Linear Accelerators

Type of physical science: Nuclear physics

Field of study: Nuclear techniques

Linear accelerators are devices that augment the energy of a beam of charged particles. Acceleration occurs in a straight line, using radio frequency electromagnetic fields.

Overview

As the name implies, a linear accelerator (linac) is a device in which charged particles travel in a straight line as they are being accelerated. The term also implies in practice that the acceleration is accomplished by means of radio frequency electromagnetic fields and not by means of electrostatic fields as in an electrostatic accelerator. Details of the design of linacs depend on whether they are intended for accelerating electrons, protons, or heavy ions.

Linacs have two basic design types: the drift-tube design and the waveguide design. A drift tube is a hollow metal cylinder, open at both ends; the particles travel along the axis of the cylinder. While they are inside the cylinder and far from either end, the particles do not experience any appreciable force because the electric and magnetic fields are shielded out by the metal of the cylinder. Since the particles experience no force in this region, they are drifting. The essence of the drift-tube method is that a large number of drift tubes are placed one after the other with short gaps between two consecutive tubes. Each tube is arranged to have either a positive or a negative voltage, with the sign alternating from one tube to the next. When particles arrive at the gap between two successive cylinders, the voltages must be arranged so that the particles are repelled from the cylinder they are leaving and attracted to the cylinder they are approaching. When they cross the gap, the particles gain a certain amount of energy. If nothing more were done, they would lose that energy at the next gap, where the force would be in the opposite direction, and the particles would be decelerated. To prevent this loss, the polarities of all the cylinders are reversed when the particles are near the center of the drift tubes. Thus, at every gap the polarity has been arranged for the particles to gain energy. The oscillation in the polarity of the drift tubes takes place at a radio frequency that is characteristic of microwaves.

The particles do not gain much energy at each gap. Nevertheless, the number of tubes (and therefore the number of gaps) can be made quite large, leading to a high value of the beam energy without the need for especially high voltage. In the upstream end of the accelerator, the particles are moving more slowly than they are at the downstream end after they have been accelerated; therefore, the length of the drift tubes must increase gradually from upstream to downstream, more or less proportional to the square root of the tube number. Each gap supplies the same energy increment, and the velocity varies as the square root of the kinetic energy, for nonrelativistic motion.

The drift tubes are all contained inside a long cylindrical tank that is maintained at a good vacuum so that the beam particles are not lost to collisions with air molecules. Devices called klystrons generate the microwaves outside the tank and conduct them to the inside, where they cause electric and magnetic fields primarily at the gaps between drift tubes, secondarily in the region between the drift tubes and the inside wall of the tank, but essentially not deep in the interior of the drift tubes.

Initially, it may seem logical to run the accelerator so that the particles arrive at the gap when the voltage is at its peak, thereby maximizing the energy imparted to the particles in the beam. If this setup is adopted, however, the beam intensity will suffer, since the particles do not all reach the gap in time to take advantage of the full voltage. As a result, the latecomers will get less than the proper gain in energy, causing them to arrive even later at the next gap. Soon, they will be lost to the beam. It is more efficient--and even essential--to design the system with enough extra voltage so that the particles arrive at the gap before the maximum voltage is reached: The particles that arrive early (the ones with too much energy) will receive less than the nominal amount of force at the gap, and their energy will be closer to the right amount. The latecomers (the ones with too little energy) will get to the gap when the voltage is higher than nominal, so they will pick up enough extra energy to get them to the next gap a little earlier. As a result, far fewer particles will be lost to the beam. This is known as the principle of phase stability.

As the particles cross the gaps, the electric forces acting on them tend not only to accelerate them but also to deflect them away from the axis of the system. The latter effect "defocuses" the beam. There are several possible remedies: One can place a small screen across the end of the drift tube to redirect the electric fields; one can use small, specially shaped pieces of metal that accomplish the same purpose as the screen but allow more particles to pass through; or one can use quadruple magnets to impose external focusing on the beam.

A waveguide linac essentially is a hollow pipe with microwaves flowing through it, with the magnetic fields perpendicular to the axis of the pipe and the electric fields at least partially parallel to the axis to impart acceleration to the charged particles in the beam. For all smooth hollow pipes, however, the phase velocity of microwaves is greater than the speed of light, and the special theory of relativity states that no particle can go faster than the speed of light (c). The particles cannot keep up with the accelerating wave. The solution to this problem is to place metal circles at regular intervals along the inside of the pipe. Each circle has a hole in its center large enough to accommodate the passage of the beam. The resulting structure is called an "iris-loaded waveguide." A wave traveling in a periodic structure can be arranged to have any phase velocity one chooses: greater than c, less than c, zero, or even negative. For linacs, the phase velocity of the microwaves is matched to the velocity of the particles being accelerated. Thus, the particles ride the wave exactly as a surfer rides a water wave in the ocean, picking up energy as the wave progresses. If the particles are slightly ahead of the region of maximum field strength, they will also have phase stability.

An alternate way to understand the working of a waveguide linac is to consider it as a large number of cavity oscillators that are connected loosely to one another by the holes where the beam goes. In each cavity there is a standing wave, with the electric field somewhere along the axis so as to provide acceleration. The timing or phase of the oscillations shifts from one cavity to the next so that it is synchronized for the arrival of the particles.

The spacing of the irises (or, alternately, the cavity sizes) varies more for proton or heavy ion linacs than for electron linacs. For the latter, a small energy gain brings the particles' velocity very close to c, and thereafter, they gain energy in regular amounts, with minimal change in the velocity. In a high-energy electron linac, the energy can be varied simply by changing the number of klystrons that drive the accelerator, since the energy is proportional to the square root of the number of klystrons.

Applications

Linacs are used as sources of particles for research in nuclear physics at low, medium, and high energies. The most spectacular example is the 3-kilometer linac at the Stanford Linear Accelerator Center (SLAC) in California. This machine is an electron linac of the waveguide type. It can also accelerate positrons on the opposite half of the cycle, the half that is useless for electrons. The positrons are made inside the accelerator itself by making some of the accelerated electrons impinge on a target located about a third of the way from the start.

At Los Alamos in New Mexico there is a large proton linac that is used for research in medium-energy nuclear physics. This accelerator is best considered as a sequence of cavity oscillators, where alternate cavities do not contribute to the energy gain, but are necessary to maintain accurate timing. These extra cavities are moved out of the beam line so as to shorten the total length of the accelerator.

Linacs are used not only as stand-alone accelerators but also as preaccelerators for other types of accelerators, such as synchrotrons. Proton synchrotrons work better if the protons are relativistic at the outset. The standard procedure is to use a linac that accepts protons at a modest energy and accelerates them to such a high energy that the synchrotron can handle them more effectively. The large accelerator at the Fermi National Accelerator at Batavia, Illinois, is a proton synchrotron built in the form of a ring that is 1 kilometer in radius. The main ring cannot operate effectively with protons direct from the ion source. Instead, the protons from the ion source are accelerated by an electrostatic accelerator of the Cockcroft-Walton type and then injected into a proton linac, which accelerates them to an energy such that they can be sent to a small synchrotron, after which they go into the main ring. The linac is one indispensable link in a chain of accelerators.

Linacs are also used in pure research as a postaccelerator to an electrostatic accelerator.

Linacs have been built for this purpose with superconducting resonant cavities, using either niobium-copper or lead-plated copper for the walls of the resonator.

The high beam intensity of linear accelerators has made them valuable for medical use, both in radiation therapy and in sterilization of numerous types of small objects used in medicine. For example, surgical thread has to be free of microbes that could cause disease in a patient who has undergone surgery. Radiation from an electron linac can be an effective replacement for either heat or chemicals, the two older methods of sterilization.

The sterilizing properties of radiation have led to varied industrial applications of linacs. They can be used to treat waste water to kill harmful organisms. They can also be used for preservation of food. For example, even a small dose of radiation will prevent the sprouting of onions, garlic, or potatoes at a cost far less than that of the energy needed to refrigerate these food items. At higher levels, the radiation can destroy insects, fungi, or microbes that cause wastage of food.

Other industrial applications exist that do not involve sterilization, such as using radiation to study wear on the surface of metal parts. Many examples of this type of application come from parts of automobile engines: piston rings, cylinder walls, and cams are all metal parts that experience wear from rubbing, in spite of lubrication with oil. It is important to know how the wear takes place and how fast. A linac can provide the radiation needed to perform such studies.

Another class of examples involves irradiation of plastics to induce polymerization and cross-linkage. For example, a plastic object may be formed by pressing the plastic into the required shape. The plastic may "remember" its original form, however, and revert to that rather than keep its new shape. If the plastic is irradiated by the beam from a linac not long after it is pressed, the structure of the polymer tends to be modified so that the plastic "forgets" its original shape.

Context

In the 1920's, the concept of a drift-tube linac was suggested in Sweden, and a small working model was built in Denmark. In the 1930's, the concepts were developed further at the University of California at Berkeley (drift tubes) and at the University of Virginia (waveguides), but no linac was then capable of enough beam energy to use for nuclear research. The energy was limited by the available technology of microwaves. During World War II, microwaves were researched extensively, mainly for their use in radar. Immediately after the war, the improved microwave methods were put to use in building new and better linacs, chiefly at Berkeley and at Stanford University. Both types of linacs were improved later both in beam energy and reliability.

At the lowest energies, linacs do not compete well with electrostatic accelerators.

Linacs have poorer duty cycles, worse energy definition, and worse definition of beam direction.

As the energy goes up, the electrostatic accelerators drop out of the competition because of their inability to hold very high voltages. The competition then takes place between linacs and circular accelerators. Linacs generally cost more per unit of beam energy, but they have higher beam intensity and better definition of beam direction; it is also easier to provide them with shielding to protect people and equipment from radiation. The beam from a linac necessarily has radio frequency structure; this feature can sometimes be turned to advantage in experiments done at linacs.

A measure of the importance of linacs is that more than six Nobel Prizes in Physics have been awarded for experiments done either with a linear accelerator as the source of the particles or with a synchrotron, where the particles were sent through a linear accelerator before reaching the main ring of the synchrotron.

Principal terms

BEAM ENERGY: the kinetic energy per particle in a beam from an accelerator

BEAM INTENSITY: the number of particles per unit time that are emitted by an accelerator

CAVITY OSCILLATOR: a hollow container made of an electrical conductor; microwaves form standing wave patterns inside, much as sound waves resonate inside hollow objects

DUTY CYCLE: the percentage of time that an accelerator actually spends accelerating particles

IRIS: a circular shield with a circular hole in the middle, as in the iris of the human eye, of which the hole corresponds to the pupil

KLYSTRON: a device for generating microwaves

LINAC: a linear accelerator

MICROWAVES: electromagnetic waves whose wavelengths range from about a millimeter to about a meter

PHASE VELOCITY: the speed at which the crest of a wave appears to travel, referenced to a specific direction in space

POSITRON: the antiparticle of the electron, with the same mass but the opposite electric charge

WAVEGUIDE: a long hollow conducting tube arranged so that microwaves can travel along the interior

Bibliography

Kapchinskii, I. M. THEORY OF RESONANCE LINEAR ACCELERATORS. Translated by S. J. Amoretty. New York: Harwood Academic, 1985. Although this book uses some mathematics, it has much qualitative material understandable by the nonspecialist.

Livingston, M. Stanley, ed. THE DEVELOPMENT OF HIGH-ENERGY ACCELERATORS. New York: Dover, 1966. This is a selection of original papers by the pioneers who originated the major types of accelerators, including linacs. Easy to read.

Livingston, M. Stanley, and John P. Blewett. PARTICLE ACCELERATORS. New York: McGraw-Hill, 1962. The standard reference on accelerators of all kinds. Contains both qualitative description and mathematical treatment. Includes a chapter on phase stability and one on linacs.

Scharf, Waldemar. PARTICLE ACCELERATORS: APPLICATIONS IN TECHNOLOGY AND RESEARCH. Translated by Oskar A. Chomicki. Taunton, England: Research Studies Press, 1989. Good survey of existing and possible future applications of linacs and other accelerators.

Scharf, Waldemar. PARTICLE ACCELERATORS AND THEIR USES. Translated by Eugene Lepa. New York: Harwood Academic, 1986. Although it has only half a chapter on linacs, this book says much about applications of accelerators in general, much of which is pertinent to linacs.

Detectors on High-Energy Accelerators

Materials Analysis with Nuclear Reactions and Scattering

Radiation: Interactions with Matter

Storage Rings and Colliders