On the Origin of Cosmic Rays

Ya. P. Terletskii

Since the discovery of cosmic rays in 1909, the most mysterious thing has always seemed to be the very fact of their existence. After the extraterrestrial nature of cosmic radiation had been definitively established, many attempts were made to explain its origin in space. However, almost all the hypotheses that were put forward were soon rejected either because of the contrived and untenable nature of their initial theoretical premises, or because they contradicted known experimental facts. The question of the origin of cosmic rays remained in this unsatisfactory state for almost forty years. As a result, some physicists even developed a prejudiced, skeptical attitude toward any new theories of the origin of cosmic rays.

In recent years, however, after reliable experimental investigations that established the basic properties of the primary component of cosmic radiation¹, and also after a number of astrophysical observations of the electromagnetic properties of cosmic objects, the question of the origin of cosmic radiation has become considerably clearer. It may now be regarded as firmly established that the “theory of cosmic induction accelerators”², developed in recent years, makes it possible to explain the basic properties of the primary component.

To the credit of this theory belongs not only the explanation of previously known facts, but also the prediction of a new phenomenon—the presence of ions of heavy elements in the composition of the primary component. The theory predicted³ this phenomenon before its discovery in 1948⁴.

According to this theory, certain cosmic objects induce in the surrounding space very extended electric fields, which accelerate the surrounding ions and electrons to the energies of cosmic particles. By analogy with laboratory accelerators, these cosmic objects may be called “cosmic induction accelerators”*; hence the name of the theory.

* Hereafter abbreviated as “CIA.”

The theory of KIU is based on the idea of the existence of magnetic fields associated with cosmic objects (stars, clouds of interstellar matter, etc.), and of the induction of extended electric fields during the motion of these cosmic objects or during changes in the magnetic fields associated with them.

These initial ideas rest on firmly established experimental facts concerning the magnetism of the Earth, the Sun, and the stars. In this connection, the discovery in 1947 of magnetized stars^5 was of especially great importance for the theory of KIU, since this discovery confirmed earlier hypothetical assumptions about the prevalence of magnetized cosmic objects in the universe^6.

The analysis of the process of particle acceleration in the theory of KIU is based on the general theoretical propositions concerning the motion of charges in electromagnetic fields developed by S. A. Boguslavskii^7.

Thus, the theory of KIU rests on firmly established experimental facts and on entirely reliable theoretical propositions.

The theory of KIU may be regarded as a chapter of cosmic electrodynamics, i.e., the theory of electromagnetic processes in cosmic objects. In other words, it is established that the origin of cosmic rays is completely conditioned by electromagnetic processes in space.

Nevertheless, despite the obvious successes of the theory of KIU, it cannot yet be considered definitively complete. Indeed, although it has already been established with sufficient persuasiveness that cosmic particles are accelerated by certain KIU, it is still unclear which of the known KIU play the chief role in the process of generating cosmic rays. Different authors give priority to different cosmic objects as the principal KIU. For example, some authors^8,9 consider the Sun, with the special type of magnetic field surrounding it, to be the principal KIU; others^10 consider moving magnetized clouds of interstellar matter; still others^3 consider magnetized stars. At present the author inclines to the supposition that the principal KIU are stars with changing magnetic fields, as primary sources of cosmic particles, and magnetized clouds of interstellar matter as KIU that redistribute the particles’ energy over the spectrum (for more detail see below).

It should also be noted here that other hypotheses concerning the origin of cosmic rays, apart from the KIU hypotheses, have in recent years generally not been taken seriously by physicists.

Before turning to an exposition of the basic propositions of the theory of KIU, we shall dwell on the principal experimental facts concerning the primary component of cosmic rays.

Ya. P. Terletsky

1. THE NATURE OF THE PRIMARY COMPONENT

According to the latest reliable experiments1, the flux of cosmic particles entering the Earth’s atmosphere from the surrounding space, i.e., the primary component of cosmic rays, consists mainly of protons. In addition to protons, the primary component includes ions of other elements in approximately the same proportion in which they are present in stars. The protons and ions of the primary component have very high energies. The mean energy of the protons is about \(10^{10}\) ev, while the mean energies of the ions are approximately \(Z\) times greater than the energies of the protons, where \(Z\) is the atomic number of the element. The energy spectrum of cosmic particles, or the distribution function of particles by energy, decreases comparatively slowly with increasing energy. It may be assumed that, for energies greater than \(10^9\) ev, the mean number of particles \(F(\mathcal E)\,d\mathcal E\) in a given energy interval from \(\mathcal E\) to \(\mathcal E+d\mathcal E\) is expressed by the power law:

\[ F(\mathcal E)\,d\mathcal E \sim \mathcal E^{-\gamma}\,d\mathcal E, \tag{1} \]

where \(\gamma\) is a positive number lying between 2 and 3. In accordance with this, particles having very high energy, of the order of \(10^{15}\)—\(10^{17}\) ev, are found in the primary component; these create in the atmosphere the so-called Auger showers.

Almost all observations, including the most recent ones1, indicate complete spatial isotropy of the primary component. So far it has not been possible to single out any preferred direction in the galaxy for cosmic particles. Cosmic particles arrive at the Earth in a uniform flux from all directions.

The intensity of the flux of cosmic particles is approximately one particle per square centimeter of surface per minute. From the energy point of view, since the particles have very high energy, this intensity is rather large: it is approximately equal to the intensity of the light emitted by all the stars. Thus, if one assumes (as is supposed in the CIU theory) that the energy of cosmic particles is drawn from the general energy source of the stars, it is necessary to suppose that, on average, each star expends approximately as much energy on the radiation of light as it expends on the acceleration of cosmic particles.

Any theory of the origin of cosmic rays must explain the facts listed above, namely:

1) the predominantly proton composition of the primary component;
2) the presence of ions of heavy elements and their percentage content in the primary component;
3) the high energy of cosmic particles, on average of the order of \(10^{10}\) ev and reaching \(10^{15}\)—\(10^{17}\) ev for Auger showers;

4) the energy spectrum of the primary component, expressed by formula (1);
5) the spatial isotropy of the primary component;
6) the considerable intensity of the flux of the primary component.

2. VARIOUS HYPOTHESES ON THE ORIGIN OF COSMIC RAYS

To explain the origin of the primary component and its properties, a large number of hypotheses have been advanced at different times. It is not possible to dwell in any detail on the content of all the hypotheses that have been put forward. We shall therefore confine ourselves to a general characterization of the content of these hypotheses, combining hypotheses of the same type into separate groups.

The first group may include hypotheses which assume that cosmic rays are remnants of some initial pre-stellar state of the universe.

Usually these hypotheses are organically connected with the theory of the expanding universe and proceed from the assumption that cosmic rays arose from the initial, infinitely dense state of the universe assumed by this theory, and have not been absorbed by interstellar matter up to the present time.

These hypotheses “explain” with seeming ease any properties of the primary component (for example, spatial isotropy); however, in essence they do not reveal the causes of the origin of cosmic rays, since they propose to solve the problem by transferring it to another unknown domain. On the other hand, even if an arbitrary pre-stellar state of the universe is assumed, it is very difficult to reconcile such hypotheses with the inevitable continuous absorption of the energy of cosmic particles in their collisions with interstellar matter. According to the estimate given by Fermi^10, the mean time for complete loss of energy by primary protons is \(6 \cdot 10^7\) years, i.e., considerably less than the age of the Earth.

The second group may include hypotheses which assume that primary cosmic radiation is generated in acts of transformation of matter into radiation.

According to these “annihilation” hypotheses, in order to explain the large energies of cosmic particles (of the order of \(10^{10}\) ev and higher), acts of simultaneous transformation into radiation of whole nuclei and even pieces of matter containing a large number of atoms are assumed, since the total energy of an individual proton is only \(10^9\) ev. It is assumed that such transformations occur not inside stars, but somewhere in interstellar space, since hard cosmic radiation cannot penetrate even through the upper layers of stellar atmospheres.

Such assumptions have no more or less satisfactory experimental or theoretical justification and can be accepted only after a radical change in the theory of elementary particles, not dictated at present by any experimental facts.

“Annihilation” hypotheses encounter insuperable difficulties when one attempts to explain the presence of heavy ions with energies of \(10^{10}\) ev in the primary component. Even if one admits that some aggregate of atoms has somehow been transformed into radiation, it does not appear possible to explain how the released energy can be transferred to an entire heavy nucleus without breaking it up into separate nucleons.

Thus, “annihilation” hypotheses are too artificial a construction, justified neither theoretically nor experimentally.

A special group is formed by hypotheses connecting the origin of cosmic rays with outbursts of novae and supernovae.

Although at first glance these hypotheses readily explain the isotropy of the primary component and its proton–ion composition, the very mechanism of acceleration of particles to energies of the order of \(10^{10}\) ev and higher is not clarified by the authors of these hypotheses. Here it is simply tacitly assumed that one grandiose phenomenon—the explosion of a nova—is the cause of another unusual phenomenon: the acceleration of particles to ultrahigh energies.

It is not excluded that, in explosions of novae and supernovae, particles with cosmic-ray energies are indeed generated by some electromagnetic processes that accelerate ions; however, there is as yet no basis for considering these hypothetical processes to be the principal source of cosmic rays.

Let us dwell, finally, on hypotheses proceeding from the assumption of acceleration of charges by electric fields.

In these “accelerating” hypotheses it is supposed that cosmic particles are ions or electrons accelerated to energies of the order of \(10^{10}\) ev and higher by cosmic electric fields.

Accelerating hypotheses meet with serious objections if they proceed from the assumption of cosmic electrostatic fields of potential character and, consequently, suppose the existence of potential differences of the order of \(10^{10}\) ev and higher between the Earth and other cosmic objects or between separate points of world space. Quite apart from theoretical difficulties, we have no astrophysical data indicating the possibility of the existence of such potential fields and of the large electric charges inevitably associated with them in the universe surrounding us.

Such objections are absent for “acceleration” hypotheses that proceed from the assumption of the existence in cosmic space of vortex electric fields caused by electromagnetic induction. Vortex electric fields capable of accelerating charged particles to energies of the order of \(10^8\) ev are induced by the general magnetic field of the Sun\(^{6}\), and also arise from the magnetic fields of sunspots. After the discovery of magnetized stars with a magnetic field exceeding 1000 gauss at the surface of the star\(^{5}\), the idea of the existence of induced electric fields capable of accelerating charges to energies of \(10^{10}\) ev and higher received a reliable experimental basis. Thus, in world space there exist real objects that are CAUs, creating fluxes of charges with the energies of cosmic particles. Consequently, there are real grounds to believe that the entire primary component is generated by CAUs of a definite type. In work\(^{3}\), as also in works\(^{6}\), the CAUs generating the primary component were identified with magnetized stars whose direction of magnetic moment is inclined to the axis of rotation. In that work it was shown that such a simplest model makes it possible to explain: the large energy of cosmic particles (\(10^{10}\) ev and higher), the predominantly proton composition of the primary component, and the presence in it of heavy ions. Thus it was shown that certain basic features of the primary component, not explained by other hypotheses without artificial assumptions, are a direct consequence of the simplest variant of the CAU theory.

Weighty arguments in favor of the developed theory were also obtained as a result of investigating the composition of the ionic constituent of the primary component predicted by the theory. Experiments have shown\(^{11}\) that the kinetic energy of nuclei present in the primary component is proportional to their charge \(Z\), and also that the dependence of the percentage content of the ionic constituent on \(Z\) coincides with the relative abundance of the elements in the universe, obtained from astrophysical data. The first fact follows directly, while the second agrees well qualitatively with the idea that the particles forming the primary component are torn out by electric fields from stellar atmospheres.

The substantial arguments cited in favor of the CAU theory confirm the correctness of its basic idea, but are not yet decisive for accepting its simplest variant.

This variant of the theory explains well only certain basic properties of the primary component—its composition and the average energies of cosmic particles. To explain the great intensity of the primary component, it is necessary either to assume a solar origin of cosmic rays\(^{8,9}\) in the presence of an additional magnetic field that holds the particles inside the Sol-

system, or else assume that the energy of the electromagnetic fields accelerating cosmic particles is drawn from nuclear processes taking place inside stars. As will be shown below, the hypothesis of the solar origin of cosmic rays does not withstand serious criticism. Consequently, from the possible types of CIE one must choose those that create variable magnetic fields at the expense of intrastellar processes.

Below we shall consider some possible types of CIE; among them one can indicate certain CIE that meet the above requirements.

Furthermore, the theory must explain the isotropy of the primary component and the specific power-law distribution of particles over energies (formula (1)). Both these facts are satisfactorily explained under the assumption that cosmic particles, passing through interstellar space, are scattered by moving magnetized clouds of interstellar matter[^10].

Thus, of all the hypotheses considered, only the CIE theory gives a satisfactory explanation of all the basic features of the primary component.

Since the CIE theory is based on the electromagnetic properties of cosmic objects and on the theory of the motion of charges in cosmic electromagnetic fields, we shall first dwell on a survey of cosmic electromagnetic fields and questions of cosmic electronics.

3. ELECTROMAGNETIC FIELDS OF COSMIC OBJECTS

In recent years it has been established that the magnetization of cosmic objects is a very widespread phenomenon in the universe. The existence of a general magnetic field has been established for the Earth, the Sun, and certain stars. Strong magnetic fields (up to 5000 oersteds) are associated with sunspots. It is also quite admissible that there exist “star spots” similar to sunspots. In some variable stars the existence of a variable magnetic field of very large amplitude was recently discovered[^12].

When the above-mentioned magnetized objects move, or when the magnetic fields associated with them change, electric fields caused by electromagnetic induction must arise.

The electromagnetic fields created by the Earth, the Sun, stars, as well as by solar and stellar spots, may approximately be regarded as fields created by separate magnetic dipoles or by aggregates of such dipoles. In the general case the magnetic moments $\mu$ of such dipoles vary both in absolute magnitude (arising and disappearing solar spots, stars with variable magnetic moment) and in direction (rotation of the Earth, the Sun, and stars). Owing to the smallness

of the periods of variation, the electromagnetic field of the dipoles under consideration may be calculated in the quasistationary approximation. Thus, in the general case one may assume that in the space surrounding a cosmic magnetic dipole having magnetic moment \(\boldsymbol{\mu}\) and rotating with angular velocity \(\boldsymbol{\omega}\) in an inertial frame of reference associated with the center of the dipole, there exists an electromagnetic field:

\[ \mathbf{H}=-\operatorname{grad}\frac{(\boldsymbol{\mu}\mathbf{r})}{r^3} =\frac{3\mathbf{r}(\boldsymbol{\mu}\mathbf{r})-\boldsymbol{\mu}r^2}{r^5}, \tag{2} \]

\[ \mathbf{E}=-\frac{1}{cr^3}[\mathbf{r}\dot{\boldsymbol{\mu}}]-\operatorname{grad}\varphi, \tag{3} \]

where \(\mathbf{r}\) is the radius vector drawn from the center of the dipole, \(c\) is the velocity of light,

\[ \dot{\boldsymbol{\mu}}=\frac{d\boldsymbol{\mu}}{dt} =\frac{\boldsymbol{\mu}}{\mu}\frac{d\mu}{dt}+[\boldsymbol{\omega}\boldsymbol{\mu}], \tag{4} \]

\(\varphi\) is the potential of the electric field created by unipolar induction.

If the magnetic dipole is regarded as a uniformly magnetized sphere of radius \(r_0\), rotating about an arbitrary axis with angular velocity \(\boldsymbol{\omega}\), then a rigorous calculation\(^{13}\) gives:

\[ \varphi=\frac{r_0^2}{5c}(\boldsymbol{\omega}\mathbf{H}) \tag{5} \]

for the region \(r>r_0\).

Thus, in the general case the electric field of a rotating cosmic dipole is expressed as

\[ \mathbf{E}=\mathbf{E}_1+\mathbf{E}_2+\mathbf{E}_3 =\frac{i}{cr^3}[\mathbf{r}\boldsymbol{\mu}]\frac{1}{\mu}\frac{d\mu}{dt} +\frac{1}{cr^3}[\mathbf{r}[\boldsymbol{\omega}\boldsymbol{\mu}]]- \]

\[ -\operatorname{grad}\left\{\left(\frac{r_0^2}{5c}\right) \frac{3(\mathbf{r}\boldsymbol{\omega})(\mathbf{r}\boldsymbol{\mu})-(\boldsymbol{\mu}\boldsymbol{\omega})r^2}{r^5}\right\}. \tag{6} \]

The first term of this expression \((\mathbf{E}_1)\) is due to the change in the absolute magnitude of the magnetic moment; the second and third terms are due to the rotation of the dipole. The field \(\mathbf{E}_2\), expressed by the second term, is caused by the rotation of the component of the magnetic moment perpendicular to the axis of rotation, and is different from zero only in the case when the direction of the magnetic moment and the axis of rotation do not coincide. The field \(\mathbf{E}_3\), expressed by the third term, is due to unipolar induction and may be represented as the field of an electric quadrupole.

Let us note that the fields \(\mathbf{E}_1\) and \(\mathbf{E}_2\), due to ordinary electromagnetic induction, decrease with distance from the center of the dipole

as \(1/r^2\), whereas the field \(\mathbf{E}_s\) of unipolar induction decreases as \(1/r^4\).

The most general theoretical considerations lead to the conclusion that magnetic fields must also exist in other cosmic objects. Since matter on stars and in interstellar space is strongly ionized, it must possess high electrical conductivity. But in large volumes of highly conducting matter the damping of electric currents is very slow. Thus, for example, for a sphere of radius \(R\), having electrical conductivity \(\lambda\), the relaxation time \(\tau\) is expressed as:

\[ \tau \simeq \frac{4\lambda R^2}{\pi c^2}. \tag{7} \]

But at large relaxation times the currents and the magnetic fields associated with them may be regarded as “frozen” into the matter. Consequently, as it moves, the matter will carry along with it the magnetic field associated with it.

Obviously, in view of what has been said above, matter ejected into space by magnetized stars will remain magnetized for a long time. Thus, in the space surrounding certain stars there will exist magnetic fields associated with clouds of ionized gas.

It is permissible to suppose that, in general, clouds of interstellar matter ionized as a result of stellar radiation carry “frozen-in” magnetic fields. In the motion of such clouds, electric fields will be induced which are capable of accelerating electric charges.

A characteristic feature of the cosmic electromagnetic fields mentioned above is their great extent and their almost complete uniformity over relatively large volumes.

4. COSMIC ELECTRONICS

To investigate the motion of a charge in the electromagnetic field of a cosmic object, we shall proceed from the relativistic equations of motion, neglecting the radiation reaction. Thus, the equations of motion of a particle with charge \(e\) and rest mass \(m\) in the electromagnetic field \(\mathbf{E}\) and \(\mathbf{H}\) we write in the form:

\[ \frac{d}{dt}\left(\frac{m\mathbf{v}}{\sqrt{1-\frac{v^2}{c^2}}}\right) = e\left\{\mathbf{E}+\frac{1}{c}[\mathbf{v}\mathbf{H}]\right\}; \tag{8} \]

where \(\mathbf{v}\) is the velocity of the particle, \(c\) is the speed of light.

The periods of variation of the electromagnetic fields of cosmic objects are measured in days and, at the very least, in hours. Dis-

The particles considered by us (electrons, protons, ions) can be accelerated to the limiting velocity in very short intervals of time, since they have a very small mass. Consequently, in the equations of motion (8) one may neglect the dependence of \(\mathbf E\) and \(\mathbf H\) on time and regard them as depending only on the coordinates. This simplification will be used everywhere in what follows, i.e., we shall imagine the electromagnetic field as if it were frozen.

An exact solution of equations (8) in the case of an electromagnetic field of the form (2), (3) does not seem possible, since the mass of a particle in the presence of an electric field cannot be considered constant, and therefore the problem becomes incomparably more complicated than the corresponding Störmer problem for a constant stationary magnetic dipole. The latter problem, as is known, is in the general case solved only by numerical integration. Analogous difficulties must also arise in an attempt to solve equations (8) exactly in the case of fields produced by clouds of interstellar matter. For investigating the question of the possibility of acceleration of charges by the electromagnetic fields of cosmic objects, however, it is not necessary always to seek exact solutions of the equations of motion. For this purpose one may successfully use approximate solutions, possible because of the great extent of the electromagnetic fields of cosmic objects\(^6\).

In spatial clouds whose linear dimensions \(l\) are small in comparison with the dimensions of the magnetized objects, the electromagnetic field may be regarded as practically homogeneous. The general solution of equations (8) in an arbitrary homogeneous electromagnetic field was comprehensively investigated by S. A. Boguslavsky\(^7\). In the case \(E < H\), this solution can be represented as the motion of a charge along a stretching spiral wound on an elliptical cylinder, with acceleration along the axis of the cylinder; moreover the entire cylinder moves with constant velocity \(\mathbf u\) in the direction perpendicular to \(\mathbf E\) and \(\mathbf H\), while the axis of the cylinder lies in a plane parallel to \(\mathbf E\) and \(\mathbf H\), between these vectors.

Owing to the quasistationary character of cosmic electromagnetic fields, in the majority of cases one may assume:

\[ E \ll H . \tag{9} \]

In this case the solution described is somewhat simplified and may be represented as the motion of a charge along a stretching spiral wound on a cylinder with its axis parallel to \(\mathbf H\) and having radius

\[ \rho=\frac{c p_n}{eH}, \tag{10} \]

where \(p_n\) is the component of the particle momentum perpendicular to \(\mathbf H\). The whole cylinder moves with velocity:

\[ \mathbf u = c\,\frac{[\mathbf E\mathbf H]}{H^2}. \tag{11} \]

The spiral is stretched as a result of the acceleration of the charge along the axis of the cylinder under the action of the component of the electric field parallel to \(\mathbf H\). If the electromagnetic field is sufficiently extended, and the dimensions \(l\) of the regions of nearly homogeneous portions of the field are sufficiently large so that one may assume

\[ \rho \ll l, \tag{12} \]

then charges already accelerated to relativistic velocities may be approximately regarded as moving along helical trajectories wound around the magnetic lines of force of the field. The displacement of the trajectory with velocity \(u\) may in this case be neglected, since, according to (9) and (11), \(u \ll c\). This picture of the motion of relativistic particles may be used in any inhomogeneous fields, provided condition (12) is satisfied along the magnetic lines of force.

When moving along a magnetic line of force, a charge will enter regions with different values of the magnetic-field intensity, as a result of which the radius of the spiral will also change. The change in the radius of the spiral can be estimated from the assumption of conservation of the adiabatic invariant when the magnetic field changes. According to this assumption, it is easy to obtain the relation

\[ \rho\sqrt{H}=\mathrm{const}. \tag{13} \]

Condition (12) can be formulated mathematically more precisely. One may assume that the motion of a charge in an inhomogeneous magnetic field has a helical character if the radius of curvature \(\rho\), determined by relation (10), changes relatively little during an imaginary traversal by the particle of a circle of radius \(\rho\). Hence, instead of (12), we obtain a condition of the form:

\[ p_n \ll p_{\mathrm{crit}}=\frac{e}{c}\,\frac{H^2}{|\nabla H|}. \tag{14} \]

In the case of fields \(\mathbf E\) and \(\mathbf H\) that are not strictly perpendicular—which occurs in most cases because of the great extent of the fields—particles acquire relativistic energy over relatively small spatial intervals, i.e. a velocity close to \(c\). Considering the particles as already having a velocity close to \(c\), one may assume that, for \(p_n \ll p_{\mathrm{crit}}\), the trajectory of the charge has the form of a stretching spiral wound around a magnetic line of force. If, however, \(p_n \gg p_{\mathrm{crit}}\), then the trajectory approaches a rectilinear one.

Applying these considerations to the motion of a charge in the field of a varying magnetic dipole (2), (3), we may approximately regard the trajectory of the particle as a spiral wound around a magnetic line of force, for regions close to the center of the dipole, where \(p_n \ll p_{\text{crit}}\), and assume that the trajectory goes off to infinity if the particle enters a region where \(p_n > p_{\text{crit}}\). Consequently, the condition

\[ p_n > p_{\text{crit}} \tag{15} \]

may roughly be regarded as the criterion for a particle to break away from the field of the magnetic dipole.

In cases where \(E > H\), the picture described for the motion of charges is no longer valid. Such cases may occur when the variable magnetic field passes through zero on changing sign. In these cases the charges will be deflected only relatively weakly by the magnetic field and will move with acceleration along trajectories having a small radius of curvature. In sufficiently homogeneous portions of the field, upon reaching relativistic energies, the motion of the charges will approach motion along electric lines of force.

The acceleration of charges in collisions with magnetized clouds of interstellar matter has a special character. In this case, charges entering a moving cloud are pushed out of it, acquiring the same energy as would be acquired by particles colliding with an infinitely heavy elastic body. This conclusion is easily reached by considering the collision of a charge with a cloud in a coordinate system moving together with the latter. In this system there is no electric field and, consequently, after the collision only the direction of motion of the particle changes, but not its energy.

5. SPATIAL DISTRIBUTION OF SOURCES GENERATING THE PRIMARY COMPONENT

Recently, in a number of works developing the theory of KIU\(^{8,9,10}\), two opposite points of view have been discussed on the question of the spatial distribution of sources generating the primary cosmic radiation that penetrates into the Earth’s atmosphere. According to the first point of view, cosmic particles arrive at the Earth from interstellar space and, consequently, the principal sources of cosmic radiation are located outside the solar system. According to the second point of view, the overwhelming fraction of particles of the primary component is generated near the Sun and is retained by a certain magnetic field within a surrounding region comparable in size to the dimensions of the solar system.

The principal argument in favor of the view that cosmic accelerators are located outside the solar system has always been the well-known fact of the isotropy of the primary component, as well as the absence of a sharply expressed dependence of the intensity of cosmic radiation on the position of the Sun and on solar activity. The weak dependence, noted by \({}^{14}\), of the total intensity of cosmic radiation on the activity of the Sun cannot yet be a substantial argument in favor of the view that the entire primary component originates within the solar system. This fact may with much greater justification be regarded as confirming that the Sun is a cosmic induction accelerator, generating, however, only the soft part of the primary component (particles with energies \(10^8\) eV, according to theory \({}^{6}\), and with energies \(10^9\) eV, according to the theory taking unipolar induction into account \({}^{15}\)), while the main, harder part comes from regions lying beyond the limits of the solar system.

The main objection raised against the first point of view rests on the fact of the very great intensity of the primary component. As Richtmyer and Teller \({}^{8}\) point out, in order to explain the observed intensity of the primary component, on the assumption that cosmic rays are emitted by stars, one would have to suppose that more than \(10^{-4}\) of all the energy radiated by stars is emitted by them in the form of cosmic radiation and not in the form of light. These authors consider this assumption improbable and choose the second point of view, believing that the entire primary component originates near the Sun and that cosmic charged particles, before reaching the Earth, wander for enormous intervals of time within the solar system, being confined by some magnetic field. To justify the latter supposition its authors have to assume the existence within the solar system of some additional field of the order of \(10^{-5}\) gauss, not caused by the magnetic moment of the Sun. It should be noted, however, that this last assumption does not save the hypothesis under consideration. The point is that the magnetic lines of force of any admissible field will either have their ends abutting on the surface of the Sun or will go off to infinity. The case of closed lines of force is possible only as an exception, under the improbable assumption of the existence of stable closed currents in interplanetary space. Consequently, according to the general picture of the motion of charges in cosmic fields (see Section 4), particles that have left the surface of the Sun will inevitably and very quickly either return to it or go off to infinity. Thus there can be no question of any prolonged wanderings of charges within the solar system, except perhaps along certain exceptional trajectories.

The hypothesis of Richtmyer and Teller is made more concrete in Alfvén’s works.^9 He assumes that the ions located around the Sun move in the Sun’s magnetic field along almost closed trajectories and are repeatedly accelerated, passing through magnetized streams of ionized matter ejected by the Sun. However, the Sun’s magnetic field is not able to hold moving charges near the Sun for any appreciable length of time, and therefore Alfvén assumes that the solar system is situated in a magnetic field “frozen” into a giant cloud of ionized matter. To explain the repeated returns of particles to the solar system, Alfvén assumes that the lines of force of the “frozen” field, penetrating the solar system, close in the form of giant rings whose dimensions far exceed the diameter of the solar system.

The artificiality of Alfvén’s hypothesis is obvious. The configuration of the “frozen” field proposed by Alfvén can exist only under a fortunate combination of circumstances, for a short time. The motion of the solar system relative to the cloud with the “frozen” field will inevitably disturb this favorable situation.

All debatable hypotheses of a solar origin of the primary component can, evidently, proceed only from the idea of accelerating charges from the surface of the Sun by fields of type (6) and of their motion to the Earth approximately along magnetic lines of force. In this case, however, no mechanisms are apparent which would provide an almost ideal isotropy of the primary component and would accelerate particles to energies considerably greater than \(10^9\) eV. Thus, only the idea of a distribution of the principal sources of the primary component outside the solar system remains, for the time being, consistent with the simplest consequences of cosmic electronics. Objections connected with the fact of the great intensity of the primary component will be removed if one indicates a type of CEU, widespread in the universe, capable of generating powerful streams of fast charged particles.

Let us proceed to consider other, more carefully thought-out types of CEU.

6. ACCELERATION OF CHARGES IN THE FIELD OF ROTATING STARS

If it is assumed that the magnetic moment of a rotating star approximately coincides in direction with the axis of rotation, then, as a result of unipolar induction, according to formulas (5)—(9), in the space surrounding the star there must exist an electric field with potential

\[ \varphi=\frac{\omega \mu r_0^2}{5c}\,\frac{3\sin\vartheta-1}{r^3}, \tag{16} \]

where \(\vartheta\) is the angle between \(\mathbf r\) and the equatorial plane. According to this expression, the potential of both poles of the star is equal to \(+2\omega\mu/5cr_0\), while the potential of the equator is \(-\omega\mu/5cr_0\). The sign of the potentials changes to the opposite if \(\boldsymbol\mu\) and \(\boldsymbol\omega\) are antiparallel.

A number of authors have pointed out the possibility of accelerating charges by the field of unipolar induction of the Sun and stars. We shall dwell only on the most consistent and complete theory \(^{15}\). According to \(^{15}\), charges that have emerged from the surface of the star far from the poles will move approximately along the magnetic lines of force (according to Section 4), first accelerating and then slowing down again and ultimately returning to the surface of the star. Only charges torn away near the poles, in accordance with condition (15), can finally leave the star. Since both poles of the star are charged with the same sign, while near the equator charges cannot detach themselves from the star, being returned by the magnetic field, the star as a whole must become charged owing to the loss of charges of one sign torn away from the poles. Thus an initially uncharged star must, in the course of time, acquire a negative charge if its \(\boldsymbol\mu\) and \(\boldsymbol\omega\) are parallel (in the case of antiparallel \(\boldsymbol\mu\) and \(\boldsymbol\omega\), the signs of all charges and potentials must be reversed). Evidently, in the idealized process under consideration the star may become charged up to a potential close to \(-2\omega\mu/5cr_0\), after which negative charges also will begin to be torn away from the star, from small annular areas surrounding the stellar poles. As a result, an equilibrium may be established when, near its poles, equal numbers of both negative and positive charges escaping into interstellar space will be torn away from the star. In this case the star will have a charge close to

\[ Q=-\frac{2\omega\mu}{5c}. \tag{17} \]

The calculations carried out showed that part of the total flux of charges emitted by the star must contain particles with very large energies (about \(10^9\) eV for the Sun and \(10^{13}\) eV for the star 78 Virginis), determined by the potential difference between the poles and the equator. It is quite obvious that the star will also emit ions of heavy elements, if such are present in its atmosphere.

The energy of the particles emitted by the star under consideration is imparted to them at the expense of the work of extraneous electromotive forces of unipolar induction acting inside the star, i.e. ultimately at the expense of the energy of rotation of the star.

Thus, stars with parallel or antiparallel \(\boldsymbol\omega\) and \(\boldsymbol\mu\), acting like a unipolar machine, must generate streams of charges with the energies of cosmic particles.

If the axis of the star’s magnetic dipole is inclined to its axis of rotation by an angle \(\theta\), as is the case for the Earth or the Sun, then in the space surrounding the star a vortical electric field \(\mathbf E_2\) is induced, along with the field of unipolar induction \(\mathbf E_3\) (see formula (6)).

If the field \(\mathbf E_3\) and the field produced by the total charge of the star do not prevent a particle with charge \(e\) from being torn away from a given point on the surface of the star (a point not lying near a pole), then the particle will begin to move with acceleration, winding around a magnetic line of force, and will again strike the surface of the star at some opposite point. The energy thereby acquired will no longer be equal to zero, as in the preceding case, when \(\theta=0\), but is expressed in the form:

\[ \mathcal E=\frac{8}{5}\,\frac{e}{c}\,\frac{\omega\mu}{r_0}\,\sin\theta\cos\psi_0\sin2\vartheta_0, \tag{18} \]

where \(\vartheta_0\) is the angle of magnetic latitude, measured from the magnetic equator, and \(\psi_0\) is the angle of magnetic longitude, measured from the meridian passing through the magnetic and geographic poles, for the point on the surface of the star from which the charge under consideration escaped. Charges leaving the surface of the star near the magnetic poles, just as in the preceding case (for \(\theta=0\)), owing to the removal of the magnetic lines of force to a large distance from the star, by virtue of condition (15), will be able to be torn away from the star and pass into outer space.

The induction effect described (\(\theta\ne0\)) differs substantially from the pure effect of unipolar induction (\(\theta=0\)) in that in the case \(\theta\ne0\) energy will be acquired both by charges that have left the surface of the star and by charges that have entered the field of the star from infinity and again gone off to infinity, since the field \(\mathbf E_2\) is vortical; whereas in the case \(\theta=0\), charges moving from infinity to infinity will not acquire energy, owing to the potential character of the field \(\mathbf E_3\) outside the body of the star. Thus the induction effect provides greater possibilities for accelerating charges than the pure effect of unipolar induction. In particular, a charge that has flown past a star with \(\theta\ne0\) at a distance \(L\) may change its energy by an amount of the order of:

\[ \Delta \mathcal E=\frac{e\omega\mu}{cL}\,\sin\theta. \tag{19} \]

As also for \(\theta=0\), the energy of particles accelerated by the induction effect will be drawn from the total energy of rotation of the star.

7. SOLAR AND STELLAR SPOTS AS INDUCTION ACCELERATORS

The possibility of acceleration of charges in the field of solar and stellar spots was first pointed out by Swann\(^{16}\). However, he did not give a correct picture of the acceleration of charges. We shall consider this question from the point of view of the theory of the motion of charges in cosmic fields set forth above.

If we abstract from the rotation of solar (or stellar) spots together with the surface of the Sun (or star), then the electric field near a spot or a pair of spots, arising upon their appearance or disappearance, will be expressed by the field \(\mathbf{E}_1\), according to formula (6). Since \(\mathbf{E}_1\) is perpendicular to \(\mathbf{H}\), determined by formula (2), then, according to the approximate picture of the motion of charges (Section 4), we should not expect any substantial acceleration of them by the field \(\mathbf{E}_1\). However, if it is taken into account that near a newly arising spot or a dipole pair of spots there is already present the field of other spots, or simply the general field of the Sun (or star), then the electric field will not be strictly perpendicular to the magnetic field and, consequently, the mechanism of acceleration of charges considered above will operate. Obviously, acceleration and separation of charges from the spots will take place mainly at the moment of their formation, when the magnetic field of the newly arising spot is still small in comparison with the already existing fields, while the electric field is sufficiently large owing to the rapid change of \(\mu\). The energy acquired by charges accelerated in the field of a newly arising pair of spots may be roughly estimated by the formula:

\[ \mathcal{E}=\frac{e}{c}\frac{\dot{\mu}}{r_1}\simeq \frac{e}{2c}\frac{a^3}{r_1}\dot{H}_m, \tag{20} \]

where \(r_1\) is the distance from the center of the magnetic dipole to the nearest portions of the charge trajectory, \(a\) is the distance between the centers of the pair of polar spots (or the length of the magnetic dipole), and \(H_m\) is the maximum value of the magnetic field on the surface of the spots.

The greatest energies will, obviously, be attained by charges initially situated near the spots, i.e. in the case \(r_1 \simeq a\). However, the magnetic lines of force emerging from this region will, as a rule, not recede to considerable distances from the Sun, and consequently the accelerated particles will for the most part return to its surface. For charges initially situated in regions of the solar surface remote from the newly arising spots, for example near the poles, the conditions for separation from the Sun will be more favorable. However, the maximum energy of the accelerated particles will correspondingly decrease by a factor of \(\frac{a}{r_1}\). For a charge leaving near the pole of the Sun, the rough estimate by formula (20) gives an energy of the order of \(10^7\) eV.

Thus, during periods of the appearance of sunspots, the Sun must emit streams of fast charged particles capable of reaching the Earth. It is possible that magnetic storms and auroras are caused precisely by these streams.

Taking into account that, on stars, magnetic fields may considerably exceed the magnetic field of sunspots, and admitting for them more intense spot-forming activity, one may suppose that the described mechanism for generating streams of fast particles is responsible for the creation of part of the primary component of cosmic rays.

8. STARS WITH VARIABLE MAGNETIC MOMENTS AS COSMIC INDUCTION ACCELERATORS

Studies of the magnetic field of the star BD-18° 3789 have shown\(^{13}\) that the magnetic field at its surface varies periodically from \(+7800\) gauss to \(-6500\) gauss with a period of 9.295 days. In other words, this star has a variable magnetic moment. Consequently, just as in the case of forming sunspots, around such a star there is induced a vortex electric field capable of accelerating charged particles.

If we consider that the field of the star is the field of a variable magnetic moment, then, because of the perpendicularity of \(\mathbf{E}\) and \(\mathbf{H}\), we cannot expect significant acceleration of charges at those times when \(E \ll H\) (as also in the case of sunspots). However, at the moments when \(\mu\) passes through zero, \(H\) is also equal to zero, while \(E\) has a maximum value (see formulas (2), (6)). Consequently, during short intervals of time in the vicinity of the star \(E > H\). When this condition is fulfilled, as was already indicated in Section 4, the charges will be only weakly deflected by the magnetic field and will move with acceleration along trajectories having a small radius of curvature and going beyond the limits of the star. Considering the trajectory to be approximately rectilinear, and \(\mu\) varying according to a sine law, one can estimate the energy imparted to the accelerated charge, according to (20), by the formula:

\[ \mathcal{E}=\frac{\pi e}{c}\frac{r_0^2 H_m}{T}, \tag{21} \]

where \(r_0\) is the radius of the star, \(H_m\) and \(T\) are the maximum value of the magnetic field and the period of its variation. According to this formula, for the star BD-18° 3789 we obtain \(\mathcal{E}=7\cdot 10^{12}\) eV, taking \(r_0=1.6\cdot 10^{11}\) cm, \(T=8\cdot 10^5\) sec, \(H_m=7000\) gauss, according to\(^{13}\). In the mechanism of acceleration under consideration, the intensity of the streams of particles breaking away from the star is evidently not limited by the conditions of detachment from the star’s magnetic field. This intensity may be very large,

If one assumes that the magnetic field of variable stars is produced not by a single magnetic dipole, but has a more complex structure, so that E and H are in general not perpendicular, then the acceleration of charges to energies of the indicated order is also possible at other periods of time.

Thus, variable magnetic stars of the type considered are also CAUs capable of generating cosmic rays.

An essential difference between the accelerators considered in Sections 7 and 8 and the accelerators considered in Section 6 is that in the second case the energy of the accelerated particles is drawn from the mechanical energy of the star’s rotation, whereas in the first case this energy is drawn from the source that creates the changing magnetic fields, i.e., ultimately from the energy produced by the nuclear reactions that sustain the activity of the stars. Consequently, variable magnetic stars and stars with intense sunspot-forming activity may be the most powerful and almost inexhaustible sources of cosmic radiation.

If one assumes that most variable stars possess variable magnetic fields, or supposes that stars with intense sunspot-forming activity are very widespread in the universe, then these stars may quite well be regarded as the principal primary sources of cosmic rays.

Such a hypothesis makes it possible to explain not only the composition and energy of the particles of the primary component, but also the high intensity of the cosmic-ray flux. However, the observed energy spectrum of cosmic particles and the isotropy of the primary component still do not follow from this hypothesis.

9. ACCELERATION OF CHARGES BY CLOUDS OF INTERSTELLAR MATTER

The energy spectrum of the primary component (formula (1)) and its isotropy are best explained on the basis of the assumption, advanced by Fermi\(^{10}\)*) that the cosmic particles emitted by primary sources are additionally accelerated in repeated collisions with chaotically moving magnetized clouds of rarefied interstellar matter. Assuming an average cloud velocity of about \(30\ \mathrm{km/sec}\) and, correspondingly, taking it that at each collision a proton acquires an energy of the order of \(10\ \mathrm{eV}\), and admitting the possibility of a very large number of collisions, Fermi derived a law of distribution of proton energies similar to

*) For a detailed exposition of Fermi’s theory, see also the article by V. S. Vavilov\(^{17}\).

experimentally observed distribution law for the primary component (1). Fermi considers the mechanism he proposed to be the basic one in the formation of the primary component. However, the latter assumption is erroneous, as can be seen from Fermi’s own calculations. According to these calculations, collisions with clouds can accelerate only sufficiently fast particles, since at low velocities the losses due to ionization of the interstellar gas exceed the increase in energy resulting from collisions with moving clouds. For each kind of ion one can indicate a minimum particle energy below which collisions with clouds do not lead to acceleration. As Fermi’s calculations showed, this threshold energy increases sharply with increasing atomic number of the particle. Thus, for example, for protons this energy is about \(2\cdot 10^8\) eV, for \(\alpha\)-particles about \(10^9\) eV, for an oxygen nucleus about \(2\cdot 10^{10}\) eV, and for an iron nucleus the threshold is \(3\cdot 10^{11}\) eV. Consequently, the acceleration mechanism by collisions with clouds cannot be the basic one for heavy ions, since their initial energy would have to be higher than the mean energy of cosmic particles. This mechanism could be accepted as basic only in the case where the primary component consisted solely of protons and heavy ions were absent from it. The supposition that protons and ions are accelerated by different mechanisms is extremely artificial. Thus, Fermi’s assumption concerning the basic character of the mechanism of collisions with clouds in the process of acceleration of cosmic particles is untenable, since it cannot explain precisely the fact (the presence of heavy ions) that was the decisive argument in favor of the KIV theory.

What has been said above does not mean, however, that Fermi’s theory is wholly erroneous. Taking account of collisions with clouds of interstellar matter explains in the most natural way the isotropy of the primary component. If the clouds move, then the acceleration mechanism proposed by Fermi also takes place, and it can ensure the correct spectral distribution. It should not, however, be assigned the principal role. If we assume that the principal primary sources are stars (for example, stars of the type considered in Sections 7 and 8), accelerating protons on average to energies of order \(10^{10}\) eV and, correspondingly, ions to energies \(Z\) times greater, while collisions with clouds chiefly redistribute this energy over the spectrum, then the principal difficulty of Fermi’s theory disappears.

Thus, we may regard moving ionized clouds of interstellar matter as a special kind of KIV, redistributing over the spectrum the energy of cosmic particles emitted by primary KIV. Collisions with clouds also ensure the isotropy of the primary component.

10. GENERAL PICTURE OF THE ORIGIN OF COSMIC RADIATION

The analysis carried out above of various hypotheses on the origin of cosmic rays leads to the conclusion that the most correct view is that the primary cosmic particles are generated in the atmospheres of the stars of the galactic system, which possess considerable magnetic fields and are cosmic-ray sources.

The acceleration of particles to energies of \(10^{10}\) eV and higher may be caused by any of the mechanisms considered in Sections 6, 7, 8, or by some new induction mechanism. Each of these mechanisms may make a definite contribution to the total flux of the primary component. However, the greatest preference may be given to the mechanisms described in Sections 7 and 8, since these mechanisms do not cease to operate as the kinetic energy of rotation decreases.

Furthermore, cosmic particles, entering interstellar space, repeatedly collide with chaotically moving ionized magnetized clouds of rarefied interstellar matter. As a result of collisions with the clouds, the particles are scattered and additionally accelerated, being distributed in energy spectrum according to law (1).

The spatial isotropy of the primary component is due both to the approximately uniform distribution of cosmic-ray stars in the nearby parts of the galaxy and to scattering by magnetized clouds of interstellar matter. Even very weakly magnetized, but very extended, clouds of interstellar matter must cause substantial curvatures of the trajectories of moving charges. Thus, the motion of cosmic particles through interstellar space is similar to the diffusion of a very light gas through an extremely heated, very heavy “gas,” whose individual “molecules” are clouds of interstellar matter.

Obviously, the effective transverse cross section for the scattering of cosmic particles in collisions with a magnetized cloud will depend on the magnitude of the mean magnetic field of the cloud and on the energy of the particle. In solving the problem of the distribution of particles over energies, this circumstance will contribute to a slower decrease of the distribution function \(F(\mathcal{E})\) with increasing energy, since for particles with large energies the magnitude of the deflection by the magnetic field of the cloud decreases and, consequently, the transverse scattering cross section decreases; thus, particles with large energies will be able to reach the Earth from more distant regions of the galaxy without being absorbed by interstellar gas.

The Fermi acceleration mechanism may be regarded as a kind of “heating” of the “cold,” light gas of cosmic particles in the “hot,” heavy “gas” consisting of cosmic clouds.

The predominance of protons in the primary component and the approximate agreement of the percentage content of ions of other elements with the relative abundance in the universe are explained by the production of primary particles in the atmospheres of stars.

When moving in the magnetic fields of cosmic clouds, charged particles must emit electromagnetic waves[^18]. In this process electrons, owing to their small mass, will lose energy to radiation much more rapidly than protons and ions of heavy elements. This may explain the practical absence in the primary component of electrons with energies of \(10^{10}\) eV and higher, since high-energy electrons will expend this energy chiefly on the emission of electromagnetic waves and, consequently, will not carry it from the stars to the Earth.

Apparently, a large part of the radio emission of the Galaxy can be explained as the electromagnetic radiation of cosmic particles moving in the magnetic fields of clouds of rarefied interstellar matter.

The analysis carried out above of the possible types of cosmic induction accelerators shows that there are no fundamental obstacles to explaining the high intensity of the total flux of the primary component within the framework of the picture we have adopted for the origin of cosmic radiation. If the total energy that can be imparted to cosmic particles by accelerators of the rotating-star type is limited by the reserve of kinetic energy of rotation of these stars, then in the case of variable-star-type accelerators no such limitation is present, since in these cases the energy of the accelerated particles is drawn from internal nuclear processes that maintain the general activity of the stars. Thus, a sufficient prevalence in the universe of magnetic variable stars can provide a very high intensity of the flux of cosmic particles in interstellar space.

The assumption that stars emit powerful fluxes of accelerated particles is in agreement with the idea, accepted recently by astrophysicists, of the existence of intense corpuscular radiation from stars[^19]. The simplest mechanism providing the general corpuscular radiation of stars may be the same as the mechanism of acceleration of cosmic particles. It may therefore be supposed that variable magnetic fields on the surfaces of stars are not an exceptional phenomenon only for special classes of stars, but are organically connected with the activity of the majority of stars.

Thus, the energy of cosmic particles is drawn chiefly from nuclear processes taking place inside stars. However, this energy is imparted to the particles not directly, but through a chain of intermediate transformations. The intranuclear energy released inside stars, under certain conditions, excites mechanical displacements of stellar matter. The displacement of large masses of well-conducting intrastellar matter in the presence of “frozen-in” magnetic fields can excite powerful magnetic fields extending beyond the surface of the star. The variable magnetic fields arising in this way accelerate ions and electrons of the star’s atmosphere up to the mean energy of cosmic particles, which fly off into interstellar space. In addition to particles accelerated to very high energies, variable magnetic fields eject streams of slower particles,^20 which constitute the bulk of the corpuscular radiation of stars and subsequently form magnetized clouds of interstellar matter.

The fast particles emitted by stars, interacting further with magnetized clouds, are accelerated still more at the expense of the kinetic energy of the clouds and acquire the energy distribution characteristic of the primary component.

Thus, the problem of the origin of cosmic rays, successfully solved by the theory of cosmic induction accelerators, is a part of cosmic electrodynamics and electronics and is organically connected with the problem of the magnetism of stars and other cosmic objects.

CITED LITERATURE

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6. Ya. P. Terletskii, ZhETF, 16, 403 (1946); DAN, 47, 104 (1945).
7. S. A. Boguslavskii, Paths of Electrons in Electromagnetic Fields, Moscow, 1929.
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1. J. W. Broxon, Phys. Rev., 75, 612 (1949).
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3. W. F. Swann, Phys. Rev., 43, 217 (1933).
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