Compensation of the Earth's Magnetic FieldG. G. Scott Citation: Review of Scientific Instruments 28, 270 (1957); doi: 10.1063/1.1715856 View online: http://dx.doi.org/10.1063/1.1715856 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/28/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A Magnet Rolling in the Earth's Magnetic Field Phys. Teach. 45, 522 (2007); 10.1119/1.2798370 Measuring Earth’s magnetic field simply Phys. Teach. 38, 113 (2000); 10.1119/1.880443 Nuclear spins in the Earth’s magnetic field Am. J. Phys. 50, 709 (1982); 10.1119/1.12735 Compensation of Earth's Field Variations by Field Controlled Rubidium Oscillator Rev. Sci. Instrum. 42, 1427 (1971); 10.1063/1.1684898 The Earth's medieval magnetic field Phys. Today

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270 H. V. NEHER AND SATYA PRAKASH

the whole system. (2) The air in the system must be thoroughly displaced by the hydrogen before any at­tempt is made to braze, or to ignite the gas. The use of some sort of flow indicator, either in the form of a water manometer or a flowmeter is desirable. A volume of hydrogen several times that of the system should be run through to thoroughly flush the containers and lines. After this is done, the hydrogen may be ignited at the outlet. The flow of hydrogen at all times should be sufficient to maintain a positive pressure inside to exclude any air.

THE REVIEW OF SCIENTIFIC INSTRUMENTS

ACKNOWLEDGMENTS

One of the authors (H.V.N.) wishes to take this opportunity of expressing his appreciation to Dr. K. R. Ramanathan and Dr. Vikram Sarabhai of the Physical Research Laboratory, Ahmedabad, for their encourage­ment and generous cooperation while this research was being carried out. He is also grateful to the United States International Cooperation Administration for financial support. The second author wishes to express his appreciation to the Atomic Energy Commission of India for financial assistance.

VOLUME 28, NUMBER 4 APRIL, 1957

Compensation of the Earth's Magnetic Field

G. G. SCOTT

Research Staff, General Motors Corporation, Detroit, Michigan (Received November 9, 1956; and in final form January 18, 1957)

A system is described for producing a highly homogeneous, variable, and directable magnetic field. This system, which was used in gyromagnetic ratio experiments, was directed against the earth's magnetic field to obtain very nearly a field free space. Horizontal fields in this working space were held to less than 0.01 % of the earth's horizontal component.

INTRODUCTION

D URING the past several years, direct gyromag­netic determinations have been made by the

General Motors Research Staff, for a number of metals and alloys.1 Successful determination of these ratios requires the accurate measurement of extremely small mechanical inertia forces. These forces were measured by suspending the ferromagnetic material being studied, in a sensitive torsional system, magnetizing it and observing the resulting rotation. Normally torques which are vastly greater than those being measured would act on the suspended system due to coupling with the earth's magnetic field. It was, therefore, of extreme importance in this work to obtain a space in which all magnetic fields were very nearly eliminated. The system to be described was capable of reducing magnetic fields in the working space to about 0.01% of the value of the earth's horiwntal component, and to hold it at this reduced value for an extended period of time.

The earth's magnetic field can be represented as a vector inclined to the vertical which is continually und~rgoing small changes both in magnitude and in direction. At a location which is remote from any con­centration of ferromagnetic material this field is highly homogeneous. The problem of compensation hence becomes one of designing a coil system capable of producing magnetic fields of high homogeneity, and also

1 G. G. Scott, Phys. Rev. 82, 542 (1951); 83, 656 (1951); 87, 697 (1952); 89, 618 (1953); 99, 1241 (1955); 99, 1824 (1955); 103, 561 (1956); 104, 1497 (1956).

of designing a system whereby the naturally occurring variations in the earth's magnetic field can be followed.

The system to be described was located in a special laboratory building so as to obtain the initial field homogeneity required. The coil array is shown in Fig. 1. It consists of three coil systems, producing magnetic fields in the vertical, north-south, and east-west direc­tions. These magnetic fields were directed against the earth's field to produce compensation. Variometers were used to follow the changes occurring in the north-south and east-west components. The vertical variations were not followed since very small vertical fields could be tolerated in these experiments. The use of a three component system also made it possible to produce highly homogeneous horizontal fields of several oersteds. This was very useful in measuring magnetic moments.

The coil system, variometers, and field detection equipment will be described in order.

THE COMPENSATING SYSTEM

Compensation of the earth's magnetic field was accomplished by an array of five different Helmholtz coils. The Helmholtz coil, which consists of two identical circular coaxial conductors having centers separated by the conductor radius, produces a highly uniform mag­netic field throughout a considerable volume. Equations expressing the field homogeneity of a Helmholtz coil have been developed by Ruark and Peters.2

Since the magnetic fields required in this work were of

2 Ruark and Peters, J. Opt. Soc. Am. 13, 205 (1926).

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COMPENSATION OF THE EARTH'S FIELD 271

the order of a few oersteds, the winding cross section could be made small compared to the radius of the coils. For this condition the formulas of Ruark and Peters can be reduced to the following:

n H,,=Hxo-0.06474r4i-(35 cos40-30 cos20+3)

A5

n H lI=0.06474r4i- sinO cos8(28 cos2(J-12)

A6

0.44959ni

A

The symbols have the following meanings:

0= angle between axis of system and line joining center of system with the particular point P at which field is to be evaluated,

r= distance from center of system to point P (centimeters),

Hx=field at P parallel to the system axis (oersteds), Hy=field at P normal to the system axis (oersteds),

Hxo=field at center of system in axial direction (oersteds),

A = radius of coil (centimeters), i= current (amperes), n=number of turns in both coils together.

The terms involving the trigonometric expressions are a measure of the inhomogeneity of the Helmholtz field. These trigonometric expressions are plotted in Fig. 2. Using values of k corresponding to a given value for 0 as shown in Fig. 2 we can write the values for H x and

FIG. 1. Coil system used in gyromagnetic ratio experiments for neutralization of the earth's magnetic field.

-l +.50 b.c

~ +.40

\ \ \""

+.30

/ \ rv \ '\ II

+.20

j \ /

II \ \ / +.'0

\ V 1\ I I

.00

\ \ / / \ \1/

-.10

~ / 1'-V '-V

-.20

-.30

200 400 800 800 8' FIG. 2. Plot of the field inhomogeneity of a single Helmholtz

system. kx=0.06474(35 cos4O-30 cos20+3). k.=0.06474 sinO cosO (28 cos20-12).

H y as follows:

Let us now consider two Helmholtz systems of differ­ent size arranged so that their axes and centers are in coincidence and connected in series opposition. A cross section of such a combined system is shown in Fig. 3. At some point P, kx, ky, r, and i will be the same for both the large and the small Helmholtz system. Now if the number of turns is proportional to the fifth power of the radii, the ratio n/ A 6 will also be the same for both systems, and since the systems are connected in opposi­tion, inhomogeneity terms of the order here considered will drop out. The main component of the field for this combined system will then be

(nl n.)

H x =0.44959i --- , Al A.

where the subscripts 1 and s refer to the large and small Helmholtz systems, respectively. It was confirmed experimentally by a measurement of field gradients that this combined system produces a very considerable

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272 G. G. SCOTT

I~ A, -I

r-A.--! T My T AI

."1' .t

FIG. 3. Diagram of double Helmholtz coil system for producing fields of high homogeneity.

improvement in homogeneity over that of the large system alone.

In this double Helmholtz system, the homogeneity correction on the field of the major coils, is accomplished with a pair of coils producing a considerably weaker field. This decreases the winding precision required on the smaller correcting pair. Also the very few turns required on the inner system makes possible a close approach to ideal current filaments.

The double Helmholtz array also gives very good access to the working space, and makes possible a convenient ar'l'angement for the mUltiple components which are necessary to eliminate the time variations occurring in the earth's magnetic field. The fact that the inner Helmholtz pair must be reversed with respect to the outer one, reduces the current-to-field efficiency of the system. However, this is not important in this particular application since only small magnetic fields are required. Other possible multiple coil arrangements for producing highly homogeneous fields have been discussed by Garrett,3 and McKeehan.4

In the coil array used to neutralize the earth's mag­netic field (Fig. 1) both the vertical and north-south components used a double Helmholtz system. The large coils in the vertical group were wound on accurately machined aluminum forms having a diameter of about 9 ft. The windings were laid in grooves having a cross section of 1 by 1 in. Each coil contained 272 turns of # 16 single Formex-single glass insulated copper wire.

aM. W. Garrett, J. Appl. Phys. 22, 1091 (1951). 4 L. W. McKeehan, Rev. Sci. Instr. 7, 150 (1936).

The small coils were about 49 in. in diameter and contained 6 turns each. It required 316 ma to neutralize the vertical component. The north-south neutralizing system was of similar construction, the large section being approximately 8 ft in diameter and the smaller internal pair being about 48 in. in diameter. The large section had 110 turns of # 12 single Formex single glass insulated copper wire in each coil. The small section had 3 turns in each coil. It required 213 ma to neutralize the horizontal component. The east-west system consisted of a single Helmholtz pair, since only very small fields were required in this direction. These coils were about 4S in. in diameter. All of the coil systems were mounted so that their magnetic axes could be easily moved through small angles, and very sensitive magnetic methods were used to determine the proper positioning. It should be noted here that it is important that all coils be placed on very solid foundations so as to prevent changes in alignment due to settling.

MAGNETIC VARIOMETERS

Since the earth's magnetic field is continually chang­ing, it is necessary to continually vary the current in the coil system to obtain proper neutralization.

The device used to follow magnetic variations in the east-west direction consisted of a magnetized rod suspended by a very fine filament, and surrounded by a coil through which an electric current could be passed. The suspended system was oil damped, and was located far enough from the main coil system so that the mag­netized rod did not produce an appreciable field in the working space. The rod, of course, pointed in a general north-south direction. The coil surrounding it had its axis in an east-west direction. The angular orientation of the rod was observed by means of an optical lever system capable of detecting angles of rotation of r\ sec of arc. When the magnetized rod turned away from some predetermined orientation it could be returned by passing a current through the surrounding coils. These coils were matched to the main east-west Helmholtz system and connected in series with it. Hence east-west magnetic variations were compensated both at the variometer and in the working space. In practice the balance point for this variometer was taken so that the rod pointed in the mean position of the earth's magnetic meridian. This minimized the field requirements of the small single east-west system.

In the device used to eliminate variations in the north-south component of the earth's field, a small coil consisting of a large number of turns of fine wire was suspended as a sensing element. Oil damping was used, and the magnetic axis of the coil was oriented in an east-west direction. Surrounding this coil was a Helm­holtz pair 4 ft in diameter pointing in the direction of the earth's total magnetic field. This orientation was used so as to also approximately eliminate the vertical component of the field surrounding the sensing element.

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COMPENSATION OF THE EARTH'S FIELD 273

The horizontal component of the field produced by this Helmholtz pair was matched to the main horizontal north-south coil system. Matching was obtained by first determining the closest integral number of turns in the variometer system; second by slight changes in the dip angle of the coil axes; and finally by using a very high resistance shunt across the 9 ohms of the main north-south field system. To determine the proper balancing current in the neutralizing coils, a current was reversed through the suspended feeler coil. If a north-south magnetic field was present, this coil turned through an angle which depended on the field strength. This angle was observed by a photoelectric multiplying system of high sensitivity. The current in the north­south system was varied until no deflection of the sensing coil was obtained. Records of time variations occurring in the earth's magnetic field are shown in Fig. 4. These records, for four different 24-hour periods, show different degrees of magnetic activity in the east­west component. The maximum variation in these charts is about 0.002 oersted. Hand-operated rheostats were used with the variometers to follow these slow variations in both of the horizontal components.

FIELD DETECTORS

In order to determine the proper alignment and matching for the neutralizing coil system, it was' necessary to have a method of detecting very small magnetic fields in the working space. To detect magnetic fields in the horizontal direction a sensing coil of 6000 turns of # 36 Formex-insulated wire was used. This coil was 22 cm in the vertical direction, and was wound on a form having an H-shaped cross section whose over-all dimensions were 1.5X 1.5 cm. This coil was suspended in a vacuum chamber located at the center of the neutralizing coil system. Oil damping was used and a 52-ft radius of curvature mirror was carried by the suspended coil for observing rotation. In detecting residual horizontal fields, a 16-ma current was re­versed through the suspended coil and the resulting rotation measured. The sensitivity of the system was such that a horizontal field of 2.5X 10-6 oersted pro­duced a scale deflection of 1 mm. The system was suspended from a torsion head so that horizontal fields in different directions could be detected. Mter eliminat­ing horizontal fields, a small inductor connected to a suitable vacuum tube amplifier was used to indicate the proper current for the vertical neutralizing system.

In addition to using the horizontal field detector for matching and aligning the various coil systems, it was also used to check the ability of the variometers to

FIG. 4. Four 24-hour records showing typical time variations in the earth's magnetic field. Records were selected from an auxiliary variometer which made a continuous plot of the east-west component.

maintain field compensation for periods of several days. This instrument showed that horizontal fields in the working space (22 cm in the vertical by about 2 cm in diameter) were continually kept below about 2X10-5

oersted. In the particular experiments for which this field

neutralizing system was designed, it was even more important to have a working space free of magnetic gradient, than it was to have the space completely neutralized. In order to study the magnetic gradient in the working space, a closely matched and accurately aligned pair of coils was made into an astatic system and supported on a critically damped torsional device as was the horizontal field detector. The individual coils had 15150 turns of # 37 wire. The matched coils were mounted on a staff so that their axes were parallel and separated by a distance of about 17 cm. They were connected in series opposition. The sensitivity of this gradient detector was such that a reversal of 16 rna in the coils gave a 1-mm deflection for a vertical gradient in the horizontal component of 8X 10-8 oersted per cm. Measurements using this instrument indicated that there was no vertical gradient in the horizontal compo­nent greater than about 2X 10-7 oersted per cm in the working space.

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