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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

001 8-9456/85/0600-0173$01.00 © 1985 IEEE

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of current, may be calculated from

Ip = f , low - y hig] I/ 2T-1 s-1. (3)

II. MEASUREMENT IN A LOW MAGNETIC FIELD

As a result of extensive calculations and investigations, theso-called Garrett coils, having a larger number of turns at theends than in the central section, have been found to be suit-able for field generation. For the same homogeneity these coilsmay be considerably smaller than solenoids produced with aconstant number of turns per unit length. A coil with a con-stant

-4TC = 9.678490 X 1W0-4

which is described in [2], has been used at the ASMW.In the determination of y' the current was equal to about

300 mA, the penrodic time was 85 Ms at a measuring time of1.5 s, polarization current being 3 A during a period of 3 s.With the errors given in reference [2] a relative measurementuncertainty of 2.1 0-6 results. Referred to AASMW-83, it ispossible to calculatey, low as

,y, low 2.675 136 9 (53) X 108 T`' s- '.

III. MEASUREMENTS IN A HIGH MAGNETIC FIELDThe high magnetic field has to meet the requirements given

below.Inhomogeneity of magnetic induction within a range of 2 cm

in the horizontal direction, 1 cm in the vertical direction, and1 cm in the axial direction <1 X 10-6.Variation with time,<1 X 10-6 per hour.Range of magnetic induction, 0.5 to 2 T.Diameter of pole piece, .25 cm.Width of air gap, >30 mm.

The most important, and also the most complex part, is thecoil to measure the high field. In the ASMW a rasotherm glassformer with one turn, which is 37 mm in width, 500 mm inlength, and 7 mm in thickness, has been used.Considering the field distribution along the turn, the effective

width of coil is equal to

X= (0.0375120 ± 0.000 000 15) m.

The calculation of the width of coil requires that the coil sur-face be perpendicular to the field lines to avoid a lateral tiltingmoment. Moreover, the point of suspension should not divergefrom the center line by more than 0.6 mm to limit the error to<1 X 10-6 in the measurement of force.An autodyne detector with a resolution of 5 X i0' is used

to detect resonance precession and to measure resonance fre-quency. A three-coordinate adjusting device rendering it pos-sible to displace the probe by ±50 mm with an uncertainty of<0.1 mm in the three axes has been constructed to take upthe measuring head, perform an accurate measurement of themagnetic field between the pole pieces and carry out a repro-ducible adjustment. Current is supplied to the measuring coilthrough two gold-coated silver strips, 15 cm in length, 2 mmin width, and 0.01 mm in thickness.

TABLE INONNEGLIGIBLE, SYSTEMATIC ERROR OF THE y'y DETERMINATION IN A HIGH

MAGNETIC FIELD

Error in ppmSource of error (P = 95%)

1. Measurement of resonance frequency 0.12. Measurement of current 0.53. Current stability 1.04. Measurement of standard resistors (including

temperature coeffilcient and load dependence) 0.5S. Measurement of standard cells (including

temperature dependence) 0.26. Gravitational acceleration 0.27. Determination of mass 1.08. Weighing 0.59. Calculation of effective width of coil 5.0

10. Adjustment of coil 1.011. Excess temperature of coil 0.512. Current distribution 0.513. Influence of stray fields 1.0

It is necessary to reverse the current in the measuring coil;this has to be done, on the one hand, to obtain double theforce, and on the other hand, to avoid the occurrence of errorsgiven below.Laminar flow of air through a temperature rise of the coil.Force actions through magnetic impurities in the coil or its

holding component.Deformation of the coil through tensile and pressure forces

on the vertical sections of conductors.Magnetization effects of the coil on the pole pieces and in-

ductive change at the measunrng point.Measurements of y' have been performed with a current of

1 A, a resonance frequency of about 39 MHz and a mass of7 g. Table I shows the nonnegligible, systematic errors. Theconfidence limit of the nonnegligible, systematic error is u. =3.2 X 10-6, that of the random error is Uf = 0.23 X 10-6 withten measurements. From that results a relative uncertainty,u 3.2 X 10-6 (P= 68 percent).In the calculation of u, the below-mentioned components

of the error have been neglected.a) Transfer of frequency to SI unit <1 X 10-7.b) Frequency drift of the equipment <1 X 10-7.c) Hysteresis effect in the magnet through current in the

measuring coil which generates a magnetic flux <1 X 10-7 .d) Permeability of the sample container and materials in

close proximity <1 X 10-7.e) Air buoyancy during weighing <5 X 10-8.

The result, referred to AASMW-83, is

'Yphigh= 2.675 150 9 (80) X 108 T -s1-'.It has been calculated for AASMW.83 with reference to A that

AASMW83 = A - 2.6 ,iAwith a total relative uncertainty of

ux =2 X 10-6 (P = 0.68).

It has been calculated for 'y that

=2.675 143 8 (48) X 108 T1 s-

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with

ux = 2 X 10-6.

or, the conversion factor K is

K =1 - (1.10 ± 2) ppm.

Taking account of the comparisons of the standards of volt-age and resistance of ASMW with the international units of theBIPM, which were completed at the BIPM in March 1983, thevalues given below result in:

VASMW = V76-BI - 1.39 pV

QASMW = n69-BI + 0.11 ,U2.From this it follows that

AASMW = ABI - 1.50 HIA.And for ABI there results

ABT=A- l.l0pA

Referred to ABI it thus follows that

'o-4,=2.675 140 9 X 108 Tr . s1

and, respectively,

YPhigh = 2.675 146 9 X 108 T-1 *s1.

REFERENCES[1 J. Forkert, and W. Schlesok, "Eine neue Fundamentalbestimmung

des A und -' mit Hilfe von Kernresonanzverfahren," Metro. Abh.des ASMW, F. 3, 1981.

[2] W. Schlesok, "Eine verbesserte z;-Bestimmung im schwachen Mag-netfeld als Ergebnis der Zusammenarbeit mit dem," WNIIM, Lenin-grad, Metrol Abh. des ASMW, H. 2, 1982.

The NBS Absolute Ampere ExperimentPAUL T. OLSEN, MEMBER, IEEE, VINCENT E. BOWER, WILLIAM D. PHILLIPS,

EDWIN R. WILLIAMS, AND GEORGE R. JONES, JR.

Abstract-We have constructed a current balance with superconduct-ing field coils for the realization of the SI ampere by comparing me-chanical to electrical work. The estimated ultimate accuracy of therealization is 0.1 ppm. We describe and present preliminary resultsobtained with a room temperature version of the apparatus.

I. INTRODUCTIONT HE practical electrical units can be maintained by a na-

- tional standards laboratory, such as NBS, with remarkableaccuracy and precision. The unit of voltage, defined in termsof the ac Josephson effect, is stable in time and routinelymaintained to a few parts in 108 [ 11. In the same way, theunit of resistance could be defined in terms of the quantumHall effect, with a reproducibility and long-term stability ofabout four parts in l'o8 [2]. Unfortunately, the relationshipbetween these "as-maintained" units and the more fundamentalSI electrical units (defined only in terms of the units of mass,length, and time) is not nearly so well established. The SIdefinition of resistance can be related to the practical defini-tion by calculable capacitor experiments [31 to a few parts in108, but the SI definition of voltage is related to the practicalor laboratory unit to an accuracy of only a few parts in 106or worse [41.Historically, the relationship between the SI and practical

units of voltage has been determined by a realization of the SI

Manuscript received August 20, 1984.The authors are with the Electricity Division, National Bureau of

Standards, Gaithersburg, MD 20899.

definition of the ampere (A): "the ampere is that current which,when passed through two parallel, infinitely long wires of neg-ligible cross section 1-m apart, produces a force between themof 2 X 10-7 N/m of length." The comparison of this SI am-pere to the practical ampere, defined by the practical volt andohm, completes the link between the SI and as-maintainedsystems of electrical units.There are also various indirect methods for arriving at the

ratio of the SI to as-maintained amperes. Generally, these in-volve combining a number of measurements of fundamentalconstants, such as the Faraday, the Avogadro constant, thegyromagnetic ratio of the proton, the Josephson frequency-voltage ratio and others, some of which involve electrical mea-surements and some of which involve force measurements.A comparison of such indirect measurements of the SI amperewith direct realization of the definition indicates large discrep-ancies [41; in fact, the value for the ratio of the SI to labora-tory ampere KA = A LAB/A given in the latest (1973) adjust-ment of the fundamental constants [51 may be in error by asmuch as 10 parts per million (ppm).The traditional method for realizing the SI definition of

the ampere has been to construct a set of coils of accuratelyknown dimensions, calculate from the dimensions the forcewhich one coil system will exert on the other for a given cur-rent in each, and then to compare the calculated force to theactual force, as measured using a balance, when a currentknown in as-maintained units is passed through the coils. Inthis case we have

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