ACCELERATORS

A. A. VOROBYOV

§ 1. Introduction

In various epochs mankind has shown interest in various large structures. The construction of accelerators in our century is compared with the construction of the pyramids in antiquity and of cathedrals in the Middle Ages.

Installations in whose electric field charged particles—electrons, positrons, nuclei, or ions—increase their energy are called charged-particle accelerators.

As a result of the braking of accelerated charged particles, radiation of a continuous spectrum of electromagnetic oscillations occurs. In this way X-rays and electromagnetic radiation are obtained whose energy considerably exceeds the $\gamma$-radiation in the radioactive decay of some atomic nuclei.

The interaction of high-energy particles, or of braking radiation from accelerators, with atomic nuclei can be used to obtain neutrons, mesons, antiprotons, and other elementary particles.

In 1919 E. Rutherford, by bombarding matter with $\alpha$-particles, carried out an artificial nuclear reaction and thereby posed the problem of obtaining fast particles for nuclear transformations.

Among the physical problems that can be developed with the aid of high-energy accelerators are nuclear spectroscopy, the scattering of protons by protons and electrons, of electrons by protons and positrons, photodisintegration, the Compton effect, problems of electrodynamics, reactions of electrons with mesons, and others.

The main argument for the construction of high-energy accelerators is the existence of high-energy particles in nature. In cosmic rays, protons with energies of $10^{12}$–$10^{14}$ eV have been detected, and even $10^{17}$ per proton has been reported. The spectrum of cosmic protons has a maximum in the region of 500 MeV.

In cyclic accelerators, electrons and protons travel cosmic distances during acceleration, at cosmic velocities. These were the first man-made structures in which cosmic scales were achieved.

Electrons and protons in accelerators, at energies of several MeV and higher, move with velocities close to the speed of light.

To control the motion of accelerated particles it is necessary to employ automatic devices operating at the correspondingly high speeds.

Previously, less attention was paid to accelerating electrons to high energies than to accelerating protons. Meanwhile, accelerated electrons possess interesting properties inherent to them and can find their own applications. The high penetrating power of fast electrons and of the photons produced when they are decelerated has found application in therapy and defectoscopy. Under the action of photons, in high-energy photonuclear reactions, the production of mesons is observed. With fast electrons it is possible to carry out nuclear spectroscopy and to study the structure of nucleons. Of no small importance here is the fact that the size of the electron itself can be neglected and it can be regarded as pointlike.

Questions concerning the structure of elementary particles began to be considered when, with the aid of accelerated particles, regions with linear dimensions of \(1\text{--}0.1\) fermi were penetrated (\(1\) fermi \(=10^{-13}\) cm). Increasing the electron energy will make it possible to penetrate regions of still smaller dimensions, of the order of \(10^{-2}\text{--}10^{-3}\) fermi, which will lead to the discovery of new physical phenomena and will create the possibility of studying the structure of the electron itself, the problems of gravitation, mass, energy, and so on.

Obtaining electrons of very high energies is as yet the only way of experimentally penetrating into the region of small linear dimensions and of deeply studying the microworld. For electron energies no upper limit has yet been named. The considerations presented above show the interest of physicists in obtaining high-energy electrons.

Accelerators ensure the progress of modern nuclear physics and solid-state physics. They are used to study the structure of atomic nuclei and internuclear forces, to obtain new elements and elementary particles, and in radiation chemistry and physics.

Electron accelerators are used for sterilizing food products and medical preparations, as well as tissues in surgical operations, etc.

To increase the energy and intensity of accelerated particle beams, storage installations are being created; accelerators are being improved in order to make fuller use of the possibilities of known acceleration methods; and fundamentally new methods of acceleration are also being proposed and developed.

In all fields connected with the construction of accelerators, various scientific and technical ideas have been put forward. For some of them, suitable conditions, the necessary technical means, materials, and apparatus proved available, and they received practical implementation. Other proposed acceleration methods were postponed until a suitable occasion or until the necessary technical means had been developed to the required level.

Sometimes “prematurely” expressed, physically possible methods of acceleration were forgotten and, after some time, were put forward again by other researchers. Authorship was then restored only after special historical investigations.

Each time a new method of acceleration was proposed, it seemed to some that an absolute solution had been found to the problem of accelerating charges to arbitrarily high energies, and that only engineering and economic problems were delaying the construction of an accelerator with any desired parameters.

Then, as each method was developed, contradictions were discovered, and finally the principal contradiction appeared. It determined the physical limit of the maximum energy attainable by particles. In the case of cyclic accelerators, the principal contradiction is ...

the radiation of electromagnetic energy by a charge moving along a curvilinear orbit.

For linear and cyclic acceleration, stability of particle motion is necessary, while in practice instabilities arise during motion, including those due to radiation. The development of each method proceeded through a struggle with the contradictions of the process. The level of development attained at each stage was determined by the level of development of related branches of science and technology and by economic factors.

It is of interest to show the main tendency in the development of acceleration methods and means as a result of the struggle of the principal contradictions, namely the required stability and the instability that arises in particle motion, and the ways of overcoming the instability. Accelerator practice over the past period well illustrates the general laws of the theory of knowledge, showing the development of the acceleration method as a result of the struggle of contradictions, taking the economic factor into account.

The level achieved at each stage in the development of accelerators was determined by the country’s material resources, the state of its economy, technology, and science.

Sharp scientific discussions of the problem of the upper energy limit attainable in accelerators have contributed to the fact that there now exist quite detailed theories of various acceleration methods.

The time when accelerators were built on the basis of rough calculations has already passed.

At present, the theory of acceleration and computer technology make it possible, before construction begins, to examine in detail linear and nonlinear problems and to model many interesting phenomena in a future accelerator on analog devices.

Experience obtained on machines already in operation shows that theoretical studies give sufficiently accurate results. Machines and accelerators built in accordance with theoretical calculations are started up easily; their operation is reliable and satisfactorily adjustable.

In compiling this survey, the author avoided describing many implemented, perfected schemes and accelerator designs, bearing in mind that in the near future they will be replaced by still more advanced ones. Such materials are appropriate for more specialized and narrower scientific studies. It was important, and difficult, to find what was essentially necessary, what determined the direction of accelerator development.

On the other hand, it was also necessary to provide factual materials so that the exposition would not become an abstract scheme devoid of practical interest.

In this work it was of interest to present the history of acceleration methods and accelerators not as a sum of separate facts, accidental discoveries, and events, but as a process of development with its own logic, resulting from the struggle of contradictions.

With such a method of presenting the subject of the study, it would be possible to obtain a coherent unity, to show the laws of development in the past, and to make scientific forecasts.

The posed problem will be considered using cyclic accelerators as an example; the various types of these A. A. Kolomensky and A. N. Lebedev combine in the following table.

Table

Types of cyclic accelerators

§ 2. Cyclotrons

The construction of very long linear accelerators entails considerable difficulties; therefore methods were developed for bending the trajectories of particles into a closed circle, an ellipse, or an expanding spiral. The trajectory is then controlled by means of a constant or time-increasing guiding magnetic field.

The first accelerator with a spiral trajectory was Lawrence’s cyclotron, built in 1931 at the University of California. In Europe the first cyclotron was put into operation in 1937 in Leningrad, at the Radium Institute.

In a cyclotron, synchronous acceleration takes place in the gap between two U-shaped electrodes, to which an alternating voltage is applied. The particles cross this gap twice during one period of the alternating voltage. While, for half a period of the current, the particle moves along an arc of a circle inside a hollow dee, the voltage in the gap changes to the opposite sign; therefore the particle, each time it passes through the gap, increases its energy.

At first it was considered necessary that acceleration in a cyclotron take place under conditions of exact resonance. Later it became regarded as possible to tune a cyclotron for operation under conditions of inexact resonance as well, with certain tolerances in the phases between the instant at which the particle appears in the accelerating gap and the phase of the voltage in the accelerating gap. Under conditions of strict resonance there is static longitudinal and transverse stability. The requirement of maintaining strict resonance limited the maximum attainable energy and the number of particles accelerated in cyclotrons.

Particles of constant mass \(m\) and charge \(e\) in a uniform magnetic field move along a circle of radius

\[ R=\frac{mc\,v}{eB}, \tag{1} \]

where \(c\) and \(v\) are the speed of light and of the particle,
\(B\) is the magnetic induction.

As the particle is accelerated, the radius \(R\) of the orbit increases.

The period of revolution of the particle

\[ T=\frac{2\pi R}{v}=\frac{2\pi mc}{eB} \tag{2} \]

does not depend on the velocity.

The maximum proton energy achieved in a cyclotron at a dee voltage of 440 kV is 22 MeV.

The relativistic increase in the mass of a particle with increasing velocity leads to a phase lag and to a violation of resonance. Resonance can be preserved if, as the radius increases, the induction also increases, so that in (2) the ratio $\frac{m}{B}$ remains constant and isochronism $T=\text{const}$ is maintained. Such a solution of the problem of stability of motion is impossible, since magnetic focusing, which ensures the transverse stability of particle motion, requires that the magnetic induction decrease with increasing radius, rather than increase. Thus a contradiction arises: measures ensuring longitudinal phase stability violate transverse stability.

In 1938 Thomas proposed a cyclotron with azimuthal variation of the magnetic field, in which the longitudinal instability characteristic of a strictly resonant cyclotron can be overcome. To preserve resonance, a periodic variation of the field strength with azimuth was proposed. The law of field variation in neighboring sectors is set so that, at their common boundary, additional components of velocity arise, directed radially toward the center and toward the median plane.

A system with spiral variation of the magnetic fields, ensuring isochronism, was also proposed. In this system the magnetic field varies periodically about a mean value not only in azimuth but also in radius.

Cyclotrons with magnetic-field variation, or with sector focusing (SCF), have in recent years attracted much attention and are already operating in many laboratories. Theory gives grounds for expecting the construction of stably operating proton accelerators to energies of 800–900 MeV.

In a ring isochronous cyclotron the central region of the poles is absent. Particles are injected into the ring at an energy of 70 MeV from an ordinary SCF, and the final energy is 500 MeV, limited by the resonance $\nu_r=1.5$. The advantages of a ring machine over an ordinary one consist in the possibility of using several extraction schemes and in the easier introduction of targets into the chamber.

A. A. Glazov, Yu. N. Denisov, and others developed an isochronous proton cyclotron for an energy of 700 MeV.

At present it appears that the most promising accelerators for obtaining beams of particles with energies up to 1 GeV at currents of the order of 1 mA, instead of 1 μA as in synchrocyclotrons, are installations with a continuous operating mode of the isochronous-cyclotron type.

§ 3. Cyclic Induction Acceleration.

Betatrons

Around a magnetic flux changing in time there is formed a vortex electric field whose lines of force are closed around the flux inducing them. Electrons, moving along the lines of force of the vortex field, acquire an increment of their energy. A patent for the method of induction acceleration was taken out in 1922 by Slepian.

In 1927 Wideröe developed the theory of the accelerator and some of its structural elements.

In 1939, Rüdenberg and Steenbeck proposed a scheme for an induction accelerator. In 1935, Steenbeck built a cyclic induction accelerator containing the basic components of the modern betatron and operating according to the same principle.

In the USSR, research on the induction method was begun in the early thirties by V. V. Yasinsky, an engineer at the Moscow Transformer Plant. In 1935 he published the results of theoretical studies of the motion of an electron in a quasi-stationary and alternating electromagnetic field of radial symmetry and proposed an accelerator scheme.

In 1935, A. A. Vorob’ev and A. K. Krasin in Tomsk began investigations of the induction method.

In 1941, Ya. P. Terletsky published theoretical studies of the motion of relativistic electrons in an alternating magnetic field of axial symmetry. He showed that in a field whose strength decreases with increasing radius and grows with time, a particle launched perpendicular to the radius of a circular orbit moves along a spiral on the surface of a cylinder whose axis coincides with the field axis. The magnitude of such a spiral decreases as the electron velocity increases. Ya. P. Terletsky gave a relativistic proof of the constancy of the radius of the equilibrium orbit \(2:1\), investigated transverse stability, and laid the foundations for a rigorous theory of induction cyclic acceleration.

The first operating betatron was built by Kerst in 1941. In the USSR, the development of betatrons for various purposes and their introduction into the practice of institutions and enterprises is associated chiefly with the work of the Tomsk Polytechnic Institute, which manufactured more than 60 betatrons; these developments began there in 1945, and at the beginning of 1947 a 5 MeV betatron began operation.

Taking into account the biological danger of radioactive isotopes, A. A. Vorob’ev proposed and calculated the possibility of replacing radioactive preparations with small-sized betatrons. Such betatrons with energies of 3–10 MeV were developed and constructed under the direction of L. M. Anan’ev and V. A. Moskalev.

B. A. Rodimov and P. A. Cherdantsev constructed a theory of electron capture into acceleration in which it is assumed that the principal influence on capture is exerted by the interaction of electron beams. They considered the possibility of non-oscillatory capture and gave proposals for constructing a high-current betatron.

V. A. Moskalev developed designs for, and built, betatrons of 15 and 25 MeV with a large accelerated charge. At the output of such betatrons a charge of more than \(10^{12}\) electrons is obtained, and the circulating current in the orbit is hundreds of amperes.

The large value of the equilibrium charge in the orbit was obtained by increasing the transverse cross section of the accelerating chamber and by raising the injection voltage by an order of magnitude. At the same time, the problem of extracting the beam from the betatrons was being solved.

At TPI, variants of three methods for extracting the electron beam from the accelerator chamber were developed and implemented:

1. By means of electrostatic deflection of the beam and various types of deflectors developed by B. A. Kononov.

2. With the use of magnetic shunts and nonmagnetic tunnels developed by L. S. Sokolov and Yu. M. Akimov.

3. By the method of perturbing the magnetic field with additional coils, developed by L. S. Sokolov.

The magnitude of the average current in the extracted beam of a 15 MeV betatron reaches \(10^{-8}\) A.

M. F. Filippov proposed a theory determining the interdependence of the principal dimensions and parameters of the betatron electromagnet, the accelerator chamber, and its tuning parameters. As a result, a simple system was obtained for the engineering calculation of accelerator variants, which proved highly successful in the practice of designing betatrons.

The works of A. P. Komar and his collaborators, who studied the conditions for electron capture into acceleration in betatrons, had a significant influence on the development of the physical theory of the betatron.

At the All-Union Special Design Bureau of the Ministry of Electrical Engineering named after V. V. Kuibyshev, under the direction of B. B. Gelfer, betatrons for defectoscopy and therapy have been developed and are being built.

Theoretical studies of the radiation of relativistic electrons in a magnetic field, published by D. D. Ivanenko and I. Ya. Pomeranchuk, showed that there exists a limit to the maximum energy attainable by electrons in a betatron. This limit is determined by the condition that the energy gain per unit path be equal to the magnitude of the electron energy losses due to classical radiation.

The works of D. D. Ivanenko, I. P. Pomeranchuk, and L. A. Artsimovich on the radiation of relativistic charged particles in cyclic accelerators played a fundamental role in their development, by determining the physically possible limits of acceleration.

§ 4. Development of cyclic accelerators of relativistic particles

The most essential feature of a cyclic accelerator at high energies is the electromagnetic radiation of the particles, whose power for electrons is proportional to the fourth power of their energy and inversely proportional to the square of the orbit radius. Radiation disturbs stability. Ensuring stability and compensating radiation losses complicate the accelerator and increase the required power.

A peculiarity of electron radiation at high energies is its quantum character. This feature was noted in 1953 by A. A. Sokolov and I. M. Ternov. They showed that the quantum character of the radiation leads to excitation of betatron oscillations of the electrons.

For high-energy particle accelerators it is important to take quantum effects into account. On the basis of the quasiclassical theory of radiation, V. V. Vladimirsky and others initially believed that quantum effects could be neglected so long as the quantum energy was less than the electron energy, i.e. up to electron energies of several thousand GeV. A. A. Sokolov and I. M. Ternov, on the basis of the rigorous quantum theory of radiation, came to the conclusion that quantum effects for a synchrotron with weak focusing should appear in the energy region of electrons of \(\sim 1\) GeV.

According to A. A. Sokolov, quantum effects influence the intensity and angular distribution of the radiation and the betatron oscillations. Quantum broadening of the orbit theoretically limits the energy attainable in a synchrotron with weak focusing to the level of 1–2 GeV.

The same results were obtained by A. A. Kolomensky and A. N. Lebedev by the quasiclassical method.

Later M. Sands, on the basis of the quasiclassical theory, considered the influence of quantum fluctuations on phase oscillations. In his opinion, quantum excitation of phase oscillations should limit the attainable energy to the level of 1–2 GeV.

of attainable energy of 1 GeV in a synchrotron with weak focusing. M. Sands, on a 1.2 GeV synchrotron, investigated the dependence of the lifetime of electrons on the amplitude of the accelerating voltage on the resonator. At an energy of 1.2 GeV, owing to the excitation of phase oscillations by quantum fluctuations of the radiation, electrons fall out of acceleration and the intensity of the radiation decreases. By the present time a theory has also been developed in detail that takes into account the influence of radiation fluctuations on phase oscillations.

Experimental work carried out by F. A. Korolev on the 680 MeV synchrotron of the Lebedev Physical Institute, using a high-speed motion-picture camera, showed that the observed transverse size of the beam is in good agreement with the theory that takes into account the influence of radiation on betatron and phase oscillations.

Work carried out on the TPI 1.5 GeV synchrotron, with simultaneous use of a high-speed motion-picture camera and an electron-optical converter with circular sweep, showed that there is good agreement between theory and experiment in determining the influence of radiation fluctuations on both betatron and phase oscillations separately.

Theoretically, variants of cyclic acceleration of electrons without removing radiation from the region of electron motion are possible, with the establishment of a regime of their self-oscillations. An electron that has emitted a quantum of energy receives it again from coherent sources. The implementation of a variant of a nonradiating cyclic accelerator would make it possible to raise the energy limit attainable in an accelerator.

In a cyclic accelerator an electron that has emitted a quantum of energy goes over to an orbit of smaller radius. This external analogy makes it possible to compare the accelerator with the Bohr hydrogen atom. In an atomic system, motion of electrons in a circle without radiation is possible.

In the forties A. A. Vorob'ev considered an accelerator and a storage ring as an analogue of the atom and sought the conditions for stable circulation of electrons without radiation.

The development of cyclic accelerators of relativistic particles proceeded in the following directions:

1. Development of a general theory of relativistic accelerators.
2. Improvement of accelerating electric and controlling magnetic systems.
3. Introduction of ideas and means of automatic regulation into accelerator technology.
4. Development of storage rings for charged particles.
5. Modernization of existing accelerators.
6. Development of new acceleration methods.

In the development of controlling and accelerating systems one may note the following interesting ideas. In 1950 N. Christofilos proposed, in accelerating particles, periodically applying measures to increase axial and radial stability. Like many other discoveries, this one had been prepared by the preceding development of science. The principle of increasing the stability of motion of a charged particle in alternating-sign fields, which received the name of strong, or hard, focusing, was most fully substantiated in the summer of 1952 by Courant, Livingston, and Snyder.

Strong focusing is a special case of the manifestation of dynamic stability in a field of rapidly varying forces for mechanical, electrical, and optical systems.

In the first resonant cyclic accelerators—cyclotrons—it proved possible to obtain particles with energies somewhat greater than ten MeV. After the formulation of the principle of phase stability, deter-

which satisfied the condition of longitudinal (azimuthal) stability, it proved possible to build synchrophasotrons with weak focusing up to 10 GeV. The use of strong focusing, which automatically ensured transverse (radial and axial) stability, made it possible to build an accelerator for several tens of GeV and, probably, to build one up to 1000 GeV.

The extension of strong focusing to phasotrons was carried out in 1953 by A. A. Kolomensky, V. A. Petukhov, and M. S. Rabinovich in the design of a ring phasotron whose magnetic field varies not in time but in space.

The designs of high-current iron-free cyclic accelerators, developed under the direction of G. I. Budker and A. A. Naumov, make it possible to obtain magnetic-field intensities of 140–200 kOe in large volumes. This made it possible to build compact accelerators whose dimensions are 14–20 times smaller than those of existing accelerators for the same energies. Since the cost of the magnet essentially determines the cost of the accelerator and decreases sharply as the radius is reduced, iron-free installations even for energies of 100–1000 GeV will still have acceptable costs and dimensions.

In the forties A. A. Vorob’ev proposed, for the purpose of controlling the motion of a particle in a cyclic accelerator, the use of the magnetic field of a cylindrical resonator or waveguide. Later the theory of such a system was developed by A. A. Vorob’ev and E. S. Kovalenko.

Among the works on improving the magnetic systems of existing accelerators are the investigations by Yu. F. Orlov on nonlinear focusing.

In accelerators with nonlinear focusing, particles execute stable oscillations because of the presence of alternating-sign focusing. In contrast to strong focusing, here the particles experience the action of alternating-sign forces not because they pass in azimuth through a sequence of focusing and defocusing sectors, but because they execute large radial oscillations. Nonlinear focusing makes it possible to obtain the same result as strong focusing, but this is achieved in time-constant, axially homogeneous magnetic fields. It also makes it possible to accelerate colliding beams of particles.

The improvement of high-frequency systems proceeded in the following directions:

a) the choice of optimum frequencies of accelerating systems;

b) the use of waveguide accelerating devices in cyclic accelerators.

At the first stage in the development of relativistic accelerators in general, and of synchrotrons in particular, little attention was paid to the choice of frequency.

The frequency of the accelerating system was chosen mainly depending on the availability of sufficiently powerful high-frequency generators. Usually the frequency of the RF generator was chosen equal to the revolution frequency of the particles.

The theoretical foundations for choosing the frequency and power of the RF supply were developed by A. A. Vorob’ev and A. N. Didenko, E. S. Kovalenko, who showed that for each synchrotron there exists an optimum frequency at which the power of the RF generator is minimal. Simple formulas were proposed for waveguide linear and cyclic accelerators, making it possible to determine the optimum frequencies not only with allowance for quantum fluctuations but also for other random factors. It was shown that for accelerators with energies of several GeV the optimum frequencies lie in the range of 500–1000 MHz.

At the Tomsk Polytechnic Institute, the electrodynamics of closed waveguide accelerating devices and the dynamics of electrons in them, proposed by A. A. Vorob’ev as an accelerating system for relativistic cyclic accelerators, have been investigated. From a comparison of a 1-GeV electron synchrotron with a 6–10-GeV synchrotron it follows that a higher-energy synchrotron is not geometrically similar to a 1-GeV synchrotron. In 1-GeV installations large resonators are used, whose transverse dimensions are considerably larger than the dimensions of the chamber. In large installations this difference decreases. This is explained by the fact that, with increasing energy, the optimal frequency at which the rf generator power will be minimal increases, and consequently the dimensions of the resonators decrease. The idea arises: could one not use such an accelerating system, which could be placed in the interpole space and would make it possible to accelerate particles not only on rectilinear sections, but continuously? This makes it possible to shorten the acceleration time and more easily compensate radiation losses. Studies have shown the possibility of acceleration in closed smooth waveguides and waveguides filled with slowing systems, which make it possible to reduce the phase velocity of the required electromagnetic wave to the particle velocity. Waveguide systems possess, in comparison with resonators, higher shunt impedances. This makes it possible in such systems to obtain the same energy increments while, on the contrary, using less powerful rf generators. Such systems can be used where resonant systems cannot be used at all, as is the case in iron-free accelerators.

The theoretical regularities studied by A. N. Didenko and others have been confirmed on the 10-MeV waveguide cyclic accelerator with diaphragm-loaded and smooth waveguides operating at the Tomsk Polytechnic Institute, and on the 3-MeV accelerator with a smooth waveguide built in Prague.

To ensure stable acceleration of protons in accelerators to energies of hundreds of GeV and more, it is necessary to seek new approaches. In accelerators at these energies, after a small amplitude of free oscillations has been ensured by the means indicated above, forced oscillations of the particles due to inhomogeneity of the magnetic field and its gradient, which increase the betatron oscillations, acquire substantial importance.

Fluctuations of the frequency and amplitude of the accelerating voltage increase the synchrotron oscillations.

In the mid-1950s, proposals on the application of the theory and means of automatic control in accelerators were made by the author in connection with an accelerator design.

E. L. Burshtein, A. A. Vasil’ev, and A. L. Mints proposed seeking a solution to the problem of damping forced oscillations and maintaining the acceleration regime by automatic regulation of accelerator parameters according to data on the instantaneous position of the beam. Automatic regulation of synchrotron oscillations has already been implemented in the 30-GeV CERN accelerator with strong focusing.

Burshtein E. L., Vasil’ev A. A., Mints A. L., Petukhov V. A., and Rubchinskii S. M. considered the possibility of automatic regulation of betatron oscillations. Automatic regulation of betatron oscillations during the acceleration process reduces to stabilizing the number of oscillations per revolution and the equilibrium orbit. Signals from the beam make it possible to establish the presence of deviations and, with the aid of a feedback system, to extinguish deviations from the calculated equilibrium motion.

The use of automatic control and stabilization of beam motion will make it possible to relax the tolerances on the accuracy of reproducing the magnetic field and the gradient, on the accuracy of magnet installation, to increase reliability, reduce the dimensions of the chamber, and so on.

§ 5. Conclusion

The use of accelerators in science is still determined by the energy and intensity of the beam of accelerated particles. In their practical use it is necessary to take into account technical-economic and operational characteristics.

A scientific methodology for comparing and selecting accelerators is still lacking. Taking as the basis for evaluation and comparison one or several properties or characteristics of accelerators, scientists have sometimes arrived at mutually opposite conclusions about the merits of the accelerators being compared.

A. A. Vorob’ev proposed a technical-economic evaluation of accelerators by expenditures referred to one accelerated particle of specified energy at the output per unit time, using formulas of the efficiency type:

\[ q = \frac{EN}{\kappa}, \]

where \(N\) is the number of particles in the pulse; \(E\) is the energy; \(\kappa\) is the expenditures subject to comparison, for example, cost, weight, power consumed by the installation, etc.

A comparison of the indices of nine synchrophasotrons for energies greater than 1 GeV led to the conclusions that the American accelerators at 12 and 12.5 GeV and the English one at 7 GeV have high economic indices. The highest indices, close to those of electron accelerators, are possessed by the Oak Ridge 12-GeV proton accelerator.

This is explained by the fact that the injector of the Oak Ridge accelerator is an isochronous cyclotron of energy 850 MeV, with \(10^{12}\) particles in the pulse and a pulse frequency of 60 pulses/sec.

Electron synchrotrons have higher indices than proton ones (synchrophasotrons). Linear electron accelerators up to energies below 10 GeV have poorer, and at energies above 10 GeV better, economic indices than cyclic ones.

Increasing the intensity of beams of particles accelerated to high energies is the most important task in the development of new methods of acceleration and new accelerators. The considerable supply power required for large accelerators, and the difficulties of delivering it, make it necessary to shift to pulsed power supply with the use of energy-storage devices. As the particle energy increases, the duty factor of the excitation pulses supplied to the accelerator electromagnet also increases. Therefore, increasing the particle energy in a cyclic accelerator is accompanied by a decrease in their number, by a rapid increase in the weight and dimensions of the installation and in the supply power. For example, to obtain particles with an energy of \(10^{16}\) eV, with a controlling field strength equal to \(10^{4}\) oersted, it would be necessary to build an accelerator whose diameter would exceed the diameter of the Earth. The output of accelerated particles from such an accelerator would be equal to one proton per day, which would be comparable with the intensity of cosmic rays.

The modern theory and practice of electron accelerators do not satisfy the demands of nuclear physics and other fields where electron beams with a long range can be used. New physical ideas and new approaches to the construction of accelerators are needed.

For acceleration up to 10 MeV, the most widely used so far have been high-voltage accelerators, cyclotrons, betatrons, linear accelerators, and microtrons.

In the range up to 100 MeV: cyclotrons, betatrons, synchrotrons, linear accelerators, and microtrons.

In the range up to 1000 MeV: synchrotrons, phasotrons, isochronous cyclotrons, and linear accelerators.

Above 1000 MeV: synchrophasotrons, synchrotrons, and linear accelerators.

In the region above 100 GeV, the following paths of development appear probable:

1. The development of a strong-focusing synchrophasotron with a radius of several kilometers, including an installation with an accelerating system in the form of a closed waveguide.

2. The creation of a cascade of synchrophasotrons, in which each preceding one serves as an injector for the next. The advantage of such an installation is as follows. As the energy of the particles increases, the beam is compressed. Therefore a smaller cross section of the accelerating chamber is used. This will lead to a significant saving in the construction of the final ring accelerator. Substantially new difficulties arise, connected with the extraction and injection of beams of high-energy particles.

3. The third path, which has been developed in many ways in recent years, is connected with regulating the acceleration regime according to signals from the particle beam. Sensors detect deviations of the beam from the calculated regime. The signals obtained act, through automation means, on the corresponding devices of the accelerator, eliminating dangerous deviations.

In the design of proton cyclic accelerators with an energy of 1000 GeV in the USSR, the following directions have emerged.

The Radio Engineering Institute of the Academy of Sciences of the USSR, E. L. Burshtein, A. A. Vasil’ev, and A. L. Mints, believe that large-scale copying of synchrotrons operating in the region of tens of GeV into the region of hundreds and 1000 GeV is impossible. They proposed building a cybernetic proton accelerator for 1000 GeV according to a three-stage scheme: an initial linear accelerator, a preliminary cyclic accelerator (booster), and a final cyclic accelerator.

Other scientists consider it possible to build strong-focusing synchrophasotrons for energies up to 500–700 GeV, raising the injection energy to 15 GeV. Such an injector may be the Serpukhov synchrotron at 70 GeV, operating in the 15 GeV regime, with an acceleration time amounting to 1/5 of the nominal value. In that case, satisfactory filling of the accelerating orbit of the large synchrotron will be obtained.

V. V. Vladimirsky, D. G. Koshkarev, and E. K. Tarasov find it possible to build strong-focusing proton synchrotrons up to 700 GeV while keeping the dimensions and cost of the installation within reasonable limits.

The path of development of installations to very high energies is suggested by the successful experience of G. I. Budker and A. A. Naumov in developing iron-free betatrons and synchrotrons. These developments were also carried out abroad, but the best results have now been obtained at the Institute of Nuclear Physics of the Siberian Branch of the Academy of Sciences of the USSR. Reliably controlled, cyclic iron-free accelerators with an orbit radius several tens of times smaller than installations with a steel magnetic circuit have great prospects for development in the region of ultrahigh energies.

Increasing the intensity of the controlling magnetic field in magnetic systems without an iron magnetic core—of the type proposed by Oliphant in Australia and developed by G. I. Budker and A. A. Naumov—or cryogenic installations with coils made of superconducting materials, is one of the paths for the development of cyclic accelerators that were outlined as early as the late 1940s and early 1950s.

The use of a closed waveguide accelerating system together with strong magnetic control fields is one of the possible ways of creating cryogenic accelerators in the near future.

Among the new methods of acceleration, let us note the work of G. I. Budker on the stabilized electron beam, the work of A. A. Kolomenskii on autoresonance acceleration by means of lasers, and especially the work of V. I. Veksler on the collective method of acceleration, which has been developed with particular success in recent years.

In the USSR, centers of scientific research in the field of acceleration and accelerators have been formed. Among them we shall mention the leading scientific institution, the Physics Institute of the Academy of Sciences of the USSR, from which came the most important theoretical investigations of V. I. Veksler, M. S. Rabinovich, A. A. Kolomenskii, A. N. Lebedev, E. L. Feinberg, and V. A. Petukhov, which defined the preceding epoch in the development and construction of accelerators. Experimental studies on electron accelerators at FIAN were carried out under the direction of Corresponding Member P. A. Cherenkov, V. E. Pisarev, and V. A. Petukhov.

At the Moscow Engineering Physics Institute, Prof. G. A. Tiagunov and O. A. Val’dner developed and built linear electron accelerators.

At the Radio Engineering Institute of the Academy of Sciences of the USSR, under the direction of A. L. Mints, the most important problems of the radio engineering of operating high-power accelerators have been solved, and an interesting idea of a cybernetic accelerator is being developed. At present there already exists an operating model of a cybernetic accelerator at 1 GeV.

At the Institute of Theoretical and Experimental Physics of the Academy of Sciences of the USSR, under the direction of A. I. Alikhanov and V. V. Vladimirsky, an accelerator with strong focusing has been developed and built, in which protons acquire an energy of 7 GeV; the world’s largest Serpukhov proton accelerator for an energy of 60–70 GeV has been built, and the first physical experiments are already being performed on it.

At the Joint Institute for Nuclear Research in Dubna, under the direction of D. V. Efremov, M. G. Meshcheriakov, and A. L. Mints, a phasotron giving protons with an energy of 680 MeV has been built, as well as a synchrophasotron at 10 GeV, built under the direction of V. I. Veksler, D. V. Efremov, and A. L. Mints. At the institute, research is being conducted on high-voltage acceleration and accelerators; a cyclotron with azimuthal variation of the magnetic field has been developed and built.

At the I. V. Kurchatov Institute of Atomic Energy, studies by G. I. Budker and A. A. Naumov on plasma acceleration, iron-free cyclic accelerators, and storage rings were begun. These studies were then transferred to Novosibirsk, where they served as the basis for the work of the Institute of Nuclear Physics of the Siberian Branch of the Academy of Sciences of the USSR.

At present, at the institute, physical experiments on electron-electron interactions with an energy of \(2 \times 160\) MeV and electron-positron interactions with an energy of \(2 \times 380\) MeV are being carried out on storage installations. A storage ring is being constructed, intended for experiments on the interaction of protons and antiproto-

…with an energy of \(2 \times 25\) GeV, at which work is also planned on electron–positron interactions with an energy of \(2 \times 6\) GeV.

In Leningrad, work on the design and construction of accelerators is being carried out at the D. V. Efremov Institute of Electrophysical Apparatus, under the direction of E. G. Komar.

Research on the physics of electron accelerators is being conducted at the Leningrad Physico-Technical Institute under the direction of A. P. Komar. A 1 GeV phasotron has been built.

In Tashkent, under the direction of S. V. Starodubtsev, powerful high-voltage ion accelerators and an original design of a cyclotron for large currents have been developed.

At the Institute for Physical Problems, under the direction of S. P. Kapitsa, microtrons for large currents are being developed.

In Tomsk, at the Siberian Physico-Technical Institute, work on high-voltage acceleration was begun under the direction of M. I. Korsunsky in 1930. He advanced several interesting ideas, including the structural combination of the accelerating tube and the high-voltage winding, and the use of vacuum for insulation purposes.

After the war, research on acceleration expanded at the Polytechnic Institute in the field of high-voltage acceleration. Pulse generators of 3.2 MeV and a pulse transformer of 1.5 MeV were created, as were electrostatic machines and parametric generators, a large number of betatrons, and a cyclotron; a 1.5 GeV synchrotron was also built and is operating successfully.

Accelerating systems for synchrotrons have been developed in the form of one or several drift gaps and closed curved waveguides; synchrotrons with such accelerating devices have been built.

In Yerevan, under the direction of A. N. Alikhanian, a 6 GeV synchrotron was developed, built, and put into operation.

The construction of accelerators, especially large ones, has become a branch of skilled electrical machine-building and radio-engineering industry.

In the creation of this industry in the USSR, a major role belongs to D. V. Efremov, A. L. Mints, and E. G. Komar, who directed the construction of the largest accelerators in the world, built in the USSR.

As thirty years ago, today the task comes down to obtaining beams of particles of high intensity and high energy, and this aspiration is driven by the desire of experimental physicists to study more deeply the phenomena of the microworld.

For technological purposes, radiation physics or chemistry requires accelerators with an energy of fifteen MeV. For therapy with hard radiation, an accelerator with an energy of up to 20–30 MeV is needed, and for therapy with an electron beam, probably up to 60 MeV.

For defectoscopy, bremsstrahlung with a maximum energy of 30 MeV is needed. In all these practical applications, installations are needed with high radiation intensity and high reliability, and consequently also productivity. This is now the main issue in the development of low-energy accelerators.

The solution of the basic task of building accelerators that provide the greatest possible number of particles at the output and ever higher energies proceeded amid many contradictions, the principal ones of which seriously impeded the development of acceleration methods and technology. They determined the achieved level of development of acceleration depending on the economic potential and the state of related branches of science and technology.