Laboratory Methods for Generating Fast Electrons and Protons

L. V. Mysovskii. Leningrad

The energy of the α-, β-, and γ-rays of radioactive elements reaches values of several million volts per electron. It is therefore quite natural that experimental physicists, in their striving to obtain radioactive radiations by artificial means, first of all sought, in order to achieve this goal, to obtain high potentials by laboratory methods. Until quite recently the most suitable instrument for this purpose could be considered the Tesla transformer, operating with spark excitation. The operating conditions of such a transformer have been examined by me in detail in the article “A Laboratory Method for Obtaining High Potentials.”* The same article describes the Tesla transformer with the aid of which the American physicists Breit, Tuve, and Dahl succeeded in obtaining a voltage of 5 million volts. In this case the length of the secondary spiral of the transformer was only 1 m, with a diameter of 8 cm. It would have been possible to go considerably further along the path of increasing the voltage. It was necessary only to resolve the question of how to retain these high potentials and how to introduce them into vacuum tubes. However, despite all the advantages of the Tesla transformer as a source of high voltage, it also has substantial shortcomings. First of all, the Tesla transformer, like any other, gives an alternating electromotive force, and consequently, if it is used for accelerating ions, one must speak not of the maximum electromotive force, but only of its effective value.

* References to the literature are at the end of the article.

Moreover, the interval of time during which the electromotive force acts in a given direction is very small (high-frequency currents).

In order to obtain a constant potential, and not an alternating one, several new and more or less original methods have been proposed. Before turning, however, to a description of the latest work in this field, we shall dwell briefly on yet another shortcoming of the Tesla transformer. If we speak not only of obtaining a high potential and of accelerating ions, but also have in mind using these accelerated ions for experiments on the splitting of atoms, then one must also reckon with another negative property of the Tesla transformer. In the article already cited above by us[^1], the reasons owing to which the Tesla transformer must operate under spark excitation were explained in detail. But under spark excitation the strength of the ion current will be comparatively small. Meanwhile, from experiments on the splitting of the atom by $\alpha$-rays we already know quite well that the probability of an $\alpha$-particle striking the atomic nucleus is very small, and therefore a large number of $\alpha$-particles is required in order to cause the splitting of a noticeable number of atoms. If, instead of using some radioactive substance, one takes a high-voltage installation as a source of fast ions, then it is evident that the splitting effect must be increased many times over, so that it can be observed with comparatively simple instruments placed near conductors charged to high potentials. On the other hand, the same experimental data on the splitting of atoms of elements by $\alpha$-particles have shown that there is no need at all to strive for very high potentials.

In the case of H-particles—protons—the potentials sufficient for splitting may be still lower, since it is much easier for a proton to penetrate into the nucleus of an atom than for a heavy $\alpha$-particle with two elementary charges. That is why, during the last two years, the attention of experimenters has been directed chiefly toward obtaining a powerful and constant beam of protons.

PRODUCTION OF FAST PROTONS BY MEANS OF A TESLA TRANSFORMER

Despite the above-mentioned shortcomings of the Tesla transformer, Tuve, Hafstad, and Dahl² nevertheless succeeded, by means of their transformer, in obtaining fast protons in a quantity sufficient not only to establish the fact of their appearance, but also to carry out some measurements. The apparatus and the discharge tube have already been described by us in the article cited above, to which we refer those wishing to become acquainted in detail with the experimental particulars. Tuve, Hafstad, and Dahl, in a letter published in Phys. Review², also refer fully to their original work with the Tesla transformer and describe only modifications in the tube that served for observing protons. The observations themselves were conducted in two ways: 1) by the method of Thomson parabolas; 2) with the aid of a Wilson chamber. Observing on a fluorescent screen the trace of a beam of protons deflected by magnetic and electric fields, the authors were able to establish that both \( \mathrm{H}^{+} \) and \( \mathrm{H}_{2}^{+} \), which had traversed a field of 1 million volts, occurred in the beam. Attempts to photograph the parabolas were not successful, since not only the trace of the beam but also the remaining parts of the screen fluoresced rather strongly under the influence of scattered electrons and light rays falling on the screen. As for the source of the protons, in the authors’ opinion the protons were obtained from hydrogen occluded by the electrodes, and also from the gas remaining in the discharge tube after evacuation.

The use of a Wilson chamber for observing proton tracks in a gas supersaturated with vapor at first also proved not especially successful. In order that the protons might pass from the tube into the chamber, openings were made in both, separated by a thin sheet of mica. Since the chamber was situated in the immediate vicinity of the discharge tube, not only protons but also fast electrons entered it through the mica window (it should not be forgotten that the Tesla transformer gives an alternating

electromotive force and, consequently, in the discharge tube ions of both signs were subjected to acceleration). When, with the aid of a magnetic field, the electrons were deflected away from the mica window, it turned out that there still remained X-rays, which in large quantity penetrated from the discharge tube into the Wilson chamber and produced intense ionization in it. Against the background of the fog formed by the X-rays, it was no longer possible to trace with sufficient definiteness the tracks of individual protons. In order to increase the number of protons an attempt was made to obtain them, according to the recipe of Dempster–Ramsauer, from lithium bombarded by electrons under a voltage of 50 V. However, the number of protons reaching the mica window from this source was so small that this arrangement had to be abandoned. Instead of improving the tube, Tuve, Hafstad, and Breit² decided to protect the Wilson chamber more carefully from X-rays. For this purpose they placed between the chamber and the tube a thick layer of absorbing material, leaving free a passage through a window for the protons. For deflecting electrons and slow ions a magnetic field was still used. Under these conditions the apparatus already gave quite definite results. Since the mica in the window had a stopping power of 1.8 cm of air, the protons entered the Wilson chamber already somewhat weakened, but nevertheless their tracks appeared quite distinctly. The number of protons observed in the chamber was different for each expansion and varied from 1 to 200. With a large number of protons (about 200) it was no longer possible to distinguish individual tracks, but the general character of the beam left no doubt as to the presence of protons. Since the protons moved under the influence of a variable electromotive force and, moreover, began their motion in different parts of the tube, the velocities of the protons entering the chamber were different. For greater definiteness of the measurements, protons with the maximum range were taken. The maximum range of a proton in air, reduced to normal conditions of temperature and pressure, proved to be equal to 2.8 cm, which is in sufficiently good

corresponds to an applied field of 1 million volts. It should be noted, however, that the authors themselves apparently regard the results they obtained as not especially reliable. At the end of their letter they point out that with a Tesla transformer and with their tube it is very difficult to obtain exact quantitative data. In their next work, Tuve, Hafstad, and Dahl intend to obtain fast protons and to make more accurate measurements by using, instead of a Tesla transformer, a Van de Graaff electrostatic generator. We shall say a few words later on about what this generator is and what its advantages are.

THUNDERSTORM DISCHARGES AS SOURCES OF HIGH VOLTAGE

The idea of using thunderstorm discharges to obtain a large potential difference occurred to the German physicists Brasch and Lange as early as 1927. At that time, works on obtaining high potentials by means of a Tesla transformer had not yet been published, nor were there works with other types of high-voltage generators, except for purely technical ones. Since Brasch and Lange set themselves the goal of obtaining ions with kinetic energy of several million volts, it seemed to them that the work could be considerably shortened by making use of the already existing enormous potential found in nature. It was only necessary to lead this potential into a laboratory adapted for this purpose and connect it to the discharge tube. Brasch and Lange indicate that usually, depending on the season, the fall of potential in the atmosphere varies from 200 to 400 volts/m. During a thunderstorm, however, the gradient can increase by more than a thousandfold. Thus, already at a height of some 100 m one could confidently expect potentials of at least on the order of 10 million volts. The principal question that had to be resolved first of all was the choice of a suitable location. Without dwelling on the various conditions that this place had to satisfy,

...we shall indicate here only that, after consultation with meteorologists, Brasch and Lange finally settled on Monte Generoso, near Lugano. Nor shall we dwell on the individual stages of the work and the difficulties that had to be overcome in assembling this ultra-high-voltage installation under unusual natural conditions*; we shall describe only the final installation 3, on which it proved possible to obtain the most powerful discharges. Schematically this installation is shown in Fig. 1, where \(d\) represents, in perspective, the antenna fastened between two summits of Monte Generoso, situated

Fig. 1.

660 m apart. To prevent the formation of a corona, hollow beads were strung on the voltage-carrying cable \(b\). Each bead was a hollow cylinder of galvanized sheet iron, about 2 m long. At the ends of the cylinders there were brass hemispheres, in the centers of which holes had been drilled for the pas—

* As the authors report, initially the work was undertaken by three physicists: Arno Brasch, Fritz Lange, and Kurt Urbano. In the summer of 1928, during work on Monte Generoso with Kurt Urbano, an accident occurred that resulted in the death of this collaborator.

of the cable. The diameters of the beads gradually increased as the cable descended toward the ground. In the upper parts the diameter of the cylinders was 2 cm; in the parts of the conductor nearest the ground, it reached 90 cm. The installation of the latter, largest beads is shown in Fig. 2. Let us now return again to Fig. 1.

The letter \(H\) denotes the last bead, which at the same time served as the high-voltage pole. The part of the cable \(a\) was intended only to support, at a certain height, the pole \(H\) and therefore had to be sufficiently well insulated. A double garland of insulators, directly adjacent to the last beads, is shown in Fig. 3. The number of these insulators had to be increased as the highest potentials were approached. However, when the number reached 120, the antenna ceased to withstand the voltage, and in the final experiments small garlands were left only in the places closest to the discharge point; in the remaining places they were replaced by non-soaking linen rope. The second pole \(E\) (Fig. 1) was suspended in an analogous manner somewhat higher on two ropes, the insulating one \(a\) and the conducting one \(b\). Through

Fig. 2.

Fig. 3.

Fig. 4.

the conducting cable to pole \(E\) was connected to ground. To observe the discharges and to regulate the magnitude of the spark gap \(HE\), a special room of corrugated sheet iron, \(4 \times 3 \times 2\ \text{m}^3\) in size, was built near the antenna (Fig. 4). The floor in this little house was also made of metal. Therefore the entire body of the house could be led to ground by means of a special cable serving to divert lightning strokes. While in this house, one could calmly observe the discharges between the poles and, by means of tensioning the cable, change the magnitude of the spark gap. The minimum distance between the poles was \(2\ \text{m}\), the maximum \(18\ \text{m}\). In the opinion of Brasch and Lange, a discharge between poles located at a distance of \(18\ \text{cm}\) corresponded to a potential difference of from 14 to 16 million volts. Thunderstorm potentials were not applied to the discharge in the vacuum tube, and the experiments described here must be regarded as a continuation of Franklin’s investigations, carried out more thoroughly and with modern technical means. To obtain fast ions, Brasch and Lange used another, already purely laboratory, apparatus, to the description of which we now turn.

IMPULSE GENERATOR

The impulse generator, in its operating conditions and in its coefficient, resembles a Tesla transformer operating under impulse excitation. Under impulse excitation of a Tesla transformer, the energy \(W\) stored in the primary circuit with capacitance \(C_1\) passes, under the most favorable conditions,\(^1\) almost entirely into the secondary circuit with capacitance \(C_2\). Consequently, we have the equality:

\[ W=\frac{C_1 V_1^2}{2}=\frac{C_2 V_2^2}{2}. \]

Hence the maximum attainable transformation coefficient is:

\[ S=\frac{V_2}{V_1}=\sqrt{\frac{C_1}{C_2}}. \]

During operation of the impulse generator, the energy \(W\) is first distributed uniformly among capacitors of capacitance \(C_1\), connected in parallel, and then the same energy is distributed among the same capacitors, but connected in series. Writing the equality:

\[ W = nC \cdot \frac{V_1^2}{2} = \frac{C}{n}\frac{V_2^2}{2}; \]

and assuming

\[ nC = C_1 \quad \text{and} \quad \frac{C}{n} = C_2, \]

we obtain

\[ C_1 \cdot \frac{V_1^2}{2} = C_2 \cdot \frac{V_2^2}{2}, \]

the maximum transformation coefficient (neglecting losses) in this case will be equal to:

\[ s = \frac{V_2}{V_1} = n, \]

or, introducing

\[ C_1 \quad \text{and} \quad C_2,\quad \text{we find} \quad s = \frac{V_2}{V_1} = \sqrt{\frac{C_1}{C_2}}, \]

i.e., the same transformation coefficient as in a Tesla transformer.

As an example, Brash and Lange cite an installation (Fig. 5) at the Physical Institute in Berlin. This installation consists of 20 glass plate capacitors, each with a capacitance of 30,000 cm. The capacitors are connected in pairs into ten elements, which are then switched by means of spark gaps from parallel connection to series connection. As a result, the potential is raised from 90,000 volts to 900,000. The circuit for switching the capacitors is shown in Fig. 6. This figure schematically depicts a high-voltage impulse generator of the firm AEG for 2.4 million volts. Its capacitance, with the capacitors connected in series through spark gaps, is 4000 cm. The duration of the discharge is from \(10^{-7}\) to \(10^{-4}\) sec. at a voltage of \(2.4 \cdot 10^6\) V and with a current during this interval of time of about 1000 A. Brash and Lange report that a generator of the same type is being built

At the Berlin Physical Institute, for \(7 \cdot 10^5\) V. This generator consists of a battery of capacitors immersed in an iron tank filled with oil. The pressure inside the tank can be brought up to 6 atm (to increase the insulating capacity of the oil). 70 spark gaps are located inside the tank, but their poles do not come into contact with the oil; instead, they are placed in special small chambers with compressed air.

Fig. 5.

The tips of the gaps had to be placed in air because in oil it is difficult to obtain simultaneous operation of all the spark intervals. In addition, by changing the air pressure in the chamber, it is possible to regulate

the magnitude of the discharge potential. Let us now turn to protecting surrounding rooms from the effects of discharges of the impulse generator. Powerful discharges of high-voltage installations cause waves to appear in surrounding conductors, under the action of which incandescent lamps, fuses, and even wires burn out. It is quite easy to protect against this unpleasant phenomenon. According to Brasch and Lange, it was sufficient to paste over the room in which the impulse generator was located with aluminum foil, of thickness

Fig. 6.

1/100 mm, for all these phenomena in adjacent rooms to cease. Concluding the description of the impulse generator, we shall point out that in the USSR we also already have assembled impulse generators which, in voltage magnitude, are analogous to the generator of the Berlin Physical Institute. For example, such a generator is located in the Physical Institute of Leningrad University, in the laboratory of Prof. P. I. Lukirskii. The operation of this generator produced the same unpleasant consequences in adjacent laboratories, and therefore the room in which the generator is located also had to be lined from the inside with metal sheets. Everything said about protecting the impulse generator applies, of course, to other high-voltage installations as well, for example, to the Tesla transformer.

L. V. MYSOVSKII

THE PLATE DISCHARGE TUBE OF BRASCH AND LANGE

Having high potentials at their disposal, Brasch and Lange undertook the construction of a discharge tube. As is known, technical medical tubes for irradiation with Roentgen rays, in the best case, withstand 300,000 V. Brasch and Lange applied gradually increasing potentials to such tubes immersed in oil, but did not obtain definite results. In some cases it was possible to raise the potential to 1 million

Fig. 7.

volts. However, for the most part, already at 300–350 kV a discharge began. In order to avoid a discharge in the gas, it is necessary to eliminate impact ionization. If all electrons are deflected by a magnetic field, then impact ionization will cease, but a new difficulty arises. The deflected electrons, settling on the walls of the tube, can greatly change the distribution of potential. It is therefore necessary not only to deflect them to the side, but also to remove them from the walls of the tube. For this purpose Brasch and Lange placed a series of nickel spring rings along the discharge tube. The walls of the tube were made not of glass, but of thick porcelain. The internal diameter of the tube was 8 cm, and the external 13. The length of the tube was calculated so that between neighboring rings the potential difference did not exceed 3000 V and so that a discharge could not occur between

external ends of the tube. Therefore, for example, the tube for \(1 \cdot 10^6\) V had to be made \(3\ \text{m}\) long, and about 300 rings had to be placed inside it, so that the distance between two neighboring rings was approximately \(1\ \text{cm}\). A segment of this tube is shown in schematic Fig. 7. In this figure the letters \(a\) denote nickel rings, and the letters \(b\) the pole pieces of magnets that served to deflect the electrons. When such a tube was tested at a voltage of 950 kV, it turned out that, at this voltage, impact ionization really did not occur in it. But the most striking circumstance was that the tube worked equally well both with the magnetic field and without it. Brasch and Lange concluded from this that the proper operation of the tube at high voltage was hindered not by discharges in the gas, but by discharges along the walls. Proceeding from this, they constructed a distinctive plate discharge tube for a voltage of 2.4 million volts. This tube is shown schematically in Fig. 8. In order to make the path of the sliding discharges from one metal ring to another as long as possible, without increasing but, on the contrary, while decreasing the length of the tube, Brasch and Lange tried to assemble the entire tube from several washers. In Fig. 8, the letter \(a\) denotes an aluminum washer, the letter \(b\) a washer of presspahn, and the letter \(c\) a rubber ring. The sequence in which they are assembled—

Fig. 8.

the washer was visible from Fig. 9. On both sides of the column of washers thick copper plates were placed. In the lower plate, connected to earth, a hole had been made, onto which a tube was fitted with an anticathode, a branch for pumping out, and a vessel for freezing out vapors.

Fig. 9.

Rubber rings were used in order to make the contact between the individual washers airtight. The metal washers had a smaller diameter of the inner opening, and thus, during discharge in the tube, protected the insulators from impacts of ions. In the last model of such a tube, designed for 2.4 million volts, the presspan was replaced by cel-

lon*. Before evacuating the tube, the washers were pressed against one another by a special device, which after pumping was removed, since the washers were then held with sufficient strength by atmospheric pressure. Strange as it may seem at first glance, the evacuation of such a tube presented no particular difficulties. By selecting certain grades of rubber, replacing presspan with cellon, and intensively condensing vapors with the aid of liquid air, it was possible to avoid spontaneous ionization of the residual gas even at a potential difference of 2.4 million volts. In Fig. 9, at the center, the final model of the plate tube is shown, with devices for pumping and for compressing the washers. The tube is connected to the surge generator AEG at \(2.4 \cdot 10^6\) V. On the right are visible the spheres of the spark gap, which served for measuring the voltage. On the left stands a hollow cylinder made of presspan, in which the tube was placed during operation. The space between the outer surface of the tube and the walls of the cylinder was filled with transformer oil. This was done in order to eliminate the possibility of external discharges.

OPERATION OF THE PLATE TUBE

The plate tube received from the generator about two pulses per second. The cathode rays that appeared thereby struck the anticathode and produced hard X-rays. To measure their hardness, Brasch and Lange used lead dishes placed one on top of another in a quantity of 22. The thickness of each such dish was 5 mm, so that together they constituted an absorbing layer of 11 cm. Between the dishes X-ray films were inserted, as shown in Fig. 10. By photometering the negatives obtained, it was not difficult to establish that the half-absorbing layer for the X-rays was equal to 0.8 cm; in other words, their hardness was

* A transparent film, resembling celluloid in appearance, but nonflammable. Recently it has also begun to be manufactured in the USSR.

already of the order of the γ-rays of radioactive elements. The intensity of these rays can be judged from the exposure time. To blacken a film placed behind 10 cm of lead, only 100 discharges of the generator were required. If one assumes that each discharge lasts \(10^{-4}\) sec., then the true exposure time turns out to be only 0.01 sec. The intensity of the cathode beam can be judged from the destructions that were observed on the anticathode.

Fig. 10. Diagram labels: “film,” “lead,” “black paper.”

Fast electrons, penetrating into the anticathode, at the end of their path caused sudden and intense heating of its inner parts. Owing to this, metal vapors formed inside the anticathode, causing bubbles to swell up on its surface. Often these bubbles burst and were pulverized.

In addition to cathode rays, Brasch and Lange also obtained canal rays from their tube. To obtain them they introduced, through steatite capillaries inserted into a copper plate on the high-potential side, water vapor at a pressure of 0.01 mm. Water vapor was chosen for the reason that its excess was easily frozen out and, consequently, did not spoil the vacuum. Experiments with canal rays were carried out only at a voltage of 900 kV. The range of the canal rays in aluminum was measured and proved to be equal to 8 μ. Brasch and Lange propose in the near future to carry out experiments with positive rays in a tube with \(2.4 \cdot 10^6\) V and an exact measurement of the range of such rays.

OBTAINING FAST IONS WITHOUT THE AID OF A HIGH POTENTIAL

The successes in obtaining high potentials achieved by means of the Tesla transformer and the surge generator so interested experimenters that proposals and even experimental works began to appear,

...which were based on entirely different principles. Very interesting in this respect is the work of Sloan and Lawrence,^4 in which fast positive ions with an energy of 1,260,000 were obtained with the aid of a potential of 42,000 V. The essence of the method proposed by the above-mentioned experimenters consists in the fact that one and the same ion passes successively through several electric fields with one and the same potential difference. Suppose that, after passing through the first field, the ion has acquired the energy \(\frac{m}{2}v_1^2\). After passing through the second field, the ion will have the energy \(\frac{m}{2}\cdot 2v_1^2\), through the third \(\frac{m}{2}\cdot 3v_1^2\), and so on. After passing through \(n\) fields its energy will be equal to \(\frac{m}{2}nv_1^2\). Let us denote the final velocity of the ion by \(v_f\); then from the equality \(\frac{m}{2}v_f^2=\frac{m}{2}nv_1^2\) we obtain \(v_f=\sqrt{n}\,v\). Thus the velocity of the ion will increase in proportion to the square root of the integers. Proceeding from this relation, Sloan and Lawrence constructed the apparatus shown schematically in Fig. 11. The source of ions was a mercury arc (the spherical tube in the lower left part of the figure). Electrode \(A\), which was a hollow tube about 8 cm long, charged to a negative potential of 10,000 V, drew in the positively charged mercury ions and directed them along the axis of the instrument. In order to reduce the divergence of the beam, adjacent to \(A\) there was another tube (the focusing electrode) of the same length, but charged to a lower potential, from 15,000 to 20,000 V. The edge of this tube facing \(A\) was sharpened in order to create a nonuniform field symmetric about the axis of the tubes. Passing through this field, the beam was straightened out and reached the accelerating electrodes already approximately parallel. The system of accelerating electrodes consisted of a series of tubes whose lengths increased in proportion to the square root of the integers.* Each—

* Strictly speaking, by the length of a tube one must understand the tube and the adjacent gap.

for the pair of these tubes was connected to opposite terminals of a tube generator with a power of 20 kW. The interval of time required for an ion to pass through any tube was equal to one half-period of the generator oscillations. Thus the ion always entered a tube with a negative potential, but left it only when this tube had already become positive. After

Fig. 11.

passing through thirty such tubes the energy of the ion increased from 42,000 V (the maximum voltage of the generator)* to

\[ 42 \times 30 = 1\,260\,000\ \mathrm{V}. \]

Undoubtedly, the greatest experimental difficulty that Sloan and Lawrence had to overcome in assembling the apparatus consisted in synchronizing the entire sys—

* As can be seen from Fig. 11, the voltage of 42,000 V was obtained by means of a Tesla transformer operating with galvanic coupling on damped oscillations.

systems. After the accelerators had been constructed according to the calculations, it would have been possible, by changing the distance between them, to achieve maximum acceleration of the ions. The maximum current would then have served as an indication that synchronism had been attained. However, moving the accelerator in such a complicated apparatus proved to be so difficult a task that it had to be abandoned. Instead, to change the phase, additional self-induction coils were introduced, and their effect on the ion beam was studied by means of a deflecting electric field placed behind the last accelerator (see Fig. 11, upper right).

Fig. 12.
Ion current in amperes \(\times 10^8\); deflecting potential.

This field was produced between two plates placed at a distance of \(1\ \mathrm{cm}\) from one another. The length of the plates was \(20\ \mathrm{cm}\). A potential difference was applied to these plates sufficient to deflect the ion beam by \(3^\circ\) and thus direct it into the Faraday cylinder located at the end of the tube. By measuring the accumulation of charge on the Faraday cylinder, it was possible to calculate the current strength, and, knowing the potential difference, it was also possible to determine the velocity of the mercury ions. In order that the negative electrons should not be able to enter the cylinder and affect the measurement, they were deflected by the magnetic field of two coils placed outside the tube (Fig. 11). The result of one such measurement is given in Fig. 12, which shows how

the change in self-induction affected the strength of the current. Along the ordinate axis is plotted the current strength in the beam in amperes, multiplied by \(10^8\). Along the abscissa axis are plotted the potential differences on the condenser that served to deflect the beam. The central curve corresponds to the most suitable value of the self-induction. When the self-induction is increased \((+L)\), and also when it is decreased \((-L)\), the curves have smaller maxima. The dependence of the ion energy on the generator frequency in the final setup is shown in Fig. 13. From

Fig. 13.

this figure it is seen that a potential of \(1\,260\,000\ \mathrm{V}\) could be obtained only at a wavelength of \(30\ \mathrm{m}\). Let us also note that in practice it proved unnecessary to select the self-induction for each accelerator separately. In Fig. 10 we see that for the first ten accelerators only one self-induction is introduced (the letter \(L\) in Fig. 10). No other special difficulties were encountered in carrying out this setup. We have already described the focusing of the beam near the mercury arc. Further along its path the beam, passing through nonuniform fields between the accelerators, became more and more parallel. Since the potential in the tube nowhere

did not exceed 42,000 V, obtaining a sufficient vacuum also presented no difficulties. With the aid of two condensation pumps, a pressure of \(10^{-5}\) mm of mercury was maintained in the tube with the accelerators. The pressure of mercury vapor near the arc was \(10^{-3}\) mm.

Since all the described acceleration experiments were carried out with mercury ions, the total length of the tube was small, only about 114 cm. Quite different dimensions would be obtained if one attempted to construct an apparatus of the same type for obtaining protons with the same energy of 1,260,000 V. In that case the velocity of the ions would be almost 15 times greater; consequently, the accelerators would have to be just as many times longer. Thus, to obtain protons with an energy of 1,260,000 V, a tube approximately 20 m long would be required. A corresponding lengthening of the accelerating system will also be obtained if we pass to faster mercury ions. Sloan and Lawrence calculate that, in order to obtain a mercury beam with an energy of 10 million volts, the length of the tube will be 8 m. This length will be reduced only if the ions are accelerated not with one charge, but with two or three. It is possible that an apparatus of this type would be much easier to use for accelerating \(\alpha\)-particles from radioactive elements. Since their mass is 4 times greater than the mass of protons, and they already possess an energy of several million volts, all this taken together would considerably shorten the system of accelerators, while at the same time we would obtain beams with which the nuclei of atoms could be acted upon with greater force.

Synchronous accelerator with a magnetic field

In order to eliminate the principal difficulty arising in the synchronous acceleration of light ions—namely, the extremely great length of the accelerating system—Lawrence and Livingston placed the accelerator in a strong magnetic field. Figure 14 gives a complete idea of the basic conception of this experiment. The accelerator \(AB\) is a

constitutes a hollow metallic cylinder cut along the diameter \(abc\). The halves of the cylinder are connected to the terminals of a tube generator and, thus, along the line of the cut an alternating potential difference is obtained. The magnetic field is directed perpendicular to the bases of the cylinder (see \(H\) in the upper part of the figure). If an ion at some

Fig. 14.

instant of time receives acceleration from the electric field near \(a\) in the direction indicated in the figure by the arrow, then its further path in half of the disk \(A\) will be a semicircle \(ab\). If the time it needs to traverse the semicircle is equal to the half-period of the generator, then near \(b\) the ion will again receive acceleration and in part \(B\) will describe a semicircle of larger radius \(bc\), etc. In order to obtain a more precise representa-

...conception of the path of the ion, let us write the equation of its motion in a magnetic field:

\[ \frac{mv^2}{r}=\frac{Hev}{c}. \]

With the aid of this formula we can find the time \(t\) required to traverse a semicircle:

\[ t=\frac{\pi r}{v}=\frac{\pi mc}{He}. \]

As we see, the time \(t\) is determined only by the mass \(m\) of the ion, its charge \(e\), and the applied magnetic field \(H\). This time does not depend on the radius \(r\) or the velocity \(v\). Since \(t\) is the half-period of the generator oscillations, for a given \(H\) we can calculate the wavelength needed for synchronism. This length will be:

\[ \lambda=2t\cdot c=\frac{2\cdot\pi mc^2}{He}. \]

From this formula we obtain, for example, that for a proton in a magnetic field of 10,000 gauss the wavelength of the generator must be \(19.4\ \text{m}\). Let us now calculate the energy that the ion will acquire in traversing a circumference of radius \(r\). If we denote by \(V_0\) the maximum value of the generator potential, then this energy will be equal to:

\[ e\cdot\frac{V_0}{300}=\frac{mv^2}{2}=m\frac{H^2r^2}{c^2}\cdot e^2. \]

Or, expressing this energy in volts per electron:

\[ V_0=150\cdot\frac{H^2r^2}{c^2}\cdot\frac{e}{m}. \]

Thus the energy will be proportional to the square of the magnetic field and to the square of the radius.

In practice it proved most expedient to take, instead of the two electrodes described above, only one \(A\) (Fig. 15). This electrode was a hollow half-cylinder with a diameter of \(24\ \text{cm}\) and a height of \(1\ \text{cm}\). Its walls were made of very thin brass. Electrode \(A\) was plac...

was placed in a box made of red copper, but was not sufficiently well polished. The internal dimensions of the box were \(26\times 28.6\times 28.6\ \mathrm{cm}^3\). A plate with a slit \(s\), metallically connected to the box, served as the second electrode. The width of the slit was \(1\ \mathrm{cm}\). Electrode \(A\) and the entire box were connected to opposite terminals of the generator.

Labels in Fig. 15: copper-to-glass seals; hydrogen; to the pump; window; deflecting potential; electrometer; filament heating \(12\ \mathrm{v}\); \(150\ \mathrm{v}\); \(110\ \mathrm{v}\).

Fig. 15.

As a result, between the slit \(s\) and the edges of the semicylinder there was obtained the same accelerating field as should have been obtained between two semicylinders. To obtain hydrogen ions, the gas located at the center of the apparatus was ionized by electrons emitted from the heated filament. The position of the filament with respect to electrode \(A\)

schematically shown in the upper part of Fig. 14. Having passed through the last circumference, the ions had to pass through a series of slits \(aa\), located in the lower part of the apparatus (Fig. 15). The slits served to filter out ions whose velocity, in magnitude or direction, could change owing to collision or reflection. Between two slits there was placed a deflecting electric field, produced by the plates \(D\). After deflection, the beam of ions entered the Faraday vessel \(C\). The charge of this vessel was measured with an electrometer. A photograph of the internal parts of the box is given in Fig. 16.

Fig. 16.

One of the most difficult tasks in the Lawrence and Livingston apparatus was the creation of an extensive, sufficiently strong, and uniform magnetic field. The poles of the electromagnet, which was made for this apparatus, were 27.5 cm in diameter, and the distance between them was 3.75 cm. The magnetomotive force was produced by two coils, each of which had 2000 turns. With the aid of this electromagnet it was possible to obtain—

Fig. 17.

obtain a field strength of 14,000 gauss. The pole surfaces were made parallel to one another with an accuracy of up to 0.2%. Investigation of various parts of the field by means of a bismuth spiral showed that the field was in fact completely homogeneous and uniform, with the exception of the region lying less than 2.5 cm from the periphery.

Fig. 18.

The successive passage of a proton beam through the field between the electrodes in the apparatus with a magnetic field produced the same focusing effect as the passage of the fields by mercury ions between the separate accelerators in the apparatus described by us earlier. For greater clarity, Lawrence and Livingston give a diagram of the motion of a positive ion in the field between the electrodes. The velocity of the ion in region \(A\) (before acceleration) is less than in region \(B\) (after acceleration), and therefore its deviation toward the line \(AB\) in the first half (Fig. 17) is greater than its deviation from \(AB\) in the second. It was established by special experiments that the focusing brings all the fast protons together into a beam having a width of only 1 mm.

The accuracy of operation of the Lawrence and Livingston apparatus (its general appearance is shown in Fig. 18) may be judged from the curves they obtained. These curves are shown on

Fig. 19. The upper curve was calculated from the formula:

\[ \lambda = \frac{2\pi mc^2}{He} \]

for \(H_2^+\), the lower one for \(H^+\). Along the ordinate axis are plotted the wavelengths in meters; along the abscissa axis, the magnetic fields in gauss that gave the maximum current values (as measured from the charge on the Faraday cylinder). The circles mark the values observed experimentally. As can be seen from the figure, all the experimental points lie on the theoretical curves.

Fig. 19.

An idea of the operation of the apparatus under various conditions is given by another figure, Fig. 20 (a drawing analogous to that for the apparatus with accelerators). The abscissas of Fig. 19 represent the deflecting potentials in volts, and the ordinates—the strength of the proton current in amperes, multiplied by \(10^9\). From the curves of this figure we see that the best result, namely a beam of protons with an energy of \(1\,220\,000\ \mathrm{V}\), is obtained at

\[ \lambda = 14.1\ \mathrm{m}. \]

Fig. 20.

In the near future Lawrence and Livingston expect, by means of a magnet with poles \(114\ \mathrm{cm}\) in diameter and with the same field strength of \(14\,000\) gauss, to obtain a stream of ions with an energy of 25 million volts.

Electrostatic High-Potential Generator

Unfortunately, the literature contains such scant information about the electrostatic generator (brief summaries in the proceedings of the American Physical Society) that only a few words can be said about it. Van de Graaff, who proposed this generator, made use of the basic fact of electrostatics concerning the distribution of charge on the surface of a conductor. This circumstance, as is known, can be used to transfer the entire charge of a small conductor to another conductor, larger in size and hollow inside. For complete transfer it is sufficient to touch, with the charged body, the inner surface of the hollow conductor; moreover, it is entirely immaterial to what potential such a hollow conductor is charged. Van de Graaff improved this elementary experiment in the following way. He mounted two hollow copper spheres, 60 cm in diameter, on Pyrex rods. Inside each sphere there was a pulley. At the lower end of the Pyrex rods there was also one pulley each. The outer pulleys were driven by a motor into rapid rotation. Over the pulley located inside and outside the sphere, and through an opening made in it, a silk belt was passed. The surface of the belt rising upward, by means of a brush connected through a kenotron to a transformer, was charged to a potential of 10,000 V. At the upper pulley this charge, by means of points, flowed onto the inner surface of the sphere. By charging in this way both spheres with opposite electricity, Van de Graaff succeeded in obtaining a potential difference of 1,500,000 V. The advantage of this installation is the constancy of the potential. With such a potential one can obtain a beam of protons moving with completely identical and constant velocities. This is why Tuve, Hafstad, and Dahl regard the electrostatic generator as the most suitable source of high voltage in work aimed at giving exact numerical values of quantities relating to protons. Let us note,

that Van de Graaff, having obtained only 1,500,000 V on his first installation, intends to go further along the path of increasing the potential. For this purpose he will need only to prepare spheres of larger diameter.

CONCLUSION

In the present review we have mentioned and discussed in greater or lesser detail four different installations. All of them were intended for obtaining fast ions, chiefly fast protons. Each of these installations has both its advantages and its disadvantages. The Tesla transformer is distinguished by the simplicity of its construction and by the possibility of easily solving the problem of introducing a high potential by placing the secondary coil directly in the discharge tube. The disadvantages of the Tesla transformer—and very substantial ones at that—are alternating voltage and the phenomena associated with high-frequency currents (for example, leakage from all nearby metallic objects).

The impulse generator is even simpler in construction, since it is, if one may put it so, only the primary circuit of a Tesla transformer (more precisely, the capacitance of the primary circuit). However, although the impulse generator gives, during periodic discharge, a potential of one sign, this potential is nevertheless not constant. In addition, for the acceleration of protons it requires the construction of a special discharge tube in which sliding discharges must be eliminated. The synchronous ion accelerator compares favorably with other installations in that it does not require a special discharge tube or an especially high vacuum, since all its operation takes place at potentials of only a few thousand volts. Another very important advantage of the synchronous accelerator is the almost ideal focusing of the ion beam. The disadvantages of the synchronous accelerator are its complexity and the dimensions of the magnetic field (or of the system of accelerators in an installation without a magnet). The electrostatic generator is simple, gives a constant po-

potential, but it is inconvenient in a laboratory setting because of the size of its spherical electrodes. It can hardly be doubted that each of these installations is quite suitable for producing a beam of protons with which one could act upon atomic nuclei. It is not accidental, however, that the first artificial disintegration of atoms by a beam of protons was achieved by Cockroft and Walton7, 8, 9 by means of a simple high-voltage transformer, the current from which was rectified and the potential oscillations smoothed by connecting capacitors.

In conclusion, let us note that although the remarkable and most successful work on splitting the atom was carried out with the aid of a simple high-voltage transformer, further work on the disintegration of heavier elements will undoubtedly require the use of protons of higher energy. It is therefore to be expected that, in the near future, installations designed to obtain fast protons will be developed by physicists with still greater intensity and thoroughness.

Literature

1. L. V. Mysovskii, Laboratory methods for obtaining high potentials, Uspekhi Fiz. Nauk, 1930, X, issue 4, p. 545.
2. M. A. Tuve, L. R. Hafstad, O. Dahl, Phys. Rev. 39, 384, 1932.
3. A. Brasch u. J. Lange, Zeitschr. f. Phys. 72, 10, 1931.
4. D. H. Sloan, and E. A. Lawrence, Phys. Rev. 38, 201, 1931.
5. E. O. Lawrence, and Livingston, Phys. Rev. 40, 19, 1932.
6. R. S. van de Graaff, Schenectady Meeting Am. Phys. Soc., 1931.
7. Cockroft J. J. a. E. T. S. Walton, Proc. Royal Soc., A, 129, 477; 1930.
8. Cockroft J. J. a. E. T. S. Walton, Nature 1932, February 13, p. 242.
9. Cockroft J. J. a. E. T. S. Walton, Nature 1932, May 7, p. 446.