Current State of the Art in Ionospheric Research

III. Some Additional Issues

Ya. L. Al’pert

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
1. Relation of ionization of the \(F_2\) layer to geomagnetic latitude . . . . . . . . . . . . . . . . . . . 310
2. Tidal phenomena in the ionosphere caused by the Moon . . . . . . . . . . . . . . . . . . . . . . . . 315
3. Meteors and their influence on the ionization of the ionosphere . . . . . . . . . . . . . . . . . . . 321
4. On the inhomogeneous structure of the ionosphere and motions within it . . . . . . . . . . . . 325
5. Plasma oscillations and their possible influence on the propagation of radio waves in the ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
6. New data on nonlinear effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Brief conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Introduction

Within the framework of the preceding articles1,2, it was not possible to consider certain still little-studied questions of ionospheric physics which may possibly play an essential role in the further development of this field. In addition, in view of a number of substantial difficulties arising in the study of the ionosphere, difficulties already partly outlined earlier2, it is important to pay especially close attention to new experimental data which at first glance may seem to us to be of only secondary importance.

Therefore, in this article some phenomena encountered in ionospheric research are considered—phenomena only briefly mentioned or not considered at all in the preceding sections. In addition, during the time that has elapsed since the publication of the articles cited above, a number of works have appeared, or have become known to the author, containing new results which, insofar as possible, are also set forth in this article.

Ya. L. Alpert

1. RELATION OF THE IONIZATION OF THE \(F_2\) LAYER TO GEOMAGNETIC LATITUDE

In the preceding sections the basic data on the \(F_2\) layer, now well studied on the basis of a large body of experimental material, have already been presented. There, too, the difficulties arising in the interpretation of experimental data were noted and partly analyzed. In particular, the existence of the so-called “longitude effect” in the ionization of the \(F_2\) layer was indicated; the physical causes and character of this effect have not yet been studied sufficiently fully. This effect consists in the fact that at two different points situated at the same latitude, the mean values of the degree of ionization of the \(F_2\) layer for the same moments of local time (say, mean monthly noon values) differ from one another. This shows that the degree of ionization of the layer changes with longitude.

In addition, from further analysis of the experimental data it also became clear that, for a fixed value of longitude, the obtained values of the degree of ionization of the \(F_2\) layer are not the same at identical latitudes of the southern and northern hemispheres.

Thus it was already established long ago\(^3\) that the course of the ionization of the \(F_2\) layer has no simple dependence on the height of the Sun above the horizon and does not coincide with that observed for the \(E\) and \(F_1\) layers.

In the light of what has been said, the recently established relation between the values of the degree of ionization of the maximum of the \(F_2\) layer and geomagnetic latitude, or magnetic inclination, is of interest.

Obtaining a sufficiently reliable dependence of this kind became possible thanks to the use of measurement results from a large number of ionospheric stations (more than 50–60), whose locations now fill the map of the globe rather densely.

For the analysis of the longitudinal or latitudinal dependence of the ionization of the layer, it is naturally expedient first to consider data corresponding to conditions of symmetrical illumination of the terrestrial globe with respect to the geographic equator. For this reason, the processing of data on the ionization of the \(F_2\) layer was carried out first of all for March and September—the months of the equinoxes. These data have been cited in the literature\(^4\)—\(^7\) for different years; some of the results are shown in the averaged curves of Figs. 1 and 2. Figure 1 gives the course of the mean monthly noon value of the ionization \(n_{eM}\) of the maximum of the \(F_2\) layer as a function of geomagnetic latitude, while Fig. 2 presents the corresponding curve of \(n_{eM}\) as a function of magnetic inclination.

The experimental points themselves, which have relatively small scatter about these curves, are not plotted in the figures.

From the figures presented it is seen that in the vicinity of the magnetic equator the degree of ionization of the maximum of the \(F_2\) layer has smaller values than in other places of the tropical zone—here the critical

frequencies of the \(F_2\) layer have a minimum. It is noted in the literature\(^5\) that a more detailed examination of ionospheric data for the equatorial zone shows that here the splitting of the \(F\) layer (into \(F_1\) and \(F_2\)) is most pronounced; moreover, it is on the whole more extended and more closely resembles in its structure the summer \(F\) layer at middle latitudes.

The maxima of the degree of ionization \(n_{eM}\) are in general situated symmetrically with respect to the magnetic equator. According to various data they are found between \(14\)–\(18^\circ\) or \(28\)–\(38^\circ\) for curves referred respectively to geomagnetic latitude (Fig. 1) or to magnetic inclination (Fig. 2). As for the magnitudes of the maxima themselves, \(n_{eM}\), although the data suggest that they may be equal (as is shown in the curves presented), there is still not sufficient certainty about this because of the incompleteness of the experimental data.

Fig. 1. Dependence of the mean monthly noonday value of the ionization \(n_{eM}\) of the maximum of the \(F_2\) layer as a function of geomagnetic latitude.

With increasing geographic latitude the longitudinal effect generally gradually disappears; therefore the course of \(n_{eM}\) at high latitudes corresponds more to the course of geographic latitude than to geomagnetic latitude.

The geomagnetic effect is observed, as some authors indicate,\(^{4,6}\) not only for the noonday values of \(n_{eM}\), but also appears in other daytime characteristics of the \(F_2\) layer. From some data relating to nighttime,\(^5\) it follows that the course of the nighttime values of \(n_{eM}\) does not have a double-humped character, but is likewise symmetric with respect to the magnetic equator.

Such are the principal known facts characterizing this effect, which, as is evident from the figures presented, is very substantial, since the values of the degree of ionization \(n_{eM}\) at the equator and in the regions of the maxima of \(n_{eM}\) differ in magnitude by more than a factor of two. Therefore analysis of this phenomenon and further comprehensive

experimental study of it may be of great interest for the study of the processes occurring in the \(F_2\) layer.

Let us dwell on an explanation of this phenomenon, which was only briefly expressed in the literature \(^{7}\) and has not been subjected to sufficient analysis.

Since the phenomenon under consideration consists in the fact that the degree of ionization of the \(F_2\) layer depends on the Earth’s magnetic field, it is natural to suppose that the ionization of the layer is partly caused by a flux of charged particles arriving in the upper layers of the atmosphere and controlled by the Earth’s magnetic field. However, here one encounters a difficulty consisting in the fact that, in order for such a corpuscular flux, originating from the Sun, to reach low latitudes, it is necessary that the velocities of its particles be close to the velocity of light; in that case their penetrating power will be very great, and they will not ionize the atmosphere in the region of the \(F_2\) layer. The available data indicate that the velocities of these particles are small \(^{8}\) (of the order of 500–600 km/sec). Moreover, it is known that, up to the present time, no strong influence of the Sun’s corpuscular radiation on the degree of ionization of the ionosphere has been detected. Thus, this possible explanation of the geomagnetic effect apparently falls away.

Fig. 2. Dependence of the monthly mean noontime value of the ionization \(n_{eM}\) at the maximum of the \(F_2\) layer as a function of magnetic inclination.

In the note mentioned above \(^{7}\), the author supposes that the flux of charged particles additionally ionizing the \(F_2\) layer is formed in the upper part of the atmosphere, above the \(F_2\) layer, where there is already a noticeable amount of gas. In this region of the atmosphere the number of collisions is small and the mean free path of the ionized particles is very large. These charged particles, forming spiral trajectories around the lines of the Earth’s magnetic field, are at the same time channeled along these lines of force. Thus the charged particles formed in the region of the magnetic equator will be directed by the magnet-

...by the Earth’s magnetic field to the north and south and, entering the region of the \(F_2\) layer, additionally ionize it. This accounts for the appearance of symmetrically situated ionization maxima in the daytime hours.

Naturally, with increasing distance from the magnetic equator the influence of these particles disappears.

In the explanation given for the effect under consideration, the author uses the so-called ultraviolet theory of aurorae, advanced in its time,\(^{9}\) which, however, proved unsuitable for explaining them. In order that the magnetic lines of force entering the lower parts of the terrestrial atmosphere near the poles should originate from the magnetic equator, it is necessary that at the equator they be located at heights of the order of \(30\)—\(40\) thousand km, where there is certainly no atmosphere and where a large number of charged particles cannot be formed. As for the effect under consideration, according to the author’s calculations,\(^{7}\) the lines of force entering the regions of maxima in the degree of ionization of the \(F_2\) layer reach, at the magnetic equator, heights of only about \(800\)—\(1200\) km, where there certainly is an atmosphere, as is confirmed at least by the polar aurorae observed at such heights.

Thus, the proposed point of view may prove quite plausible for explaining the geomagnetic effect of the \(F_2\) layer.

Let us turn to certain consequences of this theory, which it is important to elucidate for its verification and development, and also for a more complete study of the geomagnetic effect.

From the figures given above it is seen that in the regions of ionization maxima the values of \(n_{eM}\) are \(2\)—\(2.5\) times greater than the corresponding values at the geomagnetic equator. It is not difficult to show (see, for example, formulas (2.9) and (4.10) in \(^{2}\)) that the ratio of the energy \(S_\infty \cos \chi_0\), going into the ionization of a column of the \(F_2\) layer of cross-section \(1\ \mathrm{cm}^2\) at the equator, to the energy \((S_\infty \cos \chi + S_{\mathrm{add}})\), going into the ionization of the \(F_2\) layer in the region of the maximum \(n_{eM}\), is equal to

\[ \frac{S_\infty \cos \chi_0}{S_\infty \cos \chi + S_{\mathrm{add}}} = \frac{\int n_{e0}^{2}\, dz}{\int n_{e}^{2}\, dz}, \tag{1,1} \]

where \(\chi_0\) and \(\chi\) are respectively the values of the Sun’s altitude in the point considered at the geomagnetic equator and at the point where \(n_{eM}\) has its maximum, and \(S_\infty\) is the solar energy in the frequency range responsible for the ionization of \(F_2\). If we now assume that the additional ionization of the \(F_2\) layer due to bombardment by charged particles occurs uniformly throughout the whole layer, say so that \(\dfrac{n_{e0}(z)}{n_e(z)}=\mathrm{const.}\), then, using the data given in Fig. 1, we obtain for the corresponding values of \(\chi\):

\[ S_{\mathrm{add}} \simeq (3 \div 5)\cdot S_\infty, \tag{1.2} \]

i.e., that the energy \(S_{\mathrm{add}}\) of the bombarding particles is \((3 \div 5)\) times greater than the energy \(S_{\infty}\) going directly to the ionization of the \(F_2\) layer at the equator. On the other hand, since the \(F_2\) layer is ionized by the region of the spectrum \(800—900\ \mathring{\mathrm A}\) and below, in order for the energy of the bombarding particles that cause the additional ionization of \(F_2\) to be sufficient, it is necessary that these particles be produced by the ultraviolet radiation of the Sun in the spectral region \(400—450\ \mathring{\mathrm A}\) and below.

Thus it is clear that, for this effect actually to be produced by fast charged particles formed in the atmosphere itself, the total energy of these particles must be sufficiently large. If we assume, as was done above, that the entire layer as a whole is additionally ionized approximately equally at different heights and that, in the regions of the maxima of \(n_{eM}\), no significantly concentrated channeling of the bombarding particles occurs (i.e., that no focusing of these particles takes place), then a very important consequence follows from the estimates given. Namely, if one does not assume the existence in the ionosphere of an electric field accelerating the particles, then the energy of the Sun’s radiation in the frequency region \(400—450\ \mathring{\mathrm A}\) and below must be \(3 \div 5\) times greater than the energy in the frequency region

\(400 \div 900\ \mathring{\mathrm A}\).

Using the available data, we obtain the very important assumption, namely that in the region \(400—500\ \mathring{\mathrm A}\) and below

\[ S_{\infty} \simeq 3 \div 5\ \mathrm{erg}/\mathrm{cm}^{2}\mathrm{sec}. \tag{1.3} \]

Thus it is clear that a more detailed experimental and theoretical investigation of this phenomenon is very important. Apparently, along with the necessity of further verification, on a large body of data, of the regularities already obtained for the maximum of the layer during the equinox period, it is important to clarify the course of this dependence for different levels of the layer, i.e., to establish how the distribution of the ionization of the layer with height changes at different points. It is also important to trace the diurnal and seasonal character of this phenomenon.

In order to estimate more accurately the energy of the bombarding particles causing the additional ionization of \(F_2\), it is apparently necessary to calculate what the course of the ionization of \(F_2\) would be as a function of geographical latitude, if it is assumed that at the equator (because of the proximity of the geomagnetic equator to the geographical one) the ionization is caused only by absorption of ultraviolet radiation and that there is a latitudinal effect according to the law \(\cos \chi\).

In this case one obtains a course of ionization similar to the dashed curve shown in Fig. 1. The difference of the ordinates of the two curves will make it possible to estimate the additional ionization of \(F_2\) at different points of the Earth’s

sphere and, thereby, to calculate more accurately the quantities \(S_{\text{add}}\) and \(S_{\infty}\). For lack of the necessary data the author is unable to make this estimate.

It should be pointed out that the explanation considered for the geomagnetic effect of the \(F_2\) layer cannot yet be regarded as at all reliable. The already existing experimental data imply very substantial assumptions requiring serious verification. Thus, further experimental investigations and theoretical consideration of this effect are very important and will perhaps lead to the removal of a number of ambiguities arising in the study of the \(F_2\) layer.

2. TIDAL PHENOMENA IN THE IONOSPHERE CAUSED BY THE MOON

There have been reports in the literature establishing a connection between the state of the ionosphere and the motion of the Moon, namely showing the existence of a connection between the intensity of received radio signals and the phase of the Moon \(^{10,11}\). A definite dependence was also established between the time variation of the field strength of broadcasting and other radio stations and the phase of the Moon \(^{11}\).

Already from early investigations it followed that the magnitude of the observed effects was too considerable for them to be explained as a consequence of the relatively small gravitational lunar oscillations of only the lower atmosphere. However, only in 1939 was a paper \(^{12}\) published in which it was directly shown that in the \(E\) layer there are oscillations of the equivalent height having a period equal to one half of a lunar day; moreover, these semidiurnal oscillations of the height of the \(E\) layer coincide in phase with the well-known gravitational oscillations of atmospheric pressure.

Fig. 3. Semidiurnal tidal oscillations of the equivalent height of the \(E\) layer.

The results obtained in this work are shown in Fig. 3 (see also item 1 in Table 1), from which it is evident that the amplitu-

the amplitude of the oscillations \(\Delta h_E\) of the layer height reached \(\sim 1\) km, and the maximum of \(\Delta h_E\) occurred approximately \(3/4\) hour before the passage of the Moon (upper culmination). From these results it was already evident that the lunar ionospheric oscillations are independent of the barometric oscillations of the atmosphere near the Earth’s surface and that the effect of tides in the ionosphere is more significant than at the Earth’s surface. Indeed, as a result of processing these ionospheric-research data it was possible to estimate the relative change of pressure at the level of the \(E\) layer (\(\sim 100\) km), which was found to be

\[ \frac{\delta p}{p}=-\frac{\Delta h}{H}=\frac{0.93}{11.5}\simeq 0.08, \tag{2.1} \]

where \(p=p_0 e^{-\frac{h}{H}}\), and \(H=\frac{mg}{RT}\) is the height of a homogeneous atmosphere. This quantity is approximately 7000 times greater than the value of the relative pressure oscillations at the Earth’s surface at the site of the \(E\)-layer investigations, where \(\frac{\delta p}{p}\) at the Earth’s surface \(\simeq 0.0000115\).

Thus the presence of tides in the \(E\) layer of the ionosphere was demonstrated, which immediately created theoretical difficulties, since the tides in the \(E\) layer were not consistent with other tidal geophysical phenomena. Indeed, for example, on the basis of the explanation of the semidiurnal lunar oscillations of the Earth’s magnetic field it was believed that the pressure oscillations in the corresponding region of the ionosphere do not coincide in phase with the forces producing these tides; in reality, however, the ionospheric data cited above showed the opposite.

It is necessary to note that the detection of lunar oscillations on the basis of ionospheric data, especially for the \(F_1\) and \(F_2\) layers, requires analysis of a large number of measurement results and the availability of carefully checked experimental data. Since this is a second-order effect, it can be calculated only from a harmonic analysis of the deviations of the mean values of individual measurements from the smoothed diurnal variation caused by the course of solar radiation. In addition, lunar oscillations are obscured by a number of other irregular phenomena occurring in the ionosphere.

Works that have appeared recently\(^{12,13,14}\) nevertheless clarify the picture somewhat. They show that in all layers of the ionosphere semidiurnal lunar oscillations are observed not only in the height of the layer but also in the critical frequency, i.e. in the degree of ionization of the layer, and they make it possible to outline certain regularities of this phenomenon. However, it should be pointed out at once that the experimental data are still wholly insufficient, and in many respects contradictory. Therefore they do not lend themselves to any sufficiently consistent analysis in connection with the entire set of geophysical phenomena of this type. Furthermore, there is, in our view, an obvious overestimation (see \(^{13}\)) of the role of these oscillations in explaining and analyzing the principal difficulties arising in the ionosphere (see ?).

Finally, the theoretical treatment and explanation of this phenomenon and its consequences are very complex and are entangled with a number of secondary phenomena, which makes any confident conclusions impossible at the present time. For these reasons we limit ourselves here only to a summary

Fig. 4. Semidiurnal tidal oscillations of the equivalent height of the \(F_2\) layer.

Fig. 5. Semidiurnal tidal oscillations of the critical frequency of the \(F_2\) layer.

of the experimental data known from the literature and to a consideration of certain regularities that follow from them.

In Figs. 4 and 5, for illustration, oscillations of the height and critical frequency of the \(F_2\) layer, reduced in \(^{13}\) (see item 6 of Table I), are presented; and in Table I the published data on lunar tides in the ionosphere are collected. In a number of cases the quantities given in the table are semi-

derived from analysis of the results of measurements over 5–10 years, with the number of processed measurements reaching \(10^5 \div 0.5\cdot 10^6\).

In the table, \(\Delta h\) is the amplitude of the tidal oscillations of the layer height, \(\Delta f\) is the amplitude of the oscillations of the critical frequency of the corresponding layer, \(\dfrac{2\Delta f}{f}\) characterizes the amplitude of the relative change in the degree of ionization of the layer maximum, and \(t_\ell\) is the time of the lunar day (the phase of the oscillations) at which these oscillations pass through a maximum, counted from the lower culmination of the Moon.

It is evident from the table that the amplitude of the tidal effect, both for \(\Delta f\) and for \(\Delta h\), increases from layer \(E\) to layers \(F_1\) and \(F_2\), i.e., it grows with height.

The phase values (\(t_\ell\)) of the oscillations of \(h\) and \(f\), however, differ from one another; moreover, in different layers they do not coincide, at least for the oscillations of \(f\). No definite dependence of these quantities on latitude is noticeable.

In general, the more regular fact is that (although it does not coincide with the data of item 1 of the table) the phase of the oscillations of the layer height \(h\) lies midway between the transits of the Moon; as for the phase of the oscillations of the critical frequency of various layers at different places, the data here are more contradictory. There are data indicating that the phase of the oscillations of \(f\) is closer to the moment of the Moon’s transit, but there are also almost equally numerous opposite data. In one of the works\(^{12}\) (item 2 of Table I), the unexpected nature is emphasized of the fact that at almost one and the same geographical point (items 1 and 2 of Table I) the phases of the oscillations of \(h\) for \(E\) and \(F_2\) differ by 6 hours. At the same time it is pointed out that, according to analysis of the data, the time \(t_\ell\) for oscillations of the intermediate height between \(h_E\) and the height \(h_{F_2}\) of the maximum \(F_2\) for item 2 lies between 6 and 12 hours.

Some analysis has also been made of the seasonal course of these effects\(^{13}\), from which the ambiguity of the results is likewise revealed. In general it follows that the phase of the oscillations (the time \(t_\ell\)) increases, while the amplitudes (\(\Delta h\) and \(\Delta f\)) decrease, in the transition from winter to summer; but here, too, other consequences are found, namely, for example, that \(t_\ell\) for \(h_{F_1}\) in one case reaches a maximum in the equinox period, or that \(t_\ell\) for \(f_{F_2}\) decreases somewhat in the transition from winter to summer (for item 6 of Table I).

The above description of tidal phenomena in the ionosphere caused by the influence of the Moon covers almost all the data known in the literature from experimental investigations of this effect. Analysis of this phenomenon may be useful for studying the dynamics of the ionosphere, for checking a number of data on possible velocities of transport of particles in the ionosphere, etc. However, of particular importance, apparently, is a detailed study of this phenomenon for the question of the density and temperature of the atmosphere at great heights.

Table 1

Data on lunar tides in the ionosphere

For this to be clear, let us dwell briefly on the physical explanation of tidal phenomena in the atmosphere (see, for example, \(^{15}\)).

The energy acquired by the atmosphere under the action of gravitational forces is initially concentrated mainly near the Earth’s surface, owing to the great density of the atmosphere there. These forces cause displacements of atmospheric particles in both the horizontal and vertical directions, and the motions have a rather complex character, since they depend on the viscosity of the atmosphere, its density and temperature, the rotation of the Earth, and so on.

The tidal displacements of particles may be regarded as the propagation of plane waves in a medium with a refractive coefficient \(\mu\), equal to \(^{15}\)

\[ \mu^2=-\frac{1}{4}+\frac{1}{h_0}\left(\frac{dH}{dh}+\frac{\gamma-1}{\gamma}H\right), \tag{2.2} \]

where \(H=\dfrac{mg}{RT}\) is the height of a homogeneous atmosphere, \(\gamma=\dfrac{C_p}{C_v}\), and \(h_0\) is a certain parameter characterizing the equivalent thickness of the atmosphere (see \(^{15}\)). From (2.2) it is evident that in the calculations the inhomogeneity of the atmosphere is taken into account only as a function of the height \(h\) above the Earth’s surface.

Let us now suppose that, beginning from some height \(h\), the quantity \(\mu\) assumes a value equal to zero and becomes negative. This will lead to the fact that waves propagating upward from the Earth will be reflected from this region of the atmosphere back to the Earth. Thus the energy imparted to the atmosphere by gravitational forces will remain within a layer bounded by the height \(h\), in which an oscillatory motion will arise. Depending on the thickness of this layer and the parameters of the atmosphere, resonant oscillations of the atmosphere of a definite frequency may arise.

In this way the lunar tidal oscillations of the atmosphere near the Earth’s surface are explained, namely, as the result of oscillations arising between the Earth’s surface and a reflecting layer formed in the region of the first temperature minimum of the atmosphere at a height of the order of \(15\text{–}30\) km. In the calculations \(^{16}\) the influence of the second temperature minimum (\(h\sim 80\) km) on these oscillations was also taken into account.

To explain the lunar oscillations in the \(E\)-layer, the supposition was advanced \(^{15}\), see also \(^{2}\), that at a height of \(140\text{–}160\) km above the Earth’s surface there is a third temperature minimum, and that atmospheric oscillations occur here in the region between the second and third temperature minima.

From this brief consideration it is clear that the character of lunar oscillations in the ionosphere does indeed depend essentially on the density and temperature of the atmosphere at these heights. Therefore it is possible

It may be hoped that further study of these oscillations will help determine the dependence of these quantities on height above the Earth’s surface for the region of the atmosphere above the layer \(E\), for which our present information is very uncertain and contradictory (see \({}^{2}\)).

3. METEORS AND THEIR INFLUENCE ON THE IONIZATION OF THE IONOSPHERE

The development of ultrashort-wave radiolocation techniques contributed to a considerable deepening and broadening of experimental studies of the frequency of occurrence and activity of meteor bursts, information about which has grown substantially over the last two or three years. This, in turn, made it possible to investigate the role of meteors in the ionization of the ionosphere; some indications of their influence on the ionization of the \(E\) layer had already appeared in the literature in 1931. At the present time there are already a number of sufficiently well verified facts, which are briefly set forth below \({}^{16,17}\).

In \({}^{1}\) (§ 4г) it was already noted that in a number of cases an increase in the degree of ionization in the region of the \(E\) layer was observed, i.e. the appearance of \(E_{\text{spor}}\) during the passage of meteors. In addition, it was indicated there (§ 5в) that in the ionosphere there are observed, over the course of a day, flickering passing reflections, with lifetimes of 0.5 sec and more, whose heights and the intervals of time between their appearances have an irregular character. Studies of these flickering reflections—echo signals—showed that they have almost the same character by day and by night, and that the greatest number of them comes from the \(E\) layer. This is seen, for example, from Fig. 6, which gives the dependence of the frequency of occurrence of these reflections on the equivalent height for echo signals observed at a frequency exceeding the critical frequency of the \(E\) layer \({}^{18}\). Similar data were long ago obtained in other works.

Fig. 6. Dependence of the frequency of occurrence of flickering reflections on equivalent height.

From these data it thus followed that enhanced ionization in the \(E\) layer is observed both in the form of separate ionization bursts causing flickering reflections, and in the form of the well-known \(E_{\text{spor}}\) (see \({}^{1}\), § 4г), whose reflections differ from flickering reflections in that they are considerably more stable in time and arise only within a narrow interval of heights.

The question of the causes of the increased ionization of the layer and of the appearance of the so-called \(E_{\text{spor}}\) has always aroused great interest. It was therefore important to analyze the data on \(E_{\text{spor}}\) on the basis of new meteor studies.

Until recent years, the principal method of studying meteors was the visual method, which made it possible to observe them only at night under conditions of a clear sky. The use of radar devices for studying meteors by the appearance of echo signals from the places where they pass at once considerably broadened these possibilities.

However, at first it was necessary to determine whether the echo signals observed on ultra-short waves are in fact reflections from bursts of ionization arising when meteors pass through the atmosphere, or whether they are caused by other reasons. Such a check could be made by comparing data on the frequency of appearance of ionization bursts with the number of visually observed meteors. As for cases of strong meteor showers, one of which occurred, for example, on October 10, 1946, such a correspondence was established for them unambiguously and reliably.

Fig. 7. Annual variation of the monthly mean values of the number of ionization bursts during the hour at noon (curve \(a\)) and of the frequency of occurrence of \(E_{\text{spor}}\) (curve \(b\)).

However, it was also important to show that the frequency of occurrence of sporadic meteors coincides with the corresponding data of observed echo signals on ultra-short waves. Indeed, it was established that the average number of visible meteors after midnight is almost twice as great as before midnight, which coincided with the data of the study of ionization bursts. A correspondence was also shown between the seasonal variation of the frequency of occurrence of visible meteors and ionization bursts, the number of which likewise increases twofold from July to January. A correspondence was also established for certain other phenomena.

Thus confidence appeared that the echo signals observed from the upper layers of the atmosphere in the range of ultra-short-

... waves, are reflections from ionization bursts, whose frequency of appearance is determined by meteor activity.

Studies of ionization bursts have shown that the number of echo signals produced by them depends substantially on the wavelength on which they are observed; therefore measurements on a single wavelength do not yet give a complete idea of the number of meteors passing through the region of sky under study. However, these data are sufficient for establishing the basic regularities of meteor activity and, thereby, for analyzing their influence on the ionosphere. Some results of such an analysis are given in Figs. 7 and 8.

Thus, in Fig. 7^16^ the annual variation of the monthly mean values of the number of ionization bursts during one hour at noon for the period 1944–1946 is plotted (curve a), measured at a wavelength of about 11 m. In the same figure (curve b) the frequency of occurrence of reflections from \(E_{\mathrm{spor}}\) (expressed as a percentage) over the same time at a frequency of 4 Mc/s is shown. The figure shows good agreement in the course of both curves.

Even greater agreement between the course of the intensity of \(E_{\mathrm{spor}}\) and the course of the number of ionization bursts per hour is evident from Fig. 8, which gives the daily variation of the number of ionization bursts per hour (curve a) and the intensity of ionization \(E_{\mathrm{spor}}\) (curve b), corresponding to the time of passage of a strong meteor shower on October 10, 1946.^16^ In this same figure the daily variation of the number of bursts on an ordinary day is plotted (curve c).

Fig. 8. Temporal variation of the number of ionization bursts during one hour (curve a) and of the intensity of \(E_{\mathrm{spor}}\) (curve b) during a period of a strong meteor shower.

From the experimental data presented here and from a number of other studies^17^ it has now become possible to conclude that, at middle latitudes, for which measurement results are mainly available, the ionization \(E_{\mathrm{spor}}\) is apparently to a considerable extent caused by meteors. It should, however, be borne in mind that from some experimental data it is known that at high latitudes an intensification of \(E_{\mathrm{spor}}\) was observed during periods of magnetic disturbances,

thus one of the causes producing, in a number of cases, \(E_{\text{spor}}\) is apparently also corpuscular streams entering the earth’s atmosphere. Their influence on \(E_{\text{spor}}\) and on other processes is possible (see, for example, the following paragraph).

From these data it is also clear that the observed flickering reflections from the \(E\) layer may also come from ionized meteor trails.

Despite the fact that the seasonal course of ionization bursts \(E_{\text{spor}}\) is not symmetrical with respect to the summer months (see, for example, in Fig. 9 the annual mean course of the frequency of occurrence of reflections from \(E_{\text{spor}}\) at different

Fig. 9. Annual mean course of the frequency of occurrence of reflections from \(E_{\text{spor}}\) at different frequencies (Slough, at noon).

frequencies at Slough at noon for 1943–1946), and that their diurnal course likewise has no symmetry with respect to noon, nevertheless a noticeable intensification of them is observed both at times close to noon and in the summer months, indicating that the Sun to a certain extent regulates the place and frequency of occurrence of ionization bursts from meteors. This connection is manifested in the fact that, in general, the course of the frequency of these bursts in some way follows the course of the degree of ionization of the \(E\) layer, which coincides well with the change in the height of the Sun.

Thus, it may be assumed that ionization bursts from meteors apparently arise more readily in an ionized atmosphere. This is further supported by the fact that, as a more detailed analysis of the data on \(E_{\text{spor}}\) has shown, the diurnal and seasonal course of the height of \(E_{\text{spor}}\) agrees well with the diurnal and seasonal course of the \(E\) layer, while the course of \(E_{\text{spor}}\), as we have seen, for its part agrees well with the course of meteor activity.

It should be noted that during meteor showers some observations of the \(F_2\) layer were also made, but up to the present no influence of theirs on the degree of its ionization has been established.

From what has been said it is clear that at the present time it can no longer be doubted that the ionization \(E_{\text{spor}}\) is indeed regulated by meteor activity. However, the data available in the literature are still insufficient to draw definitive conclusions that it is precisely meteor activity that always determines the degree of intensity of \(E_{\text{spor}}\). Along with the remarks made above, one should also bear in mind that, as is known from a number of experiments, \(E_{\text{spor}}\) is not observed simultaneously at different points that are comparatively little separated from one another. This can hardly be attributed only to unequal meteor activity at these points. Here, probably, the influence is exerted by horizontal motions of accumulations of clouds of increased ionization in the region of the \(E\) layer. The existence of such motions is indicated by some experimental data available in the literature (see \(^{28}\) and the following paragraph).

4. ON THE INHOMOGENEOUS STRUCTURE OF THE IONOSPHERE AND MOTIONS IN IT

In the preceding sections\(^{1}\) the results of a number of experimental works have already been cited, by which it was established that in the ionosphere rather often there appear inhomogeneous regions of ionization (called ionized clouds), which lead to a complication of the character of the reflection of radio waves from the ionosphere. In a number of cases the reflections from the ionosphere are indeed such that one may picture the ionosphere, especially the region \(F\), as consisting of large inhomogeneous ionized regions and accumulations of a large number of clouds that change rather rapidly. Such cases include, for example, ionospheric storms, which are irregular and relatively short-lived phenomena.

Another type of phenomena has also led to the conception of a cloudy structure of the ionosphere—reflections from the \(E_{\text{spor}}\) layer, when the ionosphere at an altitude of the order of \(100\text{--}110\) km is represented as if by a grating, since reflections are observed simultaneously both from the ionized layer lying at these altitudes and from the higher layers of the ionosphere. This type of phenomena, although it is characterized by inconstancy in time and instability (see \(^{1}\) § 3f), can no longer be assigned to purely sporadic phenomena occurring in the ionosphere and appearing only in exceptional cases, since such reflections from \(E_{\text{spor}}\) are observed rather often.

In the preceding paragraph we saw that the intensity of \(E_{\text{spor}}\), apparently, depends significantly on meteor activity, which causes bursts of ionization, mainly in the region of the \(E\) layer. However, one may also suppose that both meteors and other phenomena occurring in the ionosphere (see below, and also § 6) contribute to the fact that ionized clouds are almost always present in the \(E\) layer. For a number of reasons there sometimes occurs a local accumulation of these ionized—

... clouds, which also leads to the fact that at the given point an intense \(E_{\text{spor}}\) appears, sometimes, as is known, completely shielding the region \(F^{19}\).

Phenomena of an analogous character are observed not only in the \(E\) layer, but also in the \(F_2\) layer, and make it possible to assume the same cloud structure of the \(F_2\) layer as of the \(E\) layer. However, this structure appears here in a somewhat different form because of the greater extent and the different dynamics of the region \(F\).

Such phenomena include those described, for example, in \(^{1}\) (§§ 3 and 5 g; see also \(^{20}\)) reflections from the so-called \(F_{\text{spor}}\), when in the region \(F\) an even multiplication of signals is observed as a result of double refraction of the signal incident on the layer in ionized regions having different degrees of ionization. Further data that have appeared in the literature \(^{21,22}\) confirm phenomena of the \(F_{\text{spor}}\) type and indicate that similar inhomogeneities and semitransparency are observed in the region \(F\) of the ionosphere under conditions when there is no basis for speaking of its disturbed state, i.e. of phenomena of a purely irregular type.

Fig. 10. Schematic height-frequency characteristic for the \(F_2\) layer, indicating the presence of a cloud structure of the layer.

Of interest in this respect are the results reported in \(^{21}\). The author of this paper observed height-frequency characteristics for the \(F_2\) layer of the type shown in schematic Fig. 10. It is evident from the figure that, in the interval of frequencies far from \(f_{F_2}^{0}\)—the critical frequency of the \(F_2\) layer—there are reflections from two heights: one height, lying in the lower part of the layer (branch \(a\) in Fig. 10), and another, of considerably greater height (branch \(b\)), apparently lying in the region of the maximum of \(F_2\) or, perhaps, somewhat above it. Characteristic in these measurements is the fact that reflections from the greater height cease at a frequency considerably smaller than the critical frequency \(f_{F_2}^{0}\), and the dependence of its effective height on frequency is the same as for a layer with a maximum, in the region of which strong penetration of the signal begins and an increase of \(h_{\partial}\), i.e. of the group-delay time of the signal, occurs. Thus, the upper branch \(b\) of the dependence of \(h_{\partial}\) also has the tails of the ordinary and extraordinary waves.

This kind of dual character of reflection, under the assumption that both branches (\(a\) and \(b\) in Fig. 10) correspond to vertical reflections, indicates, first, that the lower part of the \(F\) layer

semi-transparent, i.e., has a lattice-like character, say, a cloud structure, so that the wave incident on the layer, being partially reflected from it, penetrates into the deeper regions of the layer^20, 22. Secondly, the nature of these data indicates that the cloud structure of the layer is preserved rather high up and that the distribution of the degree of ionization with the height of the layer has a two-valued character, i.e., in it there are, essentially, two systems of ionized clouds, the degrees of ionization of which, \(n_{e1}\) and \(n_{e2}\), depend on height as indicated in Fig. 11, a. Fig. 11, b shows, for comparison, the distribution of ionization with height for the systems of clouds \(F_{\text{spor}}\) according to the experimental data given in ^1 in Fig. IV (insert)^20.

We see that both these phenomena are apparently caused by one reason, namely, the inhomogeneous cloud structure of the ionosphere,

Fig. 11. Distribution with height of the degrees of ionization \(n_{e1}\) and \(n_{e2}\) of the regular layer \(F_2\) and \(F_{\text{spor}}\).

which changes its character under different conditions, leading to different types of height–frequency characteristics.

In various experimental investigations there is a great deal of evidence testifying to the cloud structure of the ionosphere. However, most of the results of these works are mainly only qualitative in character and still do not allow one to draw a conclusion as to what this so-called cloud structure is and what the mechanism is for the formation of clouds and their accumulation at one point or another.

If, as already indicated above, during periods of ionospheric storms the \(F_2\) layer apparently really has a patchy character and consists of separate isolated accumulations of ionized clouds of both large and small dimensions, then in a number of cases there is no certainty that what are usually called ionic clouds are not in fact condensations and rarefactions of the degree

ionization caused by the motion of density waves (density oscillations) in various directions.

Thus, often, when we speak of motions in the ionosphere, there is no certainty as to whether this is the result of the drift of ionized clouds or merely the result of wave-like changes in density.

There are some experimental data which do not yet permit any generalizations to be made (since they have not been processed from the point of view of interest for the corresponding analysis), but which indicate that, in the ionosphere, there is apparently always scattering of radio waves and that the signal reflected from the ionosphere is a superposition of many elementary signals. An example of this may be the well-known phenomenon of rapid fluctuations in the intensity of a single reflected pulse[^23], when there are no grounds for speaking of fading, i.e., of the phenomenon of interference as the result of the superposition of various coherent oscillations, because of the absence of any regularity or periodicity in these oscillations. There are also other data in this direction which it does not yet seem possible to illuminate.

Thus, in the light of present-day data, the question arises whether the ionosphere does not always have, in the main, an inhomogeneous structure of a complex type, in the sense that in it there always and everywhere exist inhomogeneities of ionization both of an isolated character (clouds) and of a wave-like type (density oscillations), which in a number of cases acquire a more pronounced character owing to changes in the conditions of its dynamics (as it is customary to say—its weather). These inhomogeneities exist in the ionosphere as a “background,” which continuously changes in time—“fluctuates”—both because of the displacement (drift) of isolated inhomogeneities (clouds) and because of the appearance and disappearance of wave motions. Wave motions, in turn, may be one of the causes of cloud formation and also affect the character of the motion of these clouds.

In the following paragraph the question of plasma oscillations, which may cause wave-like motions in the ionosphere, will be considered.

We see that further experimental investigations of the ionosphere, directed toward the study of its inhomogeneous structure and of the motions occurring in it, may lead to the clarification not only of questions concerning the dynamics of these regions of the atmosphere, but also of the question of their structure.

In this light, the quantitative characteristics of the velocity of motion in the ionosphere that are available in the literature are of interest; these are given in Table II.

From the few data contained in the table it is evident that possible drift both in \(E_{\text{spor}}\) and in \(F_2\) has considerable velocities, greatly exceeding the velocities of possibly purely local

Table II

Velocities of motion in the ionosphere

of motions in the layer (Doppler effect). This makes it possible to suppose that the rapid motions are connected with the transport of large cloud-like accumulations of ionized particles, carried along by the motion of gas masses occurring at these heights, whereas the slower motions characterize the velocities of fluctuations of individual clouds and the velocities of wave-like processes occurring in the ionosphere.

5. OSCILLATIONS OF PLASMA AND THEIR POSSIBLE INFLUENCE ON THE PROPAGATION OF RADIO WAVES IN THE IONOSPHERE

The question of oscillations in plasma has been most thoroughly analyzed in several works\(^{29–33}\). However, a whole series of fundamental points is still insufficiently clarified, especially in application to the ionosphere. Therefore even the basic question of the role of these oscillations in

of the propagation of radio waves in the ionosphere and the nature of their influence on the structure of the ionosphere at the present time remains unclear.

At the same time, from a number of phenomena observed in the ionosphere, it may be supposed that plasma oscillations affect the structure of the ionosphere (see, for example, the preceding paragraph of this article). In addition, there are certain grounds for assuming that resonant plasma oscillations may actually be excited in the ionosphere (see below). Therefore, it may perhaps be expedient at present to give a brief account of plasma oscillations in a work devoted to investigations of the ionosphere.

We shall first give an elementary derivation of plasma oscillations. In these theoretical considerations it is assumed (see, for example, ^30) that the plasma is quasineutral and that only the motion of electrons is considered, i.e. it is assumed that the ions on the average remain in their places, and that their charge is uniformly distributed in space. The influence of uncharged particles is also neglected, which is possible at low gas pressure.

Let us now suppose that, for some reason, the electrons have been displaced from their initial positions by a segment $\mathbf{r}'(xyz)$. As a result of the displacement of the electrons, an excess charge is created in the given volume of plasma, whose density is

$$ \rho = e \operatorname{div}(n_e \mathbf{r}'), \tag{5.1} $$

where $n_e$ is the electron density of the plasma, and $e$ is the charge of the electron. Naturally, in expression (5.1) only the potential component of the displacement vector $\mathbf{r}'$ is considered, i.e. it is assumed that only such displacements of the electron take place.

The electric field $\mathbf{E}$ produced by the space charge $\rho$ is parallel to the displacement $\mathbf{r}'$*) and acts on each electron with the electrostatic force $\mathbf{F}_e=-e\mathbf{E}$; moreover, since

$$ \operatorname{div}\mathbf{E}=4\pi\rho=4\pi e\operatorname{div}(n_e\mathbf{r}') $$

and

$$ \mathbf{E}=4\pi n_e\cdot e\mathbf{r}', \tag{5.2} $$

then this force is equal to

$$ \mathbf{F}_e=-4\pi e^2 n_e \mathbf{r}' \tag{5.3} $$

and, as is evident, tends to return the electron back to its initial position.

On the other hand, the electron is acted upon by a hydrodynamic force $\mathbf{F}_p=-\operatorname{grad}(\Delta p)$, which tends to increase the excess pressure $\Delta p$, formed by the excess electron density and equal to

$$ \Delta p=-\varkappa T \operatorname{div}(n_e\mathbf{r}'), \tag{5.4} $$

where $T$ is the electron temperature, and $\varkappa$ is Boltzmann’s constant.

*) It is assumed that in the plasma there are no electric fields from other sources.

This force, per electron, is therefore equal to

\[ \mathbf{F}_p=-\frac{\operatorname{grad}(\Delta p)}{n_e} =\chi T \operatorname{grad}\operatorname{div}\mathbf{r}' . \tag{5.5} \]

Using (5.3) and (5.5), one can now write the equation of motion of the electron:

\[ m\frac{d^3\mathbf{r}'}{dt^2} =\mathbf{F}_e+\mathbf{F}_p =-4\pi n_e e^2 \mathbf{r}'+\chi T\nabla^2\mathbf{r}', \tag{5.6} \]

where, again, in equation (5.6) only the potential part of the vector \(\mathbf{r}'\) is used.

Equation (4.6) is a wave equation; therefore, assuming for the one-dimensional case a solution of the form

\[ x'=A\sin\left(\omega t+\frac{x}{\Lambda}\right), \tag{5.7} \]

we obtain that the frequency of the wave satisfying (5.6) is equal to:

\[ \omega=\omega_0\sqrt{1+\frac{\chi T}{4\pi n_e e^2}\cdot\frac{1}{\Lambda^2}}, \tag{5.8} \]

where

\[ \omega_0^2=\frac{4\pi n_e e^2}{m}. \tag{5.9} \]

Introducing the notation

\[ \frac{\chi T}{4\pi n_e e^2}=D^2, \tag{5.10} \]

where \(D\) is the so-called Debye radius, we obtain:

\[ \omega=\omega_0\sqrt{1+\left(\frac{D}{\Lambda}\right)^2} \simeq \omega_0\left(1+\frac{1}{2}\left(\frac{D}{\Lambda}\right)^2\right) \tag{5.11} \]

for

\[ \frac{D}{\Lambda}\ll 1. \]

From the elementary derivation presented and formula (5.11) it is clear that oscillations of individual regions of a plasma (aggregates of electrons) can arise in a plasma, and that, owing to the hydrodynamic force—the influence of the electron pressure—a wave-like process must arise in it, connecting the oscillations of electrons in different regions that occur under some initial displacement of them.

From the entire physical formulation of this question it is clear that, in order to determine the wavelength of these oscillations, additional information is necessary about the structure of the plasma itself and a concrete specification of the initial displacement of the electrons, i.e., the configuration and magnitude of the region of macroscopic inhomogeneity of the plasma that is created in the plasma at the initial instant and that will oscillate in that part of the plasma where the initial displacement is specified.

From simple considerations one can draw certain conclusions about the magnitude \(\Lambda\).

In deriving formula (5.11), the thermal motion of the electrons was not taken into account; this leads to the oscillating region of the plasma being somewhat smeared out, and if its size is comparable with the distance traversed by an electron during one period of oscillation, then the space charges causing these oscillations rapidly disappear. It follows from this that, in order for oscillations to exist in a plasma, it is necessary that

\[ \Lambda \gg \frac{\overline{v}_x}{\omega_0}, \tag{5.12} \]

where \(\overline{v}_x \approx \sqrt{\frac{kT}{m}}\) is the mean thermal velocity of the electrons (one-dimensional oscillations are being considered), and \(\omega_0\) is the zero frequency of plasma oscillations, determined by formula (5.9). Substituting the corresponding values of \(\overline{v}_x\) and \(\omega_0\) into (5.12), we obtain:

\[ \frac{\Lambda}{D} \gg 1, \tag{5.13} \]

i.e. the wavelength \(\Lambda\) of oscillations propagating in the plasma must be greater than the Debye radius (5.10). Moreover, from analogous physical considerations it is also clear that the wavelength \(\Lambda\) must be greater than the mean free path \(l\) of the gas particles; and since \(l \gg D\), this condition still further strengthens the necessity that the extent of the oscillating region of the plasma be sufficiently large.

Furthermore, it is evident from these conditions that the frequency of plasma oscillations depends little on the wavelength and is practically determined only by formula (5.9), as a result of which it may be assumed that independent oscillations can exist in separate regions of the plasma.

The elementary consideration given above is, of course, in no way suitable for the analysis of a number of fundamental questions concerning the character of plasma oscillations, the conditions for their excitation, the influence of plasma inhomogeneity, etc.,\(^{31}\) which is possible only with a more rigorous formulation of this problem\(^{29,31,32}\).

Let us now note some questions of plasma oscillations connected with the ionosphere. From formulas (5.11), (5.13), and (5.9) it is evident that the frequency of plasma oscillations, equal to \(\omega \simeq \omega_0\), represents a condition relating the frequency of the wave incident on the layer to the degree of ionization \(n_e\) of that region of the layer in which it undergoes total reflection (see \(^{1}\S 2a\)). This means that, at the point of reflection, the frequency of the wave incident on the layer and the frequency of the possible plasma oscillations almost coincide in magnitude. This gives grounds to suppose that, in the region of reflection of the wave, under certain conditions, resonant or nearly resonant excitation of plasma oscillations may occur, which should lead to absorption of the energy of the wave incident on the layer, and also to a peculiar cross-modulation of the reflected wave (oscillations of its amplitude).

Naturally, in order to excite plasma oscillations it is necessary that the amplitude of the electromagnetic field of the incident wave at the place of reflection be sufficiently large. Therefore there is no reason to suppose that such phenomena are always possible. However, on the other hand, it is clear that if, for some other reasons connected, say, with the transfer of charges occurring in the ionosphere, oscillations arise in it, then the incident wave, interacting with these oscillations, especially under conditions close to resonance, must undergo the same additional absorption and cross-modulation.

These phenomena must be greatly complicated by the inhomogeneity of the ionosphere with height, which leads to the fact that at different heights the frequencies of plasma oscillations are different; and, in view of the fact that \(n_e\) varies continuously with height, here, generally speaking, there may arise a continuum of oscillations with an upper frequency limit determined by the degree of ionization of the layer maximum. Since, as we saw above (see condition (5.13)), in different regions of the plasma there apparently may exist independent, or, let us say, weakly coupled oscillations, this must lead to the possibility of the simultaneous appearance of oscillations of different frequency in different places of the ionosphere, producing inhomogeneities in it (condensations and rarefactions of density), which may, in turn, cause cloud formation.

From the entire body of experimental data on the ionosphere it is evident (see, for example, §§ 3 and 5b) that in it, apparently, there is always a transfer both of neutral particles and of charges. Therefore there is reason to suppose that plasma oscillations, which can arise at any place in the ionosphere with various frequency and wavelength \(\Lambda\), may have a disordered, statistical character and lead to a statistical character of reflections from the ionosphere.

Thus, from what has been said above it is clear that a sufficiently detailed and rigorous theoretical analysis of this question is undoubtedly of interest.

However, this problem proves to be extremely difficult from the theoretical side. In the works cited above\(^{29,31,32}\), mainly only the linearized system of Maxwell’s equations and the kinetic equation was analyzed. At the same time, for the analysis of the questions that interest us it is necessary to investigate a nonlinear system of equations, and for a number of specifically formulated physical conditions.

Up to the present time, so far as the author knows, such work has not yet been carried out; therefore it is not possible at present to express any definite judgment on the role and influence of plasma oscillations on the propagation of radio waves in the ionosphere; it is evident, however, that interesting and important problems arise here.

6. NEW DATA ON NONLINEAR EFFECTS

Recently several experimental works[^35][^36][^37] have appeared which contain the results of studying nonlinear effects in the ionosphere. Studies of nonlinear effects, the so-called Luxembourg–Gorky effect,[^34] as was already indicated (see § 5d), are of interest not only from the methodological side, but may apparently serve for the study of certain fine details of physical processes and for the measurement of ionospheric constants, in particular the number of collisions of electrons with neutral molecules or ions.[^38] For this reason we present these still rather few results, which, however, already contain certain quantitative data. It should be noted that the measurements in the indicated works were carried out while receiving a large number of radio stations, and in one of them[^37] there are also photoscillograms of cross-modulation.

The range of waves in which the investigations in these works were carried out covers the region from 60 to 1100 km. The powers of the various stations varied within the limits from 20 to 170 kW in measurements at frequencies different from the gyroscopic frequency, while in measurements at the gyroscopic frequency stations of power \(\sim 1\) kW were also used. In all the experiments the frequency of the tone modulation of the interfering station (i.e., the one whose transmission is superposed on the reception of the main station) was varied within the limits from 50 to 2000 Hz.

The depth of cross-modulation was measured. For different cases, limits of variation of the depth of cross-modulation from 0.25% to 3% and more were obtained. In all measurements it was established that the depth of cross-modulation decreases with increasing modulation frequency \(f\) of the interfering station and at \(f \simeq 1500\) Hz and more reaches only 0.5% and less. In measurements at the gyroscopic frequency[^37] it was established that the depth of cross-modulation changes depending on the time of the experiment, which leads to the supposition of changes in the magnitude of the constant magnetic field in the ionosphere.

The processing of the experimental data was carried out on the basis of the theory of nonlinear effects developed in,[^39] and therefore they do not yet take into account a number of additional points following from the study.[^38]

From the analysis of these data[^36] the authors arrive at the supposition that the principal absorption in the ionosphere in the above-indicated range of waves occurs at night at a height of the order of 85 km, where from their experiments an effective number of collisions \(\nu_{\mathrm{eff}} \simeq 5 \cdot 10^{5}\) is obtained; in another work[^35] one obtains \(\nu_{\mathrm{eff}} \simeq (6 \cdot 10^{5} \div 1.2 \cdot 10^{6})\) for the height of the beginning of the layer \(E\).

These first quantitative results of the investigation of nonlinear effects clearly show how expedient and important further investigations in this direction are, but on the basis of a deeper and more comprehensive theoretical analysis[^38] of the results of measurements.

BRIEF CONCLUSION

With this article the review of the present state of the question of ionospheric research is concluded.

Along with setting forth already sufficiently verified experimental and theoretical data, as well as characterizing the various regions of the ionosphere and the phenomena observed in them, we considered it necessary, as far as possible, to dwell on certain phenomena that are still insufficiently investigated, and also on the difficulties and contradictions arising in this field, and to note a number of unresolved questions. Some of these questions appear to us so significant that they may possibly lead, in the near future, to substantial results and to a change in our views on a number of properties of the ionosphere.

From the material presented and considered it is clear that the problem of the ionosphere as a whole represents a broad field in which, from the scientific point of view, we encounter a great variety of physical problems and questions requiring, in theoretical treatment, both a purely macroscopic approach and, especially at the present stage of its development, the application of the methods of microphysics.

Naturally, we have not been able in these articles to cover certain works, acquaintance with which is necessary at least for the completeness of the picture.

We shall point out, for example, that data relating to the establishment of a connection between meteorological conditions at the earth’s surface and ionization in various regions of the ionosphere have not been considered here. Recently new data have been obtained on this question ^{40, 41} (see also ^{42}).

At present, however, there is still not enough material to make it possible to construct a definite picture even of a purely descriptive character, especially since the data available in the literature on this question are ambiguous and are not reproduced under different conditions. In this direction further analysis of a large, carefully obtained experimental material is necessary.

Further, one should note works in which methods and certain preliminary results are considered for investigating the ionosphere by means of the reflection of radio waves from the Moon ^{43}, or by studying the radio emission of the Sun ^{44}; these are of interest if only in the sense that they make it possible to form some idea of the upper half of the ionosphere.

There are also new interesting data on the study of the ionosphere at high latitudes ^{45, 46}, etc.

From the theoretical point of view, the attempt made in the literature to construct a general geophysical theory of the ionosphere ^{47}, certain remarks concerning diffusion and the balance of ioni-

protection in the ionosphere^48^, etc. An attempt was also made in one work to consider the ionosphere as a medium in a state of equilibrium radiation^49^. Such a consideration is legitimate, as is known, in various treatments of the solar corona and stellar atmospheres; however, when applied to the ionosphere it gives rise to a number of objections.

Thus, it did not seem possible to cover some questions in this survey. Therefore, for acquaintance with them we refer the reader to the corresponding articles cited above.

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