PROTON SYNCHROTRON

E. J. Lofgren*)

In 1910 and 1911 Geiger and Marsden carried out a series of experiments aimed at investigating the structure of the atom. They passed a narrow beam of $\alpha$-particles through a thin gold foil and observed the distribution, by direction, of the $\alpha$-particles emerging from the foil. Most of the particles were scattered through small angles. However, a certain number of particles were deflected through very large angles (about 0.01% of the $\alpha$-particles were deflected through angles exceeding 90°). This result was in complete contradiction with any notion of a continuous structure of the atom, for example, with the idea of a uniform distribution of positive charge in which electrons are embedded. Rutherford proposed an entirely different model of the atom, in which the positive charge and the greater part of the mass are concentrated in a central sphere with a radius equal to one-tenth of the radius of the whole atom. The close approach, occurring in rare cases, of the incident particles to this central nucleus leads to large deflections. In this way it was possible to explain quantitatively the experiments of Geiger and Marsden. This was the beginning of the modern theories of the structure of atoms and nuclei. Since then, and especially after 1930, one of the principal methods for studying the structure of the nucleus and its properties has consisted in bombarding the nucleus with beams of various particles. A survey of the leading ideas of nuclear physics lies beyond the scope of this article. Its purpose is to describe methods for obtaining bombarding particles. The natural sources of high-energy particles, apart from cosmic radiation, are the alpha and beta radiations of radioactive substances. $\alpha$- and $\beta$-particles possess energies of the order of several million electron-volts. As nuclear research developed, the need arose to obtain particles with higher energies, as well as fast particles of a different nature. Experimental investigations were hindered to a considerable degree by the limited possibilities of controlling the direction, intens-

*) E. J. Lofgren, Science 111, 235 (1950). Translated by V. A. Troitsky.

PROTON SYNCHROTRON

...velocity and energy of fast particles from natural sources. In order to expand the possibilities of experiment, a number of particle accelerators were developed. Table I lists the principal ones among these accelerators. By the first half of the 1930s the development of the first three types of accelerators had been brought in nuclear physics to the point of successful application. The construction of the betatron was completed in 1940. The next three accelerators were mastered in 1946, 1947, and 1948. The designs of all these machines continue to be improved at the present time. Since with their aid it is possible to accelerate various particles and to obtain different ranges of energies and intensities with varying degrees of control, each of these installations supplements rather than replaces the preceding one. As studies of the nature of cosmic radiation developed, achieving especially great successes in recent years, it became clear that cosmic radiation is a rich source of fast particles suitable for nuclear research. The study of cosmic radiation led to the discovery of the positive electron, to the detection of the family of mesons, and gave experimental confirmation of certain propositions of electrodynamics. Cosmic-ray particles may possess energies up to \(10^{16}\)—\(10^{17}\) electron-volts (if one assumes that the extensive showers of Auger are caused by a single primary particle). Primary particles of cosmic radiation fall from outer space onto the boundary of the earth’s atmosphere in an amount equal to approximately 0.6 particle per \(\mathrm{cm}^2\) per second. They are chiefly protons. Recently, however, it has been shown that a small percentage of these particles consists of nuclei of various elements occupying places in the periodic table up to its middle. Passing through the atmosphere, these particles collide with the nuclei of atoms of the air and expend their energy on interaction with already existing particles and on the creation of new particles. Thus, the passage of cosmic radiation through the earth’s atmosphere constitutes an experiment, carried out on an enormous scale by nature itself, on the study of the interaction of fast particles with matter. In order to simplify the conditions of such an experiment and to have the possibility of changing and controlling it at the experimenter’s will, it is necessary to find a way of obtaining, under laboratory conditions, particles with an energy close to that which they have in cosmic radiation. The intensity of such artificially created particles will considerably exceed the intensities that the experimenter can use in cosmic radiation. The proton cyclotron now being designed is to be a source of such particles; it will be able to create beams of particles with energies from 1 to 6 Bev (\(1\ \mathrm{Bev} = 10^9\ \mathrm{ev}\)). The mean energy of the particles of primary cosmic radiation is equal to 10 Bev.

Table I

Thus, with the aid of this machine it will be possible successfully to attain the lower limits of the energies of cosmic-ray particles. However, the upper limit of their energies is a million times greater than the limit which can be reached in accelerators now being constructed. The magnitude of the limiting energy which particles can acquire in a cyclotron is restricted by the relativistic increase of the mass of the particles as they are accelerated. This is easily shown in the following way. An ion in a homogeneous constant magnetic field of \(B\) gauss moves along a circular trajectory with radius \(r\), determined from the equality

\[ Br=\frac{v}{\frac{e}{m}}, \]

where \(\frac{e}{m}\) is the charge-to-mass ratio for the ion, and \(v\) is the velocity. Hence, for the time of one revolution one may write:

\[ t=\frac{2\pi}{\frac{e}{m}\cdot B}. \]

In the nonrelativistic region this quantity is essentially constant. An alternating electric field of frequency \(\frac{1}{t}\), applied to the dees of a cyclotron, accelerates the ions each time they pass through the space between the dees, provided only that these ions have begun to move in the corresponding phase.

The change of mass with velocity takes place according to the law \(m=\dfrac{m_0}{\sqrt{1-\beta^2}}\), where \(m_0\) is the mass of an ion at rest, and \(\beta\) is the ratio of the particle velocity to the velocity of light. If a particle is accelerated to a velocity equal to one half the velocity of light (the energy of a proton moving with such a velocity will be approximately \(150\) Mev), then its mass will be \(15\%\) greater than its rest mass, and the time \(t\) will be \(15\%\) greater than the time spent on the first revolution. Under these conditions the ions will get out of phase with the accelerating field and will not be accelerated. This difficulty was overcome by the theory of the synchrotron (an electron accelerator), and also by the theory of the synchrocyclotron (a proton accelerator), developed independently by Veksler\(^{11}\), McMillan\(^{6}\), and Oliphant\(^{7}\). These theories show that under certain conditions an ion moving in a magnetic field will possess a stable phase. Let us consider an ion whose energy lies in the extreme relativistic energy range. Let it move in a circle of radius \(r\) in a uniform magnetic field and let, as before, there be a high-frequency field between the dees. Suppose that the phase of the ion is such that, when the ion passes through the space between the dees, the accelerating field is equal to zero, whereas the preceding passage of this space by the ion was accompanied by acceleration. The radius of the trajectory is determined by the relation

\[ r=\frac{\sqrt{E^2-E_r^2}}{300B}, \]

where \(E=E_k+E_r\) is the total energy, \(E_r\) is the rest energy, equal for protons to \(935\) Mev, and \(E_k\) is the kinetic energy.

The expression for the radius may be rewritten in the form

\[ r=\frac{\sqrt{E_k^2+2E_rE_k}}{300B}. \]

If \(E_k\) is large in comparison with \(E\), then approximately

\[ r=\frac{E_k}{300B}. \]

Thus, in the relativistic region the ion velocity approaches the speed of light and the radius of its trajectory is proportional to its energy. An earlier arrival of the ion at the gap leads to its acquiring a greater energy and moving along a circle of increased radius. Its velocity, however, increases only slightly, and consequently the next time the ion will cross the space between the dees later. On the other hand, if the particle is late, it will slow down, travel along a shorter path, and the next time arrive at the gap on time. If the phase of the particle is disturbed, the particle oscillates about the stable phase and gains no energy in passing through the gap. The foregoing argument shows that a stable orbit in a magnetic field may exist for a relativistic particle. These arguments in favor of the existence of phase stability are not valid for small energies. In that case stability can be achieved by a radial decrease of the magnetic field. Such a decrease is also desirable in order to keep the accelerated particles in the median plane of the magnetic field. If one slowly changes, in the required direction, the magnitude of the magnetic field, or the frequency of the accelerating field, or both of these quantities, then the energy of the particle will increase, and the phase stability will be such that the increment of energy at each revolution will be just sufficient to keep the ion on the stable orbit as the field or frequency changes. Besides the phase oscillation, whose frequency is small in comparison with the frequency of revolution, there also occur radial and vertical oscillations of the particle’s position, whose frequency is comparable with the frequency of revolution. They are known as betatron oscillations. A large number of different accelerators have been constructed on the principle of phase stability. These accelerators differ according to which parameters are varied in them. In an electron accelerator, if the electrons have been given in some other way an energy of \(2\) Mev or slightly more, there is no need to change the frequency of the accelerating field, because in this case they possess \(98\%\) of their limiting velocity. The magnetic field is increased with time in order to ensure constancy of the orbit radius. The vacuum chamber has a toroidal shape, and the magnetic field fills the annular space. This machine is the synchrotron. For the acceleration of heavy ions there are two methods. In one of them the magnetic field is constant and its configuration is the same as in the cyclotron. In this type of accelerator the ion source is located at the center, and the accelerating dees are the same as in the cyclotron. However, as the mass of the ions increases and their period of revolution increases, the frequency of the accelerating voltage is decreased. The radius of the orbit increases, so that the entire trajectory is an expanding spiral. Such an accelerator

ions is called a synchrocyclotron*). As the dimensions of synchrocyclotrons increased, it became clear that the economic limit is represented by installations giving particles energies of the order of 500–1000 Mev. This limit is due chiefly to the very large dimensions of the magnets required for these accelerators. There remains, however, a second method, which consists in simultaneously changing the frequency and the magnetic field. The orbit radius can be kept constant and an annular magnet can be used for the accelerator, which is considerably cheaper than the corresponding magnet of cyclotron type.

At the present time three such proton synchrotrons are being built. One of them (University of Birmingham, England) is designed for 1.3 Bev. Another, being built at the national laboratory at Brookhaven, will accelerate protons to about 3 Bev and bears the name cosmotron. The third, being built at Berkeley, will initially give protons an energy of \(3\frac{2}{3}\) Bev, but provision has been made in it for such a modification of the design that it will give protons with an energy of 6 Bev. This machine has been named the bevatron. The only physical limit on the energies given by this class of accelerators is the limit imposed by the loss of energy, by a charged particle moving along a circular path, to electromagnetic radiation. For protons this limit is so high that the principal limitation in designing such an accelerator is the cost of the installation, amounting to one to two million dollars per 1 Bev. A detailed theory of the proton synchrotron is given in the literature cited at the end of the article under numbers \(^{3}\) and \(^{10}\), and design projects are described in articles \(^{1}\) and \(^{7}\). The fundamentals of the design of the Berkeley bevatron were developed by Brobeck \(^{1}\). The magnet will consist of four annular 90-degree segments arranged in such a way that the ion orbits are quarters of circles joined by straight sections. Such an arrangement of the magnet was first proposed by Crane \(^{2}\) for the synchrotron which he is now building. In the straight sections of the vacuum chamber between the magnetic segments, devices are provided for pumping out the chamber, for injecting the beam, for installing the accelerating electrode, and for experimenting with the beam. Magnetization is produced by a motor-generator, on whose shaft a large flywheel is mounted. When the magnetic field is created, the energy stored by the flywheel is converted into the energy of the magnetic field of the magnet. When the field is reduced, the generator acts as a motor and returns energy to the flywheel. Thus, the motor-

) Veksler, who proposed this method of acceleration, called an accelerator of this type a phasotron. In the American literature it is called a synchrocyclotron or a cyclotron with modulated frequency.
(Translator’s note.*)

makes up the losses, which for each pulse reach 40% of the stored energy. The protons are to be introduced from a linear accelerator with an initial energy of 10 MeV. Some of the dimensions of the betatron now being constructed are given in the first column of Table II.

Table II

In developing the design of the betatron, concern arose as to the degree of correctness of certain provisions of the theory of this installation. In particular, up to the present time not a single accelerating installation had operated with straight sections, as proposed by Crane, and it seemed likely that some unforeseen disturbance would cause oscillations of the ion beam sufficient to direct the beam onto the walls of the chamber. There also arose the extremely important question of the magnitude of a reasonable transverse cross-section for the magnetic field to be used. It was obvious that in the design of this installation there were provisions that were located in

contradictions with one another. With the given expenditures on the magnet and on the excitation equipment, it would have been possible to obtain a small aperture with a large field, which would give particles of high energy, but would allow only a very limited deviation from the ideal ion orbits. On the other hand, the choice of a large aperture reduces the value of the final energy of the particles. In order for the injected ions to fall onto their orbit, the use of electrodes is required; these must be placed in the chamber, so that many ions will inevitably collide with them.

Fig. 1.

We were not sure what measures should be taken in order to avoid these dangers. To obtain answers to these questions and to learn how to control such an apparatus, it was decided to build a working model of a size equal to \( \frac{1}{4} \) of the dimensions of the final installation. Since almost all possible difficulties were expected to arise immediately after injection, it was decided that an acceleration of the order of 6 MeV would be sufficient. This made it possible to reduce considerably the cost of the magnet and of the excitation equipment. In the second column of Table II the principal dimensions of this model are given. The general arrangement is shown in Fig. 1. In order to reduce the influence of Foucault currents, the magnet was assembled from plates \(1.25\ \text{cm}\) thick, separated by paper

with insulation. For the same reason, the vacuum chamber is assembled from stainless-steel plates 0.8 mm thick, joined into sections 30 cm long, each of which is insulated from the other sections by a rubber gasket. The atmospheric load is taken off the chamber by means of rods connected to the yoke of the magnet.

Figure 2 shows the general view of the installation, with the cyclotron serving as the injector in the foreground. The protons are accelerated to 0.7 MeV in the cyclotron, which operates for one millisecond and is started by the current of the bevatron magnet at the moment when it reaches the corresponding value. The ions pass

Fig. 2.

through a focusing magnetic field and, after they enter the region of the bevatron magnet, their trajectories are bent by the electric field of the “deflecting” electrodes in such a way that they begin to move along trajectories tangent to their orbits in the bevatron. As the magnetic field increases, and with the ion energy unchanged, they begin to oscillate around a circular trajectory of decreasing radius. Before they reach the inner wall of the chamber, the accelerating electrode is excited at a frequency equal to the frequency of rotation. This electrode is located in the straight-line part of the chamber, opposite the inflector, and consists of a copper tube with open ends, placed in such a way that the ions can pass through it. The energy imparted to the protons is equal to the change in voltage on the electrode during the time of their passage through the electrode, since the electric field at the two ends of the electrode is oppositely directed.

of sign. In the constructed bevatron model, the protons are given an energy of the order of 40 ev per revolution, in accordance with a magnetic field increasing at 4000 gauss per second. Since the velocity of the ions is certainly outside the relativistic range of velocities, the frequency of revolution is proportional to the momentum of the particles. For a constant orbit radius the momentum of the particle is proportional to the magnetic field. Therefore the radio frequency used for acceleration must change in the same way as the magnetic field changes. This change in frequency is accomplished by passing part of the current feeding the magnet through an inductance with a ferromagnetic core, connected into the radio-frequency circuit. The increasing saturation of the core as the current flowing through the magnet winding increases reduces the inductance and increases the frequency in the circuit. The required frequency interval extends from 0.4 to 1.2 megacycles per second. In the course of about a quarter of a second the magnetic field almost reaches its limiting value of 1000 gauss, and the protons acquire an energy of the order of \(6 \frac{1}{2}\) Mev. When the radio frequency is switched off, the further slight increase of the magnetic field causes a decrease in the orbit radius, and the ions are deflected onto a small target introduced through the inner wall of the annular chamber. In Fig. 3 there is shown a trace obtained on an oscillograph and showing the history of one pulse. In this case the acceleration lasts only 10 milliseconds, so that the whole course of the curve can be shown. At first the ions with an incorrect direction or energy strike the target. Of the remaining ions, those are accelerated which pass through the accelerating electrode in the proper phase. Those ions which have the wrong phase are carried to the target immediately after the radio frequency is switched on. During the long path which the ions traverse in the bevatron, they undergo many collisions with the molecules of the air remaining in the chamber. From Table II it is evident that the ions in the bevatron and its model are accelerated for 1.75 and 0.25 sec, respectively, whereas in the 184-inch

Fig. 3.

In the new synchrocyclotron they are accelerated during \(0.002\) sec. As a result of the large number of such collisions, taking place during such a long acceleration time and occurring especially often immediately after injection, when the energy is small, a substantial weakening of the beam takes place. We found that increasing the pressure by \(1.7\cdot 10^{-6}\) mm Hg led to a decrease of the beam intensity by a factor of \(1/e\). This value agrees, within the errors of the theory and the measurements, with the expected losses. The usual working pressure was \(2\cdot 10^{-6}\) mm Hg.

In Fig. 4 the change in beam intensity at high energies is shown. Here the value of the final energy is established by changing the duration of the accelerating radio-frequency pulse and by recording the integral beam collected on the target under a constant injected pulse. The greater part of the losses occurs at energies of \(3\) MeV. In Fig. 4 data are given for three transverse sections of the beam, specified by aperture diaphragms located in two straight sections of the chamber.

Fig. 4.

The middle curve in relative cross-sectional magnitude corresponds most accurately to an aperture of height \(60\) cm and width \(180\) cm, chosen for a bevatrons of natural dimensions. The oscillations of ions in the bevatron in the radial and axial directions are approximately determined by the expressions,* \(f_r=\sqrt{1-n}\,f_0;\ f_a=\sqrt{n}\,f_0\), where

\[ n=-\frac{r}{B}\frac{dB}{dr} \]

determines the radial decrease of the magnetic field, and \(f_0\) is the frequency of revolution. The constant \(n\) is equal to \(0.6\).

* The exact expressions are more complicated, since they take into account the influence of the straight sections.

From this it is clear that both frequencies are close to the revolution frequency. It is very important that there be no simple harmonic relation between these frequencies. If such a relation existed, the amplitude of one of the oscillations could increase until the ions were lost on the walls of the chamber. These frequencies were measured in an experiment proposed by Kerst, in which a radio-frequency field is established in the radial and axial directions of the vacuum chamber. At the appropriate frequency this field will increase the oscillations and destroy the beam. The calculated frequencies were confirmed in this experiment with an accuracy of about 1%; some phenomena of interest were also discovered, which, however, have not yet been quantitatively explained. Two of these phenomena concern the critical period of injection. It was found that if the applied accelerating radio-frequency voltage increases not

Fig. 5.

linearly or by a sharp jump, but as shown in Fig. 5, then the beam intensity increases by 75%. An increase in beam intensity of approximately 100% was also observed when the voltage on the deflecting electrode was switched off immediately after injection. The greatest beam intensity, with an aperture size of \(9.45\ \mathrm{cm}^2\), was \(3.5\cdot 10^{-11}\) coulombs per pulse. The intensity of the injected beam, measured at the end of the deflecting electrodes, was \(10^{-8}\) coulombs. In this case the efficiency of the apparatus was approximately \(\frac{1}{3}\%\). In a future bevatron, losses caused by scattering in the gas should be negligibly small owing to the considerably higher injection energy. In addition, the bevatron chamber should be four times larger than the chamber of the operating model, whereas the size of the deflecting electrodes will not be changed at all, and, consequently, the probability that ions after injection will not strike the deflecting electrode will increase. It is therefore natural to expect that the particle intensity in a bevatron of natural dimensions will increase by at least several percent.

References

1. W. M. Brobeck, Rev. Sci. Instr. 19, 545 (1948).
2. H. R. Crane, Phys. Rev. 69, 542 (1946).
3. J. S. Gooden, H. H. Jensen and J. L. Symonds, Proc. Phys. Soc. 59, 667 (1947).
4. Q. A. Kerns et al., Bull. Amer. Phys. Soc. 24, 8 (1949).
5. Lofgren et al., Bull. Amer. Phys. Soc. 24, 8 (1949).
6. E. M. McMillan, Phys. Rev. 68, 143 (1945).
7. M. L. Oliphant, J. S. Gooden and G. S. Hide, Proc. Phys. Soc. 59, 667 (1947).
8. D. C. Sewell et al., Bull. Amer. Phys. Soc. 24 (1949).
9. Smith, Lloyd, A. A. Garren and L. R. Henrich, Bull. Amer. Phys. Soc. 24, 8 (1949).
10. R. Q. Twiss and N. H. Frank, Rev. Sci. Instr. 20, 1 (1949).
11. V. Veksler, J. Phys. USSR 9, 153 (1945).