Variations of Cosmic Rays

L. I. Dorman and E. L. Feinberg

§ 1. Introduction

The study of changes in the intensity of cosmic rays constitutes a special branch of cosmic-ray physics. Seldom has any independent significance been ascribed to it. Several times it has attracted the attention of broader circles of physicists, when results of general physical interest “unexpectedly” grew out of it. Thus it was, perhaps, in 1926, when Myssovsky and Tuwim[^1] discovered the barometric effect—the decrease in the intensity of cosmic rays at the surface of the Earth when atmospheric pressure increases. Such a decrease confirmed the fact that cosmic rays are absorbed in the atmosphere and, consequently, provided a new possibility for studying the penetrating properties of fast particles in cosmic rays.

Then the temperature effect was discovered. In 1938, Blackett[^2] gave it an exceptionally elegant explanation. These were the years when the decay of mesons had only just been discovered, but the experiments proving its existence and making it possible to determine the lifetime were still not convincing. Blackett, as is well known, drew attention to the fact that mesons, if they are unstable, must be formed in the upper layers of the atmosphere, after the primary component has traversed a certain mass of air. Therefore, when the atmosphere is heated and correspondingly expands—for example, from winter to summer—the height of the meson-generation level should increase, their path to the Earth and their decay should increase, and the intensity should fall. The estimate gave a convincing agreement with experiment, although it later turned out that the changes from night to day—which are much smaller than the seasonal ones—have the opposite sign (see below). In those years the accuracy of registration was low, and discrepancies in the figures by factors of 2–3 could not be taken seriously. The study of temperature variations of cosmic rays yielded substantial

Variations of cosmic rays

$\lambda = 50^\circ$

) A dash denotes the absence of experimental data.
) Increase in the intensity of the hard component of cosmic rays, as distinct from other components, due to the change of temperature in the upper layers of the atmosphere.
) If it is shown that these variations really exist.
**) During the last flare of February 23, 1956, the amplitude on p. 212).

(amplitude in percent)

Table I

during small solar flares may, apparently, be caused by the atmosphere because of the change, accompanying the flare, in the flux of ultraviolet—

the increase was an order of magnitude greater than those given here (see note ...

information on the lifetime of mesons. In particular, it showed that the “atmospheric” mesons, which we now call \(\mu\)-mesons, cannot be the “nuclear” mesons that were needed to explain nuclear forces and \(\beta\)-decay according to Yukawa’s theory.

This, perhaps, exhausts the results of the study of variations that are essential for elementary-particle and cosmic-ray physics.

At the same time, however, the significance of these investigations has been increasing for other questions—for the problem of the origin of cosmic rays and for purely astrophysical problems. It is precisely these problems that are now acquiring special interest. One may perhaps say that in recent years the study of cosmic-ray variations has gradually been turning into an independent method for probing physical conditions in the interstellar medium. Here we obtain a new quantitative method which, independently of other methods (optical, radio-astronomical, etc.), makes it possible to determine certain interesting astrophysical characteristics.

At present the study of cosmic-ray variations is being carried out throughout the world by a network of special stations for continuous recording, existing alongside the solar service, the network of magnetic observatories, and other similar systems of continuous observation. These stations for the most part record the hard component of cosmic rays with the aid of large precision ionization chambers covered by a layer of \(10\ \text{cm}\) of lead, having various volumes (from 19 to \(1000\ \text{l}\)) and ensuring an accuracy of measurement of the intensity of cosmic rays from \(0.7\%\) to \(0.1\%\) per hour of recording (depending on the volume of the chamber). Continuous recording is also carried out with counter telescopes of large area (with approximately the same accuracy as that of the chambers) and recording of the neutron component with the aid of large neutron detectors constructed on the principle of local generation of neutrons in lead surrounding the neutron counters[^3]. These methods are the basic, more or less standardized ones. In addition, however, various special investigations are also being carried out.

Throughout the world there are about 35 continuous-recording stations, of which 6 are in the USSR (Moscow, Sverdlovsk, Irkutsk, Yakutsk, Cape Schmidt, Tbilisi). The first to begin operation (1949) and the best-equipped Soviet stations are the station of the Yakutsk Branch of the Academy of Sciences of the USSR and the station of the Scientific Research Institute of Terrestrial Magnetism (Moscow). During the International Geophysical Year (1957–1958) the number of stations throughout the world will increase to approximately 75. The number of published works on variations at present is measured in the hundreds. An enormous amount of material has already been accumulated, which until recently gave the impression of a weakly systematized piling-up of data. Seasonal,

daily, eleven-year, semidiurnal, 27-day oscillations, often different at different latitudes and for different components; changes during magnetic storms and during solar chromospheric eruptions; changes in the amplitude and phase of the diurnal effect during magnetic storms, etc. Some summary data on the scale of various variations can be found in Table I. Very often these data, obtained by different investigators, appeared to be mutually contradictory. However, in the very last years the whole situation has begun to become clearer; from the accumulation of facts a coherent picture is emerging. Now, on the contrary, the insufficiency of some data is already being revealed, as is the need for new measurements to refine the quantitative conclusions.

§ 2. VARIATIONS AND THE PROBLEM OF THE ORIGIN OF COSMIC RAYS

The amplitude of variations that have been reliably recorded at the present time is measured in percentages and fractions of a percent (the exception is the changes in intensity during chromospheric eruptions on the Sun; see Table I). This is true both for the main portion of the primary spectrum (particle energy \(\sim 10^{10}\) eV) and for the specially investigated energy region \(\varepsilon > 10^{13}—10^{14}\) eV (variations in the frequency of occurrence of extensive air showers). Thus, the flux of cosmic rays is fairly constant in time and isotropic.

This constancy is in itself an extremely important fact. It could be ascribed to only one of two circumstances. On the one hand, it may be that cosmic rays propagate rectilinearly and that their sources are uniformly distributed not only in our Galaxy, but also outside it (if cosmic rays, propagating rectilinearly, arrived only from our disk-shaped Galaxy, anisotropy would be observed). However, such a possibility seems improbable. In fact, from the magnitude of the intensity of the cosmic-ray flux it follows that the energy density of cosmic rays in the Galaxy is about \(1\) eV/cm\(^3\). If the same density existed not only in the Galaxy but also in intergalactic space, then this would mean that the total energy of cosmic rays in the whole universe (with an average density of matter of the order of \(10^{-28}\) g/cm\(^3\)) is approximately \(10^{-5}\) of the rest energy of all matter. This figure seems so unreasonably large that the corresponding possibility is usually rejected. Thus, there remains another possibility: cosmic rays are confined within our Galaxy, where their density is much greater than in intergalactic space. In that case a factor of order \(10^{-4}\) is added, and their total energy amounts to only \(10^{-9}\) of the rest energy of all matter (as much as,

how much at the surface of the Sun is the kinetic energy of a hydrogen atom from its rest energy).

The cause that keeps the particles in the Galaxy can only be the interstellar magnetic field. The isotropy of the cosmic-ray flux and the smallness of its variations were the first evidence in favor of the existence of such a magnetic field. At present, both theoretical considerations based on Alfvén’s magnetohydrodynamics,^4 and the direct study of the polarization of starlight upon scattering by anisotropic interstellar dust grains oriented in this magnetic field, lead, according to S. B. Pikel’ner’s estimate,^3 to a value of the strength of the interstellar magnetic field \(H \sim 3 \cdot 10^{-6}\) oersted.^5 Such a field is sufficient not to let escape from the Galaxy (dimensions \(\rho \sim 10^{22} \div 10^{23}\) cm) even particles with energy \(cp = 300H\rho = 300 \cdot 3 \cdot 10^{-6} \cdot 10^{22} \sim 10^{19}\) eV. Thereupon another question arises: can cosmic rays be of solar origin only? In that case, in order to give isotropy within the limits of the solar system, they would have to be retained in it, and consequently their trajectories must have a radius of curvature not greater than \(10^{14}\) cm.

Within the solar system the magnetic field can hardly exceed \(10^{-4}\) oersted. If this is so, then only a part of the cosmic rays with energy \(cp < 300 \cdot 10^{-4} \cdot 10^{14} = 3 \cdot 10^{12}\) eV could be of solar origin. The absence of appreciable variations for particles of higher energies thus indicates their extrasolar origin. A number of additional considerations (cf. § 9) indicate that even in the region \(cp < 3 \cdot 10^{12}\) eV cosmic rays of solar origin cannot make the main contribution.

§ 3. VARIATIONS OF ATMOSPHERIC ORIGIN

Of course, what has been said above is only one, and the crudest, example of how, on the basis of cosmic-ray variations, one can draw conclusions essential for the problem of the origin of cosmic rays. Obviously, for a more detailed analysis it is necessary to understand the nature of all the observed variations—first of all seasonal and diurnal ones, and also variations during solar flares. Yet precisely here, until very recently, the situation was extremely confused. In fact, everything that had been understood about variations up to now—the barometric and temperature effects—pointed precisely to their atmospheric origin. What, then, in the numerous variations studied has an extraterrestrial nature, and what nature exactly?

This first and quite natural question for a long time was, and to a considerable extent still remains, a subject of discussion in the world literature. To answer it, it is first of all necessary carefully to exclude from the observed variations the effects of atmospheric

origin. It is precisely here that significant discrepancies in conclusions arose.

Thus, one of the researchers, Forbush, on the basis of ten years of observations on the American network of stations of the Carnegie Institution, which he directed, came to the conclusion that seasonal variations are only half of atmospheric origin[^6],[^7]. Another, Duperier, who for many years had been carefully studying the variations in London[^8], went further. He tried to take into account the well-known fact that the decay of π-mesons, from which μ-mesons arise in the atmosphere, is facilitated when the temperature rises, since a decrease in air density reduces the capture of π-mesons by the nuclei of air atoms. Therefore, heating of the stratosphere produces an increase in the number of π-mesons and, consequently, there should exist a positive temperature effect on the intensity of μ-mesons (in contrast to the usual, negative effect, much larger in observations at sea level). However, an attempt to take it into account with the aid of empirical coefficients led Duperier to new inconsistencies. Thus, the lifetime of π-mesons required for the internal consistency of Duperier’s results under the indicated interpretation of the effect proved to be three times greater than its true value[^9].

Next, Dolbear and Elliot (Manchester)[^10], taking this positive temperature effect into account, in contrast to Forbush, came to the conclusion that the atmospheric seasonal variations merely mask true seasonal variations of extraterrestrial origin, and that these true seasonal variations have the opposite sign (and the same absolute magnitude) to those directly observed.

Many attempts were made to reconcile the different results purely empirically.

It turned out, however, that the question of the correct allowance for and elimination of meteorological variations admits a rather simple solution, and now, after numerous checks and successful applications, the corresponding method has already been used for several years on the Soviet network of stations. By excluding meteorological variations in this way, it is possible to obtain a number of new results and to understand the mutual contradictions of other authors.

First of all, it is necessary to take into account that, in addition to the effect of pressure change—simple absorption—and the effect of displacement of the meson generation level (what was usually called the temperature effect), there is still another meteorological effect[^11]. Losing energy in the atmosphere by ionization, a meson changes its lifetime. If it has lost energy at the beginning of its path, this will affect its “probability of survival” more strongly than if such a loss of energy occurs at the end of the path. Therefore, even at constant total pressure and a constant height of the generation level, vertical displacement of air masses changes the intensity of μ-mesons observed at sea level. It turns out that in a real nonequilibrium atmosphere

this effect is just as substantial as the one taken into account earlier. Therefore, wishing to take meteorological variations into account, we cannot rely only on the change of temperature at sea level, or in the stratosphere, or at some other isobaric level. It is necessary to take into account the entire temperature profile of the atmosphere above the point of observation. One can quite simply derive a formula that completely determines the observed change \(\delta N_{\mu}\) in the intensity of \(\mu\)-mesons \(N_{\mu}\) at a given level with pressure \(h_0\), if the change of pressure at this point \(\delta h_0\) and the temperature changes \(\delta T(h)\) at all levels with pressure \(h\), from the point of observation to the point of generation of \(\mu\)-mesons with pressure \(h_1\), are known. Initially such a formula was obtained\(^{11}\) for the “one-meson scheme,” which assumes the generation of \(\mu\)-mesons at one definite isobaric level (the dependence on \(h_1\) is weak, logarithmic). Application even of this approximate scheme gave good results. Both for the data of the Yakutsk station in 1949 and for the published data of the Cheltenham station (near Washington) for 1937–1946, it turned out that the seasonal variations are almost entirely reduced to meteorological ones. The correlation coefficient between the meteorological changes \(\delta N_{\mu}\), precalculated on the basis of the above-mentioned formula, into which radiosonde temperature-measurement data are substituted, on the one hand, and the observed variations \(\delta I_{\mu}\), on the other, reaches extremely high values (0.90 and above). For Yakutsk the seasonal meteorological variations are exceptionally large, the amplitude reaching 5% (at the equator the amplitude of the seasonal oscillations is ten times smaller). Therefore, such a good result for Yakutsk indicates that at high latitudes the seasonal effect is indeed practically completely reduced to the meteorological effect. Subsequently this theory was improved.\(^{12}\) It was taken into account that \(\mu\)-mesons are formed throughout the atmosphere as a result of the decay of \(\pi\)-mesons; a number of other essential circumstances were also taken into account. The conclusions of this complete theory can be represented by the formula

\[ \frac{\delta N_{\mu}}{N_{\mu}}=\beta \delta h_0+\int_{0}^{h_0} W(h)\delta T(h)\,dh . \tag{1} \]

Here \(\beta\) is the barometric coefficient, which is usually determined empirically, but in the present scheme it can be calculated theoretically and proves to be in agreement with experiment. As for the function \(W(h)\), it has the meaning of the “density of the temperature coefficient” (the former simple concept of the temperature coefficient loses its significance here). It can be split into two terms, \(W_{\mu}\) and \(W_{\pi}\), giving, respectively, the influence of the decay of \(\mu\)-mesons (negative contribution) and the influence of the decay of \(\pi\)-mesons (positive contribution). This function \(W\) is shown in Fig. 1 for two cases: in Fig. 1, \(a\)—for global observations-

Fig. 1. Density of the temperature coefficient.
a—at sea level; b—at a depth of 70 m water equivalent. Curve 1—\(W_\pi(h)\); curve 2—\(W_\mu(h)\); curve 3—\(W(h)=W_\pi(h)+W_\mu(h)\).

of the intensity of the hard component at sea level; in Fig. 1, b—for observations of the hard component underground (at a depth equivalent in absorption to 70 m of water). In calculating \(W\), no arbitrary constants are used, apart from the usual

Fig. 2. Seasonal variations of the hard component of cosmic rays at sea level: \(a\)—in Cheltenham (“one-meson scheme”), \(b\)—in Yakutsk (“two-meson scheme”). Solid curve—experiment; dashed curve—the contribution of the meteorological effect.

constants. It includes only the lifetimes of mesons, the ionization losses of particles, the absorption coefficients of the primary component in the atmosphere, and the spectral index of \(\pi\)-mesons generated in collisions of protons with nuclei (the result of the calculation is little sensitive to errors in the last two quantities). Now, knowing \(\delta T(h)\) from radiosonde measurements, with the aid of this curve it is easy

calculate \(\delta N_\mu\). This “two-meson scheme” was used over the course of several years. The results were presented in \(^{13}\). They are partly shown in Figs. 2 and 3. Some more detailed results may be found, for example, in \(^{14}\).

It becomes evident that the seasonal variations, at least at moderate and high latitudes, are almost entirely of meteorological origin. As for the diurnal variations, here the solution of the question is made somewhat difficult by the fact that their amplitude is an order of magnitude smaller than that of the seasonal ones. Therefore the errors in measuring

Fig. 3. Diurnal variations (Yakutsk, average over two years). Circles and curve—measurements, \(\odot\)—calculated meteorological effect.

the temperature become very substantial. Nevertheless, a study carried out in Yakutsk by A. I. Kuzmin \(^{14,15}\) showed (Fig. 3) that meteorological variations mask the true diurnal variations of extraterrestrial origin. After subtracting the meteorological effect, the diurnal variations increase approximately twofold. This was confirmed in a more detailed study by E. S. Glyukova \(^{16}\), who also obtained one further result.

It had long been known that the amplitude of diurnal variations is different in different seasons. It turned out, however, that if the meteorological changes are taken into account by the method described above, the diurnal effect remains constant throughout the year. In Fig. 4 is given

the difference of intensities at 14 hours and at 2 hours, and also at 17 hours and at 5 hours local time for Moscow.

The conclusion that a diurnal effect of extraterrestrial origin exists is confirmed by long-known results of acute-angle experiments with crossed telescopes^17,18,19. In the last of these, at a latitude of about \(45^\circ\), the difference was measured between the readings of two crossed telescopes directed at an angle of \(90^\circ\) to one another: one along the Earth’s axis, the other perpendicular to it. In this case the meteorological effect was automatically eliminated, and nevertheless diurnal oscillations of the intensity remained.

Fig. 4. Dependence of the diurnal variations of the hard component of cosmic rays at sea level on the time of year (Moscow): a) difference of intensities 14 h—2 h; b) difference of intensities 17 h—5 h. Dashed line—measurements; solid curve—the meteorological effect has been excluded.

In not a single case of applying the method described*) were internal contradictions found. How, then, in this case are we to understand the mutual contradictions among a number of experimenters mentioned above? It can be shown^22 that these contradictions are apparent and are connected precisely with an incorrect allowance for meteorological oscillations. In these works, which used the former method of single barometric and temperature coefficients, it could not have been

*) Subsequently this method was independently proposed by other investigators, who evidently did not know of the works^11,12,13. Thus, a one-meson scheme^11 was published by Olbert^20, and a two-meson scheme by Maeda and Wada^21. However, these methods did not find any more or less extensive application or verification among the authors mentioned.

taken into account. For example, here the circumstance that in England the stratosphere is colder in summer than in winter, but warmer by day than by night, etc., is of substantial importance. Such very widespread inversions cannot be taken into account if the concept of uniform coefficients is used.

Thus, we can take into account and exclude from the observed variations the influence of changes in meteorological conditions. At present the accuracy here is limited by the accuracy of radiosonde measurements of the atmospheric temperature. As analysis shows[^16], meteorological effects of the order of fractions of a percent can be reliably excluded only by carrying out statistical processing. In particular, if the meteorological effect is taken into account over the course of only selected days, the errors may be large. With averaging, however, for example over one month, the result is convincing.

Fig. 5. Latitudinal effect of the intensity of μ-mesons at sea level. Dashed line—measurements; solid curve—the meteorological effect is excluded.

This method was also used to study a number of other questions. Thus, for example, quite some time ago Kupferberg[^23] put forward the assumption that the latitudinal effect of the hard component at sea level can be explained to a substantial degree as a consequence of the difference in atmospheric temperatures at different latitudes. This circumstance-

...can now be accurately taken into account. Using data, averaged over many years, on the distribution of temperature in the atmosphere, it was possible to show^24 that the latitude effect cannot be explained by the temperature difference at different latitudes. However, proper accounting of meteorological conditions changes the curve of the latitude effect of the hard component and somewhat shifts the position of the

Fig. 6. Passage of a cold front (Yakutsk, April 16, 1951). Solid curve—measurements; dashed line—calculated meteorological effect.

“knee” (Fig. 5), so that the curve shows an apparent absence of primary particles with energy less than 7 Bev. Of course, this simply means that primary particles with energy less than 7 Bev cannot produce μ-mesons capable of reaching sea level. Such a conclusion agrees well with known independent results^25.

Meteorological fluctuations in the intensity of cosmic rays also arise during the passage of air fronts. This effect had already been noticed long ago^26. D. D. Krasilnikov^14,27 subjected it in Yakutsk to a careful study based on material from 107 fronts.

In Fig. 6, for one selected front, the results of measurements of the intensity of \(\mu\)-mesons \(\dfrac{\delta I_\mu}{I_\mu}\) and the meteorological changes \(\dfrac{\delta N_\mu}{N_\mu}\), calculated by formula (1) on the basis of measurements of the temperature in the atmosphere carried out every 2 hours, are compared. Of course, here the errors of the individual temperature measurements are too large for one to expect better agreement.

§ 4. CORRELATION WITH VARIOUS ASTROPHYSICAL PHENOMENA

Thus, the influence of meteorological changes can be excluded. By what path should one now proceed in explaining the remaining variations of cosmic rays?

One can study the correlation of these variations with such phenomena as solar chromospheric eruptions, the number of sunspots, and disturbances of the Earth’s magnetic field. This is the path that essentially all investigators have followed. In particular, during the four chromospheric flares on the Sun studied up to now over 20 years, sharp increases (up to hundreds of percent) in the intensity of cosmic rays were recorded. The attenuation of this effect as the flux penetrates into the atmosphere and the distribution of the effect over the terrestrial globe clearly showed that, during such a flare, an additional quantity of particles of comparatively low energies, approximately up to \(10\) Bev[^28], fell on the Earth. It may be supposed that these particles were emitted by the Sun. However, this must be proved separately.

It was further established that in many cases magnetic storms are accompanied by a significant (by several percent) decrease in the intensity of cosmic rays. However, surprisingly, in a number of cases such storms are not accompanied by changes in the flux of cosmic rays[^28].

At present it may be considered established that magnetic storms arise under the influence of ionized streams (on the whole neutral), which are constantly emitted by the Sun and in some cases sweep over the Earth. It is precisely in these cases that, at very great altitudes, they form currents that disturb the Earth’s magnetic field. The velocity of the streams in some cases can be measured from the delay of the magnetic storm relative to certain solar phenomena indicating the beginning of the emission of the stream (this velocity is small—of the order of \(10^8\) cm/sec), and the width—from the duration of the storm, from the time of the Earth’s passage through the stream. The study of these streams is of extraordinarily great importance for geophysics, for predicting the passage of radio waves, etc. The correlation of certain variations of cosmic rays with magnetic

...storms naturally suggests that they too are in some way connected with corpuscular streams. But what is this connection—does the emission of cosmic rays by the Sun also take place simultaneously with the emission of streams, or do the streams themselves affect cosmic rays arriving from afar? The latter point of view was advanced by

Fig. 7. Effect of a magnetic storm (according to Alfvén, polarization of the stream in the general magnetic field of the Sun): a—before the storm (the intensity of cosmic rays increases), b—after the storm (the intensity of cosmic rays decreases).

Alfvén\(^{4}\), and it was used by Dolgin and Elliot\(^{29}\). Indeed, such an ionized stream, moving with velocity \(u\), is polarized in the general magnetic field of the Sun \(H^{(c)}\). If \(H^{(c)}\) is perpendicular to \(u\), then an electric field directed transversely is created, such that, when a stream of width \(l\) is crossed, the energy of the particle changes by

\[ \delta \varepsilon = \mp 300\,\frac{u}{c}\, l H^{(c)} . \]

Fig. 8. Diurnal effect of cosmic rays (according to Elliot and Dolgin, polarization of the streams in the general magnetic field of the Sun). 1—the intensity of cosmic rays increases, 2—the intensity of cosmic rays decreases.

This field decelerates some cosmic-ray particles and accelerates others. Hence variations of cosmic rays may arise that correlate with the appearance of streams and, consequently, of magnetic storms (Figs. 7 and 8). However, in such a simple form, as was clear to Alfvén himself\(^{4}\), the hypothesis is still insufficient (see § 7).

The study of such correlations was undertaken by many authors. However, they encountered serious difficulties because of the distorting influence of meteorological factors.

A systematic study of this question was undertaken recently by E. S. Glokova,^16 who sought the corresponding correlations after excluding variations of meteorological origin. In doing so, substantial facts were discovered.

Fig. 9. Annual variations of cosmic rays and magnetic activity. 1 — measurements (Cheltenham); 2 — meteorological effect excluded (Cheltenham); 3 — measurements (Huancayo); C — index of magnetic activity (left-hand scale); R — relative sunspot numbers, Wolf numbers (right-hand scale).

It proved possible to study even that comparatively small residual of seasonal variations which remains after the exclusion of the large seasonal atmospheric variations.

Figure 9 shows that, for the Cheltenham station (near Washington, USA), this residual correlates well with the \(C\)-index—

with the index) of magnetic activity and correlates much worse with the index of the number of sunspots*) \(R\). At the equatorial station Huancayo the meteorological fluctuations are very small; it was not possible to take them into account because of the absence in the literature of the corresponding meteorological data. It is evident, however, that the nonmeteorological residual for Cheltenham is close to the full effect at Huancayo.

Similarly, Glokova showed that many other variations of cosmic rays as well—variations accompanying magnetic storms, 27-day variations, etc.—correlate well with fluctuations of magnetic activity. All this indicates that there exist only three kinds of variations: 1) atmospheric; 2) those associated with chromospheric eruptions on the Sun; 3) those associated with disturbances of the Earth’s magnetic field, i.e., apparently, with the emission of neutral streams of slow particles from the Sun.

Of course, however, such a purely statistical approach cannot be regarded as sufficient.

§ 5. COUPLING COEFFICIENTS AND PRIMARY VARIATIONS

First of all it is necessary to indicate a quantitative method which would make it possible, from the observed variations of different components at different levels, after the meteorological variations have been excluded, to determine the corresponding variations of the primary component at the boundary of the atmosphere, and moreover for different portions of the energy spectrum. It proved possible to solve this problem \(^{30,31}\) without carrying out any calculations of particle multiplication in the atmosphere, and relying only on already known experimental data concerning geomagnetic effects, in much the same way as was done by Neher \(^{32}\) in calculating the “multiplicity,” in \(^{3}\) for finding the “specific-yield function,” and in \(^{33}\) in calculating “effective spectra.”

Indeed, let us suppose that at latitude \(\lambda\), at a level with pressure \(h_0\), we measure the intensity of the \(i\)-th component of cosmic rays \(N_{\lambda}^{i}(h_0)\) (different values of \(i\) correspond to the hard component, the neutron

*) According to international agreement, each day at any magnetic observatory is characterized by the so-called geomagnetic characteristic, visually estimated from a tape with a recording of the field. Days with quiet magnetic conditions are denoted by the number 0. Strongly disturbed days are denoted by the number 2. Days of medium disturbance are characterized by the number 1. From the numbers 0, 1, and 2 obtained at all observatories of the world during a day, the central bureau derives an average (to an accuracy of tenths) for each day. This average has been given the name of the international geomagnetic characteristic (or \(C\)-index) of the given day.

**) The relative numbers of sunspots, or Wolf numbers (\(R\)-index), are obtained for each day by multiplying the number of groups of spots visible on the entire solar disk by 10 and adding to them the number of individual spots.

and so on). If the primary flux at the boundary of the atmosphere has an energy spectrum \(D(\varepsilon)\), then, obviously:

\[ N_{\lambda}^{i}(h_0)=\int_{\varepsilon_{\lambda}^{\min}}^{\infty} D(\varepsilon)\,m^{i}(\varepsilon,h_0)\,d\varepsilon, \tag{2} \]

where \(m^{i}(\varepsilon,h_0)\) is the “productivity factor,” showing what contribution to \(N_{\lambda}^{i}\) is made by one primary particle of energy \(\varepsilon\), and \(\varepsilon_{\lambda}^{\min}\) is the minimum energy that a primary particle must have at a given latitude \(\lambda\) in order to overcome the geomagnetic barrier.

When, as a result of some astrophysical causes, \(D(\varepsilon)\) changes by an amount \(\delta_j D(\varepsilon)\) (different values of \(j\) denote “seasonal,” “diurnal,” etc.), then the observed intensity \(N_{\lambda}^{i}\) changes by \(\delta_j N_{\lambda}^{i}(h_0)\). Varying both sides of equality (2), we have:

\[ \frac{\delta_j N_{\lambda}^{i}(h_0)}{N_{\lambda}^{i}(h_0)} = \int_{\varepsilon_{\lambda}^{\min}}^{\infty} W_{\lambda}^{i}(\varepsilon,h_0)\, \frac{\delta_j D(\varepsilon)}{D(\varepsilon)}\,d\varepsilon, \tag{3} \]

where the notation is:

\[ W_{\lambda}^{i}(\varepsilon,h_0) = \frac{D(\varepsilon)m^{i}(\varepsilon,h_0)} {N_{\lambda}^{i}(h_0)}. \tag{3a} \]

\(W_{\lambda}^{i}(\varepsilon,h_0)\) is the “coupling coefficient” (in \(\%/\text{Bev}\)), showing what “secondary variation,” measured in \(\%\) (i.e. the variation of the \(i\)-th component observed at the level with pressure \(h_0\)), will be caused by a doubling of the flux of primary particles with energy \(\varepsilon\) in the interval \(1\ \text{Bev}\). As it turns out, it can be determined without knowing the mechanism of multiplication in the atmosphere.

Indeed, differentiating equality (2) with respect to the lower limit of the integral \(\varepsilon_{\lambda}^{\min}\), we obtain:

\[ W_{\lambda}^{i}(\varepsilon_{\lambda}^{\min},h_0) = -\frac{1}{N_{\lambda}^{i}(h_0)} \frac{\partial N_{\lambda}^{i}(h_0)} {\partial \varepsilon_{\lambda}^{\min}}. \tag{4} \]

If we confine ourselves to considering that part of cosmic rays which is sensitive to the Earth’s magnetic field, then the right-hand side in equation (4) can be obtained from an empirical curve giving the dependence of the intensity of the given component on latitude. In fact, \(\varepsilon_{\lambda}^{\min}\) depends, and moreover in a well-known way, only on \(\lambda\). Consequently,

\[ \frac{\partial N_{\lambda}^{i}}{\partial \varepsilon_{\lambda}^{\min}} = \frac{\partial N_{\lambda}^{i}}{\partial \lambda} \cdot \frac{d\lambda}{d\varepsilon_{\lambda}^{\min}}. \]

Thus, if for the given component at the given altitude \((h_0)\) the study…

if the latitudinal dependence is known (and it has been well studied for many components at different \(h_0\)), then one can also compute \(W^i_\lambda(\varepsilon,h_0)\), at least for \(\varepsilon \leqslant \varepsilon_0=15\) Bev (so long as cosmic rays are sensitive to the magnetic field).

For higher energies, all that can be done for the time being is to proceed by extrapolation. Namely, one may start from some analytic form of the function \(W\). As such, the function with three arbitrary parameters \(k,a,b\) was adopted\(^{30,31}\):

\[ W^i_\lambda(\varepsilon,h_0)= k\left(\frac{\varepsilon}{\varepsilon_0}\right)^{-a+\frac{b}{\varepsilon/\varepsilon_0}}, \qquad \varepsilon \geqslant \varepsilon_0=15\ \text{Bev}. \tag{5} \]

The indicated three parameters are determined from the normalization condition

\[ \left( \text{it is easy to see that it must be } \int_{\varepsilon^i_{\lambda\min}}^\infty W^i_\lambda(\varepsilon,h_0)\,d\varepsilon=100\% \right)^{*} \]

and from the requirement of continuity of the function and of its derivative at \(\varepsilon=\varepsilon_0\).

Figure 10 gives the values of the coupling coefficients obtained in this way for four components, namely: 1) for the total intensity at high altitude (ionizing component); 2) for the neutron component at sea level; 3) for the total intensity at an altitude of \(4300\) m; 4) for the meson component at sea level. All are for three geomagnetic latitudes: \(\lambda=0^\circ, 30^\circ, 50^\circ\). The curves are shown by dashed lines in the region where extrapolation has been applied, and therefore the results are less reliable.

These curves make it possible at once to test one or another theory of the origin of cosmic-ray variations. Substituting the values of \(\delta D/D\) given by this theory, and the \(W^i_\lambda\) indicated by the graphs, into formula (3), one can compare the result with the experimental data.

But one may also try to solve the much more important inverse problem. Namely, using the observational data on variations, \(\delta_j N^i_\lambda(h_0), N^i_\lambda(h_0)\), one may try to find the primary variations. If the experimental data are sufficiently abundant, this problem can be solved with the desired accuracy. We shall now describe an attempt to apply this method to diurnal variations and to variations associated with solar flares.

The present amount of experimental data proves to be not quite sufficient for this purpose. In particular, it is desirable to have

* In fact, this integral gives the relative change of intensity corresponding to a doubling of the intensity of the primary component \(\left(\delta D/D=1\right)\).

more data concerning the variations of the neutron component at different latitudes, on the phases and amplitudes of the diurnal effect, etc. Nevertheless, we are inclined to think that the attempt undertaken \(^{30,31}\) to find the spectrum of the primary variations proved successful. The internal consistency of the results obtained suggests that these results are, at least qualitatively, sufficiently reliable. As experimental data accumulate, the results of such an analysis may change to one degree or another, and in any case the accuracy will increase. Bearing these remarks in mind, we shall proceed to present the results of the investigation \(^{30,31}\).

It is possible to show that all the diurnal variations measured up to the present time (of different components at different altitudes, about 10 effects in all) can be attributed to a diurnal variation of the primary component described by the function

\[ \frac{\delta D(\varepsilon)}{D(\varepsilon)}= \begin{cases} 0, & \text{for } \varepsilon < \varepsilon_{\text{crit}}^{(1)} \sim 7\ \text{Bev},\\ a\varepsilon^{-1}, & \text{for } \varepsilon > \varepsilon_{\text{crit}}^{(1)} \sim 7\ \text{Bev}. \end{cases} \tag{6} \]

The value of the coefficient \(a\), strictly speaking, depends on the latitude of the observation point (see § 7). For temperate latitudes \((\lambda < 50^\circ)\) one may take \(a \simeq 0.14\ \text{Bev}\). However, the dependence on latitude leads to further interesting conclusions. Of course, such a form of \(\delta D\) is given very roughly, but with the present amount of experimental data it is hardly possible to calculate more accurately. Calculations show quite definitely that a \(\frac{\delta D}{D}\) independent of energy, or having a substantially different value of \(\varepsilon_{\text{crit}}^{(1)}\), or a noticeably different exponent in \(\varepsilon\) in the region \(\varepsilon > \varepsilon_{\text{crit}}^{(1)}\), leads to contradictions with experiment. A more precise determination of \(\delta D\) requires additional experimental data.

In exactly the same way it is shown that the best agreement with the measured variations for the well-known solar flare of November 19, 1949 is obtained if one assumes that

\[ \frac{\delta D(\varepsilon)}{D(\varepsilon)}= \begin{cases} 11 \div 12, & \text{for } \varepsilon < \varepsilon_{\text{crit}}^{(2)} \approx 12\ \text{Bev},\\ 0, & \text{for } \varepsilon > \varepsilon_{\text{crit}}^{(2)} \approx 12\ \text{Bev}. \end{cases} \tag{7} \]

Other tested spectra \(\left(\frac{\delta D}{D}\right.\) independent of energy, or having a power-law character for \(\varepsilon\) exceeding some \(\varepsilon_{\text{crit}}\), or, conversely, for \(\varepsilon < \varepsilon_{\text{crit}}\), etc.\(\left.\right)\), led to contradiction with the experimental data (altogether 6 different effects).

Let us note that this spectrum agrees with the spectrum independently proposed by Firor \(^{34}\) to explain the observed

L. I. Dorman and E. L. Feinberg

[Graph]

Vertical axis label: \(W_\lambda^i(\varepsilon,h_0),\ \dfrac{\%}{\mathrm{BeV}}\)

Horizontal axis label: \(\varepsilon,\ \mathrm{BeV}\)

Panel label: b)

Curves labeled: \(1,\ 2,\ 3,\ 4\)

[Graph]

Vertical axis label: \(W_\lambda^i(\varepsilon,h_0),\ \dfrac{\%}{\mathrm{BeV}}\)

Horizontal axis label: \(\varepsilon,\ \mathrm{BeV}\)

Panel label: a)

Curves labeled: \(1,\ 2,\ 3,\ 4\)

VARIATIONS OF COSMIC RAYS

Fig. 10. Coupling coefficients: a — \(\lambda = 0^\circ\), b — \(\lambda = 30^\circ\), c — \(\lambda = 50^\circ\), d — \(\lambda = 80^\circ\).
1 — total ionizing component at high latitudes; 2 — neutral mesons at sea level or on a mountain; 3 — total ionizing component at sea level; 4 — hard component at sea level (4300 m), calculated from the latitude effect; extrapolated.

distribution of cosmic-ray variations over the terrestrial globe during large solar flares.

It is important for us that the spectrum of diurnal variations differs sharply from the spectrum of variations associated with a solar flare.

§ 6. LOCATION OF THE SOURCES OF DIURNAL VARIATIONS AND OF VARIATIONS ASSOCIATED WITH A SOLAR FLARE

Knowledge of the primary variations \(\frac{\delta D}{D}\), i.e. knowledge of the number, energy, and moment of arrival at the boundary of the atmosphere of the particles additionally reaching the Earth, makes it possible to learn much about the location, power, and character of the action of the sources of this additional radiation.

In fact, it is possible first of all to reconstruct, in the Earth’s magnetic field, the paths of these particles. In this way the direction toward the source of the additional radiation is determined. This investigation \(^{30,31}\) is carried out numerically on the basis of data available in the literature on the trajectories of charged particles in the Earth’s magnetic field \(^{35,36}\). The results show that the excess radiation arriving during a solar chromospheric eruption comes from the Sun. As for the diurnal variations, their source is located in a direction making an angle of \(82 \pm 8^\circ\) with the Earth–Sun line, to the left of it. It is noteworthy that this relative location and the character of the source are preserved throughout the entire year*). Such a location and such properties of the source not only correctly give the amplitudes of the variations of the different components at different latitudes, but also uniformly explain the scatter of the times of maximum of the diurnal effect for 10 different effects, for which the directly observed times of maximum differ within limits of up to four hours (see Table II). This means that, without such an analysis, one might have expected that the positions of the source of the variations, calculated from the different components, would be scattered within limits of the order of \(4 \times 15 = 60^\circ\).

Thus it is entirely clear that there exist at least two different sources of variations of extraterrestrial origin.

§ 7. ORIGIN OF DIURNAL VARIATIONS

The properties of the source of diurnal variations described above definitely confirm the hypothesis that these variations are caused by corpuscular streams emitted by the Sun. The spectrum found for the diurnal variations immediately makes it possible to reject a number of other

*) Here, for this reason, the fact noted above of the constancy of the diurnal effect throughout the year is important, as is revealed when the atmospheric effect is properly excluded (see Fig. 5).

hypotheses, for example, the suggestion that the azimuthal effect in the magnetic field of the Sun plays a role here ^37, or the direct arrival of particles emitted by the Sun ^38, etc.

As was noted earlier ^4, the causes considered in ^37 would have an especially strong effect in the region of low energies. Meanwhile, spectrum (6) shows that it is precisely in this region that there are no diurnal variations. The position of the source that has been found shows that the additional particles do not come from the Sun. At the same time it is necessary to explain why the flux of precisely the softest particles, \(\varepsilon < 7\) BeV, does not undergo diurnal changes. From the scheme in Fig. 11, \(a\), showing how the passage through streams in which there are magnetic fields affects cosmic rays, it is seen that, indeed, soft particles reflected by the stream do not introduce changes in the intensity: owing to the isotropy of cosmic rays, the two types of scattering always exactly compensate each other.

Faster particles coming from the left are accelerated, and those coming from the right are decelerated, if the magnetic field in the stream is directed in the same way as the terrestrial magnetic field. The deceleration of particles coming from the right at an angle \(\varphi\) to the Earth—Sun axis is equivalent to the appearance of an additional source on the left at an angle \(\pi-\varphi\) (Fig. 11, \(b\)). Together with the additional source that is due to the acceleration of particles coming from the left at an angle \(\varphi\), it gives an effective total additional flux of cosmic rays (after summation over all streams and all \(\varphi!\)), directed approximately at an angle of \(90^\circ\) to the Earth—Sun line, as required by the experiment.

Simple differentiation shows that the change of the spectrum \(D(\varepsilon)\sim \varepsilon^{-(\gamma+1)}\) as a result of acceleration caused by the crossing of a single stream is ^4

\[ \delta D(\varepsilon)\sim(\gamma+1)\frac{\delta\varepsilon}{\varepsilon}D(\varepsilon), \tag{8} \]

where \(\delta\varepsilon=\pm 300Hl\,\frac{u}{c}\). Here \(l\) is the width of the corpuscular stream, and \(u\) is its velocity. On the other hand, scattering in the stream sets the limit

\[ \varepsilon_{\mathrm{crit}}^{(1)}\sim 300Hl. \tag{9} \]

Comparing with the results of the treatment of experiment (6), we see that from \(\varepsilon_{\mathrm{crit}}^{(1)}\simeq 7\) BeV and \(a\) one can determine two characteristics of the streams: \(lH\) and \(nu\), where \(n\) is the mean number of streams,• simultaneously emanating from the Sun. The sign of the magnetic field is obtained by taking into account that the primary cosmic rays consist of positively charged particles. Further, taking from independent observations (for example, from the mean duration of a magnetic storm, and also from a number of other considerations, see ^40, p. 225) \(l\sim 2\cdot 10^{12}\) cm (which corresponds to an angular width of the stream \(\delta\simeq 8^\circ\)), we obtain from (9):

\[ H=\frac{\varepsilon_{\mathrm{crit}}^{(1)}}{300l}\sim 10^{-5}\ \text{oersted}. \tag{10} \]

Solar-daily variations

*) In the “calc.” column are given the values of the amplitude and the phase of the maximum of the sources of additional radiation indicated in the text.

**) In the experimental data cited for the hard component, an allowance for meteorological factors is impossible, since they were not

***) The data refer to the hard component at mountain level.

Table II

[[unclear: beginning of heading]] of cosmic rays

which are calculated on the basis of the energy spectrum and the location

approximately eliminates the influence of meteorological factors \(^{31}\). (The corresponding radiosonde sounding data for the atmosphere have been published.)

Figure labels: Sun; Earth; \( \varphi \); \( \pi-\varphi \); \(a\); \(b\); 1; 2; 3; 4.

Fig. 11. Production of diurnal variations of cosmic rays by streams carrying frozen-in magnetic fields.
\(a\)—scheme of the mechanism: 1—particles of low energy, \(\varepsilon < \varepsilon_{\text{crit}}\), are scattered, and their intensity on the Earth does not change; 2—particles of high energies are accelerated; their flux increases; 3—particles of high energies are decelerated, and their flux decreases.
\(b\)—production of an additional effective source of cosmic rays and its location. 1—acceleration; 2—deceleration; 3—additional flux by which the deceleration on the right can be replaced; 4—mean total effective [[unclear: continuation cut off]].

Such a large value of \(H\) indicates that this cannot be the general field of the Sun (in the Earth’s orbit, according to the latest measurements\(^{41}\), it cannot in any case exceed a value of \(\sim 10^{-7}\) oersted), but must be a field “frozen into” the stream in that region of the Sun where the stream originated, weakened as a result of the expansion of the stream*). Without entering into further discussion of this question (see \(^{31}\)), we can only emphasize that here a new possibility arises, independent of those used in astrophysics, for studying conditions on the Sun and near it. These possibilities are not exhausted by what has been said. Indeed, comparison of the quantity \((1+\gamma)\delta\varepsilon\) (one need only integrate over the angles of incidence of the particles and over all \(n\) simultaneously present streams, on the average arranged axially symmetrically\(^{31}\)) with the experimentally determined value \(a\) (see formula (6)) makes it possible, for example, taking in agreement with other determinations \(u \approx 10^8\ \text{cm/sec}\), to determine the mean number of streams \(n\). It turned out that \(n \sim 5 \div 10\). Here, however, an additional possibility opens up.

The quantity \(a\) gives the result of averaging over many streams. Moreover, as was mentioned, it differs somewhat for different latitudes on the Earth. This difference is due to the fact that at higher latitudes cosmic-ray particles arrive not in the plane of the ecliptic, but at a considerable angle \(\Phi\) to it. If, for example, for a given \(\Phi\) the particles encountered fewer solar streams on their way than for another \(\Phi\), then this reflects the distribution of streams over the surface of the Sun.

Indeed, some astrophysicists (see, for example, \(^{40}\)) have expressed the opinion that the most numerous group of solar corpuscular streams is associated with high-latitude formations on the Sun.

Although at present the experimental data concerning cosmic-ray variations and, correspondingly, concerning the values of \(a\) are still not very accurate, we can try to construct an experimental curve giving the dependence of \(a\) on the angle \(\Phi\) (Fig. 12, \(a\)). Then the curve can be recalculated so that it gives the dependence of the number of emitted streams on the heliolatitude \(\Lambda\). For this it is necessary only to make an assumption about the angular width of the streams \(\delta\). For different \(\delta\) we obtain the curves of Fig. 12, \(b\), showing that these streams are most probably indeed high-latitude formations.

Of course, the contemporary experiment gives the values of \(a\) very roughly, and we present this curve, on the one hand, in order to show

*) The presence of “frozen-in” magnetic fields in corpuscular streams is necessarily implied by the equations of magnetic hydrodynamics (see, for example, \(^{4}\)). Hypotheses about such “freezing-in” of the field in broad streams have been widely discussed in the literature (see, for example, \(^{39}\)).

the internal inconsistency of the theory, on the other—to illustrate the possibilities opened up by the study

Fig. 12. Helio-latitudinal distribution of the fluxes producing the diurnal variations of cosmic rays.
$a$—dependence of the amplitude of the primary diurnal variations $a$ on the angle $\Phi$ of the motion of particles with the plane of the ecliptic. $b$—calculated from the curve of Fig. 12, $a$, the relative number of fluxes

\[ \frac{n(\Lambda)}{n(0)} \]

as a function of the heliolatitude $\Lambda$ of the place of their emission, under various assumptions about the angular width of the fluxes $\delta$: 1—curve—$\delta = 8^\circ$; 2—curve—$\delta = 15^\circ$; 3—curve—$\delta = 30^\circ$.

heliophysical problems using data on variations of cosmic rays.

§ 8. ORIGIN OF VARIATIONS CORRELATING WITH MAGNETIC DISTURBANCES

The influence of solar fluxes is manifested not only in diurnal variations. It also appears in changes (decreases) of the intensity of cosmic rays during certain magnetic

bursts. We have already mentioned that, for some reason, in certain cases even during strong magnetic storms cosmic rays undergo no changes. A detailed analysis of the influence on cosmic rays of the streams that sweep past the Earth and thereby cause magnetic storms^31 cannot be presented here. We shall note only certain features that show the possibilities of the method.

As the diagram in Fig. 13 shows, during magnetic storms the principal role here is played by the scattering of slow cosmic-ray particles by a stream that does not let them reach the Earth. It is precisely for this reason that the intensity of cosmic rays always falls during a storm. But for this the field in the stream, or more exactly the product \(Hl\), must be considerable. From the variations of cosmic rays one may find this quantity.

Indeed, according to the scattering scheme shown in Fig. 13, one can calculate \(\dfrac{\partial D}{D}\) under various assumptions about the magnitude \(Hl\). Substituting the values found for \(\dfrac{\partial D}{D}\) into (3), one can, with the aid of the coupling coefficients shown in Fig. 10, calculate the expected decreases, during the impact of a stream on the Earth, in the intensity of the various components of cosmic rays at different latitudes. Comparison of the results of such a calculation with experimental data makes it possible to determine \(Hl\). Thus, for example, the decreases in the intensity of various components of cosmic rays at different geomagnetic latitudes, observed during the magnetic storm that followed the large solar flare of July 25, 1946, are consistently explained by the scattering mechanism considered if one assumes that the strength of the magnetic field “frozen” into the stream is \(H \sim 2\cdot 10^{-4}\) oersted near the Earth (for a stream width equal to \(2\cdot 10^{12}\) cm*).

The same mechanism can be used to explain^31 the 11-year variations of cosmic rays associated with the 11-year cycle of solar activity, during which the number of streams ejected from the Sun changes sharply; the annual variations (remaining after elimination of the meteorological effect, see Fig. 9), caused by the fact that the axis of rotation of the Sun is not perpendicular to the plane of the ecliptic, as a result of which the heliolatitude of the Earth changes during the year (the so-called Cortie effect, see^40), and this leads to a corresponding change in the number of streams striking the Earth (see Fig. 9, from which it is evident that the intensity of cosmic

*) We note that the various hypotheses discussed in the literature concerning the mechanism of the change in cosmic-ray intensity during magnetic storms, as such a detailed comparison with experiment shows, contradict the experimental data. This applies to Chapman’s hypothesis^43 (the influence of the equatorial current ring around the Earth on cosmic rays), to Alfvén’s hypothesis^4 (p. 261—the influence of the electric field of the streams on cosmic rays), etc.

rays correlates well with magnetic activity) and, finally, the 27-day tendency toward recurrence of cosmic rays, which is caused by streams emitted from the Sun over the course of several of its rotations, so that every 27 days (the time of the Sun’s rotation) the streams strike the Earth again.

Fig. 13. Effects of cosmic rays when corpuscular streams strike the Earth (schematic). 1—particles of comparatively low energy are scattered; their intensity on the Earth decreases; 2—particles of high energy are accelerated (the change is manifested on the Earth in the morning hours); 3—particles of high energy are decelerated (the change is manifested on the Earth in the night and evening hours).

From Fig. 13 it is evident that, when streams strike the Earth, in addition to the scattering of particles there must also occur acceleration and deceleration of particles of high energy arriving, respectively, from the left and from the right of the Earth–Sun line. This should lead to the appearance of additional diurnal variations with the time of maximum shifted, in comparison with the usual diurnal variations, toward the morning hours (because of the additional deflection of cosmic-ray particles in the magnetic field of the stream). This effect indeed—

...it is observed that, as is evident, for example, from Fig. 14[^28]. Since the amplitude of the additional diurnal variations is determined by the quantity \(uH\), while the decrease in intensity during a storm is determined by the quantity \(lH\), there arises the fundamental possibility of determining from cosmic-ray data the velocity \(u\) of the corpuscular stream near the Earth. Thus, for example, the velocity near the Earth, determined in this way for the stream associated with the solar

Fig. 14. Change in the diurnal variations of the hard component of cosmic rays during magnetic storms. The dashed line is the annual mean diurnal variation; the solid curve is the diurnal variation averaged over two very large magnetic storms that occurred in July 1946 and January 1949.

flare of July 25, 1946, proved to be \(u \gtrsim 10^8\ \text{cm/sec}\), which is in satisfactory agreement (if the roughness of the estimates is taken into account) with the mean velocity \(u \simeq 1.6 \cdot 10^8\ \text{cm}\), determined from the delay time of the onset of the magnetic storm relative to the onset of the solar flare.

It is easy to see that, owing to the appearance—during the arrival of the streams at the Earth—of additional diurnal variations of the indicated kind, the corresponding 11-year, annual, and 27-day changes in the amplitude and phase of the diurnal effect of cosmic rays should also be observed. The latter have indeed been detected experimentally[^44]. As for annual changes in the diurnal effect, to detect them it is necessary to eliminate carefully the influence of meteorological factors, which is at present limited by the accuracy of measuring the temperature profile of the atmosphere. Eleven-year changes in the diurnal effect have also recently been established[^42],[^45], although they were rather difficult to detect against the background of large “secular” shifts in the time of the maximum of the diurnal variations (with a period, apparently, of about 22–23 years[^45],[^46]), caused by...

apparently, a completely different cause. Such a cause could be, for example, a change in the direction of the frozen-in field in weak streams (carrying fields with \(H \sim 10^{-5}\) oersted)*) \(^{31}\). Such a cause could also be solar corpuscular streams that do not reach the Earth and carry fields parallel to the plane of the ecliptic (streams of type 2,\(^{3}\) associated with sunspots).

It should further be emphasized that, for the occurrence of a magnetic storm, it is required that the stream contain a sufficiently large number of particles; the magnetic field in the stream is immaterial, and the width of the stream affects only the duration of the storm.

Therefore a dense stream with a weak magnetic field will cause a strong magnetic storm, but will not affect cosmic rays.

This explains why even a strong magnetic storm is not always accompanied by a disturbance of cosmic rays (such, for example, was the magnetic storm of August 21, 1937 \(^{28}\)). However, on the average, as statistical analysis shows,\(^{47}\) a noticeable decrease in the intensity of cosmic rays is caused by 88% of very large magnetic storms and only 8% of moderate ones (not to mention weak storms). It follows from this that the streams causing very large magnetic storms must, on the average, carry large magnetic fields, while those causing weak storms carry, correspondingly, weak fields.

This may be connected with the circumstance that, in an ionized corpuscular stream possessing high conductivity, a certain relation must hold between the energy of the “frozen-in” magnetic field and the energy of turbulent motion in the stream. From this relation it follows that the density of the stream must satisfy the inequality

\[ \rho \gtrsim \frac{2H^{2}}{v^{2}\cdot 8\pi}, \tag{11} \]

where \(v\) is the mean velocity of the turbulent motions. Indeed, putting in (11) \(v \sim 10^{6}\ \text{cm/sec}\), we obtain for weak streams (\(H \sim 10^{-5}\) oersted), \(\rho \gtrsim 3\ \text{corpuscles}/\text{cm}^{3}\), and for strong streams (\(H \sim 2 \times 10^{-4}\) oersted), \(\rho \gtrsim 10^{3}\ \text{corpuscles}/\text{cm}^{3}\).

It is interesting that astrophysicists have also put forward the hypothesis \(^{40}\) of the existence of two types of streams genetically connected with different processes on the Sun. Some of them correlate with sunspots and other low-latitude formations on the Sun (they may be called streams of the second type according to the terminology \(^{30,31}\)) and carry, as we may now suppose, strong magnetic fields with an intensity near the Earth of \(\sim 2\cdot 10^{-4}\)

*) It is not excluded that such a change in the direction of the field could arise if the general magnetic field of the Sun changed sign, as is sometimes assumed \(^{31}\).

oersteds. Others correlate with high-latitude formations and, when they reach the Earth, cause only weak geomagnetic disturbances (“streams of the first kind”). They carry weak magnetic fields with an intensity near the Earth of \(\sim 10^{-5}\) oersted and are the main cause of the quiet solar-diurnal variations of cosmic rays.

Here, too, cosmic rays open up new possibilities for the quantitative study of these streams.

The mechanism considered for the influence of corpuscular streams on cosmic rays can evidently also explain the presence of a plateau in the latitude effect of cosmic rays at high altitudes. It was assumed that this phenomenon is connected with the scattering of low-energy cosmic rays by the general magnetic field of the Sun or by some interplanetary magnetic field of the solar system\({}^{48}\). A similar role may also be played by magnetic fields “frozen into” corpuscular streams\({}^{30,31}\). However, in that case the scattering of particles will not be stable, and at high latitudes considerable temporal fluctuations in the flux of low-energy cosmic rays are possible (which is indeed observed experimentally\({}^{49}\)). In addition, if this mechanism of plateau formation is

Fig. 15. Change in the latitude effect of the total ionizing component at high altitudes in the atmosphere at levels with pressures of 15, 20, and \(30\ \mathrm{g/cm^2}\) from the summer of 1951 (lower three curves) to the summer of 1954 (upper three curves).

main), then a decrease in the number of solar streams (during the period of decline of solar activity) should cause a displacement of the “knee” of the latitude effect at high altitudes toward high latitudes and a corresponding increase in the intensity of cosmic rays. This has recently also been observed experimentally in work\(^{50}\), where it is shown that the “knee” of the latitude effect at high altitudes did indeed shift from \(58^\circ\) in 1951 to \(68^\circ\) in 1954 (Fig. 15)*).

§ 9. VARIATIONS ASSOCIATED WITH CHROMOSPHERIC FLARES ON THE SUN

Finally, one should turn to variations associated with chromospheric flares on the Sun. They clearly show (see formula (7)) that the Sun generates cosmic rays, at least in the energy range \(\varepsilon < \varepsilon_{\mathrm{crit}}^{(2)} \sim 10—12\) Bev.

Certain characteristics of the increases in intensity during flares, obtained from experimental data by means of a rather painstaking analysis (we cannot dwell on it here, see \(^{31}\)), show that the generation of cosmic rays on the Sun can at present be explained without contradiction by Fermi’s statistical mechanism\(^{52}\), if it is applied, as proposed by V. L. Ginzburg\(^{53}\), to the conditions of the envelope of the Sun (V. L. Ginzburg developed these ideas in especially great detail for the envelopes of novae and supernovae). In this case it is required\(^{31}\) that during large chromospheric eruptions there be formations of size \(\sim 2 \cdot 10^7\) cm, moving with velocities \(\sim 3 \cdot 10^7\) cm/sec and carrying “frozen-in” magnetic fields with intensity not less than 2 oersted. If such chromospheric formations occupy a volume greater than 0.02–0.002 of the total volume of the source (with dimensions \(\sim 10^{10}\) cm, located in the upper part of the chromosphere and in the corona), then the kinetic energy of their turbulent motion proves sufficient to create the necessary additional flux of particles (in all, during the flare of November 19, 1949, \(\sim 10^{32}\) cosmic-ray particles were emitted from the Sun in the energy interval 1.5–12 Bev).

*) It is not excluded that streams of type 1, carrying weak fields, may also play a large role in producing such an effect; together with streams of type 2 they can “sweep out” some general interplanetary magnetic field, scattering particles of low energies and not admitting them into the solar system (Prof. V. L. Ginzburg kindly pointed out this circumstance to us). The field intensity will then vary with the cycle of solar activity (apparently with some delay), and such a mechanism could likewise explain the effect under discussion. It is possible that a mechanism of this kind also plays a role in producing the 11-year variations of cosmic rays.

**) A similar displacement was also found for the neutron component at an altitude of \(310\ \mathrm{g/cm^2}\)\(^{51}\).

During small solar flares there is also emission of low-energy cosmic rays from the Sun (in this case the particle flux is 2–3 orders of magnitude smaller than during large flares). Taking account of all large and small flares gives, for the mean flux of particles generated by the Sun, a value of \(\sim 10^{24}\) particles·sec\(^{-1}\). Such a small value of the particle flux makes the hypothesis of a solar or stellar origin of cosmic radiation unrealistic\(^{53}\).

True, one might suppose that all these particles become entangled in some magnetic fields near the Sun. However, during flares the particles reach the Earth from the Sun almost without being deflected. This means that the magnetic fields are very weak and the volume in which accumulation takes place must be extremely large. This is also consistent with a number of other estimates\(^{55}\).

If the Sun possesses even an insignificant general magnetic field (with an intensity of \(\sim 1\) oersted at the poles\(^{41}\)), then for particles with energies of several Bev to escape, certain special conditions are necessary (otherwise the particles, spiraling under the action of this field, will return to the Sun).

Such a condition, in particular, may be the formation of a “tunnel” in the region of forbidden directions in the field of the solar dipole owing to disturbance of this field by local fields (for example, the fields of spots\(^{54}\)). The escape of a comparatively small fraction of the generated particles from the Sun is also possible owing to their “entanglement” by the “frozen-in” magnetic fields of corpuscular streams and the ejection of these particles together with the streams to considerable distances from the Sun\(^{31}\). It is not excluded that the large difference in the fluxes of generated particles during large and small flares (by two or three orders of magnitude) is explained not only by differences in the conditions of generation, but also by differences in the conditions for the escape of particles from the Sun*).

*) After the present article had been written, a grandiose flare occurred on the Sun on February 23, 1956. The chromospheric radiation, as always accompanied by an increase in ultraviolet radiation, caused a very strong disturbance in the ionosphere, as a result of which long-distance radio communication on short waves was interrupted for several hours. At the same time the intensity of cosmic rays increased to an unprecedented extent. At a small height above sea level, in Moscow and Sverdlovsk, which fell in the zone of the maximum (in longitude), the almost instantaneous increase in the intensity of the \(\mu\)-meson component amounted to \(\sim 400\%\); then the excess over the mean level began to decrease exponentially and after 2 hours amounted to only \(20\%\). The Earth’s magnetic field prevents particles of comparatively low energies from reaching the equator. Accordingly, in Tbilisi the increase was only about \(100\% \div 200\%\). The increase was the same in Yakutsk, which, although lying to the north, was too far from the part of the Earth’s surface “illuminated” by solar cosmic rays at the time of the flare. An analysis similar to that which, for the flare of November 19, 1949, led to formula (7), showed that the spectrum of the new flare has the same character, but the absolute magnitude of the increas-

L. I. DORMAN AND E. L. FEINBERG

CONCLUSION

We have given here, of course, only a very brief account of the state of the question concerning the origin of variations of cosmic rays.

In summing up, it must once again be emphasized that at the present time, first, it has become possible consistently to exclude the influence of meteorological changes in the Earth’s atmosphere (§ 3). Secondly, a method has been developed which, when sufficiently detailed experimental data on variations of different components are available, makes it possible, on their basis, to derive the true variations in the primary spectrum of cosmic rays incident on the atmosphere (§ 5). Thirdly, the experimental data already available make it possible in this way to determine, at least roughly, the energy spectrum of cosmic rays additionally arriving at the Earth during diurnal variations and during variations connected with chromospheric flares on the Sun (§ 5). Further, it proves possible to determine the position of these sources relative to the Earth (§ 6). In other words, important characteristics of the sources of variations are determined. This makes it possible to reject a number of hypotheses that have been proposed for explaining variations.

As a result of the investigation it turns out that all variations observed up to now can be ascribed to three mechanisms (see Table I).

1) The influence of changes in the state of the atmosphere;

2) The influence of acceleration, deceleration, and scattering of cosmic rays in corpuscular streams emitted by the Sun;

3) The emission of cosmic rays by the Sun during large and small solar flares.

It is possible that, in addition, there exist variations of cosmic rays connected with the diffusion of cosmic rays from the Galaxy; however, even if they do exist, they still lie beyond the limits of accuracy of modern registration methods.

We have tried to show that the study of diurnal variations, changes in intensity during magnetic storms, and certain other variations of cosmic rays provides a new, independent method

now was 10 times greater. This means that at the boundary of the atmosphere the primary radiation at the moment of the flare exceeded the average level by approximately 100 times. However, all this increase fell in the region of comparatively low energies, and therefore at sea level the excess radiation that passed into the $\mu$-mesons capable of reaching this level (they can be produced only by primary particles with energies not lower than $\sim 7$ Bev; see Fig. 5 and the corresponding explanations in the text) exceeded the average level by only 4–5 times. Let us note that the neutron component, which more directly reflects the change in the intensity of the primary radiation (being in itself extremely weak at sea level), increased much more strongly, in Sweden, for example, by 50 times. Detailed processing by the method presented here showed that the currently known characteristics of the flare of February 23, 1956, agree with the conclusions on the nature of such flares drawn in the present article.

quantitative investigation of the properties of corpuscular streams emitted by the Sun, the distribution of their sources over the surface of the Sun, etc. The study of variations associated with solar flares also provides independent possibilities for studying certain conditions in the chromosphere of the Sun. It is already possible to determine a number of quantitative characteristics of the streams. Those of them which can also be found by other astrophysical and heliophysical methods are obtained in agreement with these determinations.

The considerations set forth in § 5 suggest precisely which variations and precisely which components of cosmic rays should be studied first of all in order to increase the reliability and accuracy of the results described and to obtain new results. The corresponding recommendations make it possible to plan more expediently the study of variations during the period of the International Geophysical Year (July 1957—December 1958).

We have not touched here on many questions, for example the explanation of such variations as semi-diurnal ones, the influence of solar flares on diurnal variations, etc.

The corresponding analysis of these variations, as well as a more detailed consideration of some other questions touched upon, may be found elsewhere31.

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