MODEL EXPERIMENTS ON STÖRMER’S THEORY OF THE AURORA BOREALIS AND THE “ECHO OF OUTER SPACE”*

Ernst Brüche, Berlin

In the July issue of Naturwissenschaften for 1928, C. Störmer reports on the so-called “echo of outer space,”¹ observed in 1927 by Hals,² and later by himself and Van der Pol,³ and interprets this “echo” in the spirit of his theory of the aurora borealis.⁴

This theory, which takes its origin from Birkeland’s magnificent experiments,⁵ reduces the phenomenon of the aurora borealis to electronic radiation from the sun. Everything else follows from this basic assumption with mathematical necessity, since the problem is in fact a mathematical one—to find the motion of electrons in the earth’s magnetic field.

* “Echoes of outer space” are repetitions, after very long intervals of time, of radio signals sent by a short-wave station (PCJJ, wavelength 31.4 m). These intervals are so great (from 3 to 25–30 sec.) that during this time the electromagnetic wave must traverse colossal cosmic distances. The well-known secondary signal that goes around the earth along the long arc of a great circle is observed \(1/7\) sec. after the main one. “Cosmic echoes” have been observed several times, by different persons and in different places, so that their existence is beyond doubt.

If Störmer’s theory is indeed correct, i.e. if these echoes really are of cosmic origin, however improbable that may be, then they are of very great interest. Here we have, essentially, a telegram sent and received back from outer space.

Translator’s note.

MODEL EXPERIMENTS TOWARD STÖRMER’S THEORY OF THE AURORA

The result of the theoretical investigation, which plays a role of special interest for us, consists in the fact that the terrestrial globe is surrounded by an annular, torus-like space into which electrons coming from the sun cannot enter. This “torus,” shown partly in section in Fig. 1, is situated symmetrically with respect to the earth’s magnetic equator. Assuming a constant velocity of the electrons, this torus bounds the earth on the outside by a curved surface, like a concave mirror. Beyond this surface there lies a bundle of electron paths that gradually diminishes with distance from the earth. Thus, in front of the earth’s equator there exists a boundary between an electrically conducting space, containing electrons, and a space containing no electrons. This boundary reflects electromagnetic waves like the Heaviside layer. Thus we have a simple explanation of the “echo of world space”—an explanation giving values of the “echo” intervals that agree well with observations. This explanation also makes understandable the comparatively large (of the order of \(1/10\)) intensity of the reflected radiation. Material on this “echo” was expanded by Halle, Talon, and Ferrié during the solar eclipse of May 9, 1929. Halle and Talon\(^6\) were able to establish at the equator—an especially favorable place opposite the electron reflector—distinct and in part very intense echoes. These echoes were delayed by up to 30 seconds relative to the signal.

Fig. 1.
Labels in the figure: “northern electron streams causing the aurora”; “reflecting wall”; “space of the torus without electrons”; “Earth”; “bounding surface of the torus (trace of the section)”; “southern electron streams”; “magnetic equator.”

It is still unclear why these echoes, observed very often on the day of a solar eclipse, were not detected during the total phase of the eclipse and for some time before it, although the Moon was not above the mountains. If one accepts that the non-observation of the echo is not an accidental phenomenon, then one must first think of some secondary processes in our atmosphere when solar illumination ceases. It could have happened, after all, that the Heaviside layer, in passing from solar illumination into shadow, changes its structure and properties and acts quite differently on electromagnetic waves during an eclipse. The waves either are “reflected” already in the Earth’s atmosphere, so that they do not penetrate into the mountain space, deprived of electrons, or they are so strongly deflected from their initial direction that the conditions of reflection at the boundary surface of the mountains—that is, the conditions for the return of the waves—are completely changed.

The long intervals between echoes that have been observed, their special frequency at the equator, and the fulfillment of certain predictions from Størmer’s theory are too strong arguments for the above-mentioned facts, which individually are not understood, to be able to lead to the abandonment of Størmer’s explanation. Størmer himself^7 therefore quite rightly points out, regarding the experiments of Van der Pol^8 and Appleton,^9 which gave negative results, that before a final conception can be constructed, the observations must first be supplemented.

Thanks to the explanation of the “echo of world space,” general interest in Størmer’s theory of the aurora borealis was again strengthened. It was therefore especially tempting to support by a model experiment this theory, which, more than any other, is suited to this by its nature and by the simplicity of its physical content. Such a model realization of the theory should not be regarded merely as an “illustration.” Not to mention that this realization may lead to electron trajectories or to features of ordered electron beams not yet discovered by calculation, it also gives the possibility of comparing the cosmic behavior of electro-

nous with laboratory experiment and to discover a possible difference between them. I therefore intended to use the possibility now available, thanks to the discovery of “thread rays,”¹⁰ for carrying out a model experiment on the theory of the aurora borealis.

Concerning these experiments, a description of which is to appear in full detail in Zeitschrift für Astrophysik, I would like to report briefly here as well. In doing so I shall remain within the framework of Størmer’s communications mentioned at the beginning, where the main features of his theory are given. I must confine myself to a few experiments, in which the quantitative aspect will recede into the background. I shall place at the forefront the “space of the torus,” which plays such an important role in explaining the “echo of world space,” and shall select and arrange the experiments from this point of view.

Experiments

Model apparatus. The terrestrial magnet is represented in the model by an electromagnet, embedded in a copper sphere and shown in Fig. 2. It can be shown that the field of such a magnet, in accordance with the theoretical assumption, agrees very well with the field of a dipole. Some experiments were carried out with other special arrangements, as will be indicated later in the text. The cosmic radiation is reproduced by electron radiation from an oxide cathode with the aid of 200 and, respectively, 250 V. Experiments were performed both with broad electron beams and with individual electron rays. Owing to excitation of the residual gas and vapors, hav—

Fig. 2.

electrons moving in the space where the experiment is carried out glow, so that they can be photographed. As individual “electron rays,” the production of which constitutes the necessary prerequisite for these experiments, “canal rays” were used, whose properties I have recently described.

The shape of the electron torus. The toroidal space inaccessible to electrons (see Fig. 1), lying, according to Störmer, around the Earth’s equator, approaches the terrestrial sphere in a funnel-like manner at the northern and southern poles. This means that electrons can reach, near the poles, all the way to the Earth’s surface. That is why the well-known luminous atmospheric phenomena are confined to the polar regions: we speak of the northern and southern lights. The fact that the space surrounding the Earth is formed in such a peculiar way without electrons becomes intelligible if one considers how the force field acts for different directions of electron paths. If an electron ray approaches in the Earth’s equatorial plane, it experiences, generally speaking, the maximum deflection, since its path runs perpendicular to the lines of force. If, on the contrary, the ray approaches along the Earth’s magnetic axis, it is completely unaffected, i.e. it reaches the terrestrial sphere. A ray coming from afar can also reach the Earth’s surface if it undergoes such a deflection in the terrestrial field that, near the Earth, its direction “by chance” coincides with the direction of a line of force descending toward the Earth. Thanks to these considerations, the space of the torus is most closely connected with the structure of the force field. It is by no means accidental that there is a far-reaching similarity (Fig. 3) between the meridional curve calculated by Störmer and the line of force of a dipole.*

* Since we found in the literature neither a diagram of the force field of a dipole nor the equation of the lines of force, we derived in the usual way the orthogonal curves from the known equations of the equipotential lines. These calculations were kindly carried out by Dr. Engel.

MODEL EXPERIMENTS TOWARD STÖRMER’S THEORY OF THE NORTHERN LIGHTS

Winding of the electron beam onto a line of force. We have seen that an electron beam can move along the magnetic axis all the way to the earth. Generally speaking, it has the greater chance of reaching the earth the more closely it adjoins a line of force leading to the earth. How, in particular, the descent to the earth takes place is shown by Störmer’s drawing in Fig. 4 on the left. In this case the electron beam winds around the line of force and thus gradually advances forward. But the approach does not go on indefinitely far. Moreover, at the end of its motion the beam turns back.

Fig. 3.

The model experiment in any case confirms the theory: Fig. 4, on the right, shows the electron path photographed in the field of the terrestrial model. As the theory requires, winding occurs around the cone of lines of force and finally a turn back. The incomplete identity of the theoretical drawing and the experimental one has its basis, on the one hand, in the fact that the field in the experiment does not quite coincide with the field of a dipole, and, on the other hand, in the fact that somewhat different initial conditions were chosen. It must be noted here, where there is the only one in this

Fig. 4.

work, a direct comparison of the theoretical and experimental trajectories, since in general I did not strive for complete coincidence of the trajectories with randomly chosen initial conditions and experiment. What is important is only that the curves belong to one family, because the point is a quantitative comparison.

Depth of penetration of the electron beam. The smaller, in our case, the angle (of the point of departure near the dipole axis) between the initial direction and the line of force passing through this point, the farther the beam can approach the surface of the earth before it turns back. If the turn occurs before the beam penetrates into the earth’s atmosphere, then we observe from the earth a beam of the “northern lights.”

Fig. 5.

I shall now show experimentally how the returning trajectory unfolds and how the beam approaches the magnetic pole more and more as the “angle of flight” decreases. Two original photographs are seen in Table I, photographs 1 and 2. For practical reasons, the point of departure of the beam is shifted here, and the influencing magnet is turned above the experimental balloon. Then, from 50 separate photographs, some were selected and drawn against the stationary magnet in Fig. 5. It is evident how, as the angle of flight decreases, the beam winds up more and more and in this way successively approaches the pole.

Trajectories going in the direction of the lines of force and perpendicular to them. To explain the form of the electronic torus, we considered the extreme

possible types of trajectories. These were the paths that passed predominantly in the direction of the lines of force and perpendicular to them. In the preceding paragraph we provided photographs and drawings for the principal representative of the first group, which can descend into the funnel-shaped depression as far as the earth. Many other curves could also have been shown; much could also be said about the “zone of encounter” on the earth, about the influence of the circular current around the terrestrial equator, etc. But in this report we shall not dwell on experiments intended for the study of the theory of the polar aurora. For the “echo of world space,” what is chiefly important are the paths running perpendicular to the lines of force. These paths lie opposite the terrestrial equator on the far side of the boundary of the torus. Between the terrestrial sphere and them extends the torus space, free of electrons, beginning with a sharply expressed boundary surface.

Electron-free region of a permanent magnet. Not only our earth, but also every other magnet of sufficient strength has regions free of electrons. This can be shown by the following experiment with a permanent horseshoe magnet, which reveals a substantially sharper curve delimiting the free region than can be obtained with the aid of a dipole. A balloon, only a few centimeters deep, was placed parallel to the plane of the table. The horseshoe magnet was set up in such a way that one pole was in front of the vessel and the other behind it. A beam of electrons was sprayed out in the form of a fan from an incandescent cathode, chiefly in the plane of the table, and was immersed in a magnetic field perpendicular to it. With various positions of the magnet there arise (shown in photograph 3 of plate I) sharply separated regions: with electrons and empty.

These experiments, it is true, give a rough picture of the interaction of the sun and the earth, since here too we are dealing with a point source at a finite distance. But these experiments, nevertheless, do not disclose the mathematical concept of the torus space, because this space pertains only

to rays that come from infinity from all directions. However, in this case as well we can try to illuminate the matter with our permanent magnets. To do this, we shall “bombard” the magnet not from one point in various directions, but from different points, always perpendicular to the lines of force and, moreover, so that the ray passes as far as possible.

From experimental considerations the experiment was again carried out in such a way that not the source of the rays changed its position relative to the stationary magnet, but the magnet rotated with the source stationary. From 16 separate photographs (an example of which is given by photo 4 of Table I), Fig. 6 arose in this way; it already gives a fairly correct mathematical picture of the boundary curve of the torus, both in form and in position.

Fig. 6.

A region free of electrons in the equatorial plane of the earth. For a dipole it is incomparably more difficult to show the boundary curve lying in the equatorial plane, since electrons not flying quite exactly toward this plane are deflected, wander, for example, toward the poles, and in this way blur the contours of the boundary curve. The best photograph that I obtained is reproduced in photo 11 of Table 2. It is especially valuable because the boundary circle of the torus visible here (slightly outside the dotted equator of the earth model) corresponds in every respect to the mathematical concept of an electronic torus.

After we have seen how the boundary circle separates the equatorial plane into a region free of electrons and a region filled with them, it is also of interest to see where this boundary circle lies for the Earth. Observation of the “echo” enables us, in the simplest way, to estimate the distance sought. If we assume, moreover, that the longer intervals of the “echo” are caused by confused reflections or by some other secondary influences, then for direct reflection we must take one of the shortest observed intervals of the “echo”—about \(3\frac{1}{2}\) sec. From this interval of time it follows that

\[ d=\frac{c\cdot t}{2}=\frac{300\,000\cdot 3.5}{2}=5.3\cdot 10^{5}\ \text{km}=83 \]

terrestrial radii, \(\sim 1.5\) times the distance of the Moon.

Nonperiodic trajectories in the equatorial plane. Plane trajectories lying on the far side of the boundary circle in the equatorial plane are distinguished, in comparison with spatial paths, by their simplicity and by their importance for the consideration of scales. They are of interest insofar as they are all directed to one and the same side, as is shown in Fig. 7. At first sight it is not entirely clear how, with a continuous change in the direction of flight (see again Fig. 7), the dipole passes from one side of the trajectory to the other.

Fig. 7.

As examples of such trajectories, Table I shows photographs 7, 8, and 9—three curves obtained in the field of a dipole. Then Fig. 8 shows a picture composed of a number of such experimentally obtained trajectories. Here we cannot pause to prove that this drawing is in quantitative agreement with the drawing obtained by Störmer from theory.

The question indicated above finds its resolution in the presence of a certain flawless circular path, to which-

... as the direction of emission is changed, the electron trajectories asymptotically approach them from both sides.

The circular path and the limiting circle. Between the radius \(c\) of this circular path and the radius \(d\) of the limiting circle, according to the theory there is the relation:

\[ d=(\sqrt{2}-1)c=0.41c. \]

Experiment makes it possible to verify this relation. From photograph 11 of Table 2, in which both circles enclose the region filled with electrons, it follows that \(d=0.42c\). Since we now know the relation between the radius \(c\) and the radius of the limiting circle \(d\), it is possible to calculate its value from the value of \(d\) already known for the earth. Hence it follows:

\[ c=\frac{5.3\cdot 10^{5}}{0.41}=1.3\cdot 10^{6}\ \text{km}. \]

Fig. 8.

The circular path and the velocity of the electrons. If, as in our experiment, the velocity of the electrons and the magnetic moment of the dipole are known, then the position of the circular path is thereby also given. This path will appear precisely when the deflecting force of the field is so great that the center of curvature falls exactly at the dipole, i.e. when:

\[ H=\left(\frac{m}{e}\right)\frac{v}{c}=\frac{M}{c^{3}}. \]

Whence it follows

\[ c=\sqrt{\left(\frac{e}{m}\right)\frac{M}{v}}, \]

where \(M\) is the magnetic moment of the dipole, \(H\) is the field intensity

TABLE I.

1

2

3

4

5

6

7

8

9

TABLE II.

10

11

12

13

14

15

16

17

in gauss, $\frac{e}{m}$ is the ratio of charge to mass, $v$ is the velocity of the electrons.

Since in phot. 10 the current strength $=0.6\ a$, and hence the magnetic moment was $6500\ \mathrm{cm}^3$ gauss, and since a beam was used having velocity $8.6 \cdot 10^8\ \mathrm{cm/sec}$, corresponding to 200 V, then $C = 11.2\ \mathrm{cm}$, which is in good agreement with the experiment, for which $C = 10.5\ \mathrm{cm}$. If $M$ and $C$ are known, the velocity of the electrons can conversely be calculated from the above equality.

Since for the earth $M = 8.4 \cdot 10^{25}\ \mathrm{cm}^3$ gauss, and from observations of the “echo” we compute $d$ and, correspondingly, $c$, then for the velocity of cosmic electrons there follows the value $v = 0.95$ the velocity of light. And this value is in any case comparable with the values obtained by other methods.

Consideration of scales. Our experiments will have quantitatively complete significance only when we form an entirely clear conception of the relation of the cosmic scale to the experimental one. It no longer requires more detailed explanation that the circular path has the greatest importance for such investigations. The radius $c$ is at the same time a natural unit of the whole problem and will therefore be taken in the theory in general as equal to 1. If $c$ is equally large for two experiments, then all corresponding trajectories are identical, whatever the magnetic moment and the velocities of the electrons may be. If the model experiment is to be carried out in a terrestrial sphere one thousand times smaller, then, having correspondingly chosen $M$ and $v$ for this experiment, $c$ must also be decreased 1000 times.

Using exact numerical values, one can draw the comparative picture given in Fig. 9. To the left of the beginning 0 the cosmic scale is plotted, to the right—the scale of the experiment. The drawing was obtained by photographing a beam deflected in the equatorial plane of the dipole. If our experiment is in all details a true picture of reality, then we must conceive of the earth’s sphere as reduced to $0.6\ \mathrm{mm}$, as indicated in Fig. 9. In

with this reduction of our spherical magnet, the magnetic moment would have had to retain its magnitude. This requirement, of course, cannot be fulfilled experimentally. However, even without this reduction we obtain the correct picture up to the point where the rays begin to interact with the surface of the monstrously enormous terrestrial model.

Fig. 9.

Fig. 9 supplements the investigation further in that it shows that the photographed electron ray has, at the point of intersection with the “circle of scales,” the same curvature. This is as it should be, for equal field strengths at a given point determine an equal curvature of the path.

Periodic trajectories in the equatorial plane. We designated the circle of radius \(= 0.41 c\) as the boundary of approach of all electrons and as the region within it free of them. What will happen, however, if we let electrons into this region? In that case, naturally, electron trajectories again result, which differ fundamentally from those considered in that they do not extend to infinity. And precisely this means that, conversely, in accordance with our reasoning, not a single electron can penetrate from infinity into the interior of the boundary circle.

To illustrate the “periodic paths” it is first necessary to report on a comparatively easily performed experiment. In a field

of a large coil placed behind or in front of the plane of the drawing, an electron beam is sent out perpendicular to the lines of force, i.e. in the plane of the drawing. Since the magnetic field increases near the axis of the coil, with a suitable choice of current strength there appear more or less strongly curved periodic trajectories. Photographs 5 and 6 of Table 1 give an approximate view.

It was more difficult to obtain periodic paths in the equatorial plane of the dipole. Photographs 12 and 13 of Table 2 show such paths in good agreement with the theory. In the photograph a circular path was subsequently drawn in. The figures show the two limiting circles that are very characteristic of periodic trajectories.

Spatial trajectories. Finally, let us leave aside the equatorial paths, which have already given all that is essential about the regions free of electrons around the Earth’s equator, and turn to those spatial paths which pass outside the limiting circle and whose totality forms the reflecting wall of the torus.

The consideration of the non-periodic plane paths alone has already led us to a large number of different curves, so that for demonstration only a few of them had to be selected. It is easy to understand how much greater the number of paths will be in space. If in the plane an infinite set of paths is possible, then in space there is an infinite number of such infinite sets. However, just as all plane trajectories adjoin a “special” circular trajectory, so groups of spatial curves are connected with a certain spatial periodic path, to which they asymptotically approach.

Non-periodic spatial paths. As a typical representative of spatial paths we shall give only one example. This is a trajectory which lies at the same time midway between the plane paths of the equatorial plane considered up to now and the spatial trajectories obliquely intersecting this equatorial plane.

The result of the experiment is shown in phot. 16, plate 2. Near the limiting circle the electron beam describes an almost sharply defined figure, approximately perpendicular to the preceding and following planes of the orbits.

Periodic spatial trajectories. A periodic path, obtained experimentally and belonging to the simplest group of periodic trajectories calculated by Störmer, is shown in phot. 14, plate 2. This photograph was obtained when the beam was let in perpendicular to the equatorial plane and for a quite definite current strength in the electromagnet. The possibility of obtaining such curved paths with such an initial direction of the beam becomes perfectly clear if one considers the pattern of the field of force and all the components of the forces acting on the beam in such a field. Of the intricate periodic spatial curves only now calculated by Störmer, we shall consider one more comparatively simple case.* This is the self-twisted path presented in phot. 15, plate 2.

The more intricate the trajectories become, the more closely, generally speaking, they adjoin the outer surface of the torus space. Rising from the equatorial plane, they reach the highest point and then, following the curvature of the torus, descend more or less deeply toward the Earth. In doing so they make one, two, or even more loops, depending on how deeply they penetrate. Usually these trajectories are symmetrical with respect to the plane of the equator. The electrons thus describe loops near the northern pole, then “travel” to the southern pole, where they de—

* Prof. Störmer kindly placed his curves at my disposal even before publication, for which I sincerely thank him. The calculated and experimentally obtained curves agree with one another, insofar as they belong to one family of curves. One part of the calculated paths was too complicated for experimental representation. On the other hand, the experiment yielded paths that have not yet been found by calculation. (At present published in: Z. Astrophysik 1, 237, 1930.)

the very same loops coincide, and so on. There are, however, paths that are not symmetrical with respect to the plane of the equator, and moreover such that the successive “loops” do not correspond.

The space of the torus. The paths discussed pass together in close proximity to the boundary circle. If we draw the infinite set of possible paths that occur in nature all together, then they fill, outside the dipole, a region with a sharp boundary surface opposite the dipole. We obtain the reflecting surface of the torus, so important for the “echo of world space.” Its meridional curve can also be shown directly in experiment. In doing this, the terrestrial model is “shelled” not by a single ray, but by an entire bundle of such rays. As early as 1900, Birkeland successfully carried out such experiments.

It is impossible in any case to show the meridional curve quantitatively correctly, since the electronic “pillow” embraces the equator of the dipole on all sides, and the meridional curve disappears amid this “pillow” because it must be photographed through it. It was therefore necessary to abandon quantitative agreement and to choose a suitable position for the point source of electrons, with the aid of which the boundary curve appears clearly, although also too far from the sphere. Thus photograph 17 in Table 2 was obtained, where the electrons must be considered as coming from the right.

Near the earth the space of the torus certainly does not have such a sharp boundary, since the tacit assumption that what is involved is electronic radiation with a single velocity is hardly fulfilled. This boundary is also expressed differently in strength (intensity), probably practically disappearing entirely at certain moments. At the same time, assuming that the sun emits electrons, the very existence of the “torus,” and hence the possibility of using it with full justification to interpret the “echo of world space,” does not seem subject to doubt.

The experiments reported here have shown that those calculated by Störmer, down to details, are astonishing in their…

in the form of trajectories permit verification by model experiment. One may even say that, in originality and beauty, nature has surpassed the curves calculated by Störmer.*

LITERATURE

1. C. Störmer, Naturwissenschaften 17, 643, 1929; cf. also the first communication, 122, 681, 1928, and C. r. 187, (4), 811, 1928.

2. J. Hals, cited according to Störmer’s communication; cf. note 1.

3. V. d. Pol, Nature 122, 878, 1929.

4. Similar, though not so sharply expressed, echo delays were already known earlier. Cf. A. H. Taylor and L. C. Young, Prac. Inst. Radio Eng., 16 May 1928.

5. Kr. Birkeland, The Norwegian Aurora Polaris Expedition 1902/3, London, 1913.

6. J. B. Galle and G. Talon, and Ferrié, C. r. 190, 48, 1930; cf. J. B. Galle, Londe Electrique 9, 257, 1930.

7. C. Störmer, C. r. 190, 106, 1930.

8. Cf. also G. Ferrié, C. r. 190, 48, 1930.

9. V. d. Pol, Nature.

10. Brüche, in collaboration with W. Ende, Z. Physik 64, 180, 1930.

11. Cf. C. Störmer, Arch. Sci. Physic. natur. [4] 24, 862, 1907.

(Fig. 21.)

* Experimentally found periodic spatial trajectories have, since the writing of this work in August 1930, provided new confirmations of the theory and further, as yet theoretically uncalculated, forms of paths.