STUDY OF THE EARTH’S MAGNETIC FIELD ON ARTIFICIAL SATELLITES AND ROCKETS

N. V. Pushkov and S. Sh. Dolginov

The program of the International Geophysical Year (IGY) provides for geomagnetic measurements to be carried out on artificial satellites and rockets, as a result of which experimental data should be obtained on the spatial distribution of the Earth’s magnetic field at great altitudes. In the present article, some geophysical and technical aspects of such measurements are considered.

PRINCIPAL TASKS OF GEOMAGNETIC MEASUREMENTS ON ARTIFICIAL SATELLITES AND ROCKETS

a) The Earth’s magnetic field and its features

Around the Earth there is a natural magnetic field, the nature and origin of which remain unexplained to this day. Many theories—or, more precisely, hypotheses—have been proposed that have attempted to explain one or another feature of the Earth’s magnetic field, but none of them can be regarded as fully reliable.

The Earth’s magnetic field influences the motion of charged particles located in the upper ionized layers of the terrestrial atmosphere, arriving to us from the Sun and from outer space; this leads to the formation of such geomagnetic effects as the polarization of radio waves reflected from the ionosphere, latitude effects in cosmic rays and auroras, the orientation of auroral rays along the lines of force of the magnetic field, and so on.

It has also been established that large irregular changes in the Earth’s magnetic field, known as magnetic storms, are clearly correlated with changes in the intensity of cosmic rays, the heights and critical frequencies of ionospheric layers, the appearance of auroras at low latitudes, and certain other helio- and geophysical phenomena. All this indicates that the action of the Earth’s magnetic field on charged particles may be manifested at very great distances from the Earth.

The Earth’s magnetic field is divided into a constant field and a variable field. The constant field also includes very slow, so-called secular variations of the Earth’s magnetic field; all other, more rapid changes—such as magnetic storms, pulsations, diurnal variations, etc.—are assigned to the variable field. The distribution of the magnetic field and its changes in time have so far been studied only at the Earth’s surface, and even there insufficiently. Comparatively few measurements have been carried out in the polar regions. Measurement data at sea have reduced accuracy.

Using data from ground-based observations, one can, by the method of spherical harmonic analysis, separate the constant and variable fields into parts whose sources are located inside the Earth and outside it. Numerous analyses of the constant field carried out up to the present time show that the greater part of it is produced by sources located inside the Earth, and only a small part of the field (about 1%) by sources outside the Earth’s surface. In reality, the external part of the constant field is doubtful, since its magnitude lies within the limits of the errors of the expansion, given present knowledge of the field distribution.

The separation of the fields of daily variations and magnetic storms shows that the greater part of them, approximately \(2/3\), is produced by sources outside the Earth’s surface, and the smaller part, approximately \(1/3\), by sources inside the Earth. The latter may be electric currents induced in the conducting layers of the Earth when the external field changes.

The external part of the field of daily variations and magnetic storms can also be represented in the form of an equivalent system of electric currents assigned to one or another altitude. The problem of determining the location of the field sources from a given distribution of it on the surface is many-valued. Many systems of currents can be proposed that give the same distribution of the variable field on the Earth’s surface, as well as currents induced in the Earth. Therefore, the calculated equivalent current systems assigned to an arbitrary altitude should be regarded rather as a convenient way of representing the field than as a physical reality.

Equivalent current systems of solar daily variations were first constructed by Bartels on the basis of the data of an analysis of solar daily variations carried out by Chapman. He assigned them to a thin spherical layer at an altitude of 100 km. Later, current systems of daily variations based on observations of the 2nd International Polar Year were calculated by Benkova[^1]. Idealized systems of electric currents of magnetic disturbances, based on mean data and assigned to altitudes of 100–150 km, were first constructed by Chapman and subsequently refined by him together with Vestine. Among the recent works connected with the calculation of current systems of magnetic storms, one should mention the works of Vestine[^2] and Benkova[^3]. In them, current systems are presented for the first time for individual magnetic storms and disturbances.

A characteristic feature of the currents of magnetic storms is their great concentration along the zone of maximum frequency of auroral visibility. They may be considered here as a linear or cylindrical current (a jet of electric current) included in a current layer of lower density. On the evening side of the Earth the linear current flows westward, and on the morning side eastward. Chapman[^4] assumes that anomalously large values of the daily variations of the field in the region of the geomagnetic equator may be caused by a linear current flowing here in the daytime from west to east. The magnitude of the field produced by such a current at a distance \(R\) from it will be:

\[ \Delta F = 0.2 \frac{I}{R}, \]

where \(\Delta F\) is expressed in gammas, \(I\) is the current strength in amperes, and \(R\) in km.

The discovery of the ionosphere and the establishment of a close connection between changes in the Earth’s magnetic field and in the ionosphere have made most probable the assumption that daily variations and magnetic storms are caused by electric currents in the ionosphere. At the same time, some investigators do not exclude the possibility that the final phase of storms (after-effects of the disturbance) is determined by a system of electric currents in the form of a closed ring surrounding the Earth in the equatorial plane at a distance of several Earth radii from the center of the Earth[^5].

b) Problems Solved by Magnetic Measurements
on Rockets and Satellites

Magnetic measurements on satellites and rockets can reveal systems of currents in the ionosphere, estimate their density, and make it possible to draw conclusions about the existence of electric currents outside the ionosphere.

The magnetic field of a system of currents can be determined as the difference between the measured values of the field and those calculated under the assumption of the action of a single constant field. In these calculations we neglect the magnetic field of currents induced in the Earth. To compute the constant field at altitude, we may use an empirical formula expressing the potential of the Earth’s magnetic field in terms of a series of spherical functions:

\[ V=a\sum_{n=1}^{\infty}\sum_{m=0}^{n}\left\{g_n^m\cos m\lambda+h_n^m\sin m\lambda\right\}P_n^m(\cos\theta)\left(\frac{a}{r}\right)^{n+1}, \tag{1} \]

where \(r,\theta,\lambda\) are the spherical coordinates of the point, \(a\) is the mean radius of the Earth, \(P_n^m(\cos\theta)\) are Schmidt’s associated functions, and \(g_n^m\) and \(h_n^m\) are numerical coefficients. These coefficients are found so that the field components calculated from formula (1) for \(r=a\) correspond as well as possible to the observed distribution of the field on the Earth’s surface.

The calculated values of the field components—northern, \(x\), eastern, \(y\), and vertical, \(z\)—for the epoch 1945, for altitudes of 100, 300, 500, 1000, and 5000 km, for a grid of points every \(10^\circ\) in latitude and \(30^\circ\) in longitude, are given in Vestine’s work\(^{2}\). In the calculation, series having 48 terms and containing spherical functions up to and including the 6th order were used.

In many cases, when calculating the field at altitude, one restricts oneself only to terms of the first-order function. The potential of the field of the first-order function \((n=1)\) will be:

\[ V_1=g_1^0\cos\theta+g_1^1\sin\theta\cos\lambda+h_1^1\sin\theta\sin\lambda . \tag{2} \]

The potential of the field of a uniformly magnetized sphere and of the field of a central dipole has an analogous expression. On the basis of this formal analogy, the field of the three terms of the first-order function is regarded as the field of uniform magnetization of the Earth.

The calculated values of the field components—the northern, \(x\), eastern, \(y\), field of the Earth. The axis of uniform magnetization passing through the center of the Earth intersects the Earth’s surface at the geomagnetic poles. The north geomagnetic pole was located in 1945, according to Afanas’eva’s data\(^{6}\), at the point \(\varphi=79.4^\circ N;\ \lambda=292.6^\circ E\), and according to Vestine’s data\(^{2}\), at the point \(\varphi=78.6^\circ;\ \lambda=289.9^\circ E\).

Sometimes, instead of a central dipole referred to the geometric center of the Earth, one uses an eccentric dipole referred to the so-called magnetic center of the Earth. The north pole of the eccentric dipole is located at the point \(\varphi=80.1^\circ N;\ \lambda=277.3^\circ E\).

The eccentric dipole corresponds somewhat better to the distribution of the field observed on the Earth’s surface. The field of functions of higher orders will be given by the difference between the observed field and the field of uniform magnetization. This “residual field” has a clearly expressed regional character and is regarded as the field of magnetic anomalies.

It follows from expression (1) that the fields of functions of higher orders must decrease with distance from the Earth significantly faster than the field of uniform magnetization.

Taking this circumstance into account, as well as the small magnitude of the residual field, the Earth’s field at large distances from it is taken to be the field of uniform magnetization. However, calculation of geomagnetic effects with allowance only for uniform magnetization sometimes leads to a discrepancy between theoretically calculated and actually observed effects. Thus, in particular, it had long been noted that the region of minimum values of cosmic-ray intensity did not coincide with the geomagnetic equator. Analyzing measurement data for the intensity of the neutron and meson components of cosmic rays in the equatorial region, Simpson \(^{7,8}\) indicated that better agreement could be obtained by shifting the point of intersection of the geomagnetic equator and the geographic equator westward by \(45^\circ\) and transferring the north pole of the eccentric dipole to the point \(\varphi = 80.2^\circ N\) and \(\lambda = 246.8^\circ E\). The discrepancy in the position of the geomagnetic poles, determined from magnetic data and from cosmic-ray intensity data, indicates the necessity of taking into account the influence of the anomalous field and of the field of the ionospheric ring current \(^{9}\).

Magnetic measurements on satellites and rockets can provide experimental data on the attenuation of magnetic anomalies and other features of the field with distance from the Earth. These data can be used to test various assumptions about the depth of the sources of regional magnetic anomalies. More precise information about the depth of the sources of regional anomalies will be of great importance for the study of the Earth’s internal structure. Comparison of magnetic measurements on satellites with determinations of the distribution of masses within the Earth from observations of perturbations of the satellite orbit may also be used to establish a connection between gravitational and magnetic anomalies produced by an inhomogeneous distribution of masses at great depths.

From what has been said it is clear that the data of magnetic measurements on satellites and rockets may be used for solving a number of problems. At the present initial stage of their development, when the scalar quantity of the total field-intensity vector is being measured, they may be used mainly to investigate the general distribution of the field at great heights, to detect and evaluate systems of electric currents of solar-diurnal variations and magnetic storms. The idea of the possibility of detecting current systems by means of magnetic measurements on a rocket was first expressed by Vestine \(^{2}\). Vestine indicated that, in a vertical crossing of a current layer, it would be possible to detect it with a magnetometer from the discontinuity of the horizontal components of the magnetic field of the currents at the boundaries of the layer.

The first detection of currents in the \(E\)-layer of the ionosphere was made by Zmter and his collaborators \(^{10,11}\) near the geomagnetic equator.

Two ascents were made to an altitude of \(105\) km. One of them was carried out after noon, when small changes in the horizontal component were observed on the Earth, and the other—several days later at midday. During the first ascent, the usual decrease of the field with altitude was observed, complicated by the influence of a local magnetic anomaly present in the launch region. During the second ascent, at altitudes of \(93\)—\(105\) km, a jump in the change of the field intensity of about \(400\ \gamma\) was detected. It is assumed that this change is equivalent to a jump in the change of the horizontal components of the field when passing through a thin current layer,

\[ \Delta F = \Delta H = 0.4\pi I, \]

where \(\Delta F\) is the jump in gammas and \(I\) is the current intensity in amperes per kilometer. The jump in the change of the field observed in the measurements corresponds to that which could be expected when the magnetometer passed through the current system of diurnal

variations in the equatorial region. Its magnitude proved to be greater than expected.

The possibility of detecting current systems by means of magnetic measurements on rockets as the rocket passes through the layer is considered in detail in Chapman’s paper^12, where the following program of rocket investigations is recommended:

a) Study of the linear current flowing along the auroral zone during magnetic disturbances.

b) Study of the branches of this current that may flow in the arcs of the aurorae.

c) Verification of the hypothesis that, during magnetic storms, an extra-ionospheric ring of currents arises in the equatorial plane.

d) Study of the height, thickness, and density of the current layer in the polar cap.

e) Studies of the currents of daily variations during magnetically quiet days at low and middle latitudes.

Magnetic measurements on rockets will be carried out during the IGY in a number of countries at high and low latitudes. The ionospheric layers are located at various heights ranging from 90 to 300 km. The F2 layer of the ionosphere rises even higher during magnetic disturbances. In order to clarify the role of each of the ionospheric layers in creating current systems, it is necessary to carry out at least some of the measurements on large rockets capable of raising magnetometers above the ionosphere.

A disadvantage of rocket measurements is that they last for a very short time and pertain to a small region near the rocket launch site. In order to study the spatial distribution of the field and its temporal changes, it is necessary to make a large number of repeated measurements at many points, which entails great expense. It may therefore be supposed that magnetic measurements on rockets will be carried out only in the most interesting places and at the most interesting moments in time.

The most interesting places for measuring the magnetic field on rockets may be the zones of maximum frequency of visible aurorae in the Arctic and Antarctic, with the aim of detecting and estimating the intensity of linear currents arising there during magnetic disturbances. The most suitable time for launching rockets may be chosen on the basis of forecasts of magnetic disturbances and data from visible recordings of changes in the magnetic field at observatories. The IGY falls in the years of maximum solar activity and, consequently, is the most favorable period for detecting the current systems of daily variations in temperate latitudes. Magnetic measurements on rockets should be made there in summer, when the daily variations are greatest.

c) Possibilities offered by satellites in the study of the Earth’s magnetic field

Magnetic measurements on satellites will apparently be less accurate than those on rockets. The smaller dimensions of a satellite do not allow the sensitive elements that detect the field to be placed at large distances from magnetic masses and other sources of interference. An unoriented satellite will, in addition, be less stable than a rocket. It will also be considerably more difficult to tie the measurements on the satellite to ground-based measurements. A major advantage of the satellite will be that measurements on it can be carried out over the course of a long—

at the same time. Artificial satellites can therefore be used not only for studying the spatial distribution, but also the temporal variations of the field when repeated measurements are made over the same place.

Measurements of the magnetic field on artificial satellites are considered in \(^{13,14,15,16}\). The following tasks are envisaged for these measurements \(^{13}\):

a) Study of the spatial distribution of the permanent magnetic field around the Earth.

b) Evaluation of the spatial distribution and heights of systems of electric currents in the ionosphere and beyond it.

c) Study of the inhomogeneous structure of the ionosphere.

Detection and evaluation of current systems can be carried out by various methods depending on whether the satellite crosses the current layer, moves above it, below it, or within it. The motion of the satellite in the layer can be established in the case of an inhomogeneous distribution of ionization in it, in the horizontal and vertical directions. Observations of winds in the ionosphere indicate that such an inhomogeneous distribution of ionization does indeed occur. In the presence of inhomogeneities in the ionosphere and the associated local strengthening or weakening of currents in the ionosphere, the magnetometer signal will fluctuate strongly. By isolating from these fluctuations the slower fluctuations caused by inhomogeneity in the distribution of the permanent field, it will be possible to judge the dimensions of ionospheric inhomogeneities and their intensity. Apart from the time of ascent and descent, a short-lived satellite can be in the ionosphere only when it moves along an elliptical orbit, and then at perigee.

The magnetic variations produced by currents in the ionosphere will be measured with different signs on the ground and above the ionosphere; this circumstance can be used as a criterion for determining the location of linear currents and of the current layer when the satellite moves outside the ionosphere. The field of an annular extraterrestrial current will be measured on the satellite everywhere with one sign.

Since the field of the current will be determined from differences between the measured and calculated values of the field, particular attention must be paid to the accuracy of determining the position of the satellite at the moment of measurement. An error in determining the satellite’s altitude of \(1\) km leads to an error in determining the field of \(18\)—\(20\) gammas. The same error in the satellite’s position in latitude leads to an error in determining the field of about \(4\) gammas. The most accurate values of the permanent field at altitudes can apparently be obtained by averaging repeated measurements at altitudes on magnetically quiet days.

From the point of view of studying the general distribution of the magnetic field and polar current systems, the most suitable orbit for a satellite is an orbit passing through the geographic poles of the Earth. As the satellite moves around the Earth, owing to the Earth’s rotation the satellite’s orbit will shift westward. The instruments installed on the satellite will thereby carry out a magnetic survey of the Earth. If the satellite is launched at some angle to the Earth’s axis of rotation, then it is desirable that this angle be no more than \(10^\circ\), so that measurements can be made in the region of the pole of uniform magnetization of the Earth.

However, polar orbits and those close to them will require a considerably larger number of ground stations than an equatorial orbit and those close to it. An equatorial orbit can be used, however, for solving a smaller number of problems, chiefly for

checking the hypothetical equatorial ring current outside the ionosphere.

For interpreting the results of magnetic measurements on satellites and rockets it is very important to have data on auroras and on changes in the magnetic field and ionosphere at as many stations as possible. The IGY offers the greatest opportunities for this. Of great value may be such simultaneous observations from satellites of the ultraviolet and corpuscular radiation of the Sun beyond the limits of the ionosphere.

The interpretation of magnetic measurements on satellites will be connected with a very large amount of computational work, but in return it may yield very valuable results. The use of these measurements will expand considerably when it becomes possible to increase their accuracy and to pass from measurements of the scalar magnitude of the field intensity to measurements of the field components. In particular, they may then be used to determine the normal field and to determine more accurately the locations of the sources of secular variations. It is not excluded that these measurements will lead not only to a refinement of present ideas, but also to the emergence of new ideas and new concepts.

MAGNETOMETERS FOR MEASUREMENTS ON SATELLITES AND ROCKETS

The most valuable results in measurements of the magnetic field on satellites and rockets could be obtained with the aid of magnetometers measuring the field components or the scalar magnitude of the field vector and its direction. The possibility of using such magnetometers will appear in the future. In the near future, however, magnetometers based on nuclear induction and with magnetically saturated sensors, measuring the scalar magnitude of the total field intensity, will apparently be used.

a) Proton magnetometer

(magnetometer based on measuring the frequency of free precession of protons)

The nuclear-induction method of measuring field intensity is based on the use of the phenomenon of free precession of protons in an external magnetic field. The precession frequency of protons, which possess magnetic and mechanical moments, is determined, as is known, by the Larmor relation $\omega=\gamma H$, where $\gamma$ is the gyromagnetic ratio and $H$ is the magnetic-field intensity.

Using this relation, one can, by finding the frequency of free precession of protons and knowing the gyromagnetic ratio, determine the field intensity. The precession frequency is usually measured in liquids rich in protons, whose gyromagnetic ratio is known most accurately: $\gamma_p=2.67528\pm0.00006\cdot 10^4\ \text{sec}^{-1}\ \text{oersted}^{-1}$.

In 1954 Packard and Varian[^17][^18] described a convenient method for observing the free precession of protons in a weak magnetic field, making it possible to measure this field with high accuracy. This method consists in the following: a sample—a liquid with a high proton content, situated in a field $H_0$—is subjected for a short time to a strong field $H$ (of the order of 100 oersteds), which is then rapidly switched off. The field $H$ is produced in an excitation coil surrounding the sample and directed approximately perpendicular to the field $H_0$. Under the action of the field $H$ the sample acquires a macroscopic magnetization, whose intensity will be equal to $I_{\text{n}}=\chi_{\text{n}}H$, where $\chi_{\text{n}}$ is the nuclear susceptibility. After

after the field \(H\) is switched off, the macroscopic magnetic moment arising in the sample begins to precess freely around the field \(H_0\) with frequency \(\omega=\gamma_p H_0\). The magnitude of the macroscopic magnetic moment of the sample gradually decreases, but the relaxation time is about 3 sec and is sufficient to allow measurement of the frequency of the voltage induced by the precessing moment of the sample in the signal coil (which is also the excitation coil), now connected to an amplifier. The alternating electromotive force induced in the coil will be
\[ E=K\chi_{\mathrm{я}}\gamma_p H_0 H\sin^2\theta e^{-t/T_2}, \]
where \(K\) is a constant depending on the parameters of the coil, the filling factor, and the \(Q\)-factor of the circuit; \(\theta\) is the angle between the field \(H\) and \(H_0\); \(t\) is the time from the moment of switching off the field \(H\); and \(T_2\) is the relaxation time.

The method of measuring the field on the basis of nuclear induction has remarkable advantages in comparison with other methods: 1. In it, measurement of the field is reduced to measurement of frequency. 2. The accuracy of the measurement does not depend on the design parameters of the sensor and of the channels forming the signal. 3. The magnetometer readings are obtained in absolute measure. 4. The sensor and the channels forming the signal are, in principle, free of zero drift. The accuracy of measurement is determined only by the accuracy of determination of the frequency standard. 5. The measurement results, when the sensor is in a fixed position, do not depend on the orientation of the sensor in the measured field. 6. The sensor signal, amplified by an audio-frequency amplifier, can be transmitted by telemetry and measured accurately at a distance (the signal may be used directly to modulate a transmitter). The accuracy of measurements by proton magnetometers in an observatory is estimated at \(1\ \gamma\) and is limited only by the accuracy of the determinations of \(\gamma_p\).

When this method is used on moving objects, certain complications may arise that make the measurements more difficult and increase their error: 1. Although the precession frequency does not depend on the orientation of the excitation coil with respect to the measured field, the signal strength will be proportional to \(\sin^2\theta\) and, for small \(\theta\), will be close to zero. 2. When the coil rotates together with the moving object with angular velocity \(\dot\varphi\) about an axis perpendicular to the coil axis, the field will be measured with an error \(\Delta H'=\pm 3.7\dot\varphi\), where \(H\) is in gammas and \(\dot\varphi\) is in radians per second[^19]. 3. Inhomogeneity of the magnetic field in the volume of the magnetometer sensor greatly reduces the relaxation time \(T_2\). At large field gradients, it is practically impossible to measure the signal.

A proton magnetometer can be very convenient for measurements on a rocket, since the measurements are confined to a comparatively small range of field variations, and signal transmission is carried out within line of sight. In the case of measurements on satellites, the onboard equipment of the proton magnetometer becomes much more complicated.

1. The magnetometer amplifier must provide a sufficiently large signal-to-noise ratio in the frequency range 1200–2800 cps.

2. With a limited number of ground stations, there arises the necessity for a storage device and for an onboard generator of reference marks, which must be stored together with the magnetometer signals.

3. The satellite must be equipped with three mutually perpendicular coils and a switching device so that the field can be measured at any position and rotation of the satellite relative to the field[^15].

4. In the immediate vicinity of the coils there must be no sources of extraneous magnetic fields with gradients greater than \(5\ \gamma\) per \(1\ \mathrm{cm}\).

b) Self-Orienting Total-Vector Magnetometer

The first measurements of the Earth’s magnetic field on rockets[^10] were carried out with three-component magnetometers having magnetically saturated sensors. The sensors were rigidly fastened to the rocket body and were provided with a squaring device for obtaining the scalar value of the total field vector. Such a simple design operated successfully because the sensors on the rocket were oriented to some extent, and the range of measured quantities was comparatively small.

In measurements of the field on satellites, such a design cannot be satisfactory. For installation on a satellite, an instrument of the self-orienting total-vector type is necessary. The suitability of using instruments of this type on a satellite is determined, at least in the first experimental measurements, by the following circumstances:

1. If it were possible to create a self-orienting magnetometer with magnetically saturated sensors of small dimensions, low weight, and low power consumption, which would have high sensitivity and stability over time, then such a magnetometer could not only measure the scalar value of the magnetic field, but also determine the orientation of the satellite.

2. Magnetometers with magnetically saturated sensors are less sensitive to inhomogeneity of the magnetic field. Field inhomogeneity affects only the stability and accuracy of their operation, but does not prevent the formation of a signal.

3. Magnetometers with magnetically saturated sensors will not create significant interference for the operation of other instruments on the satellite, which cannot be said of proton magnetometers.

A total-vector magnetometer with magnetically saturated sensors consists of three main parts: a measuring channel, a mechanical orientation unit, and two orienting channels. The measuring and orienting channels contain a number of analogous functional elements: sensors, selective amplifiers, and phase-sensitive rectifiers. These elements serve to convert the signal of the Earth’s constant magnetic field into a direct-current electrical signal of sufficient power.

In the simplest case, a magnetically saturated sensor consists of a permalloy plate and primary and secondary windings wound on it. When the plate is magnetized by the field \(H = H_0 + H_m \sin \omega t\), where \(H_0\) is the magnetic field being measured and \(H_m \sin \omega t\) is the auxiliary excitation field that magnetizes the sensor core to saturation, a nonsinusoidal voltage arises in the secondary winding, containing both even and odd harmonics. The even harmonics are an odd function of the measured field \(H_0\) and an even function of the auxiliary excitation field. The odd harmonics, conversely, depend in an odd manner on the phase of the excitation field and in an even manner on the sign of the constant field \(H_0\).

As sensitive elements it is advisable to use sensors of even harmonics[^20]. The greatest stability is exhibited by magnetometers in which not all even harmonics are used, but only the second. The circuit of a sensor of the second-harmonic type consists of two parallel permalloy plates, on which are wound two primary windings connected in series—

but connected in opposition, and one common secondary winding embracing both plates. With this method of connection the odd harmonics are compensated in the secondary winding, while the even harmonics add.

The cores of the sensors are made in the form of thin strips or wires. The demagnetizing factors of such cores in the transverse direction are thousands of times greater than in the longitudinal direction. Therefore, they are practically magnetized by the projection of the field onto the longitudinal axis of the sensor. For this reason, the voltage of the second harmonic on the winding of a sensor installed perpendicular to the field is equal to zero. When the sensor is deflected to one side or the other from the direction perpendicular to the field, a second harmonic of the corresponding phase appears on the sensor winding, whose amplitude, within considerable limits, is proportional to the angle of deflection. Thus, sensors of the indicated type possess two important properties: direct sensitivity to the sign of the measured constant field and selectivity with respect to the direction of the field.

In magnetometers of the total vector, three mutually perpendicular sensors are used, fastened on the platform of the orientation unit. The sensor installed perpendicular to the platform is the measuring one; the other two, lying in the plane of the platform, serve to set it perpendicular to the total field vector. The sensors are supplied from a special generator with a frequency of 2000 cps. Its voltage is free from even harmonics. The signals from each sensor are amplified by selective amplifiers tuned to a frequency of 4000 cps, after which they are fed to phase-sensitive rectifiers. The magnitude and sign of the constant component of the rectified current of each of the three phase-sensitive rectifiers depend on the magnitude and sign of the magnetic field acting on the corresponding sensor.

Subsequently the circuits of the measuring and orienting channels differ substantially. The output signals of the phase-sensitive rectifiers of the orienting channels are fed to the input of the magnetic amplifiers of the servosystems of the orienting channels. In the servosystems these signals are converted into signals of frequency 400 cps and amplified in power. The output terminals of the servosystems of the orienting channels are connected to the control windings of low-inertia phase-sensitive motors of the mechanical orientation unit. The constant phases of the low-inertia motors are supplied from a special 400 cps generator, from which voltage is also supplied for exciting the magnetic amplifiers.

Thus, the channels that convert the magnetic-field signal into an electrical signal, and the servosystem, operate at different frequencies. This increases the noise immunity of the circuit. The servosystem contains no selective elements, and its operating mode does not depend on changes in the voltage of the power sources over wide limits. The motors of the servosystem rotate the platform with the sensors fastened to it, through a mechanical transmission, until the voltage on their control windings becomes equal to zero, which occurs when the sensor of the measuring channel is oriented along the total vector.

When the platform is deflected from the normal to the direction of the total vector by an angle \(\alpha\), a mismatch signal proportional to \(\sin \alpha\) appears on the orienting sensors. The associated error of the measuring sensor will be proportional to \(\sin^2 \alpha/2\). Consequently, with an error in the orientation of the platform of \(1^\circ\), the error of the measuringablytyped

The sensor does not exceed 4 gammas. The satellite magnetometer orientation unit must permit any number of rotations about both axes. Therefore, it must have slip rings with reliable contacts.

On the shafts running from the motors to the platform of the orientation unit, movable contacts of two potentiometers may be mounted; their position will depend on the orientation of the satellite body with respect to the Earth’s magnetic field. The position of the movable contacts can be transmitted by two telemetry channels.

In the measuring channel of the magnetometer, a compensation method of measurement is used. A field within the limits of \(\pm 2500\ \gamma\) can be compensated automatically by introducing deep negative feedback. Changes within these limits can be transmitted by two telemetry channels. The remaining part of the field can be compensated by a current supplied to the compensation winding from a stable current source. The compensation current can be changed automatically when the field deviates by more than \(\pm 2500\ \gamma\) from the specified levels. The position of the range switch must be transmitted by a fifth telemetry channel.

If all the electronic units of this very complex system are made with semiconductor elements, then the weight of the magnetometer together with the orientation unit will not exceed 12–13 kg. The power consumed by the magnetometer will be about 20 watts. Obviously, such a circuit is possible only if the temperature conditions inside the satellite permit the use of semiconductor elements. It is expected that the temperature of the satellite, with small internal energy sources, may fluctuate within the range \(0\text{–}10^\circ\)C.

However, even in this case the question may arise of the stability of the zero point of the magnetometer. Analysis of individual circuit elements and experimental verification of the stability over time of the zero points of analogous magnetometers made with germanium triodes, diodes, and magnetic amplifiers show that the zero drift of magnetometers at room temperatures does not exceed 60 gammas per day. In the temperature range \(0\text{–}20^\circ\), the temperature coefficient of such magnetometers may be on the order of 10 gammas per degree, which appreciably exceeds the temperature coefficient of ordinary magnetometers. However, the temperatures inside the satellite can be measured and transmitted by telemetry, and corrections for temperature changes can be introduced during processing.

CITED LITERATURE

1. N. P. Benkova, Trudy NIIZM, ser. 6, issue 1 (1941).
2. E. H. Vestine, L. Laporte, L. Lange and W. E. Scot, Carnegie Inst. of Wash. Pub. No. 580 (1947).
3. N. P. Benkova, Trudy NIIZM, issue 10 (20) (1953).
4. S. Chapman, Archiv. f. Meteorol. geophys. u. Bioklimatol. 4, 368 (1951).
5. V. C. A. Ferraro, In International Association of Geomagnetism and Aeronomy Bulletin No. 15b, 166–186, Paris (1956).
6. V. I. Afanas’eva, Izv. AN SSSR, ser. geogr. i geof. 11, No. 1 (1947).
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