автореферат диссертации по приборостроению, метрологии и информационно-измерительным приборам и системам, 05.11.01, диссертация на тему:Разработка и исследование измерительного комплекса для определения гиромагнитного отношения протона в воде методом "слабого поля"

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On the rights of the manuscript.

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KOREA RESEARCH INSTITUTE OF STANDARDS AND SCIENCE

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Po Gyu Park £ ^ й n^ jc

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Development and research of the measuring complex for determination of the proton gyromagnetic ratio in water

by low field method

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Jc *........ ^

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f}ts T ■■■("' " ? б -VV vZ-(•Л

Speciality 05.11.01: - Instruments and measurement methods on the fields of

measurements

Dissertation on awarding of a scientific degree of the candidate of engineering

science.

The scientific adviser: Professor Vladlen Ya. Shifrin

Taejon, 2001 R. Korea

Contents

Introduction ............................................ 4

Chapter 1. Review and determination of research subject............ 10

§1.1. Review of a y'P - measurements ------------------------ 10

§ 1.2. Grounding of common structure of the measuring system------ 18

Chapter 2. Measuring system and technique for determination

of the solenoid constant via winding dimensions.....-..... 21

§ 2.1. Multi-current precision uniform field solenoid with

constant independent from averaged diameter ............- 21

§ 2.2. Measuring system for determination of a solenoid

dimensions ..................................... 35

§ 2.3. Absolute determination of a constant of a solenoid .......... 55

Chapter 3. Apparatus and experiment on measurement of the gyromagnetic ratio of 4He atoms in terms of that of the 3He nuclei ................................. 61

§ 3.1. Applied magnetic resonance technique with the

polarization by a optical pumping method .............— 61

§ 3.2. Measurement of the gyromagnetic ratio of 4He

atoms in terms of that of the 3He nuclei ................. 70

Chapter 4. Measuring system for determination of the 4He

atoms gyromagnetic ratio .....-..........................79

§4.1. Nonmagnetic environment--------------------------------79

§ 4.2. General structure of the measuring system ....................81

§4.3. Atom-resonance based current source —.....................86

3

§ 4.4. The system for automatic compensation of the

Earth magnetic field......-......------------------ 93

§ 4.5. Results of the 4He atoms and proton gyromagnetic

ratio determination ------------------------------ 100

Conclusion ............................-............... 102

References ...............-............................ 104

Introduction

Topicality of work

The proton gyromagnetic ratio in water - y'p represents the physical interconnection of the magnetic field and the Zeeman magnetic resonance frequency in the system of fundamental physical constants.

The y'p is one of the basic constants for establishing of the main standards of the electromagnetic SI units, for example, the quantum Hall resistance:

RH =

fiy(^'p/fiB)[RH]LAB[2e/h]

4I/3

iLAB

16 R

\-yp\ab

(1)

and for testing of the fundamental physical theory via the determination of the fine-structure constant(a) in particular, according to the following relation:

a =

(M'p/Mb)[RH ]ub >/Ь]ив

2 Mo R«[r'p_ LAB

\V3

(2)

where is a magnetic susceptibility of vacuum, с is the speed of light in vacuum, ц'р/^в is a magnetic moment of a proton in terms of Bohr magneton, Rm is a Ridberg constant, RH is a the quantum Hall constant, 2e/h is a Josephson constant; the index LAB means, that the constants are measured in comparable laboratory units.

Therefore knowledge reliability increase of this world constant, to which the researches of the given work were directed, without any doubts remains an actual problem of the fundamental metrology.

Along with a value of y'P for the fundamental metrology, this constant plays a crucial role in achieving of a high accuracy magnetic measurements.

For magnetic measurements y'P serves as a conversion coefficient for proton magnetic resonance instruments. It determines the absolute accuracy of this kind of measurements. Quantum interconnection between magnetic flux density (В) and Zeeman proton magnetic resonance frequency (cop) is defined by the well-known ratio:

Ур=сор-В (3)

The measurements of a magnetic field parameters prevail in magnetic measurements. They can be applied in the following spheres, important for human beings: study of a physical nature of earth magnetism, its dynamic development and its influence both on global and local physical processes, including deep tectonic, climatic and medical effects, and earthquake prediction; in geophysical researches of natural time-space distribution of parameters of a magnetic field on the Earth's surface with the purpose of mineral resources discovering and estimation of natural resources of human being's life; in searching for hidden technical objects and determination of their magnetic parameters, including the defense aspects and in other spheres.

By the period of realization of this work in KRISS, the most precise y'P-experiments were made atNIST (USA) in 1988[1] and VNIIM in 1987[2]. However, the difference of these results, which is greater than the sum of the standard deviation, points to the lack of coordination between them. So, this new experiment was actual for a more precise y'P - determination. This work was accomplished in KRISS (Korea Research Institute of Standards and Science) with collaboration with of the VNIIM (D. I. Mendeleyev Institute for Metrology in Russia).

The purpose of researches

The purpose of the dissertation is the development and research of the measuring system for determination of the proton gyromagnetic ratio in water by low field method inKRISS.

The research problems

To achieve the purpose of the present dissertation it was necessary to fulfil the following tasks:

- to develop the common structure of the measuring system;

- to fulfil the absolute determination of a constant of a precision solenoid;

- to develop atom resonance based precision current source and current measurement in the adopted units of Volt and Ohm;

- to develop measuring complex and make the experiments for obtaining more precise determination of the gyromagnetic ratio of the 4He atoms in terms of that of the 3He nuclei, gyromagnetic ratios of the 4He atoms and protons.

Methods of researches

Both theoretical and experimental methods of researches were used in this work. The theoretical methods of researches are based on the use of elements of differential and integrated calculus, and of mathematical statistics.

The experimental methods of researches, are based on the application of the principles of the atomic and nucleus quantum magneto-resonance phenomena, electromagnetic induction, methods, worked out in the process of work and some auxiliary devices.

Scientific novelty

The scientific novelty of the results acquired is as follows:

- on the basis of generalization of methods and measuring systems, used before, the original structure of experiment for y'P - determination were developed in KRISS ;

- theoretical proof and experimental realization of the modification of a non-contact electromagnetic method for dimensional measurements of the solenoid, allowing to decrease uncertainty due to the current injection system;

- theoretical analysis of the optimized parameters of a five-current system of a calculable high uniform field solenoid with independent coil constant from averaged diameter and homogeneous solenoidal systems for the atom-resonance current stabilizer;

- offered and realized method of calculation and measurement of the amendments of the nuclear resonance sensor magnetization effect, realized for the first time at the definition of the constant of connection of gyromagnetic ratio of the 4He and helion;

- the new values of the gyromagnetic ratio of the 4He, helion and proton, in included by CODATA into the bulletin "Values of the Fundamental Physical Constants", as recommended in 1998.

Practical importance

The practical importance of the results is as follows:

- the acquisition of the one of the most precise experimental determinations of the proton, 3He helion and 4He atoms gyromagnetic ratios, the significance of which was confirmed by including in official new adjustment of the basic physical constants, carried out by the International Committee on Data for Science and Technology (CODATA) in 1998;

- the reduction of the uncertainty of tesla reproduction in KRISS about 100 times and the creation on its basis of a new primary standard unit of magnetic flux density in KRISS, used for calibration of all kind of industrial magnetometers in Republic of Korea.

The results of work

The dissertation was executed in KRISS in 1991-1998. The stated results were used by CODATA in bulletin the "CODATA Recommended Values of the Fundamental Physical Constants: 1998", at realization of several research projects in KRISS, and in VNIIM at the coordination of the size of tesla VNIIM and KRISS.

Approval of the results

The basic results of the dissertation were discussed at the following International Conferences:

- Conference of Precision Electromagnetic Measurements (CPEM 2000), Sydney, Australia, 2000;

- InterMag-99 , Kyungju, R. Korea, 1999;

- Conference of Precision Electromagnetic Measurements (CPEM 98), Washington, USA, 1998;

- Committee Consultative de Electricitee (CCE/97), Paris, France, 1997;

- Conference on Precision Electromagnetic Measurements (CPEM 96), Braunschweig, Germany, 1996;

- International Symposium on Test and Measurement (ISTM 95), Taiywan, 1995;

- International Symposium on Advanced Computational and Design Technique in Electromagnetic Systems (ISEM-Seoul), Seoul, R. Korea, 1994;

- Conference on Precision Electromagnetic Measurements (CPEM 94), Boulder, USA, 1994;

- IEEE Instrumentation and Measurement Technology Conference (IMTC/94), Hamamatsu, Japan, 1994.

The publications

The materials of dissertation were used in 35 magazines publications and in conference digests.

9

Topics to be covered:

1. Research and development of a measuring system for determination of the proton gyromagnetic ratio in water by low field method in KRISS;

2. Results of the determination of the gyromagnetic ratio of proton, helion and helium-4 atoms;

3. Development of the modification of a noncontact electromagnetic method for dimensional measurements of the solenoid, allowing to decrease uncertainty, that appears due to the uncertain configuration of the current injection system;

4. Development of the optimized parameters of a winding for the five current system of a calculable solenoid and of the solenoidal system for the atom-resonance current stabilizer;

5. Development of a method to the effect of a magnetization of winding of the nuclear magnetic resonance sensor;

Volume and structure of the dissertation

This dissertation consists of introduction, 4 chapters, conclusion, references,

list of the literature and applications. The volume is 112 pages, including 58 figures

and 6 tables.

The list of the literature contains 100 names on 9 pages.

Chapter 1. Review and determination of research subject

§ 1.1. Review of a y'P - measurements

The proton gyromagnetic ratio y'P (the prime indicates protons in a spherical sample of pure H20 at a temperature of 25°C) of a particle having the spin quantum number i and magnetic moment M(Fig. 1.1) is given by

where f is the precession frequency and cop is the angular precession frequency of the particle in magnetic flux density B, h = h/2л, h - Planck constant. The SI

2к fP _coP _M

(1.1)

В В iti

unit[3],[4] of y'p is s^T"1 = Askg"'[5].

• Ratio of magnetic dipole moment to spin angular momentum

M=Y fi/

M

• Measurement of precession

frequency by NMR method

(0 = ДЕ/Й - 2M B/ft

= Ур в (,- = 1/2)

Fig. 1.1. Schematic representation of the proton magnetic resonance.

The role of y'P - measurement in the fundamental metrology[6]-[24] is shown in Fig. 1.2 by the schematic diagram.

Fig. 1.2. The purpose of y'P - measurement.

The y'p-experiments started opened about 45 years ago in the series metrology institutes of different countries - NBS-NIST (USA); VNIIM, KhGNIIM (Russia); NPL (England); PTB, ASMW (Germany); ETL (Japan); later NIM (China) and KRISS (Korea) also joint to this work [25]-[42]. The uncertainty of the y'P-determination was decreased more then 100 times during this period and reached (0.1-0.3) xlO"6 for different experiments.

To determine the gyromagnetic ratio of a proton in practice two methods were used - "low-field"method and "high-field" method[43].

In the low-field method {у'Р{1о)) the magnetic flux density В is of the order of 1 mT and is usually generated by a single-layer precision solenoid carrying an electric current I as it is shown on Fig. 1.3. The magnetic flux density В is calculated from the dimensions of the solenoid and the current :B = juJCJ, where KB is the measured

Current sources for zero-field

Helmholtz coil

Standard Resistor

Main and aux. currents for solenoid

MMn

°x° о о

о о

Voltage Standard

Solenoid

m

NMR Signal detector

H20 sample

Fig. 1.3. The ^-measurement by low-field method.

Balance system

Standard Resistor

AW

Electromagnet

power supply

NMR Signal detector

Electromagnet pole

H20 sample

I

mg

Fig. 1.4. The yp -measurement by high-field method.

solenoid constant and has the dimension of reciprocal length, ju0 is magnetic constant: [л = 4 7txlO"7N/A2. Thus the equation for measurement y'P by this method is as follows:

Low-field method was carried out NIST, VNIIM, NPL, NIM, ETL, PTB and KRISS.

In the high-field method (yP(hi)) the magnetic field with an induction В about 0.5 T is reproduced by an electromagnet and is determined by measurement of the dimensions of a rectangular frame with a current / and mechanical force operating on it field of this electromagnet as it is shown on Fig. 1.4. Simultaneously in the same working space the resonance frequency of protons in a sample with a water is measured by a method of a induced precession. The gyromagnetic ratio of protons is determined according to the ratio:

. ., 2лfpIL mg

where / is the current which is flowing past on a conductor, m is the weighed mass, g is the acceleration of force of weight, L = <^dlxB/B0- effective dimension of a frame

with a current I, В is the magnetic flux density in the working space of an electromagnet, dl is the element of a conductor with a current.

This method allows to make the measurements of y'P with a smaller accuracy, than the low-field method and, that's why consequently it was not developed during last 20 years. The highest accuracy of measurements yP(hi) was reached in 1979 in Kibble experiment[30] from NPL(England). The uncertainty of determination of a constant were estimated as 1 x 10~6.

Anyway, the current / is measured in terms of a practical laboratory unit of current AUB =Vlab/ Qlab, where VLAB and QLAB are practical laboratory units of voltage and resistance. The unit VLAB may be based on the Josephson effect [44],[45], or probably on the mean emf of a group of standard cells, and the unit QLAB may be based on the quantum Hall effect[46]-[49] or possibly on the mean resistance of a group of standard resistors.

As we see from eq(1.2) and eq(1.3) in the low-field method the y'P is inversely proportional to the current /, while in the high-field method it is directly proportional to I. Thus joint determination of y'P by two methods with use of the identical size of ampere [7],[16],[17],[19],[50],[51], is independent from uncertainty of Alab in SI:

Yp =

■ . • I1/2

Y p{lo) • Y P{hi)

~|!/2

cop{lo)cop{hi)- L M0KBmg

(1.4)

In table 1.1 the results of the proton gyromagnetic ratio experiments which are used in the 1998 COD ATA adjustment are summarized [5]. Also included in the table is the value of fine-structure constant (a) inferred from each low-field result and the value of plank constant (h) inferred from each high-field result, as discussed in connection with each experiment. Each inferred value is indented for clarity and is given for comparison purposes only; in actuality the values of y'P are taken as input data for the 1998 COD ATA adjustment. Fig. 1.5 shows the values of y'P from various laboratories, having most precision results, compared with CODATA 86 and CODATA 98[5],[52].

The NIST (National Institute of Standards and Technology) reported its first low-field measurement of y'P, which had a relative standard uncertainty of about 4 xlO"6, in 1958[25] - Bender and Driscoll. Its most recent low-field result was reported by Williams et al.[l] and has a relative standard uncertainty of l.lxlO"7. In this experiment, the single-layer precision solenoid had a length of 2.1 m, a diameter

Table 1.1. Summary of data related to y'P, and inferred values of a an h.

Relative standard

Quantity Value uncertainty uT Identification

2.675 154 05(30)x 108 s" -l j-i 1.1X10"*7 NIST-89

V1 137.035 9880(51) 3.7X10-8

r;_9o(io) 2.675 1530(18)Xl08s"1 T-i 6.6ХНГ7 NIM-95

a'1 137.036 006(30) 2.2X10-7

rp-9o(hi) 2.675 1525(43)xl08s"1 T-i 1.6X10"6 NIM-95

h 6.626 071(11)X10~34 Js 1.6X10"6

JWhi) 2.675 1518(27)xl08s"1 T-i l.OxlO"6 NPL-79

h 6.626 0729(67)X 10~34 J s 1.0X10"6

2.037 895 37(37)x lOV •l j-i 1.8X10"7 KRISS/

tf"1 137.035 9853(82) 6.0X10"8 VNIIM-98

/WIo) 2.037 897 29(72)X10V •l j-i 3.5X10"7 VNIIM-89

a"1 137.035 942(16) 1.2X10"7

of 0.3 m, and was wound with 2100 turns of gold-plated copper wire 0.8 mm in

diameter. The current through the solenoid was about 1 A, but additional current was

added to segments of the winding in such a way that the magnetic flux density was

insensitive to the diameter of the solenoid to the same extent that that it would be for

a 1.5 km long solenoid. Five current sources were used to energize to solenoid. A non-contact probe system was used in order to determine variations in the diameter and pitch of the windings [53].

The VNIIM in Russia, group has reported in 1981 a value of yP(lo)[32]. They were used a four segment solenoid and mechanically located the wires, using a laser interferometer to measure the dimensions. They used a two-coil free induction decay method to measure the NMR signal. In 1988 the VNIIM low field helion experiment was performed [37] in air at 23°C with spherical low-pressure 3He samples. The NMR frequency was measured by free precession with the 3He atoms first polarized

by optical pumping as was done in the VNIIM experiment that determined the shield helion to shield proton magnetic moment ratio. The magnetic field was produced by a four-section, single-layer precision solenoid 294 mm in diameter and 500 mm long with a total of 256 turns that generated a magnetic flux density of 0.57 mT with a current of 1 A. Many improvements were incorporated in the helion gyromagnetic ratio experiment based on the experience gained in the earlier proton gyromagnetic ratio experiment[54]. The result reported by [37] was 0.37xl0"6.

yp = 2.675 154 30xl08 s'T1 -4-3-2-10 1 2 3

KRISS/VNIIM(lo)-97 * ->

NIM(lo)-95 j

NIM(hi)-95

NIST(lo)-89 i

VNIIM(lo)-88

ETL(lo)-86

ASMW(lo)-85

NPL(hi)-79

CODATA-98 i

CODATA-86 i

Fig. 1.5. The values of y'P from different laboratories in comparison with data of COD ATA 86 and CODATA 98.

The Chinese group from NIM (National Institute of Metrology) have measured y'p in both methods starting in the 1970. Chiao, et al.[17] has reported a value of yP{lo) and YP{hi) in 1980. In the NIM experiment, the dimensions of a precision single layer Helmholtz coil were measured in comparison with length standards. The end standards in their turn were measured by an interferometer. The significant part of the NIM work is the precision obtained in the NMR part of the experiment, 7xl0"8, considering the low field, about 2xl0"4T, produced by the Helmholtz coil. The final 0.8x10"6 uncertainty was primarily limited by the dimensional measurements. A number of significant improvements in technique and auxiliary equipment have been incorporated over the years [55] -Liu et al., 1988; [39] -Liu et al., 1995. The most recent NIM measurements yielded in 1995 [39], results of yP(lo), yP{hi) are

0.7xl0"6 and 1.6xl0"6, accordingly.

P. Vigoureux and N. Dupuy at the NPL (National Physical Laboratory in England) have spent many years obtaining their results [16] -Vigoureux et al. in 1980. In measuring the pitch of their solenoid they use a unique technique to located the wire position. Their solenoid is bifilarly wound and to measure the pitch they place a voltage between the two windings. A metal sphere that is attached to one end of an interferometer is moved along a generator of the solenoid, shorting out the double helix as it goes. The pulse that results from this short triggers the recording of the position of the sphere by the laser interferometer. This information is recorded for different generators by rotating the solenoid. These data are then combined to describe the average position of each turn of the solenoid. The most accurate high-field у'р-experiment was carried out at NPL by Kibble and Hunt in 1979 [30]. In this experiment, the current-carrying conductor used to measure the 0.47 T magnetic flux density В of the electromagnet was a rectangular coil. The current in the coil was from 0.5 A to 5 A, the number of ampere turns used was 1.5 to 15, and the maximum force on the coil, was equal to the weight of a 250 g standard of mass. The uncertainty was evaluated 1 .Ox 10"6.

A low-field experiments were made also at the ETL (Electrotechnical Laboratory in Japan)[36],[56] -Nakamura et al. in 1987, 2xl0"6 and at the PTB(Physikalisch-Technische Bundesanstalt in Germany)[34] - Weyand in 1985, 3.4x10"6. Low- and high-field experiment simultaneously have executed at the ASMW(Amt fur Standartisierung, Messwesen und Warenprufung) [18],[19] -Forkert et al. in 1986 with the estimated uncertainty of 2.1xl0"6 and 3.2 xlO"6 respectively.

§ 1.2. Grounding of common structure of the measuring system

The y'p-determination by low-field method includes two independent experiments coupled to measurement of two different quantities. The first experiment is an absolute determination of a constant of a solenoid having dimension T/A and consisting in measurement of the geometrical parameters of a current-carrying winding of a solenoid and calculation of a conversion coefficient. The second experiment is a determination of the quotient of a Zeeman frequency of a sample, located in working space of a solenoid, to its magnetic flux density.

The main distinguishing feature of the measuring system, developed in this work, is the application of the more accurate 4He AMR technique for determination of the Zeeman magneto-resonance frequency and development the modification of a non-contact electromagnetic method for measurements of the solenoid dimensions, allowing to attain a lower uncertainty owing to the current injection system [40]-[42],[57].

The usual nuclear magnetic resonance (NMR) method for water samples has been used during last 45 years without substantial changes in all previous yp experiments except for [2]. But that method has some limitations which effect the accuracy. One limitation is a low signal-to-noise ratio owing to the very low effectiveness of the thermal nuclear spin polarization and high-noise induction methods for NMR signal monitoring. Other limitations are derived from reference-to-NMR signal phase shifts, phase shift through the signal damping, and NMR-

frequency dependence upon temperature or sample shape. It impedes the reduction of the proton magnetic resonance(MR) frequency shifts below lxlO"7.

On the other hand, the MR-technique based on optical pumping[58] provides higher sensitivity and accuracy for the transformation of the magnetic flux density into resonance frequency. There were developed that may be used in higher precision experiments than by conventional NMR methods in water. One of the two methods is NMR in optically pumped low-pressure 3He [59] with an induction method of NMR signal monitoring. The advantages of this method are much higher signal-to-noise ratio, small signal damping factor, negligible diamagnetic susceptibility and absence of the NMR frequency shifts, that arise because of temperature or sample shape. Gyromagnetic ratio of the 3He nuclei has been measured relatively to the gyromagnetic ratio of the unbound proton and the proton in a spherical water sample[60],[61].

The most accurate determination of the y3He / y'P was made in 1993 by Flowers et. al.[61] with one-standard-deviation uncertainty of 4xl0"9.

A second alternative to the proton NMR is the 4He AMR technique is based on OP polarization by means of metastable exchange with OP-polarized atoms of alkaline metal[62],[63],[64]. Results of experiment obtained in low magnetic fields have shown [65] that 4He AMR-frequency shifts are reduced to the level of random errors. This makes possible to determine y4He in fixed units with a less than lxlO"8 error at a 1 mT magnetic field.

The 4He AMR technique has important advantages for low field range in comparison with not only proton NMR but also with 3He NMR. AMR frequency is hundreds times higher than NMR and more effective optical method of AMR-signal monitoring makes higher relative accuracy in the actual AMR frequency determination. In this experiment the 4He technique was chosen for conversion of the magnetic flux density to the resonance frequency.

Experimentally measured ratios [61] and у4не/узне [66] were applied for

transition from y4He to y'P. The most accurate determination of the gyromagnetic ratio

20

of 4He atoms in terms of that of the 3He nuclei was made with essential participation of the author of this work and as a part of this work in 1996[66] (chapter

3).

The y'p - determination at NIST [ 1 ] provides two important ideas for this work in obtaining higher accuracy of the magnetic field determination by more precise measurement of the solenoid winding dimensions. Those ideas are the multi-current solenoid, constant which is not sensitive to the average diameter and the induction technique[l] for dimensional measurements with the importance modification made in this work.

Chapter 2. Measuring system and technique for determination of the solenoid constant via winding dimensions

§ 2.1. Multi-current precision uniform field solenoid with constant independent from averaged diameter

The solenoid, intended for determination of y'P with uncertainty about 1 x 10"7 must satisfy very high requirements on the field homogeneity and on the opportunity of precise dimension measurements. Fig.2.1 shows the results of our calculation where an error of 1 (im in 10-turns groups at central part of the five-current solenoid causes a resultant uncertainty up to (3-4) xlO"7 [57].

Fig. 2.1. Effect of 1 (im measuring error on the solenoid constant.

It demonstrates the necessity of diameter- and pitch-measurements with uncertainty of less than 0.1 fim. Generally, the measurement of pitch with such absolute accuracy is possible but the same measurement of winding diameter at this moment is practically impossible. Therefore, a construction of solenoid, which ensures insignificant dependence of its constant on averaged diameter of the winding, was developed.

The non-uniformity of the solenoid field should be less than 1 x 10"7 in a sphere of 40 mm in diameter to ensure the necessary measuring accuracy of the Zeeman magneto-resonance frequency.

The simple solenoid with the practical ratio of the winding length to diameter (about 5) can provide at best 1000 times bigger non-uniformity for that size of sample. Combination of the required field homogeneity with a rather weak dependence of coil constant on the winding diameter is observed for the simple solenoid if it has the huge ratio of length to diameter - about 1000, it means that the length must be up to 0.2 km. However, it is not used in practice.

Complete equivalence to the essential source of a magnetic field is achieved in this work by application of a practical solenoid of 1 m in length, due to the development of the optimized multi-current winding, the analysis of which is considered below.

Precision solenoid, made in this work, consists of a winding of silver plated copper wire laid along a helical groove on a fused silica cylinder. The winding length is 1020 mm; average radius R=l 14.67 mm; pitch Р=1.0001 mm; wire diameter is 0.799 mm.

Much effort has been directed toward developing a method of fabrication of a solenoid carcass of fused silica by the grinding and lapping processes. A rough cylindrical tube was mounted on a lathe between the head and tailstocks. The precision surface of the tube was obtained by a diamond-grinding wheel, mounted on the carriage. The helical groove of 1 mm pitch was machined by a diamond screw wheel in the same lathe.

The temperature-controlled grinding fluid was showed on the surface of the former during the machining. The depth of the groove is estimated to 0.3 mm after final screw grinding.

The lapping was continued by using a copper block with a diamond paste to smooth out the variations in radius and pitch. Several times the silica cylinder was cleaned, and a measurement was taken of the radius and the pitch by a three-

dimensional machine, equipped in the Length group at KRISS. This machine is able to measure the surface variations and the distance from the reference point, that is, radius and pitch, with a resolution of ±0.2 jam. The variations of surface and pitch were measured to be a few micrometers, but there is an eccentric part along the former axis.

The copper wire of 99.99 % purity was coated with silver by an electroplating method to reduce the contact resistance for current injection. The wire of 1 mm diameter was cleaned to remove the dust and rinsed, a