prof. Dr. H. Capptuller for
many helpful discussions, and P. Berke, W. Heine, and E. Simonfor their assistance in constructing the measuring equipmentand performing the measurements.
REFERENCES
[1] P. Vigoureux and N. Dupuy, "Realisation of the ampere and mea-surement of the gyromagnetic ratio of the proton," NPL Rep.,DES 59, 1980.
[2] W. Chiao, R. Lunand, and P. Shen, "The absolute measurement ofthe ampere by means of NMR," IEEE Trans. Instrum. Meas., vol.IM-29, pp. 238-242, 1980.
[3] E. R. Williams and P. T. Olsen, "New measurement of the protongyromagnetic ratio and a derived value of the fine structure con-stant accurate to a part in 107," Phys. Rev. Lett., vol. 42, pp.1575-1579, 1979.
[4] W. Braunbek, "Die Erzeugung weitgehend homogener Magnet-felder durch Kreisstrome," Z. Phys., vol. 88, p. 299, 1934.
[5] K. Weyand, "Ein neues Verfahren zur Bestimmung des gyromag-netischen Koeffizienten des Protons," PTB Rep. E-26, ISSN0341-6674.
[6] H.-J. Petrick and H. K. Cammenga, Ber. Bunsenges. Phys. Chem.,vol. 8,p. 1105, 1977.
[7] B. Theile et al., "Magnetische Vermessung im Sudgelande derPTB," private report.
[8] A. L. Bloom and D. J. Innes, "Octagonal coil system for cancellingthe Earth's magnetic field," J. Appl. Phys., vol. 36, p. 2560, 1965.
A New Determination of the Ampere and theGyromagnetic Ratio 'yp' in a Low and High Magnetic Field
WOLFGANG SCHLESOK AND J. FORKERT
Abstract-A new improved fundamental determination of the ampereand gyromagnetic ratio '4 was carried out in the Amt fur Standardisie-rung, Messwesen und Warenprufung (ASMW) in 1983. Taking the re-sults of measurements in a low magnetic field of about 1 mT and in ahigh magnetic field of about 1 T as a basis, it has been calculated forAASMW-83 with reference toA
AASMW-83 = A - 2.6 ,uAwith a relative uncertainty of ± 2 ppm. For .y results a value of
ap= 2.675 143 8 (48) X 108 T * s
which is independent of the reference value of current.
I. INTRODUCTIONAMONG the most important tasks which have to be per-
formed by the national standards institutes at presentis the fundamental determination of the base unit, the ampere,because of its fundamental importance to electrical and mag-netic measurements as well as more accurate determinations offundamental physical constants such as N, a, hle, and F. As aresult of international efforts to realize units which are inde-
Manuscript received August 22, 1984.The authors are with the Electricity Divison, Amt fur Standardisierung,
Messwesen und Warenprufung, Furstenwalder Damm 388, DDR-1 162Berlin, German Democratic Republic.
pendent of time and place and to derive the base units fromatomic constants, there obviously exists a clear tendency toproceed from traditional to quantum mechanical methods.For this purpose the method of nuclear magnetic resonanceis applied at the ASMW. The objective of this task has beenthe determination of the ampere and a value of -4 with anuncertainty of .2 X 10-6 (P = 68 percent) the latter beingindependent of the reference values of current.The determination of the ampere is based on the measure-
ment of resonance angular frequency X in two magnetic fieldsof different strength [1]. In it the gyromagnetic ratio -y, is,in the one case proportional, and in the other case, inverselyproportional to current. It has been calculated for the ampere:
A= 4'high ILAB'4,low
and for AASMW, in particular:
AASMW = }7PlOW Ay'high
(1)
(2)
The currents in the two magnetic fields may be different, theyhave only to be referred to the same unit. Without any addi-tional effort, 'y,, which is independent of the reference value
