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Accelerators
Chapter 18
Accelerators Chapter Outline 18.1 Introduction 18.2 Accelerators for Radiation Technologies 18.3 Linear Accelerators of Direct Action (High-Voltage Accelerators) 18.3.1 X-Ray Tubes 18.3.2 The CockcrofteWalton Generators 18.3.3 Dynamitron and Tandetron 18.3.4 The Van de Graaff Generators 18.3.5 Pelletrons 18.3.6 Transformer Systems
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18.4 Linear Resonance Accelerators 18.5 Rhodotrons 18.6 Cyclic Accelerators 18.6.1 Cyclotrons 18.6.2 Betatrons 18.6.3 Microtrons 18.6.4 Synchrotrons 18.7 Synchrotron Radiation References
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18.1 INTRODUCTION Since the discovery of X-ray radiation and radioactivity and before the beginning of the 1930s, engineers, as well as physicians, used natural radionuclides, mainly 226Ra, and X-ray tubes as sources of radiation. Sources of natural activity are provided only by gamma quanta, fast electrons, and alpha particles in a limited energy range. With the help of nuclear reactions, neutrons can be obtained. Researchers in physics had at their disposal also cosmic radiation. Among nuclides of natural radioactivity in the 232Th decay chain, there is a 208Tl nuclide emitting gamma quanta with an energy of 2.614 MeV. This is the maximum energy of the nuclide gamma source. The maximum energy of alpha particles (Ea ¼ 8.779 MeV) emits 212Po (T1/2 ¼ 3$107 s), a nuclide from the same decay chain. The maximum energy of the beta spectrum of the nuclide 12N is 16.6 MeV. But 12N is a short-lived nuclide (T1/2 ¼ 1.3$102 s) and is far from the nuclear stability region. Usually, the boundary energy of the beta spectrum of nuclides of natural activity does not exceed w5 MeV. Let us recall that the average energy of beta particles is about one-third of the maximum. In cosmic rays, particles are observed in a very wide energy range, up to energies unavailable in modern accelerators, up to 1021 eV. But the density of the flux of cosmic particles drops sharply as their energy increases. For example, the particle flux density with an energy of 1019eV is one particle per year per km2. The flux density of particles with an energy of one TeV (1012 eV) is equal to w1 m2/s. Besides, which is quite important for the experiment, cosmic particles arrive at random instants. Even with this meager set of radiation energies, it was possible to find out rather much of the structure of an atomic nucleus, and to spot the nucleus itself inside the atom. However, to study the atomic nucleus and elementary particles, as well as to use radiation in technical applications, it is necessary to have a wider range of bombarding particles, higher energy, to have such a controlled device that would give out the flows of the necessary particles of the required energy, and the required intensity, continuously or in pulsed mode. Thus, science and technology required the creation of controlled sources of nuclear radiation. Because the main task was to increase the energy of the particles, such devices were called accelerators. To date, a large number of different types of accelerators have been developed. In principle, all possible accelerators can be divided into accelerators for industrial applications and accelerators for scientific research. However, such a division is somehow arbitrary, because applied works are carried out on typically scientific accelerators and scientific research is carried out on industrial accelerators.
Radiation. https://doi.org/10.1016/B978-0-444-63979-0.00018-5 Copyright © 2019 Elsevier B.V. All rights reserved.
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By the principle of action, accelerators can be divided into linear and cyclic. The electron accelerators and accelerators of heavy charged particles, protons and ions, quite noticeably vary in structure and design. But they can be both cyclical and linear. In general, large and very large accelerators are intended for research in high-energy physics. Here the word “very big” is not a stylistic device, but a literal name. Large accelerators are well known; they are often mentioned by the press. It is on such accelerators that new fundamental information is obtained on the structure of matter at the deepest level. These are very complex and expensive installations, there are rather few of them. For a long time, only the most highly economically developed countries could afford to produce a large accelerator. At present, this became completely impossible for one country, and the largest accelerators are being built and used on the basis of broad international cooperation. For a long time, accelerated particles bombarded stationary targets. In such collisions and at relativistic particle energies, the relative energy is much lower than the relative energy in the nonrelativistic case (Section 3.2.3, Eq. 3.25). In this, the total collision energy is equal, approximately (2E$mc2)1/2. For example, protons with an energy of 1000 GeV, colliding with protons of a stationary target, cause reactions characterized by an energy of w45 GeV. In the collision of two particles of equal mass with an energy of 1000 GeV each, the collision energy is 2000 GeV. It is seen that it is more effective to bring two accelerated beams of particles in collision. Accelerators in which beams collide are called colliders [1]. Therefore, the progress of higher energies in physics occurs mainly due to colliders. And research in the field of already mastered energies is more profitable to carry out by the accelerators with a fixed target. In this case, it is possible to operate with beams of unstable or neutral particles, which is very difficult or even impossible on colliders. Besides, accelerators with fixed targets can be studied more rare phenomena, as it is possible to obtain a much larger number of collisions. Accelerator technology is widely demanded in various spheres of modern industry. Currently, there are about 26,000 accelerators in the world, of which only 5% are installations for scientific research, the rest are used in medicine, in the production of semiconductors, in the processing of materials, industrial tomography, etc.
18.2 ACCELERATORS FOR RADIATION TECHNOLOGIES To date, there has been an extensive set of clearly defined areas in which the use of accelerators is technologically and commercially justified. According to experts in the field of beam technologies [2,3], the total amount of annual costs for the use of industrial accelerators for production, sterilization, and control currently exceeds $ 500 billion. According to estimates from the same sources [2,3] over the past 60 years, more than 24,000 accelerators for industrial applications have been built in the world. Moreover, more than 11,000 accelerators were built specifically for medical needs. There are major areas where ray technologies play an important role. Most of the accelerators (w10,200) were used for ion implantation; approximately on 7000 accelerators, the radiation treatment of materials for their modification was conducted. Approximately 2600 accelerators were used for sterilization and other similar treatments. By use of 1500 accelerators, nondestructive testing of products is carried out, at least 1500 accelerators operate as neutron generators. Approximately 1000 accelerators are engaged in the production of radionuclides. And we also have to specify accelerators as sources of synchrotron radiation. It is assumed that about 70 such sources are currently in operation. Of course, these figures are not quite exact. There are multifunctional machines by which a variety of operations can be done, but nevertheless the trend toward specialization is quite evident. Most of the industrial accelerators have a service life of 20e40 years; it is believed that at least 75% of the created accelerators are still used. The use of radiation technology is continuously spreading. New accelerators are developed and produced by approximately 70 companies around the world. According to recent estimates, approximately 1100 industrial irradiating systems are coming to the market for a total of $ 2.2 billion a year. To solve the problems in nuclear physics, accelerators are required for ever higher energies, which produce beams of ever increasing intensity and accelerate ever heavier ions. Currently, the greatest accelerator is the Large Hadron Collider (LHC), with maximum energy of 7 þ 7 TeV; it can produce up to one billion protoneproton collisions per second. It can accelerate nuclei up to 208Pbþ82. To solve various industrial problems, accelerators with energy in the range from 75 keV to 30 MeV are required. Particles with a lower energy spend a significant part of the energy in the accelerator window and in the air, radiations with higher energy are capable of inducing radioactivity. Usually this rather wide range of energies is divided into three groups: 1. high-energy acceleratorsdfrom 5.0 up to 30 MeV; 2. medium-energy acceleratorsdfrom 300 keV up to 5.0 MeV; and 3. low-energy acceleratorsdfrom 75 keV up to 300 keV.
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Accelerators with energies above 300 keV are usually equipped with beam scanning systems; accelerators for smaller energies produce a wide beam with the help of an extended cathode and an anode. In the radiation technologies and in medicine, both cyclic and linear accelerators are used. In industrial applications, several types of cyclic accelerators are used, mainly cyclotrons, synchrotrons, betatrons, microtrons, and a wide range of linear accelerators The new types or new modifications of known types of accelerators appeared. They are, rhodotrons, pelletrons, dynamitrons, etc., possessing a whole complex of useful qualities for industrial applications.
18.3 LINEAR ACCELERATORS OF DIRECT ACTION (HIGH-VOLTAGE ACCELERATORS) 18.3.1 X-Ray Tubes The simplest theoretically and the first historically were linear accelerators of direct action. In linear accelerators, particles are accelerated by a constant electric field and they move rectilinearly in a vacuum chamber, between accelerating electrodes. The energy that the particles received was determined by the potential difference that could be provided in such installations. Since then, the main problem was in generating high voltage; the first successful designs of accelerators were called generators. Though it has to be pointed out that conventional X-ray tubes are also accelerators, they accelerate electrons that by slowing down in the anode material generate X-rays (Fig. 18.1). In high-voltage accelerators, as a rule, three circuits for obtaining high voltage are used: (1) Cascade generators (the CockcrofteWalton generator, etc.). (2) Mechanical charge transfer (Van de Graaff generator, pelletron, etc.). Accelerators built on this basis are sometimes called “electrostatic generators.” (3) Various transformer circuits.
18.3.2 The CockcrofteWalton Generators The first linear accelerators (the CockcrofteWalton generator and the Van de Graaff generator) appeared almost simultaneously in the early 1930s of the last century. In 1932, two scientists from Cambridge, John Cockcroft and Ernst Walton, built a cascade voltage multiplier, converting the alternating voltage into a high constant. The accelerator with this high-voltage source was called the CockcrofteWalton generator; the voltage multiplication scheme is shown in Fig. 18.2. As early as in the first experiment on the accelerator they built, the researches directed a beam of protons accelerated to an energy of 800 keV toward a 7Li target, and then they observed a nuclear reaction in which a lithium nucleus captured a proton and disintegrated into two alpha particles. 7 3 Li
þ p/42 He þ 42 He þ 17 MeV.
(18.1)
This was the first reaction of nuclear fission by artificially accelerated particles, and due to this achievement the authors received the Nobel Prize in Physics in 1951 for “transmutation of atomic nuclei with artificially accelerated atomic particles.”
FIGURE 18.1 Scheme of the X-ray Coolidge side-window tube (scheme). C is the cathode, A is the anode, and Win and Wout are water inlet and outlet of the cooling device. Figure from Roentgen-Roehre.svg. Hmilchderivative work: Coolth (talk) - Roentgen-Roehre.svg, Public Domain. https://commons. wikimedia.org/w/index.php?curid¼11691922.
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FIGURE 18.2 The simple multiplier of CockcrofteWalton generator, consisting of two sections.
FIGURE 18.3 Marx generator: (A) Charging, (B) Discharging.
There are many different cascade voltage multiplication schemes. One of them is the Marx generator (Fig. 18.3). In it, the capacitors are charged in parallel from the common source, and then by means of spark discharges, they are switched to serial and the voltage on the capacitors is summed. It is clear that such generator can only operate in a pulsed mode.
18.3.3 Dynamitron and Tandetron Several other versions of cascade generators got special names. Thus, the company IBA Industrial (formerly Radiation Dynamics Incorporated) in the 1960s developed accelerator, called “Dynamitron,” that can accelerate either electrons or positive ions. Dynamitron’s accelerating column is within a vessel filled with sulfur hexafluoride insulating gas under high pressure. The main advantage of the electrical circuit used in Dynamitron is to allow a much higher beam current to be transported than a typical the CockcrofteWalton style accelerator. Dynamitron can produce an electron beam with an energy of up to 5 MeV and a power of up to 300 kW. Dynamitron has a very large installed base, with more than 200 units, primarily in the United States [5]. A whole series of cascade accelerators of ELU type, similar to Dynamitron, is produced by the G.I. Budker Institute of Nuclear Physics in Novosibirsk (Siberian department of the Russian Academy of Science). Accelerators of ELU series have been issued since 1971, and they dominate in the market of accelerators for radiation technologies in Russia and Eastern Europe. A range of electronic accelerators of constant action such as ELU creates electron beams in the energy range from 0.2 to 2.5 MeV and beam current up to 200 mA.
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The cascade generator of the tandem type is called “tandetron.” This accelerator achieves two-step acceleration with a single voltage by converting the electric charge of an accelerating ion. Negative ions, extracted from an ion source, inject into the accelerator, where it accelerates ions in two steps. First, the injected negative ions are accelerated due to the applied electrostatic field (positive high voltage). After they collect the maximum possible energy, the negative ions are passed through a thin foil, where they are “stripped off,” i.e., each is deprived of a pair of electrons and converted into a positive ion. The beam of positive ions accelerates toward ground potential and gains energy again. Thus, the total energy can be twice as large as in a single stage of the CockcrofteWalton generator. The tandem machine can produce ion beams with energies in the range from 400 keV to 24 MeV of almost all elements of the periodic system with the current in the mA area.
18.3.4 The Van de Graaff Generators In 1931, the American scientist Van de Graaff built an electrostatic generator in which electrical charges from a special charger are transferred to a high-voltage electrode by a tape of insulating material. The high potential (up to 10 MV) allows to accelerate both electrons and heavy particles, i.e., protons, deuterons, and alpha particles. Various Van de Graaf generators are by now manufactured industrially. The beam intensity reaches 100 mA, the beams can be well collimated, and the output energy can be easily stabilized with an accuracy of 10 keV. The maximum energy achieved is now about 30e40 MeV for protons. As is known, the breakdown voltage of dry air at atmospheric pressure is w30 kV/cm, and the electric field strength depends rather considerably on the radius of curvature of the electrode. Therefore, the high-voltage electrodes must be large in size with a well-polished surface and to stand far enough from other installations and walls of the premises. In modern accelerators that use high voltage, the high-voltage part of the plant is placed in a reservoir with a high pressure of electrically insulating gas, so at present such accelerators look much more compact. As in the case of the CockcrofteWalton generators, the Van de Graaff generators are produced in a tandem version.
18.3.5 Pelletrons A more advanced modification of the Van de Graaff generator is the so-called pelletron. In the pelletron, the electric charge is transferred not by a dielectric belt conveyor but by a chain consisting of electrically conductive links (pellets) connected by an insulator. Besides, the charging system of the conveyor has been changed. As a result, a high stability of the charging current and a long service life are achieved; the danger of spark breakdowns and spraying of the tape material is eliminated. Pelletron allowed to increase the received high voltage up to 25 MV. The form of the charge transfer chain and the animation of the pelletron are shown on the NEC website [6].
18.3.6 Transformer Systems High voltage in direct-acting accelerators can be obtained by means of various transformer circuits. One of the types of such system is a conventional high-voltage transformer, powered by a sinusoidal voltage. A special device ensures the passage of a beam of accelerated particles only when the voltage on the secondary winding of the transformer has the necessary polarity and is close to the maximum. Such schemes make it possible to obtain powerful beams with the energy of accelerated particles up to 2e3 MeV. In pulsed accelerators, voltage sources are pulsed transformers of various types, for example, the Tesla transformer.
18.4 LINEAR RESONANCE ACCELERATORS The production of high-energy particles can be achieved by a resonant method. Historically, the first accelerator of the resonance type was the Wideröe accelerator, developed in 1928 by the Norwegian physicist Rolf Wideröe. The resonant linear accelerators became known as the “linac” (LINear ACceleration). The particle beam moves along the axis of the subsequent line of tubes, as shown in Fig. 18.4. A high-frequency electric field with a voltage of the order of hundreds of kV is active in the gaps between the tubes. Inside each tube, the electric field equals zero. In each flight between the tubes, a cluster of particles accelerates. The frequency of the generator and the dimensions of the tubes are selected so that the bunch of accelerated particles approaches the next gap at the moment when the accelerating voltage acts there.
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FIGURE 18.4 Scheme of the linear resonant accelerator. S e particle source, G e voltage generator.
Because the velocity of the particle increases while passing through the next accelerating gap, the lengths of the accelerating tubes also increase. When the particle reaches relativistic velocities, the length of the tubes becomes constant. Calculations show that for protons to reach an energy of 10 MeV at an accelerating voltage frequency of 10 MHz, the length of the last tube has to be 2.2 m. The simplest version of the Wideröe accelerator makes it possible to accelerate only the particles in the area of nonrelativistic energies. To eliminate the problems inherent in the Wideröe accelerator, resonator accelerators were developed. A simple resonator accelerator with a standing wave serves to accelerate electrons. Another version of a resonator accelerator with a transit tube, the so-called Alvarez accelerator, preferably accelerates protons and other heavy particles. There are accelerators using so-called loaded waveguides in which a traveling electromagnetic wave is formed. The traveling wave carries particles along the accelerating field. If the velocity of a particle differs insignificantly from the light speed, it keeps on the crest of the wave for a long time, continuously being accelerated by it. A series of resonance pulsed accelerators ILU has been manufactured since 1970 by the G. Budker Institute of Nuclear Physics. Accelerators overlap the energy range from 0.7 to 4 MeV with a maximum beam power of up to 50 kW. Accelerators of the “linac” type can accelerate both electrons and heavy particles. The largest linear accelerator today is the Stanford Linear Accelerator at Menlo Park, California, which is 3 km long. It has about 80,000 accelerating electrodes and could accelerate electrons and positrons to about 50 GeV. The next step in the creation of linacs is the perspective International Linear Collider, where electron and positrons will collide. It is expected to be 30e50 km long. It is planned to achieve initially collision energy of 500 GeV, with a perspective of a later upgrade to 1000 GeV (1 TeV). The supposed location of its construction is the Kitakami highlands, in the Iwate prefecture of Northern Japan.
18.5 RHODOTRONS A relatively new type of accelerator, which appeared at the end of the twentieth century, rhodotron, can be attributed to both a group of cyclic accelerators and that of linear accelerators. In accelerators in which particles pass successively and repeatedly in the accelerating region along the same path, there are serious limitations of the beam current due to the increasing role of the space charge. The French scientist Jacques Pottier (1989), who proposed a new type of accelerator, named “rhodotron,” was able to overcome this difficulty. Pottier drew attention to the fact that in the coaxial cavity in the median plane the magnetic field equals zero, so it does not reject the beam, and the electric field is directed radially and is able to accelerate electrons. Turning off a beam of electrons at the exit from the resonator and returning it to the accelerating cavity, as shown in Fig. 18.5, it is possible to drive the particles several times through the accelerator, gradually increasing their energy. The name “rhodotron” has the Greek origin (“rhodon” means “a rose”), as the trajectory of the accelerated electrons resembles a rosette. Parameters of the resonator and high-frequency equipment allow the electrons to transmit energy up to 2 MeV in one pass, and the total number of passes is limited by 10. It is possible to withdraw the beam also at intermediate stages of acceleration. Thus, rhodotron makes it possible to obtain continuous beams of electrons with an energy of 5e10 MeV of considerable power (hundreds of kW). Turning magnets make rhodotron a very compact accelerator.
18.6 CYCLIC ACCELERATORS 18.6.1 Cyclotrons The first cyclic accelerator, the cyclotron, was constructed by E. Lawrence and M.S. Livingston in 1929, and in 1939, for which E. Lawrence was awarded the Nobel Prize in Physics. The first Lawrence cyclotron had a diameter of 4 inches (10 cm), and in 1932 a 27-inch diameter machine was built in which protons were accelerated up to an energy of 5 MeV. The principle of operation of the cyclotron is clear from Fig. 18.6.
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FIGURE 18.5 Scheme of the rhodotron. E is the electron source, L is the magnetic lens, C is the high-frequency resonator, and M is one of the bending magnets. Figure from Rhodotron.svg. Author Patrick87. https://commons.wikimedia.org/wiki/File:Rhodotron.svg.
FIGURE 18.6 Diagram of cyclotron operation from Lawrence’s 1934 patent. The “D”-shaped electrodes are enclosed in a flat vacuum chamber, which is installed in a narrow gap between the two poles of a large magnet. Figure from Cyclotron. Wikipedia. https://en.wikipedia.org/wiki/Cyclotron. Cropped from U.S. Patent 1,948,384, Ernest O. Lawrence, Method and apparatus for the acceleration of ions (1934).
In the cyclotron, the particle source is located in the center of the vacuum chamber between the poles of the magnet. A high-frequency alternating voltage applies between two hollow “D”-shaped electrodes called “daunts” inside a vacuum chamber. The particles that are emitted from the source perpendicular to the direction of a uniform magnetic field B (constant magnitude and direction) move along a spiral trajectory as their energy increases in every passage between the daunts. In the circular motion, centripetal force and magnetic Lorentz force are equal (18.2) mv2 r ¼ eBv; where m is the particle mass, e is its charge, v is velocity, and r is the circular path radius. The frequency of the particle motion in the constant magnetic field, the so-called cyclotron frequency f, does not depend on the particle energy and the radius f ¼ v=2pr ¼ eB=2pm.
(18.3)
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All particles with the same charge-to-mass ratio rotate around magnetic field lines with the same frequency. By choosing the frequency of high-frequency electric field, one can achieve multiple resonance acceleration of the particle. Cyclotrons became very popular type of accelerators. According to the MEDraysintell “The global cyclotron market is expected to reach US$ 245 million in 2030 showing an annual growth of 3%, with an estimated yearly average sale of 60 cyclotrons over the years 2015 to 2030.” [9]. Up to 2015, over 1200 cyclotrons are used in nuclear medicine worldwide for the production of radionuclides [9]. The synchronization of particle motion and the frequency of the accelerating field are obtained only in the nonrelativistic case (for protons only up to an energy of tens of MeV). With increasing energy, the mass of particles starts to depend on their velocity. In order to keep the particles in phase with the oscillations of the electric field, the change of either the magnetic induction or of the frequency of the accelerating field in the process of acceleration is needed. The first option is the basis of the synchrotron, and the second is the basis of the phasotron (synchrocyclotron).
18.6.2 Betatrons An attempt to create the first cyclic accelerator of electrons was undertaken by the Norwegian scientist Rolf Wideröe back in 1926, i.f., earlier than the idea of a cyclotron emerged, but the first reliably functioning betatron appeared only in 1940. The author of the operating model of betatron was the American scientist D. Kerst. Betatron is an induction accelerator in which electrons are held in equilibrium on a circular orbit by the magnetic field increasing synchronically with the increase of electron energy. Acceleration occurs due to the vortex electric field created by an alternating magnetic flux inside the equilibrium orbit. To create the necessary magnetic field, large electromagnets with an iron core are used. In betatrons, the energy of accelerated electrons can reach hundreds of MeV, but the magnets of such betatrons turn out heavy and consume a lot of energy. For example, the 300-MeV betatron of the University of Illinois weighed more than 300 tons. Now betatrons with an energy of 20e50 MeV were most widely used.
18.6.3 Microtrons In his search for a way to overcome the problem of phasing the beam in a cyclotron, the Soviet scientist V.I. Veksler invented a new type of accelerator, a microtron. In the microtron (Fig. 18.7), the particles are introduced into the accelerator chamber not in the central part of the magnetic field, as in the cyclotron, but at its edge. An accelerating cavity is located at the particle entrance. At each turn, the electrons receive energy on the order of the rest mass of the electron (w0.5 MeV). This means that, after the first turn, relativistic electrons move inside the microtron. They enter the resonator by each turn exactly at the moment of acceleration. Electrons move around the circle with the radius increasing, and all circles contact inside the resonator. Because of the need to ensure a large increase in energy for each turn, a powerful microwave electronics is used to operate the microtron, which is indicated by the prefix “micro” in the name of the accelerator. The maximum energy of the accelerated electrons is limited by the dimensions of the permanent magnet. The microtron turns out a fully operational accelerator of medium-energy electrons (up to 30 MeV), which plays an important role in many applications.
FIGURE 18.7 The scheme of microtron. Figure on the basis of B.S. Ishkhanov, I.M. Kapitonov, E.I. Kabin, Particles and Nuclei. Experiment, MAKS Press, Moscow, 2015, in Russian. Web-publication. http://nuclphys.sinp.msu.ru/experiment/index.html#cont.
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18.6.4 Synchrotrons For researches in high-energy physics, high-energy particles are required. It is known from optics that to distinguish the structural details of an object with linear dimensions of the order of d, the wavelengths of radiation comparable or less than d must be used: ƛ d. Taking into account that the de Broglie wavelength of the particle is equal to ƛ ¼ Z/p, and the relation of the kinetic energy and momentum in the nonrelativistic case has the view F ¼ r2/2M, one finds that for probing atomic nuclei w1013 cm, particles are needed with energy (in units of Mc2) not less than 2 E 1 Z ¼ 2 . (18.4) Mc2 2d Mc If the bombarding particle is a proton, then Z/Mrc ¼ lr ¼ 0.21$1013cm is the Compton wavelength of the proton and Mrc2 ¼ 938 NeV w 1 GeV, then F/Mrc2 0.02 and for probing details with linear dimensions w 1013 cm, protons with an energy of not less than w 20 MeV are required. To improve the spatial resolution, the energy of the particles should be increased inversely proportional to the square of the required resolution. In Section 3.2.5.4, the variation of the potentials with which the bombarding particle occurs as its energy increases and the corresponding change in information on the structure of the object are described in detail. Because the energy values of nuclear levels are tens of MeV, for the study of nuclei, accelerators with particle energies of hundreds of MeV are required. It is important that the distance between the nuclear levels is of the order of several keV; therefore, beams with a high-energy resolution are required. There are no restrictions on the upper limit for research investigations in the physics of elementary particles. The problem of increasing the energy of accelerated particles was solved by the creation of synchrotrons. The principle feature of the synchrotron, which distinguishes it from the cyclotron and the phasotron, is that the particles move in the annular channel and only within this channel it is necessary to create a magnetic field. This dramatically reduces the size and weight of the magnet, as well as the energy consumed by it. The arrangement of the elements of the synchrotron is shown in Fig. 18.8. In some parts of the ring, accelerating electrodes are installed, on which a high-frequency accelerating field is supplied. For continuous acceleration of particles, it is necessary that at the moments of acceleration the direction of particle motion and the electric field coincide; for this, it is necessary to provide resonance between the motion of particles and the change in the electric field. Because the accelerator simultaneously accelerates a huge number of particles with spread of energies, and therefore also in masses, the particles have different frequencies of turning. Therefore, an insignificant fraction of the accelerated particles fall into resonance with the accelerating field. This problem was solved with the discovery of the autophasing principle (V.I. Veksler, E. McMillan). In a synchrotron, in which the magnetic induction changes synchronously with the motion of particles, it is possible to accelerate only the relativistic particles that move with the constant velocity, i.e., electrons. To accelerate protons and ions,
FIGURE 18.8
Schematic of a synchrotron.
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before they become relativistic, it was also necessary to change the frequency of the accelerating electric field, as was done in the synchrocyclotron (phasotron). Such a device was called proton synchrotron. In the Russian scientific publications, the proton synchrotron is called synchrophasotron. In order to secure reliable operation of the proton synchrotron and to reduce the dimensions of the vacuum chamber, and hence the magnet, it was required to ensure the stability of the particle motion in the directions that are perpendicular to beam trajectories. A specially selected rather complex configuration of the magnetic field makes it possible to rapidly quench the particle vibrations both in the radial and in the vertical direction. In order to strengthen the axial focusing, a field sharply decreasing along the radius is necessary. On the contrary, to increase the focusing along the radius, a sharply increasing field along the radius is necessary. The simultaneous requirements here are impossible, but they can be implemented alternately. A system that realizes this sequential focusing is called a system with “hard” focusing. A decrease in the transverse oscillations is also promoted by a specially designed so-called “cooling” of the beam. After the discovery of the autophasing principle, the era of the construction of accelerators for ever greater energy began. In 1952, in Brookhaven, USA, the so-called Cosmotron was commissioned for proton energy of 3.3 GeV. In 1954, in Berkeley, USA, the Bevatron was constructed for energy of 6.2 GeV (by now it could be called Gigatron). The limiting energy of this accelerator was calculated for the production of antiprotons. Indeed, measurements have shown that these particles actually exist. For this discovery, E. Segre and O. Chamberlain were awarded the Nobel Prize in Physics in 1959. At that time, the antiprotons seemed absolutely exotic particles. The authors of the discovery reported about the discovery when only 40 antiprotons were registered. Slightly more than 50 years passed, and now the use of antiprotons for radiation therapy are quite seriously discussed [10]. In 1957, in Dubna, the USSR began to operate a synchrophasotron with a “weak” focusing on the energy of 10 GeV. The vacuum chamber of the Dubna synchrophasotron with weak focusing had dimensions of 2 m by 40 cm. The author of this book personally observed how the personnel while repairing and adjusting the facility had to crawl inside the vacuum chamber. In 1961, the strong focusing mode was used in the accelerator ITEP, Moscow, USSR, for 7 GeV, which served as the basis for the creation of the U-70 accelerator in Protvino, USSR, for 70 GeV. The super proton synchrotron at CERN, which started to operate in 1976, accelerated protons up to 400 GeV, sufficient for the production of W and Z bosons, carriers of weak interaction. The discovery of these particles in 1983 proved to be an important stage in making of a modern conception of the world; it confirmed the theory of combining electromagnetic and weak interactions. C. Rubbia and S. Van der Meer in 1984 were awarded the Nobel Prize for this discovery. Van der Meer’s major contribution was the development of a cooling system for the beams. Without this achievement, the discovery of W and Z bosons would not be possible. The greatest for today (summer 2018) is the LHC at CERN (CERN) on the border of Switzerland and France. In the collider mode, the energy of colliding protons is 7 þ 7 TeV. The LHC can also accelerate heavy ions, in particular, lead ions 208Pbþ82 up to an energy of 2.76 TeV per nucleon. Let us note that the inside diameter of each of the two vacuum chambers of the LHC for proton beams moving in opposite directions equals 5.0 cm [11]. The LHC was actually designed for searching the last elementary particle of the Standard Model of Elementary Particles, i.e., the Higgs boson. During 2013, in experiments by the two different facilities on the LHC collider, the data were obtained proving the existence of this particle. P. Higgs was awarded the Nobel Prize in Physics in 2013 for his prediction of a particle that could be responsible for the inertial mass of elementary particles, made back in the 1960s of the 20th century. The particle was later called the Higgs boson. Scientists and engineers around the world are looking ahead, and they are working hard for upgrading the LHC, and to obtain the High-Luminosity LHC. The upgrading is planned to be accomplished in 2026, and it is planned to increase the number of collisions by a factor of five to ten. The next step is currently in progress; the scientists are developing designs for a higher performance particle collider, the Future Circular Collider (FCC). It is going to greatly increase the energy and intensity of a particle collider and is going to reach collision energies of 50 þ 50 TeV. It is expected that the FCC will approach the maximum of its potential around 2035. The length of the tunnel for the proposed accelerator will be approximately 80e100 km [12]. Thus, it can be seen that cyclic accelerators can be divided into accelerators in which the particles move in a spiral during acceleration (cyclotron, phasotron, microtron), and accelerators in which the particles move along an unchanged, closed, nearly circular path (betatron, synchrotron). One of the most serious problems that have arisen in the acceleration of electrons in cyclic accelerators is the loss of energy by radiation. If electrons and protons of the same energy move in the orbits with equal radiuses, then the energy
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losses of electrons for synchrotron radiation are (mp/me)4 z 1013 times greater. Therefore, it is not possible to accelerate electrons up to energies of more than 100 GeV on cyclic accelerators. To accelerate electrons (and positrons) up to higher energies, huge linear accelerators are constructed. On the other hand, it turned out that magnetic bremsstrahlung (synchrotron) radiation of accelerated electrons has many useful properties, so now special accelerators are being built, designed to produce beams of synchrotron radiation (Section 18.7). Different types of cyclic accelerators are preferable for accelerating different types of particles. Synchrotrons, betatrons, and microtrons are designed to accelerate electrons, and cyclotrons, phasotrons, and proton synchrotrons are designed to accelerate heavy particles. Large modern accelerators are usually compound systems. Before particles are injected into the large ring of the accelerator, where they receive the final energy, they sometimes go through several stages of preliminary acceleration and at some stages, usually initial, they are accelerated in a linear accelerator. If the necessary number of particles is not obtained from the injector at one stage, the accumulation and storage regime is applied.
18.7 SYNCHROTRON RADIATION When moving in a magnetic field along a curvilinear trajectory in accelerators, the charged particle undergoes radial acceleration perpendicular to its trajectory and, in accordance with the laws of electrodynamics, emits electromagnetic quanta. The energy lost to radiation is inversely proportional to the square of the particle mass. This leads to the conclusion that heavy particles emit significantly less energy than the light ones. For example, a proton emits an energy 3.4$106 times less than an electron. Therefore, the radiative energy losses are most important for lightest charged particles, i.e., electrons. This magnetobremsstrahlung is called synchrotron radiation, because experimentally the radiation was first discovered by F. Haber, a graduate student, on the 80-MeV synchrotron of General Electric in 1947. For the sake of justice, it should be noted that synchrotron radiation was predicted by theorists even before the discovery. Synchrotron radiation was first negatively perceived as an obstacle to the acceleration of particles, as it sets the energy limit of electrons accelerated in cyclic accelerators, i.e., betatron, synchrotron. At present, synchrotron radiation is widely used in scientific research, as well as in applications of great practical importance. Synchrotron radiation is used in microlithography, for the photosynthesis of hydrocarbons, nitrogen oxides, etc. It is used to study the radiation impact on materials and instruments outside the atmosphere, which is very important for space materials science. X-ray monochromatized synchrotron radiation is used in X-ray diagnostics, what allows to significantly reduce the radiation load per person during X-ray examination. There are interesting applications of synchrotron radiation in radiation technology and radiation-chemical processes. These vast possibilities of using synchrotron radiation are determined by a set of remarkable properties. The maximum intensity of the radiation is shifted to the high-frequency area with respect to the rotation frequency of the electron in the orbit. The maximum intensity occurs in the X-ray region and even in the gamma ray region in modern synchrotrons and storage rings. The radiation has a sharp directionality along the tangent to the electron orbit. The time structure of the radiation depends on the specific accelerator. On the synchrotron, the acceleration cycle is usually repeated at a frequency of 50 Hz, and with the same frequency the bursts of radiation pulses are repeated being modulated inside the packets with the frequency of the electron motion in orbit. The length of a bunch of electrons in an orbit is determined by the duration of those bursts that reach hundreds of picoseconds. Initially, synchrotron radiation was obtained on synchrotrons. But when the extremely interesting and useful problems that can be solved with the help of this radiation became clear, special storage devices appeared. In storage rings, due to repeated injection, intense particle beams can be accumulated, maintained in the continuous circulation mode. Prior to entering the actual storage ring, the electrons need to be preaccelerated to their final energy and speed (in the actual storage ring their energy is only maintained). The scheme of the storage ring with injection, undulator, wiggler, etc., is shown in Fig. 18.9. The real storage device has a lot of beamlines. For example, the ring of the ESRF (European Synchrotron Radiation Facility, Grenoble, France) has a length of 844 m and 49 bunches. The energy of the electrons in the storage ring is 6 GeV [13]. At present, synchrotron radiation is one of the most important tools in radiation technology. To increase the intensity of synchrotron radiation and to use it more efficiently, special synchrotron radiation generators are built, undulators and wigglers. These devices proposed by V.L. Ginzburg in 1947, and now called “insertion devices,” are really inserted in straight sections of electron storage rings [15]. An alternating periodic magnetic field is created in these devices, and electrons move along a trajectory that looks like a snake. The spectral and angular distribution of the radiation from an undulator essentially depends on the
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FIGURE 18.9
The scheme of storage ring and synchrotron radiation emission.
relationship between the angle of rotation of the electron in the magnetic field and the characteristic angle of divergence of radiation from each point of emission of the electron. Depending on this relationship, either an undulator or wiggler mode is realized. At present, there are undulators of a few tens of meters in length. The undulators 150e200 m long are in the development stage. Considering the large number of synchrotron radiation sources in the world that require undulators, the production of the latter has become a notable branch of scientific instrumentation [15]. Until now, the most brilliant and energetic source of light is the European X-ray Free Electron Laser (European XFEL) now in operation at Hamburg, Germany. It generates ultra-short X-ray flashes at a rate of 27,000 per second with a peak brilliance, one billion times higher than the best conventional X-ray sources. Electrons are accelerated up to the energy of 17.5 GeV by a 2.1-km long linear accelerator with superconducting RF cavities in the 3.4-km long tunnel. The X-rays are generated by self-amplified spontaneous emission, where electrons interact with the radiation that they or their neighbors emit. The wavelength of the X-ray laser may be up to w250 keV (from 0.05 to 4.7 nm).
REFERENCES [1] B.S. Ishkhanov, I.M. Kapitonov, E.I. Kabin, Particles and Nuclei. Experiment, MAKS Press, Moscow, 2015 in Russian. Web-publication. http:// nuclphys.sinp.msu.ru/experiment/index.html#cont. [2] R.W. Hamm, M.E. Hamm (Eds.), Industrial Accelerators and Their Applications, World Scientific, 2012. http://www.worldscientific.com/ worldscibooks/10.1142/7745. [3] T.K. Kroc, R.D. Kephart, Industrial Acceleratorse Beyond Transformers and Cyclotrons, More Power, FERMILAB-CONF-15-131-A, 2015, 4 p. http://lss.fnal.gov/archive/2015/conf/fermilab-conf-15-131-ad.pdf. [4] Roentgen-Roehre.svg. Hmilchderivative work: Coolth (talk) - Roentgen-Roehre.svg, Public Domain. https://commons.wikimedia.org/w/index.php? curid¼11691922. [5] Dynamitron. Wikipedia. https://en.wikipedia.org/wiki/Dynamitron. [6] National Electrostatic Corporation. http://www.pelletron.com/charging.htm. [7] Rhodotron.svg. Author Patrick87. https://commons.wikimedia.org/wiki/File:Rhodotron.svg. [8] Cyclotron. Wikipedia. https://en.wikipedia.org/wiki/Cyclotron. Cropped from U.S. Patent 1,948,384, Ernest O. Lawrence, Method and apparatus for the acceleration of ions (1934). [9] MEDraysintell identifies more than 1200 medical cyclotrons worldwide. http://www.einnews.com/pr_news/300008215/medraysintell-identifiesmore-than-1-200-medical-cyclotrons-worldwide. [10] H.V. Knudsen, et al., Antiproton therapy, Nucl. Instr. Meth. B 266 (2008) 530e534. [11] LHC Machine Outreach. LHC Vacuum System. http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/components/vacuum.htm. [12] F. Zimmermann, M. Benedikt, D. Schulte, J. Wenninger, Challenges for highest energy circular colliders, in: Proceedings of IPAC2014, Dresden, Germany, MOXAA01, 6 p. http://accelconf.web.cern.ch/AccelConf/IPAC2014/papers/moxaa01.pdf.
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[13] ESRF, The European Synchritron. http://www.esrf.eu/UsersAndScience/Experiments/Beamlines. [14] P. Barnes, J.K. Cockcroft, S. Jacques, M. Vickers. How do Synchrotron Work? Instrumentation II: Synchrotron Sources and Methods, School of Crystallography, Birkbeck College, University of London. http://pd.chem.ucl.ac.uk/pdnn/inst2/work.htm. [15] G.N. Kulipanov, Ginzburg’s invention of undulators and their role in modern synchrotron radiation sources and free electron lasers, Phys. Usp. 50 (2007) 368e376.
Accelerators Chapter Outline 18.1 Introduction 18.2 Accelerators for Radiation Technologies 18.3 Linear Accelerators of Direct Action (High-Voltage Accelerators) 18.3.1 X-Ray Tubes 18.3.2 The CockcrofteWalton Generators 18.3.3 Dynamitron and Tandetron 18.3.4 The Van de Graaff Generators 18.3.5 Pelletrons 18.3.6 Transformer Systems
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18.4 Linear Resonance Accelerators 18.5 Rhodotrons 18.6 Cyclic Accelerators 18.6.1 Cyclotrons 18.6.2 Betatrons 18.6.3 Microtrons 18.6.4 Synchrotrons 18.7 Synchrotron Radiation References
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18.1 INTRODUCTION Since the discovery of X-ray radiation and radioactivity and before the beginning of the 1930s, engineers, as well as physicians, used natural radionuclides, mainly 226Ra, and X-ray tubes as sources of radiation. Sources of natural activity are provided only by gamma quanta, fast electrons, and alpha particles in a limited energy range. With the help of nuclear reactions, neutrons can be obtained. Researchers in physics had at their disposal also cosmic radiation. Among nuclides of natural radioactivity in the 232Th decay chain, there is a 208Tl nuclide emitting gamma quanta with an energy of 2.614 MeV. This is the maximum energy of the nuclide gamma source. The maximum energy of alpha particles (Ea ¼ 8.779 MeV) emits 212Po (T1/2 ¼ 3$107 s), a nuclide from the same decay chain. The maximum energy of the beta spectrum of the nuclide 12N is 16.6 MeV. But 12N is a short-lived nuclide (T1/2 ¼ 1.3$102 s) and is far from the nuclear stability region. Usually, the boundary energy of the beta spectrum of nuclides of natural activity does not exceed w5 MeV. Let us recall that the average energy of beta particles is about one-third of the maximum. In cosmic rays, particles are observed in a very wide energy range, up to energies unavailable in modern accelerators, up to 1021 eV. But the density of the flux of cosmic particles drops sharply as their energy increases. For example, the particle flux density with an energy of 1019eV is one particle per year per km2. The flux density of particles with an energy of one TeV (1012 eV) is equal to w1 m2/s. Besides, which is quite important for the experiment, cosmic particles arrive at random instants. Even with this meager set of radiation energies, it was possible to find out rather much of the structure of an atomic nucleus, and to spot the nucleus itself inside the atom. However, to study the atomic nucleus and elementary particles, as well as to use radiation in technical applications, it is necessary to have a wider range of bombarding particles, higher energy, to have such a controlled device that would give out the flows of the necessary particles of the required energy, and the required intensity, continuously or in pulsed mode. Thus, science and technology required the creation of controlled sources of nuclear radiation. Because the main task was to increase the energy of the particles, such devices were called accelerators. To date, a large number of different types of accelerators have been developed. In principle, all possible accelerators can be divided into accelerators for industrial applications and accelerators for scientific research. However, such a division is somehow arbitrary, because applied works are carried out on typically scientific accelerators and scientific research is carried out on industrial accelerators.
Radiation. https://doi.org/10.1016/B978-0-444-63979-0.00018-5 Copyright © 2019 Elsevier B.V. All rights reserved.
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By the principle of action, accelerators can be divided into linear and cyclic. The electron accelerators and accelerators of heavy charged particles, protons and ions, quite noticeably vary in structure and design. But they can be both cyclical and linear. In general, large and very large accelerators are intended for research in high-energy physics. Here the word “very big” is not a stylistic device, but a literal name. Large accelerators are well known; they are often mentioned by the press. It is on such accelerators that new fundamental information is obtained on the structure of matter at the deepest level. These are very complex and expensive installations, there are rather few of them. For a long time, only the most highly economically developed countries could afford to produce a large accelerator. At present, this became completely impossible for one country, and the largest accelerators are being built and used on the basis of broad international cooperation. For a long time, accelerated particles bombarded stationary targets. In such collisions and at relativistic particle energies, the relative energy is much lower than the relative energy in the nonrelativistic case (Section 3.2.3, Eq. 3.25). In this, the total collision energy is equal, approximately (2E$mc2)1/2. For example, protons with an energy of 1000 GeV, colliding with protons of a stationary target, cause reactions characterized by an energy of w45 GeV. In the collision of two particles of equal mass with an energy of 1000 GeV each, the collision energy is 2000 GeV. It is seen that it is more effective to bring two accelerated beams of particles in collision. Accelerators in which beams collide are called colliders [1]. Therefore, the progress of higher energies in physics occurs mainly due to colliders. And research in the field of already mastered energies is more profitable to carry out by the accelerators with a fixed target. In this case, it is possible to operate with beams of unstable or neutral particles, which is very difficult or even impossible on colliders. Besides, accelerators with fixed targets can be studied more rare phenomena, as it is possible to obtain a much larger number of collisions. Accelerator technology is widely demanded in various spheres of modern industry. Currently, there are about 26,000 accelerators in the world, of which only 5% are installations for scientific research, the rest are used in medicine, in the production of semiconductors, in the processing of materials, industrial tomography, etc.
18.2 ACCELERATORS FOR RADIATION TECHNOLOGIES To date, there has been an extensive set of clearly defined areas in which the use of accelerators is technologically and commercially justified. According to experts in the field of beam technologies [2,3], the total amount of annual costs for the use of industrial accelerators for production, sterilization, and control currently exceeds $ 500 billion. According to estimates from the same sources [2,3] over the past 60 years, more than 24,000 accelerators for industrial applications have been built in the world. Moreover, more than 11,000 accelerators were built specifically for medical needs. There are major areas where ray technologies play an important role. Most of the accelerators (w10,200) were used for ion implantation; approximately on 7000 accelerators, the radiation treatment of materials for their modification was conducted. Approximately 2600 accelerators were used for sterilization and other similar treatments. By use of 1500 accelerators, nondestructive testing of products is carried out, at least 1500 accelerators operate as neutron generators. Approximately 1000 accelerators are engaged in the production of radionuclides. And we also have to specify accelerators as sources of synchrotron radiation. It is assumed that about 70 such sources are currently in operation. Of course, these figures are not quite exact. There are multifunctional machines by which a variety of operations can be done, but nevertheless the trend toward specialization is quite evident. Most of the industrial accelerators have a service life of 20e40 years; it is believed that at least 75% of the created accelerators are still used. The use of radiation technology is continuously spreading. New accelerators are developed and produced by approximately 70 companies around the world. According to recent estimates, approximately 1100 industrial irradiating systems are coming to the market for a total of $ 2.2 billion a year. To solve the problems in nuclear physics, accelerators are required for ever higher energies, which produce beams of ever increasing intensity and accelerate ever heavier ions. Currently, the greatest accelerator is the Large Hadron Collider (LHC), with maximum energy of 7 þ 7 TeV; it can produce up to one billion protoneproton collisions per second. It can accelerate nuclei up to 208Pbþ82. To solve various industrial problems, accelerators with energy in the range from 75 keV to 30 MeV are required. Particles with a lower energy spend a significant part of the energy in the accelerator window and in the air, radiations with higher energy are capable of inducing radioactivity. Usually this rather wide range of energies is divided into three groups: 1. high-energy acceleratorsdfrom 5.0 up to 30 MeV; 2. medium-energy acceleratorsdfrom 300 keV up to 5.0 MeV; and 3. low-energy acceleratorsdfrom 75 keV up to 300 keV.
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Accelerators with energies above 300 keV are usually equipped with beam scanning systems; accelerators for smaller energies produce a wide beam with the help of an extended cathode and an anode. In the radiation technologies and in medicine, both cyclic and linear accelerators are used. In industrial applications, several types of cyclic accelerators are used, mainly cyclotrons, synchrotrons, betatrons, microtrons, and a wide range of linear accelerators The new types or new modifications of known types of accelerators appeared. They are, rhodotrons, pelletrons, dynamitrons, etc., possessing a whole complex of useful qualities for industrial applications.
18.3 LINEAR ACCELERATORS OF DIRECT ACTION (HIGH-VOLTAGE ACCELERATORS) 18.3.1 X-Ray Tubes The simplest theoretically and the first historically were linear accelerators of direct action. In linear accelerators, particles are accelerated by a constant electric field and they move rectilinearly in a vacuum chamber, between accelerating electrodes. The energy that the particles received was determined by the potential difference that could be provided in such installations. Since then, the main problem was in generating high voltage; the first successful designs of accelerators were called generators. Though it has to be pointed out that conventional X-ray tubes are also accelerators, they accelerate electrons that by slowing down in the anode material generate X-rays (Fig. 18.1). In high-voltage accelerators, as a rule, three circuits for obtaining high voltage are used: (1) Cascade generators (the CockcrofteWalton generator, etc.). (2) Mechanical charge transfer (Van de Graaff generator, pelletron, etc.). Accelerators built on this basis are sometimes called “electrostatic generators.” (3) Various transformer circuits.
18.3.2 The CockcrofteWalton Generators The first linear accelerators (the CockcrofteWalton generator and the Van de Graaff generator) appeared almost simultaneously in the early 1930s of the last century. In 1932, two scientists from Cambridge, John Cockcroft and Ernst Walton, built a cascade voltage multiplier, converting the alternating voltage into a high constant. The accelerator with this high-voltage source was called the CockcrofteWalton generator; the voltage multiplication scheme is shown in Fig. 18.2. As early as in the first experiment on the accelerator they built, the researches directed a beam of protons accelerated to an energy of 800 keV toward a 7Li target, and then they observed a nuclear reaction in which a lithium nucleus captured a proton and disintegrated into two alpha particles. 7 3 Li
þ p/42 He þ 42 He þ 17 MeV.
(18.1)
This was the first reaction of nuclear fission by artificially accelerated particles, and due to this achievement the authors received the Nobel Prize in Physics in 1951 for “transmutation of atomic nuclei with artificially accelerated atomic particles.”
FIGURE 18.1 Scheme of the X-ray Coolidge side-window tube (scheme). C is the cathode, A is the anode, and Win and Wout are water inlet and outlet of the cooling device. Figure from Roentgen-Roehre.svg. Hmilchderivative work: Coolth (talk) - Roentgen-Roehre.svg, Public Domain. https://commons. wikimedia.org/w/index.php?curid¼11691922.
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FIGURE 18.2 The simple multiplier of CockcrofteWalton generator, consisting of two sections.
FIGURE 18.3 Marx generator: (A) Charging, (B) Discharging.
There are many different cascade voltage multiplication schemes. One of them is the Marx generator (Fig. 18.3). In it, the capacitors are charged in parallel from the common source, and then by means of spark discharges, they are switched to serial and the voltage on the capacitors is summed. It is clear that such generator can only operate in a pulsed mode.
18.3.3 Dynamitron and Tandetron Several other versions of cascade generators got special names. Thus, the company IBA Industrial (formerly Radiation Dynamics Incorporated) in the 1960s developed accelerator, called “Dynamitron,” that can accelerate either electrons or positive ions. Dynamitron’s accelerating column is within a vessel filled with sulfur hexafluoride insulating gas under high pressure. The main advantage of the electrical circuit used in Dynamitron is to allow a much higher beam current to be transported than a typical the CockcrofteWalton style accelerator. Dynamitron can produce an electron beam with an energy of up to 5 MeV and a power of up to 300 kW. Dynamitron has a very large installed base, with more than 200 units, primarily in the United States [5]. A whole series of cascade accelerators of ELU type, similar to Dynamitron, is produced by the G.I. Budker Institute of Nuclear Physics in Novosibirsk (Siberian department of the Russian Academy of Science). Accelerators of ELU series have been issued since 1971, and they dominate in the market of accelerators for radiation technologies in Russia and Eastern Europe. A range of electronic accelerators of constant action such as ELU creates electron beams in the energy range from 0.2 to 2.5 MeV and beam current up to 200 mA.
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The cascade generator of the tandem type is called “tandetron.” This accelerator achieves two-step acceleration with a single voltage by converting the electric charge of an accelerating ion. Negative ions, extracted from an ion source, inject into the accelerator, where it accelerates ions in two steps. First, the injected negative ions are accelerated due to the applied electrostatic field (positive high voltage). After they collect the maximum possible energy, the negative ions are passed through a thin foil, where they are “stripped off,” i.e., each is deprived of a pair of electrons and converted into a positive ion. The beam of positive ions accelerates toward ground potential and gains energy again. Thus, the total energy can be twice as large as in a single stage of the CockcrofteWalton generator. The tandem machine can produce ion beams with energies in the range from 400 keV to 24 MeV of almost all elements of the periodic system with the current in the mA area.
18.3.4 The Van de Graaff Generators In 1931, the American scientist Van de Graaff built an electrostatic generator in which electrical charges from a special charger are transferred to a high-voltage electrode by a tape of insulating material. The high potential (up to 10 MV) allows to accelerate both electrons and heavy particles, i.e., protons, deuterons, and alpha particles. Various Van de Graaf generators are by now manufactured industrially. The beam intensity reaches 100 mA, the beams can be well collimated, and the output energy can be easily stabilized with an accuracy of 10 keV. The maximum energy achieved is now about 30e40 MeV for protons. As is known, the breakdown voltage of dry air at atmospheric pressure is w30 kV/cm, and the electric field strength depends rather considerably on the radius of curvature of the electrode. Therefore, the high-voltage electrodes must be large in size with a well-polished surface and to stand far enough from other installations and walls of the premises. In modern accelerators that use high voltage, the high-voltage part of the plant is placed in a reservoir with a high pressure of electrically insulating gas, so at present such accelerators look much more compact. As in the case of the CockcrofteWalton generators, the Van de Graaff generators are produced in a tandem version.
18.3.5 Pelletrons A more advanced modification of the Van de Graaff generator is the so-called pelletron. In the pelletron, the electric charge is transferred not by a dielectric belt conveyor but by a chain consisting of electrically conductive links (pellets) connected by an insulator. Besides, the charging system of the conveyor has been changed. As a result, a high stability of the charging current and a long service life are achieved; the danger of spark breakdowns and spraying of the tape material is eliminated. Pelletron allowed to increase the received high voltage up to 25 MV. The form of the charge transfer chain and the animation of the pelletron are shown on the NEC website [6].
18.3.6 Transformer Systems High voltage in direct-acting accelerators can be obtained by means of various transformer circuits. One of the types of such system is a conventional high-voltage transformer, powered by a sinusoidal voltage. A special device ensures the passage of a beam of accelerated particles only when the voltage on the secondary winding of the transformer has the necessary polarity and is close to the maximum. Such schemes make it possible to obtain powerful beams with the energy of accelerated particles up to 2e3 MeV. In pulsed accelerators, voltage sources are pulsed transformers of various types, for example, the Tesla transformer.
18.4 LINEAR RESONANCE ACCELERATORS The production of high-energy particles can be achieved by a resonant method. Historically, the first accelerator of the resonance type was the Wideröe accelerator, developed in 1928 by the Norwegian physicist Rolf Wideröe. The resonant linear accelerators became known as the “linac” (LINear ACceleration). The particle beam moves along the axis of the subsequent line of tubes, as shown in Fig. 18.4. A high-frequency electric field with a voltage of the order of hundreds of kV is active in the gaps between the tubes. Inside each tube, the electric field equals zero. In each flight between the tubes, a cluster of particles accelerates. The frequency of the generator and the dimensions of the tubes are selected so that the bunch of accelerated particles approaches the next gap at the moment when the accelerating voltage acts there.
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FIGURE 18.4 Scheme of the linear resonant accelerator. S e particle source, G e voltage generator.
Because the velocity of the particle increases while passing through the next accelerating gap, the lengths of the accelerating tubes also increase. When the particle reaches relativistic velocities, the length of the tubes becomes constant. Calculations show that for protons to reach an energy of 10 MeV at an accelerating voltage frequency of 10 MHz, the length of the last tube has to be 2.2 m. The simplest version of the Wideröe accelerator makes it possible to accelerate only the particles in the area of nonrelativistic energies. To eliminate the problems inherent in the Wideröe accelerator, resonator accelerators were developed. A simple resonator accelerator with a standing wave serves to accelerate electrons. Another version of a resonator accelerator with a transit tube, the so-called Alvarez accelerator, preferably accelerates protons and other heavy particles. There are accelerators using so-called loaded waveguides in which a traveling electromagnetic wave is formed. The traveling wave carries particles along the accelerating field. If the velocity of a particle differs insignificantly from the light speed, it keeps on the crest of the wave for a long time, continuously being accelerated by it. A series of resonance pulsed accelerators ILU has been manufactured since 1970 by the G. Budker Institute of Nuclear Physics. Accelerators overlap the energy range from 0.7 to 4 MeV with a maximum beam power of up to 50 kW. Accelerators of the “linac” type can accelerate both electrons and heavy particles. The largest linear accelerator today is the Stanford Linear Accelerator at Menlo Park, California, which is 3 km long. It has about 80,000 accelerating electrodes and could accelerate electrons and positrons to about 50 GeV. The next step in the creation of linacs is the perspective International Linear Collider, where electron and positrons will collide. It is expected to be 30e50 km long. It is planned to achieve initially collision energy of 500 GeV, with a perspective of a later upgrade to 1000 GeV (1 TeV). The supposed location of its construction is the Kitakami highlands, in the Iwate prefecture of Northern Japan.
18.5 RHODOTRONS A relatively new type of accelerator, which appeared at the end of the twentieth century, rhodotron, can be attributed to both a group of cyclic accelerators and that of linear accelerators. In accelerators in which particles pass successively and repeatedly in the accelerating region along the same path, there are serious limitations of the beam current due to the increasing role of the space charge. The French scientist Jacques Pottier (1989), who proposed a new type of accelerator, named “rhodotron,” was able to overcome this difficulty. Pottier drew attention to the fact that in the coaxial cavity in the median plane the magnetic field equals zero, so it does not reject the beam, and the electric field is directed radially and is able to accelerate electrons. Turning off a beam of electrons at the exit from the resonator and returning it to the accelerating cavity, as shown in Fig. 18.5, it is possible to drive the particles several times through the accelerator, gradually increasing their energy. The name “rhodotron” has the Greek origin (“rhodon” means “a rose”), as the trajectory of the accelerated electrons resembles a rosette. Parameters of the resonator and high-frequency equipment allow the electrons to transmit energy up to 2 MeV in one pass, and the total number of passes is limited by 10. It is possible to withdraw the beam also at intermediate stages of acceleration. Thus, rhodotron makes it possible to obtain continuous beams of electrons with an energy of 5e10 MeV of considerable power (hundreds of kW). Turning magnets make rhodotron a very compact accelerator.
18.6 CYCLIC ACCELERATORS 18.6.1 Cyclotrons The first cyclic accelerator, the cyclotron, was constructed by E. Lawrence and M.S. Livingston in 1929, and in 1939, for which E. Lawrence was awarded the Nobel Prize in Physics. The first Lawrence cyclotron had a diameter of 4 inches (10 cm), and in 1932 a 27-inch diameter machine was built in which protons were accelerated up to an energy of 5 MeV. The principle of operation of the cyclotron is clear from Fig. 18.6.
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FIGURE 18.5 Scheme of the rhodotron. E is the electron source, L is the magnetic lens, C is the high-frequency resonator, and M is one of the bending magnets. Figure from Rhodotron.svg. Author Patrick87. https://commons.wikimedia.org/wiki/File:Rhodotron.svg.
FIGURE 18.6 Diagram of cyclotron operation from Lawrence’s 1934 patent. The “D”-shaped electrodes are enclosed in a flat vacuum chamber, which is installed in a narrow gap between the two poles of a large magnet. Figure from Cyclotron. Wikipedia. https://en.wikipedia.org/wiki/Cyclotron. Cropped from U.S. Patent 1,948,384, Ernest O. Lawrence, Method and apparatus for the acceleration of ions (1934).
In the cyclotron, the particle source is located in the center of the vacuum chamber between the poles of the magnet. A high-frequency alternating voltage applies between two hollow “D”-shaped electrodes called “daunts” inside a vacuum chamber. The particles that are emitted from the source perpendicular to the direction of a uniform magnetic field B (constant magnitude and direction) move along a spiral trajectory as their energy increases in every passage between the daunts. In the circular motion, centripetal force and magnetic Lorentz force are equal (18.2) mv2 r ¼ eBv; where m is the particle mass, e is its charge, v is velocity, and r is the circular path radius. The frequency of the particle motion in the constant magnetic field, the so-called cyclotron frequency f, does not depend on the particle energy and the radius f ¼ v=2pr ¼ eB=2pm.
(18.3)
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All particles with the same charge-to-mass ratio rotate around magnetic field lines with the same frequency. By choosing the frequency of high-frequency electric field, one can achieve multiple resonance acceleration of the particle. Cyclotrons became very popular type of accelerators. According to the MEDraysintell “The global cyclotron market is expected to reach US$ 245 million in 2030 showing an annual growth of 3%, with an estimated yearly average sale of 60 cyclotrons over the years 2015 to 2030.” [9]. Up to 2015, over 1200 cyclotrons are used in nuclear medicine worldwide for the production of radionuclides [9]. The synchronization of particle motion and the frequency of the accelerating field are obtained only in the nonrelativistic case (for protons only up to an energy of tens of MeV). With increasing energy, the mass of particles starts to depend on their velocity. In order to keep the particles in phase with the oscillations of the electric field, the change of either the magnetic induction or of the frequency of the accelerating field in the process of acceleration is needed. The first option is the basis of the synchrotron, and the second is the basis of the phasotron (synchrocyclotron).
18.6.2 Betatrons An attempt to create the first cyclic accelerator of electrons was undertaken by the Norwegian scientist Rolf Wideröe back in 1926, i.f., earlier than the idea of a cyclotron emerged, but the first reliably functioning betatron appeared only in 1940. The author of the operating model of betatron was the American scientist D. Kerst. Betatron is an induction accelerator in which electrons are held in equilibrium on a circular orbit by the magnetic field increasing synchronically with the increase of electron energy. Acceleration occurs due to the vortex electric field created by an alternating magnetic flux inside the equilibrium orbit. To create the necessary magnetic field, large electromagnets with an iron core are used. In betatrons, the energy of accelerated electrons can reach hundreds of MeV, but the magnets of such betatrons turn out heavy and consume a lot of energy. For example, the 300-MeV betatron of the University of Illinois weighed more than 300 tons. Now betatrons with an energy of 20e50 MeV were most widely used.
18.6.3 Microtrons In his search for a way to overcome the problem of phasing the beam in a cyclotron, the Soviet scientist V.I. Veksler invented a new type of accelerator, a microtron. In the microtron (Fig. 18.7), the particles are introduced into the accelerator chamber not in the central part of the magnetic field, as in the cyclotron, but at its edge. An accelerating cavity is located at the particle entrance. At each turn, the electrons receive energy on the order of the rest mass of the electron (w0.5 MeV). This means that, after the first turn, relativistic electrons move inside the microtron. They enter the resonator by each turn exactly at the moment of acceleration. Electrons move around the circle with the radius increasing, and all circles contact inside the resonator. Because of the need to ensure a large increase in energy for each turn, a powerful microwave electronics is used to operate the microtron, which is indicated by the prefix “micro” in the name of the accelerator. The maximum energy of the accelerated electrons is limited by the dimensions of the permanent magnet. The microtron turns out a fully operational accelerator of medium-energy electrons (up to 30 MeV), which plays an important role in many applications.
FIGURE 18.7 The scheme of microtron. Figure on the basis of B.S. Ishkhanov, I.M. Kapitonov, E.I. Kabin, Particles and Nuclei. Experiment, MAKS Press, Moscow, 2015, in Russian. Web-publication. http://nuclphys.sinp.msu.ru/experiment/index.html#cont.
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18.6.4 Synchrotrons For researches in high-energy physics, high-energy particles are required. It is known from optics that to distinguish the structural details of an object with linear dimensions of the order of d, the wavelengths of radiation comparable or less than d must be used: ƛ d. Taking into account that the de Broglie wavelength of the particle is equal to ƛ ¼ Z/p, and the relation of the kinetic energy and momentum in the nonrelativistic case has the view F ¼ r2/2M, one finds that for probing atomic nuclei w1013 cm, particles are needed with energy (in units of Mc2) not less than 2 E 1 Z ¼ 2 . (18.4) Mc2 2d Mc If the bombarding particle is a proton, then Z/Mrc ¼ lr ¼ 0.21$1013cm is the Compton wavelength of the proton and Mrc2 ¼ 938 NeV w 1 GeV, then F/Mrc2 0.02 and for probing details with linear dimensions w 1013 cm, protons with an energy of not less than w 20 MeV are required. To improve the spatial resolution, the energy of the particles should be increased inversely proportional to the square of the required resolution. In Section 3.2.5.4, the variation of the potentials with which the bombarding particle occurs as its energy increases and the corresponding change in information on the structure of the object are described in detail. Because the energy values of nuclear levels are tens of MeV, for the study of nuclei, accelerators with particle energies of hundreds of MeV are required. It is important that the distance between the nuclear levels is of the order of several keV; therefore, beams with a high-energy resolution are required. There are no restrictions on the upper limit for research investigations in the physics of elementary particles. The problem of increasing the energy of accelerated particles was solved by the creation of synchrotrons. The principle feature of the synchrotron, which distinguishes it from the cyclotron and the phasotron, is that the particles move in the annular channel and only within this channel it is necessary to create a magnetic field. This dramatically reduces the size and weight of the magnet, as well as the energy consumed by it. The arrangement of the elements of the synchrotron is shown in Fig. 18.8. In some parts of the ring, accelerating electrodes are installed, on which a high-frequency accelerating field is supplied. For continuous acceleration of particles, it is necessary that at the moments of acceleration the direction of particle motion and the electric field coincide; for this, it is necessary to provide resonance between the motion of particles and the change in the electric field. Because the accelerator simultaneously accelerates a huge number of particles with spread of energies, and therefore also in masses, the particles have different frequencies of turning. Therefore, an insignificant fraction of the accelerated particles fall into resonance with the accelerating field. This problem was solved with the discovery of the autophasing principle (V.I. Veksler, E. McMillan). In a synchrotron, in which the magnetic induction changes synchronously with the motion of particles, it is possible to accelerate only the relativistic particles that move with the constant velocity, i.e., electrons. To accelerate protons and ions,
FIGURE 18.8
Schematic of a synchrotron.
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before they become relativistic, it was also necessary to change the frequency of the accelerating electric field, as was done in the synchrocyclotron (phasotron). Such a device was called proton synchrotron. In the Russian scientific publications, the proton synchrotron is called synchrophasotron. In order to secure reliable operation of the proton synchrotron and to reduce the dimensions of the vacuum chamber, and hence the magnet, it was required to ensure the stability of the particle motion in the directions that are perpendicular to beam trajectories. A specially selected rather complex configuration of the magnetic field makes it possible to rapidly quench the particle vibrations both in the radial and in the vertical direction. In order to strengthen the axial focusing, a field sharply decreasing along the radius is necessary. On the contrary, to increase the focusing along the radius, a sharply increasing field along the radius is necessary. The simultaneous requirements here are impossible, but they can be implemented alternately. A system that realizes this sequential focusing is called a system with “hard” focusing. A decrease in the transverse oscillations is also promoted by a specially designed so-called “cooling” of the beam. After the discovery of the autophasing principle, the era of the construction of accelerators for ever greater energy began. In 1952, in Brookhaven, USA, the so-called Cosmotron was commissioned for proton energy of 3.3 GeV. In 1954, in Berkeley, USA, the Bevatron was constructed for energy of 6.2 GeV (by now it could be called Gigatron). The limiting energy of this accelerator was calculated for the production of antiprotons. Indeed, measurements have shown that these particles actually exist. For this discovery, E. Segre and O. Chamberlain were awarded the Nobel Prize in Physics in 1959. At that time, the antiprotons seemed absolutely exotic particles. The authors of the discovery reported about the discovery when only 40 antiprotons were registered. Slightly more than 50 years passed, and now the use of antiprotons for radiation therapy are quite seriously discussed [10]. In 1957, in Dubna, the USSR began to operate a synchrophasotron with a “weak” focusing on the energy of 10 GeV. The vacuum chamber of the Dubna synchrophasotron with weak focusing had dimensions of 2 m by 40 cm. The author of this book personally observed how the personnel while repairing and adjusting the facility had to crawl inside the vacuum chamber. In 1961, the strong focusing mode was used in the accelerator ITEP, Moscow, USSR, for 7 GeV, which served as the basis for the creation of the U-70 accelerator in Protvino, USSR, for 70 GeV. The super proton synchrotron at CERN, which started to operate in 1976, accelerated protons up to 400 GeV, sufficient for the production of W and Z bosons, carriers of weak interaction. The discovery of these particles in 1983 proved to be an important stage in making of a modern conception of the world; it confirmed the theory of combining electromagnetic and weak interactions. C. Rubbia and S. Van der Meer in 1984 were awarded the Nobel Prize for this discovery. Van der Meer’s major contribution was the development of a cooling system for the beams. Without this achievement, the discovery of W and Z bosons would not be possible. The greatest for today (summer 2018) is the LHC at CERN (CERN) on the border of Switzerland and France. In the collider mode, the energy of colliding protons is 7 þ 7 TeV. The LHC can also accelerate heavy ions, in particular, lead ions 208Pbþ82 up to an energy of 2.76 TeV per nucleon. Let us note that the inside diameter of each of the two vacuum chambers of the LHC for proton beams moving in opposite directions equals 5.0 cm [11]. The LHC was actually designed for searching the last elementary particle of the Standard Model of Elementary Particles, i.e., the Higgs boson. During 2013, in experiments by the two different facilities on the LHC collider, the data were obtained proving the existence of this particle. P. Higgs was awarded the Nobel Prize in Physics in 2013 for his prediction of a particle that could be responsible for the inertial mass of elementary particles, made back in the 1960s of the 20th century. The particle was later called the Higgs boson. Scientists and engineers around the world are looking ahead, and they are working hard for upgrading the LHC, and to obtain the High-Luminosity LHC. The upgrading is planned to be accomplished in 2026, and it is planned to increase the number of collisions by a factor of five to ten. The next step is currently in progress; the scientists are developing designs for a higher performance particle collider, the Future Circular Collider (FCC). It is going to greatly increase the energy and intensity of a particle collider and is going to reach collision energies of 50 þ 50 TeV. It is expected that the FCC will approach the maximum of its potential around 2035. The length of the tunnel for the proposed accelerator will be approximately 80e100 km [12]. Thus, it can be seen that cyclic accelerators can be divided into accelerators in which the particles move in a spiral during acceleration (cyclotron, phasotron, microtron), and accelerators in which the particles move along an unchanged, closed, nearly circular path (betatron, synchrotron). One of the most serious problems that have arisen in the acceleration of electrons in cyclic accelerators is the loss of energy by radiation. If electrons and protons of the same energy move in the orbits with equal radiuses, then the energy
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losses of electrons for synchrotron radiation are (mp/me)4 z 1013 times greater. Therefore, it is not possible to accelerate electrons up to energies of more than 100 GeV on cyclic accelerators. To accelerate electrons (and positrons) up to higher energies, huge linear accelerators are constructed. On the other hand, it turned out that magnetic bremsstrahlung (synchrotron) radiation of accelerated electrons has many useful properties, so now special accelerators are being built, designed to produce beams of synchrotron radiation (Section 18.7). Different types of cyclic accelerators are preferable for accelerating different types of particles. Synchrotrons, betatrons, and microtrons are designed to accelerate electrons, and cyclotrons, phasotrons, and proton synchrotrons are designed to accelerate heavy particles. Large modern accelerators are usually compound systems. Before particles are injected into the large ring of the accelerator, where they receive the final energy, they sometimes go through several stages of preliminary acceleration and at some stages, usually initial, they are accelerated in a linear accelerator. If the necessary number of particles is not obtained from the injector at one stage, the accumulation and storage regime is applied.
18.7 SYNCHROTRON RADIATION When moving in a magnetic field along a curvilinear trajectory in accelerators, the charged particle undergoes radial acceleration perpendicular to its trajectory and, in accordance with the laws of electrodynamics, emits electromagnetic quanta. The energy lost to radiation is inversely proportional to the square of the particle mass. This leads to the conclusion that heavy particles emit significantly less energy than the light ones. For example, a proton emits an energy 3.4$106 times less than an electron. Therefore, the radiative energy losses are most important for lightest charged particles, i.e., electrons. This magnetobremsstrahlung is called synchrotron radiation, because experimentally the radiation was first discovered by F. Haber, a graduate student, on the 80-MeV synchrotron of General Electric in 1947. For the sake of justice, it should be noted that synchrotron radiation was predicted by theorists even before the discovery. Synchrotron radiation was first negatively perceived as an obstacle to the acceleration of particles, as it sets the energy limit of electrons accelerated in cyclic accelerators, i.e., betatron, synchrotron. At present, synchrotron radiation is widely used in scientific research, as well as in applications of great practical importance. Synchrotron radiation is used in microlithography, for the photosynthesis of hydrocarbons, nitrogen oxides, etc. It is used to study the radiation impact on materials and instruments outside the atmosphere, which is very important for space materials science. X-ray monochromatized synchrotron radiation is used in X-ray diagnostics, what allows to significantly reduce the radiation load per person during X-ray examination. There are interesting applications of synchrotron radiation in radiation technology and radiation-chemical processes. These vast possibilities of using synchrotron radiation are determined by a set of remarkable properties. The maximum intensity of the radiation is shifted to the high-frequency area with respect to the rotation frequency of the electron in the orbit. The maximum intensity occurs in the X-ray region and even in the gamma ray region in modern synchrotrons and storage rings. The radiation has a sharp directionality along the tangent to the electron orbit. The time structure of the radiation depends on the specific accelerator. On the synchrotron, the acceleration cycle is usually repeated at a frequency of 50 Hz, and with the same frequency the bursts of radiation pulses are repeated being modulated inside the packets with the frequency of the electron motion in orbit. The length of a bunch of electrons in an orbit is determined by the duration of those bursts that reach hundreds of picoseconds. Initially, synchrotron radiation was obtained on synchrotrons. But when the extremely interesting and useful problems that can be solved with the help of this radiation became clear, special storage devices appeared. In storage rings, due to repeated injection, intense particle beams can be accumulated, maintained in the continuous circulation mode. Prior to entering the actual storage ring, the electrons need to be preaccelerated to their final energy and speed (in the actual storage ring their energy is only maintained). The scheme of the storage ring with injection, undulator, wiggler, etc., is shown in Fig. 18.9. The real storage device has a lot of beamlines. For example, the ring of the ESRF (European Synchrotron Radiation Facility, Grenoble, France) has a length of 844 m and 49 bunches. The energy of the electrons in the storage ring is 6 GeV [13]. At present, synchrotron radiation is one of the most important tools in radiation technology. To increase the intensity of synchrotron radiation and to use it more efficiently, special synchrotron radiation generators are built, undulators and wigglers. These devices proposed by V.L. Ginzburg in 1947, and now called “insertion devices,” are really inserted in straight sections of electron storage rings [15]. An alternating periodic magnetic field is created in these devices, and electrons move along a trajectory that looks like a snake. The spectral and angular distribution of the radiation from an undulator essentially depends on the
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FIGURE 18.9
The scheme of storage ring and synchrotron radiation emission.
relationship between the angle of rotation of the electron in the magnetic field and the characteristic angle of divergence of radiation from each point of emission of the electron. Depending on this relationship, either an undulator or wiggler mode is realized. At present, there are undulators of a few tens of meters in length. The undulators 150e200 m long are in the development stage. Considering the large number of synchrotron radiation sources in the world that require undulators, the production of the latter has become a notable branch of scientific instrumentation [15]. Until now, the most brilliant and energetic source of light is the European X-ray Free Electron Laser (European XFEL) now in operation at Hamburg, Germany. It generates ultra-short X-ray flashes at a rate of 27,000 per second with a peak brilliance, one billion times higher than the best conventional X-ray sources. Electrons are accelerated up to the energy of 17.5 GeV by a 2.1-km long linear accelerator with superconducting RF cavities in the 3.4-km long tunnel. The X-rays are generated by self-amplified spontaneous emission, where electrons interact with the radiation that they or their neighbors emit. The wavelength of the X-ray laser may be up to w250 keV (from 0.05 to 4.7 nm).
REFERENCES [1] B.S. Ishkhanov, I.M. Kapitonov, E.I. Kabin, Particles and Nuclei. Experiment, MAKS Press, Moscow, 2015 in Russian. Web-publication. http:// nuclphys.sinp.msu.ru/experiment/index.html#cont. [2] R.W. Hamm, M.E. Hamm (Eds.), Industrial Accelerators and Their Applications, World Scientific, 2012. http://www.worldscientific.com/ worldscibooks/10.1142/7745. [3] T.K. Kroc, R.D. Kephart, Industrial Acceleratorse Beyond Transformers and Cyclotrons, More Power, FERMILAB-CONF-15-131-A, 2015, 4 p. http://lss.fnal.gov/archive/2015/conf/fermilab-conf-15-131-ad.pdf. [4] Roentgen-Roehre.svg. Hmilchderivative work: Coolth (talk) - Roentgen-Roehre.svg, Public Domain. https://commons.wikimedia.org/w/index.php? curid¼11691922. [5] Dynamitron. Wikipedia. https://en.wikipedia.org/wiki/Dynamitron. [6] National Electrostatic Corporation. http://www.pelletron.com/charging.htm. [7] Rhodotron.svg. Author Patrick87. https://commons.wikimedia.org/wiki/File:Rhodotron.svg. [8] Cyclotron. Wikipedia. https://en.wikipedia.org/wiki/Cyclotron. Cropped from U.S. Patent 1,948,384, Ernest O. Lawrence, Method and apparatus for the acceleration of ions (1934). [9] MEDraysintell identifies more than 1200 medical cyclotrons worldwide. http://www.einnews.com/pr_news/300008215/medraysintell-identifiesmore-than-1-200-medical-cyclotrons-worldwide. [10] H.V. Knudsen, et al., Antiproton therapy, Nucl. Instr. Meth. B 266 (2008) 530e534. [11] LHC Machine Outreach. LHC Vacuum System. http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/components/vacuum.htm. [12] F. Zimmermann, M. Benedikt, D. Schulte, J. Wenninger, Challenges for highest energy circular colliders, in: Proceedings of IPAC2014, Dresden, Germany, MOXAA01, 6 p. http://accelconf.web.cern.ch/AccelConf/IPAC2014/papers/moxaa01.pdf.
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[13] ESRF, The European Synchritron. http://www.esrf.eu/UsersAndScience/Experiments/Beamlines. [14] P. Barnes, J.K. Cockcroft, S. Jacques, M. Vickers. How do Synchrotron Work? Instrumentation II: Synchrotron Sources and Methods, School of Crystallography, Birkbeck College, University of London. http://pd.chem.ucl.ac.uk/pdnn/inst2/work.htm. [15] G.N. Kulipanov, Ginzburg’s invention of undulators and their role in modern synchrotron radiation sources and free electron lasers, Phys. Usp. 50 (2007) 368e376.