ACCELERATOR

Particle accelerators are scientific instruments used to accelerate elementary particles to very high energies. They are of paramount importance for the study of elementary particle physics because the fundamental structure of matter is most clearly revealed by observing reactions of elementary particles at the highest possible energies. Historically, the development

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of elementary particle physics has been strongly coupled to advances in the physics and technology of particle accelerators. The first modern particle accelerators were developed in the 1930s and led to fundamental discoveries in nuclear physics. From 1930 to 1990, the energies attainable in particle accelerators have increased at an exponential rate, with an average doubling time of about two years. This progress has been due to a remarkable synergy between accelerator physics concepts (such as resonant acceleration, alternating gradient focusing, and colliding beams) and accelerator technology developments (such as microwave cavities, superconducting magnets, and broadband feedback systems). The consequence has been enormous progress in our understanding of the fundamental forces and constituents of matter.

Types of Accelerators

The large varieties of high-energy accelerators all share two basic common features. The first feature is the way that they accelerate the collection of moving charged particles within the accelerator (which is called the beam). In all accelerators, the energy of the beam is increased by passing it through electric fields, which exert a force on the beam parallel to its direction of motion. This force causes the beam's energy to increase. The second common feature is the method of controlling the direction of motion of the beam. All accelerators do this by the use of magnetic fields, which exert a force perpendicular to the direction of motion of the beam.

Accelerators can be usefully classified according to their geometry. A linear accelerator is a straight- line arrangement of many electric fields, with a few magnetic fields interspersed between the electric fields to focus the beam. A circular accelerator typically has only a few electric fields. Many magnetic fields bend the orbit of the beam into a closed, roughly circular path, as the beam particles pass through the electric fields once each revolution. Over many revolutions, the energy of the beam increases. As explained below, the magnetic field strength required to deflect a particle beam through a given angle is proportional to the momentum of the beam. In a synchrotron (the most common form of circular accelerator), the strength of the magnetic field is increased with the beam energy to maintain a constant radius orbit.

Accelerators may also be distinguished according to the species of particle that they accelerate: electrons or heavier particles such as protons (also called hadrons). One of the features of circular electron accelerators is the production of large amounts of electromagnetic radiation due to the centripetal acceleration of the electrons. This radiation, called synchrotron radiation, complicates the design of circular electron accelerators, since the radiated energy must be restored to the beam particles, increasing the requirements on the accelerator's electric fields. However, the radiation (a highly directional source of X rays) has been found very useful for applications in condensed matter physics, chemistry, and biology. Many accelerators (called synchrotron radiation sources) have been built whose sole purpose is the production of such radiation. For a fixed-radius accelerator, the power dissipated in synchrotron radiation increases as the fourth power of the beam energy, placing a very severe limit on the ultimate energy of circular electron accelerators. To achieve very high-energy electron beams, linear electron accelerators are required.

In hadron accelerators, protons or heavier ions are accelerated. Because of their larger mass, the synchrotron radiation of protons in circular accelerators is much weaker than that of electrons. Consequently, much higher energies are possible in circular proton accelerators than in circular electron accelerators. However, unlike the electron, the proton is not a true elementary particle: it is a composite system of three quarks and multiple gluons. The energy carried by a proton is shared among the quarks and gluons, so the energy of a single quark is much lower than the proton beam energy.

Accelerators may also be classified in terms of the final use of the accelerated beam. In accelerators prior to the 1960s, the high-energy beam struck a stationary target, in which the reactions to be observed took place. This was done either by placing the target within the accelerator or by manipulating the orbit of the accelerated beam so that it emerged from the accelerator (a process called extraction) and struck the target. In either case, an accelerator that is used in this way is called a fixed-target accelerator. The energy E_R available for a reaction in a target is given byin which E_b is the total beam energy, m is the rest mass of the target atom, and c is the speed of light.

Starting in the 1970s, circular accelerators were developed in which two counter-rotating beams were made to collide with reactions occurring at the collision point. Such an accelerator is called a collider. If both beams share orbits controlled by a single set of magnetic fields, one of the beams must be composed of the antimatter partner of the other (e.g., protons and antiprotons, or positrons and electrons). The advantage of a collider lies in the fact that the energy available for a reaction is given in this case bySince typically E_b » mc² , the energy available for a reaction is much larger than in a fixed-target accelerator. Colliders may also be built using two separate accelerators, which share a small overlap region where collisions take place; in this case, antimatter is not required. All current and planned accelerators operating at the energy frontier are colliders.

Circular colliders often utilize a special type of accelerator called a storage ring. This is a circular accelerator in which the beam simply circulates at a fixed energy. Collisions take place during the storage time of the beam, which is usually in the range of several hours. During this time, the beams may undergo billions of collisions. Nevertheless, the number of particles in the beam is diminished very slowly, since the probability of a high-energy reaction occurring in a single collision is very low.

Very high-energy electron circular colliders are not feasible due to excessive synchrotron radiation. To obtain very high energies in the collisions of electron beams, it is necessary to collide the beams from two opposing electron linear accelerators. Such a machine is called a linear collider.

Although the beam energy of a collider is a key measure of its usefulness for the study of elementary particle reactions, it is not the only figure of merit. Equally important is a measure of the rate at which reactions will occur: this measure is called the luminosity. For a collider, the luminosity is proportional to the density of the beams at the collision point and to the rate at which collisions take place. The design of a high-energy collider is often dominated by the need to attain sufficient luminosity to permit the observation of an adequate number of high-energy reactions.

Injector

The injector is the source of the particles for an accelerator. The injector is required to deliver to the accelerator a beam of a specified quality and energy. The quality of a beam is a measure of the beam's intensity and size: a high-quality beam will typically have a large number of particles (perhaps 10¹⁰) and a relatively small transverse size (ranging from millimeters to nanometers, depending on its energy and its location within the accelerator). For low-energy accelerators, the injector may be a small device, such as a hot-filament electron source or a discharge ion source. For high-energy accelerators, the injector is itself a complex arrangement of lower-energy accelerators. For hadron colliders, the luminosity is influenced heavily by the beam quality delivered by the injector.

Colliders that utilize beams of antimatter require very specialized injectors that can efficiently collect antimatter. The antimatter is typically produced in a fairly diffuse, low quality state from a target illuminated by the beam of an auxiliary fixed-target accelerator. The quality of the antimatter beam must be increased by orders of magnitude, in a process called beam cooling. For electrons and positrons, specially designed storage rings, called damping rings, are used, in which the process of synchrotron radiation reduces the size and increases the density of the beam. For antiprotons, an artificial process (called stochastic cooling) involving sophisticated micro- wave signal processing is often employed. After sufficient cooling has occurred, the injectors can deliver high-quality antimatter beams to a collider.

Acceleration System

For accelerators used in elementary particle physics, the acceleration system is a set of resonant cavities or waveguides carrying time-varying electromagnetic fields. The beam passes through the cavities, and the electric fields increase the energy of the beam. The frequency of the electromagnetic cavity fields can range from below 50 MHz to above 30 GHz. The electric field strengths can range from below 5 MV/m to above 100 MV/m. The beam is accelerated in "bunches" whose length is related to the wavelength of the cavity fields, ranging from meters (for accelerators using 50 MHz fields) to fractions of a millimeter (for high-frequency accelerators).

A key concept in an acceleration system is that of resonant acceleration. This requires that each bunch arrive at each cavity at about the same phase of the electromagnetic field, so that each bunch always receives roughly the same energy gain. The cavity spacing and the field's frequency must be appropriately matched to the beam velocity to achieve resonant acceleration. An important feature of the beam dynamics is called phase stability. This guarantees that, under the appropriate circumstances, the beam is stable under small deviations from the resonant acceleration condition (that is, if displaced from the resonant condition, the beam will oscillate stably about it, rather than continue to deviate further from it).

Orbit Control System

The orbit control system in an accelerator is a set of magnets placed along the beam's trajectory. The magnets do not change the energy of the beam but exert forces on the beam that define its orbit. The magnets are most often electromagnets, with fields that are either constant in time (in storage rings) or which increase in strength as the beam's energy is increased (in synchrotrons). Permanent magnets, with fixed magnetic fields, may also be used in storage rings. The most common types of magnets used in an accelerator are dipole magnets and quadrupole magnets.

Dipole magnets produce a spatially uniform magnetic field and are used to deflect the orbits of all particles in the beam by the same amount. The fundamental orbit control system in a circular accelerator is a series of dipole magnets that bend the orbit of the beam into a roughly circular path. The Lorentz force exerted by the dipole's field provides the centripetal force required for circular motion. This leads to the following relation between the momentum of the beam particle p , the magnetic field B , the beam particle's charge q , and the beam's orbit radius R :This equation shows that for a high-energy beam, with a large value of p , either a large magnetic field or a large orbit radius is required. The need to limit the accelerator's size, for economic reasons, puts a great premium on the use of high magnetic fields for high-energy circular accelerators. Very high magnetic fields can be generated without excessive power dissipation through the use of magnets whose conductors are made from superconducting materials. This is why today's largest high-energy circular accelerators rely on superconducting magnet technology for their orbit control system.

Quadrupole magnets are used to focus the beam. A useful analogy may be made between the orbits of charged particles in an accelerator and the paths of light rays in an optical system. Prisms deflect all the rays in a monochromatic light beam by the same amount in the same way that dipole magnets deflect all the orbits in a monoenergetic charged particle beam by the same amount. Optical lenses focus light beams by providing a deflection of a light ray that is proportional to the distance of the ray from the lens' axis. Similarly, charged particle beams are focused using quadrupole magnets, which have a magnetic field strength that is proportional to the distance from the magnet's axis. The use of quadrupole magnets is essential to the operation of all types of accelerators. Their focusing properties ensure that the beam will oscillate stably about the ideal orbit if displaced from it.

Optical lenses are cylindrically symmetric and can focus simultaneously in both transverse planes. Unfortunately, the equations of electrodynamics do not allow this for quadrupole magnets: if they focus in one transverse plane, they must defocus in the other. Nevertheless, it is possible to construct a system of alternating focusing and defocusing magnets whose net effect is focusing. This is called the principle of alternating gradient focusing. Accelerators with a focusing system based on this principle were first developed in the 1950s, and since then all accelerators make use of this feature in their orbit control system.

Final Use Systems

In a fixed-target accelerator, the high-energy beam is usually extracted from the accelerator prior to its use in the creation of high-energy reactions. Extraction is very simple from a linear accelerator. Extraction from a circular accelerator can be more challenging. It is usually not desirable to extract the entire beam from the accelerator in one revolution, as the resulting instantaneous rate of reactions in the target may be too high to be useful. Generally, the beam must be extracted "slowly," over many thousands of revolutions. Such a procedure often relies on the generation of small nonlinear disturbances in the accelerator's magnetic fields, which slowly divert the beam from its stable orbits. The location of these disturbances must be carefully controlled to ensure that the entire beam emerges from the accelerator at a single location from which it can be transported by a linear array of quadrupole and dipole magnets (called a beam line) to the target.

In a collider, the beams do not need to be extracted but must be tailored to have very specific features at the collision point. Since the luminosity is proportional to the density of the beams at the collision point, the beams must be focused very tightly to as small an area as possible. A system of very strong quadrupole magnets, placed within the accelerator very close to the collision point, provide this focusing. When the high-density beams collide, the electromagnetic fields of one beam can strongly perturb the motion of the other beam. This beam-beam interaction is one of the fundamental limitations on the achievable beam density, and hence luminosity, in a circular collider. In a linear collider, the beams interact only once, and so the density can be made much higher. Nevertheless, the luminosity is comparable to that in a circular collider because the rate at which collisions occur is much lower in a linear collider.

To record the results of the colliding beam reactions, a system of high-energy particle detectors is installed surrounding the collision point. These particle detectors often have their own magnetic fields, which can influence the orbits of the colliding beams, and must be considered in the design of the accelerator. Conversely, background reactions from stray particles in the beam can severely comprise the performance of the particle detector. The need for careful and close integration of the particle detector and the accelerator is an important feature of a collider.

See also:Accelerators, Colliding Beams: Electron-Positron; Accelerators, Colliding Beams: Electron-Proton; Accelerators, Colliding Beams: Hadron; Accelerators, Early; Accelerators, Fixed-Target: Electron; Accelerators, Fixed-Target: Proton; Beam Transport; Detectors; Extraction Systems; Injector System

Bibliography

Bryant, P. J., and Johnsen, K. The Principles of Circular Accelerators and Storage Rings (Cambridge University Press, New York, 1993).

Conte, M., and MacKay, W. W. An Introduction to the Physics of Particle Accelerators (World Scientific, Singapore, 1991).

Edwards, D. A., and Syphers, M. J. An Introduction to the Physics of High Energy Particle Accelerators (Wiley, New York, 1993).

Lawson, J. D. The Physics of Charged-Particle Beams (Oxford University Press, New York, 1988).

Livingood, J. J. Principles of Cyclic Particle Accelerators (Van Nostrand, Princeton, NJ, 1964).

Livingston, M. S., and Blewett, J. P. Particle Accelerators (McGraw-Hill, New York, 1962).

Reiser, M. Theory and Design of Charged Particle Beams (Wiley, New York, 1994).

Wangler, T. P. Principles of RF Linear Accelerators (Wiley, New York, 1998).

Wiedemann, H. Particle Accelerator Physics I: Basic Principles and Linear Beam Dynamics, 2nd ed. (Springer-Verlag, New York, 1998).

Gerald F. Dugan

ac·cel·er·a·tor / akˈseləˌrātər/ • n. something that brings about acceleration, in particular: ∎  the device, typically a pedal, that controls the speed of a vehicle's engine. ∎  Physics an apparatus for accelerating charged particles to high velocities. ∎  a substance that speeds up a chemical process ∎  Comput. short for accelerator board.