MEASUREMENT OF POSITIVE ION CONCENTRATION ALONG THE ORBIT OF AN ARTIFICIAL EARTH SATELLITE

K. I. Gringauz, M. Kh. Zelikman

1. INTRODUCTION

The information presently available on the altitude variation of ion and electron concentrations in the ionosphere is very uncertain and contradictory, especially in the upper part of the ionosphere—at altitudes greater than 250–300 km, about which sounding of the ionosphere by radio waves, as a rule, cannot provide any information. Some authors, such as Bates[^1], believe that there are grounds for a substantial revision of the generally accepted data on the heights of the \(F\) layer, obtained by processing the results of radio sounding of the ionosphere. Rocket measurements of electron concentrations (for example,[^2]) have led a number of authors[^2][^3] to cast doubt on the established ideas concerning the layered structure of the ionosphere.

Equally uncertain is the information on inhomogeneities in the upper part of the ionosphere. Observations of scintillation of radio stars have led to the conclusion that ionospheric inhomogeneities exist which cause changes in the phase of cosmic radio emission passing through the ionosphere. According to Hewish’s estimate[^4], the typical size of these inhomogeneities, located at an altitude of approximately 400 km, is \(\sim 5\) km; these inhomogeneities move, carried by ionospheric winds, at a velocity of \(10^4\) cm/sec. Rapid variations in the amplitudes of individual radio pulses reflected from the ionosphere make it possible to suppose the existence in the \(F\) layer of considerably smaller inhomogeneities, with linear dimensions on the order of hundreds of meters and even less[^5][^6]. There are several possible explanations for the origin of these inhomogeneities, none of which can be regarded as reliable.

Since the orbits of artificial Earth satellites will pass through regions of the ionosphere lying above 200 km, i.e., mainly in its least studied parts, the question naturally arises of the possibility of using artificial satellites as a means for studying the structure of the ionosphere.

A comparison of the possibilities of geophysical investigations with the aid of artificial satellites and rockets makes it possible to note certain obvious advantages of satellites over rockets. These include, first of all, the possibility of prolonged observations and of obtaining statistically more complete results, and the possibility of obtaining information on the geographical variability of the quantities being studied (over the short time of the satellites’ revolution around the Earth).

As in the case of rocket experiments, the possible methods of investigating the ionosphere with the aid of satellites may be divided into two main groups.

K. I. Gringauz, M. Kh. Zelikman

1. The study of the propagation of radio waves between a satellite and the Earth, i.e., the study of radio signals emitted from the satellite (or from the Earth) and received on the Earth (or on the satellite; for this variant the use of radio telemetry is necessary).

2. Measurement of the characteristics of the ionosphere near the satellite by means of onboard instruments, with transmission of their readings to the Earth through a radio-telemetry system (or with storage by onboard recording devices).

The principal disadvantage of the methods of the first group is the influence, on the character of the received signals, of the entire thickness of the atmosphere located between the satellite and the Earth, which makes it extremely difficult to determine the location of inhomogeneities along the path of propagation of the radio wave that have caused a given change in the signals under study. In rocket experiments, in order to avoid this difficulty, observations are conducted so that the direction of propagation of the radio waves coincides with the direction of motion of the rocket; it is then assumed that during each measurement the ionosphere along the rocket trajectory remains unchanged. In this case changes in the radio signals may be attributed to the influence of newly appearing portions of the ionosphere in the path of propagation of the radio wave, and thus the vertical cross-section of the ionosphere may be determined.

In the case of an artificial satellite, the direction of radio communication with it from a given ground station will change continuously and will not coincide with the direction of motion of the satellite; therefore it becomes impossible to determine at what altitude those regions of the ionosphere are located that cause the observed changes in the signals received on the Earth (at any rate, without simultaneous observations from a number of ground stations). For this reason, the use on a satellite of apparatus for studying local characteristics of the ionosphere by the method of studying radio-wave propagation appears inexpedient.

The principal advantage of the methods of the second group is the complete independence of the measurement results from the characteristics of the thickness of the ionosphere lying between the satellite and the Earth, and from the processes occurring in it; in this case the instrument readings are determined entirely by the small region of the ionosphere surrounding the satellite. However, the appearance in the ionosphere of a moving body causes disturbances in the region surrounding it and, generally speaking, changes the values of the quantities to be measured in this region. This gives rise to a skeptical attitude toward the possibilities of studying the properties of the medium surrounding a flying satellite. Thus, for example, Newell\(^7\) expressed the opinion that such measurements on satellites are inexpedient.

The study of the concentrations of charged particles in the ionosphere is associated with a number of specific difficulties that do not affect the study of other parameters of the medium. Thus, the measurements will be affected by the electric potential acquired by the satellite; under the action of various radiations, electrons are emitted from the surface of the satellite; air particles are ionized as a result of the satellite’s motion.

However, the considerations that will be presented below make it possible to believe that, with the proper choice of the physical parameter to be measured and of the measurement procedure, the direct study of the properties of the ionosphere by means of artificial Earth satellites can yield valuable results. It seems to us that the most convenient parameter for such measurements is the concentration of positive ions. Let us note that in the literature there is an almost unanimous opinion that at the altitudes through which satellite orbits will pass (the region of the \(F\) layer,

and above), negative ions are practically absent; if this is so, then the determination of the concentration of positive ions is equivalent to the determination of the concentration of free electrons—the principal physical characteristic of the ionosphere.

2. SOME CHARACTERISTICS OF THE IONOSPHERE AT THE ALTITUDES UNDER INVESTIGATION

Knowledge of the approximate characteristics of the ionosphere in the region of interest to us is important for the correct formulation of the experiment in two respects: from the standpoint of the expected range of values of the quantity being measured, and from the standpoint of taking into account the conditions under which the measuring apparatus must operate, and of assessing the phenomena connected with justifying the choice of measurement of the concentration of positive ions as a means of studying the structure of the ionosphere. Below are given some data based on the concepts contained in the literature of recent years and partially taking into account the results of rocket investigations of the upper atmosphere.

Figure 1 presents graphs of the distribution of air temperature with altitude, obtained by various authors^8. The ion temperature \(T_i\) is taken to be equal to the temperature of the neutral molecules \(T\). The question of the relation between the ion temperature in the ionosphere and the electron temperature \(T_e\) was considered by G. Drukarev^9 and V. L. Ginzburg^10,5. According to these authors, although the velocity distributions of ions and electrons are Maxwellian, their temperatures \(T_i\) and \(T_e\) are in principle different. However, according to V. L. Ginzburg’s estimate, for the \(F\) layer \(\Delta T = T_e - T_i \approx 10^\circ \mathrm{K}\), and since \(T_i \approx 1000^\circ \mathrm{K}\), the practical difference between the electron temperature and the ion temperature in the \(F\) layer is very small. In a thorough review of data on the temperature of the ionosphere, published by Gerzon^11, the conclusion is also drawn that the electron temperature is in fact equal to the gas temperature (although there are indications of the possibility of briefly higher temperatures under the action of certain factors, for example in aurorae). It should be noted, however, that the considerations of the authors cited refer to altitudes below 400 km and do not take into account the changes in data on the altitude variation of the concentration of neutral molecules introduced in recent years by rocket investigations.

Fig. 1.

Bearing in mind the curves shown in Fig. 1, and assuming that the quantities \(T_i\) and \(T_e\) are practically identical, the order of magnitude of the thermal velocities of neutral molecules and ions may be estimated as \(v_i \approx 10^5\ \mathrm{cm/sec}\), and of electrons as \(v_e \approx 10^7\ \mathrm{cm/sec}\). Thus, the velocity of motion of an artificial Earth satellite \((v_{\mathrm{sp}} = 8 \cdot 10^5\ \mathrm{cm/sec})\) is an order of magnitude lower than the thermal velocity of electrons, but an order of magnitude higher than the velocity of ions.

According to data on mean free paths \(\lambda\), based on rocket experiments, at an altitude of 200 km \(\lambda \approx 3 \cdot 10^4\ \mathrm{cm}^{12}\). Assuming that the order of magnitude of the linear dimensions of the satellite is \(L \approx 10^2\ \mathrm{cm}\), one may assert that along the entire orbit of the satellite the condition \(\lambda \gg L\) is satisfied and that, from the point of view

from the standpoint of aerodynamics, the motion of the satellite takes place in the region of free molecular flow[^13].

From many years of observations of the ionosphere by the method of radio sounding it is known that the critical frequency of the \(F_2\) layer, even in years of maxima of solar activity, does not exceed \(16 \cdot 10^6\) cps, which corresponds to an electron concentration of \(2 \cdot 10^6\ \text{cm}^{-3}\). It should be borne in mind, however, that the data of ionospheric stations are determined by the extensive region of the ionosphere participating in the formation of the reflected signal, and cannot serve as proof of the absence of large \(N_e\) in small inhomogeneities. The altitude variation of \(N_e\) above the maximum of ionization of the \(F_2\) layer should be regarded as practically unknown. The results of the only rocket experiment of Berning[^14] published up to the present time, carried out above the maximum of the \(F\) layer, cannot, in our opinion, serve as a guide in preparing new experiments, if only because of the lack of statistics.

3. ON THE DISTRIBUTION OF CHARGED PARTICLES AROUND THE SATELLITE

Since the motion of the satellite, as was noted above, must occur in the region of free molecular flow, and since its velocity exceeds by an order of magnitude the thermal velocities of molecules, the perturbations produced by the satellite in the surrounding region of the ionosphere will differ considerably from the perturbations produced by rockets in lower layers of the ionosphere. Thus, near the satellite there will be no substantial changes in the temperature and concentrations of ions and electrons associated with aerodynamic effects such as shock waves and the boundary layer. Nor will there be any diffusional depletion of the plasma by charged particles near the surface of the body, which usually occurs when the dimensions of the body are large in comparison with the mean free paths of the particles (or are comparable with them).

Like any body situated in an electron–ion plasma, the satellite must acquire a negative charge as a consequence of the difference between the velocities of electrons and ions. The field of the charged body is screened by the adjoining layer of positive space charge, in which the electron concentration is considerably reduced in comparison with the undisturbed value. However, unlike the case in which an immobile or slowly moving body (in comparison with the thermal velocities of the gas particles) is placed in a plasma, this layer of positive charges will not adjoin the surface of the artificial satellite directly on all sides, since behind the satellite (in the direction opposite to the velocity vector) there will be an airless space that will not have time to be filled by particles of air. The dimensions and shape of this region will depend on the dimensions and shape of the projection of the satellite onto a plane normal to the velocity vector, and on the temperature of the air.

Since the thermal velocities of electrons exceed the velocity of the satellite by an order of magnitude, the indicated region will be filled with electrons until the field of the negative space charge that has formed prevents any further increase in the electron concentration within it. The entry of positive ions into the airless region depends on the magnitude of the satellite’s negative potential and on the field of the negative space charge located behind the satellite. For small values of these quantities, ions will not enter there, just as neutral particles do not. Thus, the layer of positi-

tive charges surrounds the satellite together with the airless volume behind it, filled with electrons; part of it adjoins the surface of the satellite, and part adjoins the indicated volume. The thickness of the layer increases as the concentration of charged particles decreases.

4. POTENTIAL OF THE SATELLITE

The condition for establishing the potential of the conducting surface of a body located in a plasma consists in the total current of charges collected by the entire surface being equal to zero, i.e.

\[ I_{\Sigma}=I_{+}+I_{-}=0. \tag{1} \]

The current of positive ions may be taken equal to

\[ I_{+}=eN_{+}v_{\mathrm{cn}}S_{+}, \tag{2} \]

where \(e\) is the electron charge, \(N_{+}\) is the concentration of positive ions, and \(S_{+}\) is the area of the projection of the satellite onto a plane normal to the velocity vector.

At \(T \approx 1000^\circ\mathrm{K}\) (see Section 2), expression (2) is valid if the satellite potential is not very large, and \(S_{+}\) is of the same order of magnitude as the surface of the satellite. A sufficient condition for relation (2) to hold is that the thickness of the layer of volume positive charge be small in comparison with the linear dimensions of the satellite.

The magnitude of the electron current to the surface of the satellite, owing to the presence of the Earth’s magnetic field, depends on the ratio of the Larmor radius to the mean free path and to the linear dimensions of the satellite. In the altitude region under consideration, for the values of the electron temperature indicated in Section 2, the mean Larmor radius is much smaller than the mean free path and the dimensions of the satellite, and, for a negative potential \(\varphi\) of the satellite, the expression for the electron current has the form

\[ I_e=I_{e0}e^{-\frac{e\varphi}{kT_e}}, \tag{3} \]

where

\[ I_{e0}=S_eN_e\frac{v_e}{2} \tag{4} \]

is the electron current to the satellite when the satellite potential is equal to zero; \(S_e\) is the surface, approximately equal to the projection of the satellite onto a plane normal to the magnetic meridian; \(v_e\) is the mean thermal velocity of the electrons and, in the absence of negative ions, \(N_e=N_{+}\).

From (2) and (3) we obtain

\[ \varphi=-\frac{kT_e}{e}\ln\frac{S_ev_e}{2S_{+}v_{\mathrm{cn}}}. \tag{5} \]

This formula has been derived under the assumption that there is no photoemission from the surface of the satellite (which may be caused by hard ultraviolet or other radiation). It is clear from the formula that, in this case, the satellite potential is practically determined only by the electron temperature. Thus, for \(T_e \approx 1000^\circ\), for a spherical satellite, \(\varphi \approx 0.3\ \mathrm{V}\).

On the portion of the orbit illuminated by the Sun, in the presence of a photoemission current from the surface \(I_{\phi}\), the expression for the potential takes the form

\[ \varphi=-\frac{kT_e}{e}\ln\frac{I_e}{I_{+}+I_{\phi}}. \tag{6} \]

If \(I_{\phi}>I_{+}\), the potential may increase substantially. At comparatively small electron concentrations, cases are possible in which \(I_{\phi}\gg I_{+}\); then the satellite will acquire a positive charge, and the pattern of the distribution of space charges around the satellite will change sharply.

The expressions given above yield the value of the “effective” potential, i.e., the value that an equipotential surface of the satellite would have. However, when the satellite moves with velocity \(v_{\mathrm{sp}}=8\cdot 10^{5}\ \mathrm{cm/sec}\) in the Earth’s magnetic field, its surface becomes substantially nonequipotential. The potential difference between two points on the satellite surface separated from one another by \(\Delta L\ \mathrm{cm}\) may reach the value

\[ \Delta \varphi = 10^{-8} v_{\mathrm{sp}} H \Delta L, \tag{7} \]

where \(H \simeq 0.4\) oersted is the strength of the Earth’s magnetic field. Taking the linear dimensions of the satellite to be \(L \simeq 10^{2}\ \mathrm{cm}\), we find that \(\Delta \varphi\) may reach \(0.4\ \mathrm{V}\).

Thus, it may be assumed that under ordinary conditions of the \(F\) layer, at \(T=1000^\circ\mathrm{K}\) and in the absence of photoemission, the potential at all points of the satellite surface will be negative and will not exceed \(1\ \mathrm{V}\), whereas the kinetic energy of ionized diatomic nitrogen or oxygen molecules moving relative to the satellite is \(\sim 10\ \mathrm{eV}\).

At such values of the potential, according to approximate calculations, the thickness of the layer of positive space charge \(\delta\) at \(N\simeq 10^{5}\ \mathrm{cm}^{-1}\) does not exceed \(3\ \mathrm{cm}\), and at \(N\simeq 10^{4}\ \mathrm{cm}^{-1}\), respectively, \(\sim 10\ \mathrm{cm}\).

It should be borne in mind, however, that during rocket experiments carried out in the USA with a radio-frequency mass spectrometer, phenomena were observed in the ionosphere that could have been explained by a high negative potential of the rocket (up to \(20\ \mathrm{V}\),\(^{15}\)). The occurrence of such a potential was not explained and cannot be explained from the standpoint of existing ideas about electron temperatures in the ionosphere; however, the possibility of significant negative potentials of a satellite cannot be considered excluded.

Recently, data were published indicating that during another daytime rocket launch into the \(F\) layer, in experiments with radio-frequency mass spectrographs permitting positive and negative ions to be studied separately, no positive ions were detected, while only negative ions were observed.\(^{16}\) No explanation of this result is given. It seems to us that it could be explained by the fact that, owing to photoemission from the rocket surface, the latter acquired a positive potential, which prevented positive ions from entering the mass spectrometer. Therefore, in developing the methodology to which this article is devoted, the possibility that the satellite, on the illuminated part of its orbit, might acquire a positive potential was also taken into account.

5. PRINCIPLE OF MEASUREMENTS

From reports appearing in the press beginning in 1949,\(^{17,18,19}\) it is known that attempts were made to measure ionospheric parameters by means of dynamic probes installed on rockets. This method, known as the Langmuir–Mott-Smith method and widely used for studies of gas-discharge plasma under laboratory conditions, makes it possible to determine both the electron and ion concentrations, as well as

electron temperature in an equilibrium plasma. Without dwelling on the advantages and disadvantages of the indicated method under the specific conditions of a flying satellite, we shall note only one feature which, in our opinion, makes its application inexpedient for studying such an important characteristic of the ionosphere as the size of inhomogeneities. This feature consists in the fact that, in order to take one volt-ampere characteristic (by processing which the measured quantities can be obtained), with the present capabilities of radiotelemetric systems (which make it possible to record up to several hundred points per second; see 20), a time of the order of tenths of a second is required, i.e., a time during which the satellite will cover a distance measured in hundreds of meters. Over this section of the path, the properties of the medium and the conditions in which the probe is located may change. As a result, the probe characteristic may be distorted. Moreover, this characteristic makes it possible to determine the concentration essentially at one point along the indicated distance.

Therefore, for studying the concentration of charged particles in the ionosphere by means of artificial satellites, it appears more expedient to use a method based on continuous measurement of the current of charges of one sign flowing onto a certain section of the satellite surface, by means of a device with a screened collecting electric field.

Such a device may be a trap for positive or negative charges with a collector collecting charges of the corresponding sign. The trap is connected with the external medium by means of an aperture covered by a metal mesh which is at the potential of the satellite surface (and which is, in essence, a part of this surface). Charges from the external medium strike the mesh in the same way as the remaining parts of the satellite surface and pass through the mesh into the trap.

The field produced when a certain constant potential is applied to the collector relative to the satellite surface ensures the collection of charges of one sign and the repulsion of charges of the other sign, but does not affect the magnitude of the current to the collector, which is determined by the free flux of charges of the given sign onto the mesh.

Although the field current of positive charges to the entire surface of the satellite, \(I_+\), is equal to the total current of negative charges, \(I_-\) (according to (1)), nevertheless there is a fundamental difference between the measurement by the indicated method of the electron and ion concentrations, since what is involved is, in essence, the measurement of the local density of the electron current \(j_e\) or ion current \(j_+\) on some section of the satellite surface, which are not equal to each other, for they depend differently on the potential of the given section of the surface and on the orientation of the satellite. For a negative surface potential, \(j_e\) and \(j_+\) on one and the same section of the surface are expressed as follows:

\[ j_e=\frac{1}{4}eN_e v_e \cos(\widehat{\mathbf{H},\mathbf{n}})\,e^{-\frac{e\varphi}{kT}} \tag{8} \]

and

\[ j_+=eN_+v_{\mathrm{sp}}\cos(\widehat{\mathbf{v}_{\mathrm{sp}},\mathbf{n}})\,f(\varphi), \tag{9} \]

where \(\varphi\) is the potential of the given point of the surface, \(v_e\) is the mean thermal velocity of the electrons; \(\mathbf{H}\) is the vector of the magnetic-field intensity, \(\mathbf{v}_{\mathrm{sp}}\) is the vector of the satellite velocity; \(\mathbf{n}\) is the normal vector to the surface at the given point.

K. I. GRINGAUZ, M. Kh. ZELIKMAN

The function \(f(\varphi)\) may be regarded as a correction coefficient. To express \(f(\varphi)\) analytically is quite complicated: the form of this function depends on the curvature of the given surface element, on its orientation relative to the velocity vector, and on the mass spectrum of the ions. In the theory of the stationary probe an analogous function describes the change in current in the sloping part of the probe characteristic. In the case under consideration, the dependence of \(j_{+}\) on \(\varphi\) must be still weaker than in the case of a stationary probe, because of the considerably greater flight effect at the same potentials \(\varphi\). Expressions (8) and (9) are valid for surface elements not adjoining the airless space behind the satellite. In the case of a satellite oriented relative to its velocity vector, \(\cos(\mathbf{v}_{\mathrm{sp}}, \mathbf{n})\) becomes a constant coefficient.

As for the density of the electron current, it not only depends directly on the orientation of the given surface element relative to the Earth’s magnetic field and on the thermal velocity of the electrons, but also depends very strongly on the potential of the given surface element (which, as noted earlier, may differ by tenths of a volt for different surface elements). At small positive potentials of the satellite surface (such that \(\sqrt{2e\varphi/m_i} \ll v_{\mathrm{sp}}\)), expression (9) for \(j_{+}\) remains valid, whereas (8) must be changed. If in the ionospheric regions being studied there were appreciable concentrations of negative ions, the dependence of the current density of negative charges on the electron concentration (or on the total concentration of negative charges) would become ambiguous. For these reasons, continuous measurement of ionization along the satellite orbit, based on the principle set forth above, can be carried out only as a measurement of the concentration of positive ions. Since, in measurements of the current of charges of one sign by means of traps, the results of the measurements may be affected by the orientation of the traps relative to three directions—the velocity vector, the intensity of the Earth’s magnetic field, and the direction toward the Sun (the latter affects the magnitude of the photoeffect from the collector)—it is essential, when setting up the experiment, to take into account how the satellite is oriented relative to these directions.

Since a constant orientation of the satellite relative to all three of the indicated directions is in principle not feasible, without considering the question of the preference of one or another orientation of the satellite, we assume that the orientation of any surface element of the satellite in flight may change relative to each of these directions.

Fig. 2.

6. SETTING UP THE EXPERIMENT

Below is a description of an experiment based on the measurement principle set forth in the preceding paragraph. Two mesh spherical ion traps, fastened on a thin rod, are installed above diametrically opposite portions of the satellite surface (Fig. 2) in such a way that, for any orientation of the satellite, at least one of them is outside the airless space behind the satellite. In the case of a satellite oriented relative to the velocity vector, it is sufficient

one ion trap, located in front of the satellite. These mesh metallic spheres are connected with the electrically conducting part of the satellite surface through a small resistance \(R\) (of the order of \(10^3\ \Omega\)) and during most of the experiment are, as it were, part of the satellite surface, having the corresponding potential.

At the center of each mesh sphere there is a small collector, also spherical in shape, to which, relative to the outer sphere, a voltage is applied that creates a field which repels particles with negative charge beyond the limits of the sphere. The collector is connected through a resistance \(R'\) (of the order of \(10^6\ \Omega\)) to the conducting shell of the satellite (Fig. 3).

Fig. 3.

The current of positive ions flows from the collector to the shell, causing a corresponding increase in the electron current to the satellite surface. The voltage from the resistance \(R\) is fed to the input of an amplifier, from whose output the voltage is recorded on the Earth with the aid of a radiotelemetric system.

In addition to the two-channel amplifier \(I\), the apparatus installed on the satellite includes a sawtooth voltage-pulse generator \(II\), which, at intervals of the order of 2 sec, produces pulses of two polarities with amplitudes of the order of 20 V and total duration of the order of 0.2 sec, loaded on the resistance \(R\), through which, as indicated, the spherical traps are connected with the conducting part of the satellite shell (Fig. 3).

The voltage \(V_k\) applied to the collector is chosen so that it is sufficiently high to ensure the collection of all positive ions entering the trap (i.e., so that the trap operates “in the saturation regime”), but not so high as to cause appreciable emission of electrons from the collector surface bombarded by ions.

It follows from relation (9) that the measured current of positive ions is equal to

\[ I_+ = N_+ e v_{\mathrm{sp}} \pi r^2 f(\varphi_l)\alpha, \tag{10} \]

where \(r\) is the radius of the trap shell, \(\varphi_l\) is its potential relative to the neutral plasma, \(f(\varphi_l)=1\) when \(\varphi_l=0\), and \(\alpha\) is the transparency coefficient of the mesh shell.

This relation is valid for any orientation of the satellite until the trap enters the airless region behind the satellite. The use of two traps arranged in the manner indicated above makes it possible to obtain continuous recording of the ion current independently of the orientation of the satellite.

It follows from (10) that, when \(\varphi_l=0\), the measured current to the collector is related to the concentration of positive ions by a simple relation in which all quantities except \(N_+\) are known.

As was already indicated, if the existing ideas about the regions of the ionosphere of interest to us are correct, then the potential \(\varphi_l\) must be such that the function \(f(\varphi_l)\) differs little from 1. Nevertheless, it is highly desirable to take into account the influence on the measurements of \(\varphi_l\), i.e., the change in the velocities of the particles entering the trap due to the electric field of the shell.

When voltage pulses are applied to the mesh spheres, the system consisting of the mesh sphere and the satellite is transformed into a so-called “double probe” in the plasma. In order that one of the electrodes of such a double probe may acquire a potential of either sign relative to the neutral plasma, its surface must be in a definite relation to the surface of the second electrode—namely, such that the current of charges of one sign to this electrode, at any of its potentials, can be compensated by the current of charges of the opposite sign to the other electrode. Practically, taking into account the velocities of electrons and ions, in our case this means that the surface of the metallic part of the mesh shell of the trap must be two orders of magnitude smaller than the area of the conducting part of the satellite surface. This limits the size of the trap and requires good conductivity of the corresponding part of the satellite surface.

During the application of bipolar voltage pulses (Fig. 4) to the shells of the traps, once every two seconds the volt-ampere characteristics are recorded

Fig. 4.

\[ I_k=f_1(U), \tag{11} \]

where \(U=\varphi_l-\varphi_{\mathrm{sp}}\) is the known potential difference between the section of the satellite surface to which the output of the pulse generator is connected and the mesh sphere*).

To find on this characteristic the point at which the potential of the trap shell relative to the neutral plasma is equal to zero (i.e., \(U=\varphi_l-\varphi_{\mathrm{sp}}=-\varphi_{\mathrm{sp}}\)), it is necessary either to find some characteristic point

*) The value \(U\) is known to within the emf induced, during motion in the Earth’s magnetic field, in the wire connecting the generator output with the trap shell (i.e., to fractions of a volt).

on characteristic (11), in which the value \(\varphi_l\) would be known, or to determine the value \(\varphi_{\mathrm{sc}}\) by some independent method. The point \(\varphi_l=0\) is easily determined on Langmuir probe characteristics as the point of inflection of the \(\ln I\) curve. However, on characteristics (11) it will not have special features. Nevertheless, there exists a characteristic point on curve (11) at which the potential \(\varphi_l\) can be determined. This is the point \(\varphi_{\mathrm{br}}\), corresponding to complete retardation of the positive ions (point \(A\) on

Fig. 5.

the curve of Fig. 5), starting from which the registered current ceases to decrease as the positive potential of the grid shell of the trap is increased. At this point the obvious condition is satisfied

\[ e\varphi_l=\frac{m_{i\max}v_{\mathrm{sp}}^2}{2}, \tag{12} \]

where \(m_{i\max}\) is the mass of the heaviest ions entering the trap, which, apparently, may be either \(NO\) ions \((m_i=30)\), or \(N_2\) ions \((m_i=28)^*)\). To refine the mass of the heaviest ions present in this section of the orbit, data obtained with a radio-frequency mass spectrometer\({}^{21}\) may be used.

Having determined \(\varphi_{\mathrm{br}}\) and knowing the value of \(\varphi_l-\varphi_{\mathrm{sc}}\) at this same point, one can find the value \(\varphi_{\mathrm{sc}}\) and, consequently, determine the point of the characteristic at which \(\varphi_l=0\), i.e. \(f(\varphi_l)=1\). This makes it possible to measure the corresponding value \(N_{+0}\) at this point, undistorted by the electric field of the grid shell of the trap.

*) Obviously, the form of characteristic (11) depends not only on the mass of the heaviest ions, but also on the mass spectrum of all ions. It is possible that on this characteristic it will be possible to determine the points of retardation of ions with different masses; in that case it could be used for mass-spectrometric purposes. This question, in our opinion, deserves special consideration.

Let us denote by \(k\) the ratio of the quantity \(N_{+0}\) to the quantity

\[ N_+ = \frac{N_{+1}+N_{+2}}{2}, \]

where \(N_{+1}\) and \(N_{+2}\) are the values of \(N_+\) calculated from relation (10) under the condition \(f(\varphi_l)=1\), for the points corresponding to the beginning and end of the bipolar voltage pulse applied to the traps. If \(k_1\) and \(k_2\) are the values of \(k\) determined from two successive current–voltage characteristics, then the values \(N_+\), determined from the currents recorded in the interval between the taking of these characteristics, can be corrected by multiplication by the correction factor

\[ k_{\mathrm{av}}=\frac{k_1+k_2}{2}. \]

Another method of determining, on the characteristic (Fig. 5), the point corresponding to \(\varphi_l=0\) may be based on the use of experimental data on measuring the satellite’s own electric charge[^22]. In this experiment the electric-field strength \(E\) at a given portion of the satellite surface is measured directly. The quantity \(E\) is related to the potential of this portion of the satellite surface relative to the neutral plasma by the relation

\[ E\delta=\varphi_{\mathrm{sp}}, \tag{13} \]

where \(\delta\) is the thickness of the space-charge layer surrounding the satellite, which in turn depends on the ion concentration in the undisturbed plasma \(N_+\). Taking as \(N_+\) the value measured by the instrument described in the present article at the moment of the beginning of the sawtooth pulse, and thus determining \(\delta\), and then, according to (12), \(\varphi_{\mathrm{sp}}\), one can, with the aid of the current–voltage characteristic (11), find the point corresponding to \(\varphi_l=0\), and then, having obtained the refined value \(N_{+0}\), apply the method of successive approximations and obtain new, more accurate values of \(\delta\), \(\varphi_{\mathrm{sp}}\), etc.

Taking into account that the ion concentration in inhomogeneities may exceed the maximum values observed during radio sounding of the ionosphere, the instrument must be able to measure ion concentrations \(N_+\) up to \(10^7\ \mathrm{cm}^{-3}\) (as the upper limit). The lower limit will in practice be determined by parasitic effects (see below).

The need to measure values of \(N_+\) differing from one another by several orders of magnitude requires the use of an amplifier with automatic gain switching (of the measurement ranges).

In conclusion of this section, let us dwell on considerations concerning the choice of the time operating mode of the ion traps. The short duration of the voltage pulses applied to the trap shells is necessary in order to be able to assume that the ion current has changed because of the change in the potential of the grid sphere, and not because of a change in the ion concentration in space. Reduction of the pulse duration is limited by the capabilities of radio-telemetry systems with respect to polling frequency, owing to the need to obtain a sufficiently detailed current–voltage characteristic. Long pauses between pulses are needed for recording inhomogeneities of the ion concentration, since for this purpose the ion current must be measured at a stable potential of the trap shell.

7. ON ACCOUNTING FOR EFFECTS THAT DISTORT THE MEASUREMENTS

In the description of the experiment, a method was indicated for accounting for the influence of the electric field of the grid shell of the trap on the measurement results. On the illuminated part of the orbit the measurements may be substantially distorted

photoemission from the collector. When a spherical trap is used, at the center of which there is a small collector, the surface collecting the ions is the surface of the mesh sphere, while photoemission proceeds from the surface of the collector. Therefore the influence of photoemission on the recorded current decreases in proportion to the increase of the ratio

\[ \frac{r^2}{r_0^2}, \]

where \(r_0\) is the radius of the collector.

When voltage pulses are applied to the mesh shell of the trap, the potential \(\varphi_l\) exceeds the retarding potential of the positive ions; the recorded current will then be the total current produced by processes not associated with the presence of ions in the trap.

The magnitude of the secondary emission of electrons from the collector under bombardment by ions with energy determined by the collector potential, \(\varphi_k\), can be partially determined by changing the value of \(\varphi_k\) during the experiment. It can be studied beforehand in the laboratory on samples of collectors made of various materials.

Among the effects that may distort the measurements is the ionization of air produced by the flying satellite itself. The possibility of such ionization is evident from the fact that a molecule elastically reflected from the surface of the satellite may acquire an energy of \(40\text{--}45\) eV, whereas the ionization potentials of gas molecules are \(12\text{--}15\) eV, and for ionization in the collision of particles of equal mass an energy \(P>2W\) is required (see, for example, \({}^{23}\)).

Comparison with data on meteor ionization in the lower part of the ionosphere leads to the conclusion that the expected effect is insignificant; however, this does not take into account the specific features of the upper part of the ionosphere (the degree of excitation of molecules, etc.). Therefore, in order to estimate the ionization produced by the satellite itself and its influence on the results of measurements of ion concentration, one should make use of the measurement data themselves, as well as carry out certain control observations.

There are grounds to believe that, all other conditions being equal, the concentration of ions produced by the satellite should increase in proportion to the density of the air. Consequently, the minimum value of the concentration of positive ions measured when the satellite passes through the lower part of the orbit will be the upper limit of the possible values of the ion concentrations produced by the satellite along the entire orbit. It is difficult, however, to say to what extent this effect is determined solely by the density of the air. Moreover, if the lower part of the orbit passes near the maximum of the \(F\) layer, then small values of the ion concentration can hardly be expected there. Therefore observations by ionospheric stations installed along the orbit of the artificial satellite may be very useful.

Comparison of the results of radiosonde measurements with the results of direct measurements on the satellite, carried out at altitudes below the maximum ionization of the \(F\) layer, will make it possible to estimate the ionization due to the satellite’s motion (to the extent that it is possible to determine the altitudes to which the radiosonde data correspond, and the reliability of the assumption that negative ions are absent at the altitudes under investigation).

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