Cyclotrons

Type of physical science: Nuclear physics

Field of study: Nuclear techniques

The cyclotron, invented in 1932, is a device designed to accelerate charged particles to high velocities and energies in a spiral path. Cyclotrons have found application in basic nuclear research and nuclear medicine with the development of radioactive elements.

Overview

Cyclotrons are machines designed to accelerate charged particles to very high energies by keeping them confined to a tight spiral path. In early nuclear research, natural radioactivity provided α or β particles that were used as projectiles for exploring the atomic structure.

The radioactive decay of radium resulted in the production of α particles, which were applied by Ernest Rutherford in 1911 in his investigations into the scattering properties of the gold atom.

Natural decay did not create enough energy, however, for later research in artificial radioactivity, transmutation, and the production of neutrons.

Breakthroughs in accelerator design were made in 1931 by Robert Van de Graaff and in 1932 by John Cockcroft and Ernest Walton. The Van de Graaff generator, as it was called, consisted of a moving belt which charged a hollow sphere. Energies of 750 kiloelectronvolts were initially achieved by these machines. They were not nearly as powerful as the accelerators that were to follow, but these early generators were important because relatively large currents could be generated that proved to be essential to the calibration of threshold energies in nuclear reactions. High-output voltages were also reached by the Cockcroft-Walton device, which doubled transformer output through an elaborate system of condensers and rectifiers.

Energies of an increased order of magnitude are possible with machines that apply a potential difference or voltage many successive times to the same particle before it bombards a target. The linear accelerator was such a device, as it employed an alternating voltage in a stepwise fashion between successive tubes. The length of the tubes increased along the path, with the exact values depending on the alternating voltage frequency and desired output voltage of the particles.

Ernest Orlando Lawrence developed the idea of a circular path after carefully researching the linear accelerator concept theorized by Rolf Wideroe, a Norwegian engineer.

Wideroe's design involved accelerating particles through a series of separate metal cylinders inside an evacuated tube. The difference in Lawrence's concept was that the particles, after being bent into a circular path by a strong magnetic field, pass through the same accelerating point or gap many times rather than through a series of successive gaps, as Wideroe had proposed.

Lawrence called the machine a "magnetic resonant accelerator." The term "cyclotron," first used as laboratory slang, became official in 1936. The cyclotron made possible the resonant acceleration of protons and other small charged particles without long tubes.

The principle behind the cyclotron is relatively simple. Ions are injected from a source containing hydrogen gas above a filament. Upon entering side D, which is free from electric fields, the ions or particles are pulled over to the other semicircle labeled C, charged to the opposite potential by the high frequency oscillator.

Immediately upon arrival at C, the polarity again reverses, forcing the ions to accelerate back across the gap to the first semicircle, which is also called a "dee." The speed of the particle inside the cyclotron dees is constant; acceleration can occur only between the dees in the region of the potential difference.

The path of the particles is confined to a semicircle because of the presence of a strong vertical magnetic field shown at position B. As the ion picks up speed, it moves in ever-widening spirals, eventually reaching the circumference of the dees after a hundred or more turns (positions 1, 2, and 3 in the figure). By this time, the particles may have acquired a total energy of 1 million volts or more from a radio oscillator source, which is one hundred or more times weaker. Yet, the energy of the spiraling particles does not directly depend on the applied voltage.

For small voltages, the ions make many turns, but for high voltages, the number of turns completed is small.

The actual construction of the first cyclotron started in the fall of 1930 when Lawrence called upon the help of his graduate assistant, M. Stanley Livingston. There were many design problems that needed solutions. First, resonant voltage which could keep the ions in step with the magnetic field was required. A high-voltage radio frequency oscillator was acquired which was able to time the voltage changes between the dees correctly. Second, a source was needed to produce ion currents in the milliamp range. Experiments showed that this goal could be accomplished by firing electrons from a radio tube filament in the center of the chamber into the hydrogen gas liberated within the chamber. Third, the pressure within the cyclotron had to be low enough to not allow undesirable collisions between the hydrogen ions and the air molecules within the chamber. A vacuum pump was designed which could produce the required low pressures, but it needed to run continuously. Fourth, the entrance aperture to the chamber for the ions was redesigned from a rectangular screen to a series of parallel slits for absorbing less of the beam current. Fifth, to deflect the beam at the periphery of the spiral into the collector for study, the experimentor needed to determine the appropriate electrostatic forces. The passageway size of this emergent beam was restructured so that only ions of a narrow range of energies could be focused.

The first cyclotron model measured only 10 centimeters in diameter, with a magnet capable of 550 gauss to confine the ions. With the machine, Livingston recorded resonantly accelerated protons (hydrogen gas ions), each having an energy of 6,000 electronvolts. Later, he replaced the magnet with one capable of 13,000 gauss and recorded energies of 80,000 electronvolts. During this last run, the ions had completed eighty-two crossings of the dee gap, or forty-one complete turns. With a second and larger model, which was 28 centimeters in diameter with a magnetic field strength of 15,000 gauss and a short wave 500-watt power oscillator, Lawrence and Livingston produced protons in excess of 1 million volts. More precise controlling of the magnetic field allowed protons to attain energies of 1.22 million electronvolts which, for 4,000 volts applied to the dees, was an amplification factor of more than three hundred.

Lawrence received the Nobel Prize in Physics in November, 1939, for his invention and development of the cyclotron. Within five months, a grant from the Rockefeller Foundation arrived to build a giant 100-million electronvolt cyclotron with a huge magnet, which measured 4.6 meters in diameter.

With these higher-energy machines, a problem surfaces which Albert Einstein had predicted some years before concerning relativity. The first problem is that, when any particle speeds up, its mass will increase. If a particle's velocity increases substantially with respect to the speed of light, then the particle's mass will increase over its normal or rest mass by a divisional quantity known as the relativistic factor, which approaches zero close to the speed of light. For a proton of 25 million electronvolts traveling at one-fifth the velocity of light, an increase in mass of around 2 percent was expected. At 100 million electronvolts or approaching one-half the speed of light, however, protons are 10 percent more massive than they are at rest.

The angular velocity (ω) of the particle is inversely proportional to its mass (M) and directly proportional to the product of its charge (q) multiplied by the strength of the magnetic field B (ω = qB/M). This relationship causes the angular velocity or required oscillator frequency for the particle to decrease with increasing mass and, as a result, the particle will lag farther and farther behind the oscillator frequency. This lag will soon cause the particle to reach the gap between the dees when the polarity of the voltage has already reversed and will result in a progressive decrease in velocity.

A second problem arises from the magnetic field factor. To prevent particles from moving out of the horizontal plane because of their velocity, a restoring force is required to push the particles back into the plane. This process, termed "axial focusing," requires that the magnetic field bend toward the axis of motion of the particle. If the field must be bent toward the axis, however, then the magnetic field strength perpendicular to the plane of motion must decrease as predicted from theory. This decrease forces a slowing down of the angular velocity of the particles, as it did before because of relativistic effects.

Lawrence had hoped in 1939 to overcome the increase in mass by using a very high-accelerating voltage, accelerating the protons to maximum speed in only a few turns by essentially a brute force technique. Rather than battling against nature's forces, however, new techniques had emerged to move particles far beyond those limits without allowing the particles to fall out of step with the accelerating voltage.

Applications

The basic design of the cyclotron was used to create other particle accelerators. The synchrocyclotron was built to avoid the relativistic problems of the cyclotron. The concept behind this machine is to slow down the oscillator frequency applied to the particle--that is, to match the driving frequency of the voltage to the angular velocity of the particle. Particles that arrive at the gap sooner than the reference particle receive a greater accelerating voltage, gain energy, and increase their mass, which in turn, causes them to slow down. Conversely, particles that reach the accelerating gap too late receive a smaller energy increase than the reference particle and increase their mass more slowly, which in turn causes them to rotate faster.

During World War II, Ed McMillan, from Berkeley, California, and Vladimir Veksler, of the Soviet Union, independently thought of this principle of frequency modulation, which adjusts the frequency of the applied voltage to allow it to remain in sync with the particles. The problem with the synchrocyclotron is that the variable frequency does not allow for the acceleration of a beam of particles, which had been possible with the fixed-frequency cyclotron.

If one changes the frequency to keep the voltage in step with the higher-energy particles, then the particles are compressed into batches and do not arrive at the gap between the dees at the same time. New ions emerging from the source are held back until the reference batch is accelerated up to the ions' full energy, so that the new batch can be matched to the proper rotational frequency.

As a contrast, every oscillating frequency of the cyclotron is identical, and particles may leave the ion source at any time. The synchronized cyclotron or synchrocyclotron concept takes groups of particles at one time and accelerates them out to the periphery of the magnet. The total or final energy is limited only by the size and strength of the magnet.

The idea for varying the cyclotron frequency was applied to the design of a 4.6-meter machine. A large magnet which was used for uranium enrichment was incorporated into the particle accelerator design. In November, 1946, the synchrocyclotron produced its first beam of deuterons with an energy of 195 million electronvolts. The new accelerator found its way into cosmic-ray research by producing a large supply of charged particles called pions, which were discovered in 1947. Also in 1947, the kaon and other exotic particles were discovered from the analysis of cosmic-ray tracks. The Berkeley machine was not powerful enough to produce these particles, however, and the 4.6-meter magnet was as large as was practical to construct.

The isochronous cyclotron or sector cyclotron was built in the late 1950's as a solution to the requirement of a curved magnetic field near the periphery of the accelerator which kept the particles in the desired orbital plane. By using three wedge-shaped magnets that met at a point in the center, the particles were constrained to follow a noncircular orbit, straight between the magnets and bending at 120 degrees within the magnets. The magnetic field lines were bowed outward at the edge of the magnets away from the plane, pushing particles that are out of the median plane back inward. The complicated shape given to the magnetic poles caused a sinusoidal variation in the pole strength and in the focusing of the particle beam. Later computer studies, however, demonstrated that many different forms in the magnetic field variation also produced beam focusing. A large isochronous cyclotron located in Vancouver, British Columbia, is 17 meters in diameter and applies a spiral shape to its sector designs, reaching energies of 500 million electronvolts for negative hydrogen ions.

Context

The cyclotron as conceived by Lawrence in 1930 is still the basis for major developments in accelerator design. The basic cyclotrons of the 1930's evolved into the synchrocyclotrons of the late 1940's and early 1950's, then into the synchrotron and isochronous cyclotrons dating from the early 1950's and finally into the superconducting cyclotrons that appeared in the late 1970's. The idea of the cyclotron survived because of the application of the basic theory to a succession of later improvements. Some of the advancements have included superconductivity and higher-energy ion sources.

The superconducting cyclotron, a major evolutionary development of the cyclotron, employs conventional components that are immersed within superconducting coils, which operate at the very low temperatures of liquid nitrogen and helium. The superconducting coils permit the increase of the strength of the magnetic field up to 50,000 gauss, or approximately three times higher than the typical cyclotron. The linear size of the superconducting cyclotron needs to be only one-third that of the conventional cyclotron, and the corresponding cross-sectional area is only one-ninth the size. This technical improvement greatly reduces operating costs. Superconducting cyclotrons that can produce energies of 500 million electronvolts and 800 million electronvolts have been installed at Michigan State University.

These machines are designed to accelerate the very heavy nuclei, such as lead and uranium, that are required in certain types of nuclear reactions.

The energies of cyclotrons and other accelerators are being boosted because of developments in heavy-ion sources. Advanced sources include confining microwave-heated electrons in a magnetic plasma and using electron beams to ionize heavy ions such as nitrogen, which increases the charge state of the source and the energy level for the beam.

There are almost one hundred cyclotrons in worldwide operation, which are generally used for research in nuclear physics and atomic chemistry. These high-energy accelerators investigate the atomic structure, nuclear forces, and many different kinds of nuclear reactions.

Practical use of cyclotrons has occurred in laboratories in the production of radioactive isotopes for medicine. Neutron beams from secondary reactions are generated for cancer therapy and environmental analysis. Many cyclotrons are in operation strictly for medical applications.

Principal terms

BEAM CURRENT: the electron-current equivalency of charged particles within a cyclotron, usually measured in milliamps or microamps

ELECTRONVOLT: a unit of measurement equivalent to an electron which has moved through a potential difference of 1 volt

FREQUENCY MODULATION: the practice of varying the frequency of applied potential difference or voltage in order to keep the particles in step or phase

GAUSS: a unit of magnetic field strength

PHASE: referring to wave motion, the position of a wave with respect to a reference wave

RELATIVISTIC: moving at very high speed comparable to the speed of light

RESONANCE: motion which matches the natural vibrational frequency of a system

Bibliography

Boorse, Henry, Lloyd Motz, and Jefferson H. Weaver. THE ATOMIC SCIENTISTS: A BIOGRAPHICAL HISTORY. New York: John Wiley & Sons, 1989. The significant achievements of Ernest Lawrence, including awards and honors, are presented in the chapter entitled, "New Particles and Atomic Accelerators." Contains considerable biographical information.

Close, Frank, Michael Marten, and Christine Sutton. THE PARTICLE EXPLOSION. New York: Oxford University Press, 1987. The general reader should find the brief chapter "The Whirling Device" on Lawrence's cyclotron fascinating. Included are photographs from the early and late versions of the cyclotron. The development of the synchrocyclotron and its limitations is addressed, as well as the work in nuclear science that was ongoing in Berkeley, California, during this period.

Kaplan, Irving. NUCLEAR PHYSICS. Reading, Mass.: Addison-Wesley, 1962. A comprehensive description of the principles behind both the cyclotron and the synchrocyclotron. Formulas are presented showing the relationships between the speed, mass, radius of orbit, charge, magnetic field strength, and the voltage encountered in these accelerators. The relativistic problem at high energies is thoroughly discussed by Kaplan.

Requires a basic mathematics background to understand. Kevles, Daniel J. THE PHYSICISTS. New York: Alfred A. Knopf, 1978. In chapter 15, "Miraculous Year," Kevles portrays Lawrence as being on the fast track to notable achievements. The reader will appreciate the emphasis on the thought process that Lawrence used in designing a machine which kept particles moving indefinitely in a circle, rather than the conventional straight line that accelerators had used previously. An excerpt from one of Lawrence's lecture series on radioactive tracer elements shows how he solicited audience participation.

Heilbron, J. L., and Robert W. Seidel. LAWRENCE AND HIS LABORATORY. Vol. 1 in A HISTORY OF THE LAWRENCE BERKELEY LABORATORY. Berkeley: University of California Press, 1989. A complete history of Lawrence, his staff, and his contributions in a detailed format. Many figures and tables are included, as well as photographs of the staff and the various cyclotrons. Items from Lawrence's experimental notebook are provided, as are additional tables on the operating costs of the various sized cyclotrons.

Oldenberg, Otto. INTRODUCTION TO ATOMIC AND NUCLEAR PHYSICS. New York: McGraw-Hill, 1961. This text on atomic physics illustrates the principles of the linear accelerator, the fixed-frequency cyclotron, the synchrocyclotron, the betatron, and the synchrotron in a style that can be comprehended by the reader without a strong mathematical background. Diagrams and photographs accompany the descriptions of these accelerators.

Wehr, M. Russell, James A. Richards, Jr., and Thomas W. Adair III. PHYSICS OF THE ATOM. Reading, Mass.: Addison-Wesley, 1985. A brief history of accelerators covers Ernest Rutherford's α-particle scattering, the Cockcroft-Walton accelerator, the Van de Graaff electrostatic generator, the linear accelerator, the cyclotron, the synchrocyclotron, and the synchrotron up to the modern superconducting varieties. Short but succinct. Also provides ample photographs and diagrams.

Schematic of a cyclotron

Nuclear Reactions and Scattering

Radiation: Interactions with Matter