Betatrons

Type of physical science: Particle accelerators, Elementary particle (high-energy) physics

Field of study: Techniques

The betatron is a device that accelerates electrons to very high energies in a very short time while the electrons move around in a fixed circular path. The high-energy electrons can produce deeply penetrating x-rays.

Overview

Betatrons are particle accelerators that are specially designed to accelerate electrons to very high energies using the principle of magnetic induction. When radioactivity was discovered in 1896, the three types of radiation emitted by radioactive material were called alpha, beta, and gamma rays. Beta rays were subsequently identified as electrons. Electrons are still sometimes referred to as beta particles, and hence electron accelerators are known as betatrons.

Michael Faraday discovered in 1831 that a time-varying magnetic field induces an electric potential. For example, if a magnet is quickly moved into a coil wire, a current is generated in the coil as a result of the induced electric potential. It is also well known that the negatively charged electrons are accelerated in an electric field such that they move toward the positive terminal. In a television tube or a computer monitor, millions of electrons are accelerated from the negative cathode to the positive screen (anode) when there is an applied voltage between the two electrodes. These two properties of magnetic induction and field acceleration are gainfully employed in a betatron. An electric voltage is induced by a time-varying magnetic field, and this induced voltage is used to accelerate the electrons.

The basic principle of operation of the betatron is similar to that of the transformer that is commonly used in electrical power transmission. The transformer consists of two sets of coils wound on a common magnetic iron core. The primary coil carries the input alternating voltage. This varying voltage produces a varying magnetic flux, which then induces an alternating voltage in the secondary coil. By increasing the number of turns in the secondary coil, the output voltage can be increased. If the secondary coil has one thousand times more turns than the primary, the voltage will increase one thousand times. It should, however, be remembered that the current will simultaneously decrease a thousand times. According to the laws of physics, energy can be neither created nor destroyed. With careful design and considerable difficulty, high voltages on the order of two million volts have been produced using powerful step-up transformers. The high-voltage breakdowns that always plague such electrical devices set a limit on the voltage attainable through this technique.

A betatron does not employ many turns of wire to form the secondary coil; instead, electrons are made to circle the magnetic core repeatedly. Every time an electron completes one circle around the magnet, it is accelerated by a voltage equal to the induced voltage in one turn of wire. Electrons are extremely light particles, and they can travel at velocities close to the speed of light. Within a few milliseconds, they can circle a million times around the magnetic core, thereby generating a very high energy of millions of electronvolts. Hence, the betatron is basically a step-up transformer in which the secondary coils have been replaced with circulating electrons so that high-voltage breakdown is no longer a problem. As the energy increases, the electrons will start spiraling out of the initial orbit. However, a separate guide field can be used to keep the electrons in a stable orbit as long as they are inside the accelerating chamber.

The betatron consists of a doughnut-shaped accelerating chamber located between the pole pieces of an electromagnet. The chamber is evacuated to a very high order of vacuum so that the electrons circling inside the chamber are not scattered by air molecules. The magnetic field of the electromagnet performs a dual function in the betatron. First, as the field direction is perpendicular to both the plane of rotation and the movement of the electrons, it bends the electrons around to move in a circular path. Secondly, the variation of the magnetic field induces an electric field, which accelerates the electrons in a tangential direction. Theoretical calculations show that to maintain the electrons in a circular orbit of constant radius, the electromagnet should be designed such that the average magnetic field over the area of the orbit is twice the field at the circumference.

The exciting coil of the electromagnet is powered by the conventional alternating voltage at a frequency of fifty or sixty hertz. The alternating current in the excitation coil follows a sinusoidal waveform with a smooth crest and a trough. This varying current induces a magnetic flux with a frequency and time variation that correspond to that of the excitation current. As mentioned before, this induces the electric field needed to accelerate the electrons to high energies. The acceleration should take place in the first half of the wave crest—that is, within five milliseconds in the case of the fifty-hertz alternating voltage. Within that short time, the electrons will circulate a million times, each time gaining more energy. The energy per revolution may be small, in the range of only tens of electronvolts. However, within five milliseconds, this energy is multiplied about a million times, and the resulting electron velocity can reach 99.9 percent of the speed of light. Once the excitation voltage reaches the top of the wave crest, it is necessary to wait until the start of the wave trough, when the acceleration can happen in the opposite direction. The electrons, therefore, have to be injected into the betatron in pulses.

At the beginning of an acceleration cycle, a burst or pulse of electrons must be injected at the right time and right energy into the circular orbit inside the chamber. In Robert R. Wilson and Raphael Littauer's Accelerators: Machines of Nuclear Physics (1960), the authors make the observation that the electrons in a betatron "must make their first trip around the guide field like fully seasoned accelerator travelers—no breaking in or warming up allowed!" A pulsed electron gun of relatively high energy is used as the injector. For example, for a betatron capable of accelerating electrons to fifty megaelectronvolts (MeV), the electrons are injected with an initial energy of fifty to one hundred kiloelectronvolts (keV). The injector electron guns are of a simple design; they are like those used in a television tube, except that they are operated in pulses through suitable switching mechanisms.

To begin the operation in a betatron, electrons are injected when the excitation current in the electromagnet reaches a small initial value. The magnetic field bends the electrons into the circular orbit inside the accelerating chamber; as the magnetic field increases in the first half of the wave crest, the electrons gain energy from the accelerating electric field produced by magnetic induction. Both half periods of the supply voltage can be used to accelerate the electrons. When the sinusoidal wave changes direction and becomes a wave trough, the acceleration process described above can be repeated with the beam traveling in the opposite direction. Betatrons that use both half periods of the supply voltage use two separate electron injector guns that operate alternately during the individual half periods, resulting in two output beams of electrons. Such devices are known as dual-beam betatrons.

Once the electrons have reached their maximum energy, they should be removed from their stable orbit. For this purpose, the electromagnet of the betatron is fitted with an auxiliary coil called an expansion coil. Just before the end of the acceleration cycle, the expansion coil is energized by a strong current pulse. The duration of this pulse is very short, lasting only a few microseconds. The magnetic field induced in the expansion coil causes the radius of the electron orbit to increase. The electrons leave the stable orbit and are taken out through a suitable window built into the chamber wall. When the betatron is used to generate x-rays, the accelerated electron beam is deflected by means of the expansion coil to strike a suitable metal target placed inside the chamber itself. When the high-energy electrons are stopped by the target, a part of their energy is converted into x-rays. The x-rays, being electromagnetic waves, are not deflected by the magnetic field, and they can penetrate outside the chamber.

When electrons are accelerated around a circular orbit, they emit electromagnetic radiations such as light or x-rays. This radiation, called synchrotron radiation, leads to energy loss that can be substantial at high energies. Based on this and other factors, the theoretical limit of the maximum energy attainable in a betatron has been calculated to be about 500 MeV, and the largest betatron ever built could produce 340 MeV. However, the energy range typically does not exceed 50 MeV.

Applications

Though betatrons have largely been replaced by synchrotrons, which are capable of producing significantly more energy, they are widely used in the fields of medicine and industry, especially when space is limited. The principal areas in which betatrons are employed are radiotherapy, radiography, and photoactivation.

In radiotherapy, betatrons are mostly used to treat malignant tumors. As betatrons produce highly penetrating x-rays, they are more effective in this kind of treatment than other sources. In one study, patients with bladder tumors who were given radiation therapy with 200-kilovolt x-rays showed a five-year survival rate of 14 percent, while radiation therapy using x-rays from a 35 MeV betatron raised the survival rate to 55 percent.

Therapeutic betatrons are designed to generate both hard (highly penetrating) x-rays and high-energy electrons. In the case of x-rays, the absorption dose builds up steadily over the first one to four centimeters of penetration. Therefore, the sensitive layers of the skin receive only a fraction of the dose received at full depth. Normally, high-energy x-ray beams from a betatron or another device are aimed at the tumor inside the body from a number of directions. This will produce a concentration of radiation at the tumor region without introducing harmful doses in the rest of the patient's body.

High-energy electrons that are used directly for treatment are absorbed by tissues within a short distance in the patient's body. A two-megaelectronvolt beam is absorbed within one centimeter of body tissue. Electron irradiation is therefore very useful in treating surface tumors without affecting internal organs. For example, a chest tumor can be treated by a carefully controlled electron beam from a betatron without affecting the lungs inside.

Betatrons are generally highly reliable and durable. The most problematic elements are the evacuated accelerating chamber and its electron source. Electron guns have long lifespans, depending on the high-order vacuum inside the chamber. When an electron gun is worn out, replacement requires the dismantling of the chamber, which is usually sealed. This is a tedious and time-consuming process. In newer designs, the chamber is constructed so that it can be evacuated continuously by a high-vacuum pump, thus speeding up the process of replacing worn-out parts. The mobility and maneuverability of the instrument also are significant factors, depending on the applications.

Radiographic betatrons have been used for industrial flaw detection for many decades. Since they produce highly penetrating x-rays, these devices can be used to inspect steel up to half a meter in thickness. The hard x-rays from the betatron are passed through the material to be examined and strike a radiographic film behind it. Flaws such as fractures and bubbles contain less-dense material, typically air, so they appear darker in the film. As the photosensitive emulsion of the film has a relatively low absorption coefficient for x-rays, multiple-layer films or other techniques must be used to get a good picture.

Neutron activation analysis is an important nondestructive way to trace even tiny amounts of elements present in samples. The neutrons hitting the sample can turn neutral atoms radioactive. The subsequent gamma-ray emissions can help to identify the trace elements present and measure their amounts. When neutron activation is not plausible, either because the cross section of the element is too small or the substance in which the trace element is located is too large, then photoactivation is the method commonly used.

Photoactivation is similar to neutron activation, but instead of neutrons, high-energy photons are used to make the neutral atoms radioactive. These photons are obtained as x-rays from a betatron. A major advantage of photon activation is that it can be applied to samples of up to five hundred grams, and the entire sample can be activated, increasing the possibility of detecting even very small amounts of trace elements.

Context

In a thought-provoking article published in the March 1958 issue of Scientific American, Robert R. Wilson called the building of accelerators "an obsession of our own time" and compared it with the "magnificent preoccupation" with building cathedrals in twelfth- and thirteenth-century France. He added, "Like nuclear physics today, religion at that time was an intense intellectual activity. It seems to me that the designer of an accelerator is moved by much the same spirit which motivated the designer of a cathedral."

Particle accelerators are the products of basic scientific research. Even though they have found practical applications in many fields, these machines were originally built to help understand matter at the most basic level. Particles were accelerated to higher and higher energies by these mighty nuclear machines to probe the secrets of the atom, just as bigger and bigger telescopes were built to probe the cosmos.

In 1910, Ernest Rutherford used the energetic alpha particles from a radioactive source to perform scattering experiments and discovered the nuclear model of the atom. In 1919, Rutherford, still using the same natural ammunition, carried out the first artificial transmutation of an element. He was able to turn nitrogen atoms into oxygen atoms by bombarding nitrogen gas with alpha particles, which had a maximum energy of about eight megaelectronvolts. It was subsequently realized that the acceleration of atomic and subatomic particles to high energies could lead to tremendous progress in nuclear research.

In 1922, Joseph Slepian filed a US patent application in which he described how a device similar to the electrical transformer could be used to accelerate electrons. The next step in developing the theory was taken by Norwegian physicist Rolf Wideröe, who showed how to arrange Slepian's iron-core system with a slowly varying magnetic field to reach high flux linkages and high energies. Around the same time, Ernest Walton's experiments in Britain helped lead to an understanding of the techniques needed to focus and stabilize the electron orbit. The first successful betatron was built by Donald W. Kerst at the University of Illinois in 1940. His first machine accelerated electrons to an energy of 2.35 MeV, and his second machine reached energies of 20 MeV. In 1950, he built the largest ever betatron, which produced pulses of 340 MeV electrons.

The betatron was the first accelerator to achieve stable circular orbits for the accelerated particles and to use a simple property such as magnetic induction to energize them. Its development involved a tremendous amount of technological innovation. The two magnetic fields—the guide field acting over the annular chamber and the energizing field acting on the central core—have to increase steadily in synchronization. The whole process takes place within a few milliseconds.

High-energy betatrons have contributed to basic scientific research. However, the importance of this machine lies in its ability to produce hard x-rays and provide a well-focused electron beam. Because of this capability, betatrons are being extensively used in many industries and medical establishments.

The electron synchrotron has superseded the betatron in terms of high-energy capability. These machines can accelerate electrons to billions of electronvolts. The electron synchrotron combines the accelerating system of the highly successful cyclotron with the ring-shaped, pulsating guide field of the betatron. Betatrons have nevertheless found their own niche in medical and industrial applications, where their smaller size makes them preferable to synchrotrons when higher energy levels are unnecessary.

Principal terms

alternating current (AC): electrical current that periodically rises and falls in positive and negative directions, in contrast to the steady direct current (DC)

beam energy: the kinetic energy per particle in the beam from an accelerator

electronvolt: the energy acquired by a particle of unit charge, such as an electron, when it is accelerated by a potential of one volt; because accelerator beam energies are huge, they are typically measured in terms of kiloelectronvolts (one thousand electronvolts) or megaelectronvolts (one million electronvolts)

magnetic flux: the magnetic lines going through a given area; the density of these lines is an indication of the strength of the magnetic field

magnetic induction: the creation of an electric field by varying the magnetic flux; the magnitude of the induced electric field is proportional to the rate at which the flux changes

transformer: an electrical device that can increase or decrease an alternating voltage through the principle of magnetic induction

Bibliography

Bhandari, R. K., and Malay Kanti Dey. "Applications of Accelerator Technology and Its Relevance to Nuclear Technology." Energy Procedia 7 (2011): 577–88. Print.

Kerst, Donald W. "Historical Development of the Betatron." Nature 157.3978 (1946): 90–95. Print. Written by the builder of the first successful betatron. Kerst gives a good account of the work that went ahead of his own in the development of the machine.

Lei, Han, et al. "Optimal Application of the Betatron." Advanced Composite Materials. Ed. Wenzhe Chen et al. Spec. issue of Advanced Materials Research 482–84 (2012): 2170–73. Print.

Livingston, Stanley M. High-Energy Accelerators. New York: Interscience, 1959. Print. This work does not have a separate section on betatrons; however, it does discuss some of the important techniques used in the acceleration of electrons.

Livingston, Stanley M. Particle Accelerators: A Brief History. Cambridge: Harvard UP, 1969. Print. Gives only a brief account of the betatron, but puts its development in a sound historical perspective.

Oldenberg, Otto. Introduction to Atomic and Nuclear Physics. New York: McGraw, 1961. Print. Contains a brief overview of the betatron. Written in a simple style that should be accessible to the lay reader.

Scharf, Waldemar. Particle Accelerators and Their Uses. 2 vols. New York: Harwood, 1986. Print. Part 1 has an excellent chapter on the betatron, with many diagrams and photographs. Part 2 lists many of its applications. A little technical in approach, but can be followed by laypersons.

Scharf, Waldemar. Particle Accelerators: Applications in Technology and Research. New York: Wiley, 1989. Print. Contains a brief, nontechnical section on betatrons. Includes a simple and elegant diagram helpful in understanding how the guide magnetic field and main field work. Also contains much relevant material on accelerator techniques and the applications of accelerators in general.

Semat, Henry. Introduction to Atomic and Nuclear Physics. 3rd ed. New York: Rinehart, 1954. Print. Provides a simple account of the theory and construction of the betatron. Includes a good diagram and a photograph of the original machine.

Takayama, Ken, and Richard J. Briggs, eds. Induction Accelerators. Heidelberg: Springer, 2011. Print.

Wilson, Robert R., and Raphael Littauer. Accelerators: Machines of Nuclear Physics. New York: Doubleday, 1960. Print. Features an extremely well-written chapter on betatrons; informative and easy to follow. The principles behind the machine are discussed in several places, with interesting examples.