ACCELERATORS, FIXED-TARGET: PROTON

Particle accelerators invariably accelerate either protons or electrons because they are the only stable, electrically charged particles. Copious synchrotron radiation of electron beams at high energies tends to make the design of proton and electron accelerators very different, and a given accelerator is normally only used for one type of particle. Many proton accelerators are, however, capable of accelerating heavy nuclei.

Proton Accelerators

Proton accelerators begin with an ion source. The most commonly used sources produce either protons or H^- ions. An H^- ion consists of a proton with two bound electrons. Proton sources can result in higher currents, but the advantage of H^- sources is that they enable the use of a special technique known as "multi-turn injection." While the pulse of protons that can be injected into a circular accelerator is limited to one turn (i.e., the time it takes for a particle to traverse the circumference), an H^- pulse can be injected for many turns. Multi-turn injection is achieved by passing the H^- beam through a thin foil inside the circular accelerator to strip off the two electrons and thereby create a proton beam. A variety of techniques are available to produce heavy atoms in various states of ionization. The ions emitted by a source may be accelerated initially by a static electric field. However, it is impractical to obtain static fields with the billions of volts that are required to produce high-energy beams.

In modern, high-energy accelerators, the first step toward high energy takes place in a linear accelerator (linac). A linac stores the energy required for acceleration in radio frequency (rf) cavities. In these cavities the electrical field changes sign at a rate determined by the cavity frequency. Particles arriving at the correct time are accelerated while particles arriving half an rf cycle later are decelerated. The beam is bunched so that all particles are accelerated; no beam passes through the cavities during the decelerating cycle. If no countermeasures were taken, the beam would expand its transverse dimensions indefinitely, like the beam from an ordinary flashlight. In practice, the beam is continually refocused by a series of quadrupole magnets that are used to bend the diverging beam inward, resulting in a beam whose size oscillates between somewhat larger and smaller sizes but does not grow over distance. The linac technique can be continued indefinitely, but the amount of acceleration is proportional to the number of rf cavities, which are a dominant component of the cost.

Circular accelerators are used to overcome the limitations of proton linacs. The principle of operation is similar to the linac except that dipole magnets are used to bend the beam in a circle. The beam passes through the rf cavities thousands or even millions of times, dramatically reducing the number of rf cavities required. Circular accelerators tend to be dominated by the need for a large number of high-field magnets to bend the beam; the rf cavities, because they are used more efficiently, typically occupy only a small fraction of the circumference.

A large number of proton accelerators have been built. Table 1 lists some of the higher-energy proton accelerators that are used for fixed-target experiments. The beam energy is given in terms of the total voltage of the static electrical field that would be required to achieve the beam energy measured in billions of volts (giga electron volts or GeV).

Comparison of Fixed Targets and Colliding Beams

High-energy physics creates new forms of matter by colliding particles at extremely high energy using two basic techniques. The first technique, the colliding beam technique, involves colliding one beam of particles with another. The second involves the interaction of a particle beam with a fixed target made of gaseous, liquid, or solid material. A major difference between these techniques is that the conservation of momentum significantly affects the amount of collision energy that can be converted into mass. For example, a 1,000-GeV proton beam colliding head-on with another 1,000-GeV proton (or anti-proton) beam can produce a state with masses up to 2,000 GeV/c² because the momenta of the two beams are equal and opposite. The same proton beam colliding with a stationary target nucleon can create at most 43 GeV/c² of mass. For this reason, experiments intending to produce high-mass particles (such as the recently discovered top meson) are performed with colliding beam accelerators.

Fixed-target experiments have the advantage of producing higher interaction rates. In a proton-proton collider, a proton beam might circulate for hours and still not be exhausted. In a fixed-target experiment, the same beam can be produced repetitively every few seconds, each pulse being completely exhausted in a dense target. Even more important is the possibility of creating a wide variety of secondary beams from interactions of protons in the target. The higher interaction rates with fixed targets is crucial in making secondary beams, but, ironically, the need to conserve the momentum of the primary proton beam is an advantage in this case: the secondary particles are produced mainly along the initial direction of the proton beam.

Types of Targets

A variety of targets are used. Some experiments (where the protons are used to produce a secondary beam, for example) do not require a particular nuclear

TABLE 1

composition. In these cases, a copper target might be used because of its attractive mechanical and thermal properties. Occasionally, targets are chosen because of the number of protons in the target: beryllium is often used when a nucleus with a small number of protons (Z = 4) is desired. Lead (Z = 82) or tungsten (Z = 74) may be used when a large number of protons per nucleus or high material density is desired. Many experiments want the simplest nuclear target possible, namely, hydrogen atoms, whose nucleus consists of a single proton. In order to make a high-density target, the hydrogen is usually cooled to cryogenic temperatures ( -255°C). When a neutron target is desired, deuterium is used. The deuterium nucleus, known as "heavy hydrogen," consists of a proton and a neutron. Comparison of hydrogen and deuterium targets allows experimenters to deduce the characteristics of beam interactions with neutrons.

Nuclei possess an intrinsic angular momentum known as "spin." When the nuclear spins point in a common direction, a material is said to be "polarized." Since interactions generally depend on spin, it is an advantage to be able to control the target polarization. Special targets, using special materials, have been built that allow creation of significant polarization. The techniques are not generally applicable to all nuclei, and practical considerations restrict polarized target usage to those experiments that require them.

Types of Beams

Protons interact with nuclei via the "strong" force and are therefore very effective in producing a wide variety of particles. Particles that are stable except for decays mediated by the weak force can generally form beams suitable for experiments. The very massive bottom (and top) mesons, however, are rarely produced and have lifetimes that are too short (at currently available energies) to make beams. Particle beams that decay via weak interactions can also be used to produce tertiary products (like neutrinos) that are not produced in strong interactions.

Secondary beams produced by protons generally consist of more than one particle type. A bending magnet is used almost universally with charged particle beams to select a specific momentum range. Often this simple technique produces a beam of the correct momentum and adequate purity, but it may be possible to restrict beam particles to a particular velocity. When combined with momentum selection, the velocity selection can be restrictive enough to specify the particle mass, uniquely identifying the particle type. More commonly the velocity (or some other property) of the particle is measured, but undesired particles are not removed from the beam; the information is used later in the analysis of the interactions.

Primary Proton Beams

The simplest fixed-target experiment at a proton accelerator involves steering the primary beam onto a fixed target. Proton beams can be used to study elastic and total cross-sections of proton-nuclei interactions. The rates of production of various particles can be studied, and particles produced by proton interactions can be used to form secondary beams. In many cases, the nature of neither the target nor the projectile is important: only the amount of energy that can be converted into mass is important. For these experiments, the high-intensity primary beam can be an overwhelming advantage in studying rare processes. The challenge is to design an experiment that is sensitive to the rarely produced state but able to ignore more common states.

Charged Meson Beams

When a high-energy proton beam hits a target, the most prolifically produced charged particles are pi-mesons (π⁺ and π^-), and K mesons (K⁺ and K^-). These mesons have long lifetimes (τ_π = 2.6 × 10^-8 second and τ_K = 1.2 × 10^-8 second), so they can be focused into beams and transported a hundred meters at high energy, where the lifetime is stretched by the relativistic effect known as time dilatation.

Meson beams have been used extensively to analyze meson production at a wide variety of momenta and from a wide variety of nuclei. Meson beams have also been used to study interactions with nuclei, including total and elastic cross-sections. Interactions with electrons in the target have been used to measure the distribution of quarks in mesons. The decays of mesons have been studied extensively, including extremely rare processes, as infrequent as one in many billion decays.

Antiprotons

Antiprotons are produced in the same way as mesons, but at much lower rates. Since antiprotons are stable, they can be collected in specially designed storage rings. These storage rings have been used mainly to collect antiprotons for proton-antiproton colliding beam accelerators but have also been used with internal, gas jet targets to produce charmonium states (bound states of a charm quark and an anticharm quark) and to form antihydrogen atoms (the bound state of an antiproton and a positron). Antiproton beams have been extracted from storage rings at controlled rates, and their interactions have been studied. Antiproton beams have also been produced at high energy for scattering experiments similar to those performed with π and K mesons.

Hyperon Beams

Proton beams can be used to produce hyperon beams. Hyperons are baryons (protonlike particles) with the strangeness quantum number equal to -1(Σ⁺, Σ^-, Λ⁰), -2 (Ξ^- and Ξ°), or -3 (Ω^-). The Σ° is unstable against electromagnetic interactions (decaying Σ° → Λ⁰γ) and has a lifetime that is too short(7.4 × 10^-20 second) to form a beam. Hyperon lifetimes (typically 10^-10 second) are much shorter than those of π and K mesons (about 10^-8 second), so hyperon beam lines tend to be much shorter.

Hyperon beams have been used to study decays and hyperon properties including precise measurements of magnetic moments. Hyperon beams can also be used to study hyperon-nuclei interactions.

Neutral Beams

A proton beam impinging on a target will produce neutral particles, such as π⁰'s, K⁰'s, and neutrons. The charged particles produced by proton interactions can be swept out of the beam by a magnetic field, leaving only the neutrals. The π⁰ is unstable against electromagnetic decays (π⁰ → γγ), and its lifetime is too short (8 × 10^-17 sec) to make a beam. The π⁰ decays, however, can be used to produce a photon (γ) beam. The γ's can also be used to produce a tertiary electron beam via the reaction γN → e⁺ e^- N . While it might seem much easier to produce electrons with an electron accelerator, proton accelerators tend to have higher energies, and it has been attractive to produce high-energy (albeit low-intensity) electron beams at proton accelerators.

Photon beams interact electromagnetically with nuclei; at high energies they probe the nuclear quark distribution. Since the electromagnetic interaction is probably the most studied, and best understood, of all interactions, it is a great advantage to study nuclei with this well-understood probe.

Neutral K mesons have been a subject of intense study, because the neutral K meson system is one of the few ways that a property known as CP violation can be studied. The K -meson system consists of two particles: K⁰_s (K short) and K⁰_L (K long). The K⁰_s has a short lifetime (0.9 × 10 second) and decays rapidly, leaving a beam of primarily (K⁰_L lifetime 5.2 × 10^-8 second). However, the K⁰_s can be "regenerated" by the interaction of a K⁰_L beam in a nuclear target.

Muon and Neutrino Beams

Neutrinos are particles that interact only weakly and are not produced directly in proton nuclei interactions. A muon neutrino beam can, however, be produced by a decay of a meson beam via π⁺ → μ⁺ν_μ and K⁺ → μ⁺ν_μ. Some electron neutrinos are also produced via decays such as μ⁺ → v̄_μ e⁺ ν_e and K⁺ → π⁰ e⁺ν_e. Tau neutrinos can be produced at low rates from short-lived, heavy meson decays. Antineutrino beams can be produced from mesons of the opposite sign.

Neutrinos are an especially good probe of nuclei since they mainly interact with individual quarks via the weak interaction. A key disadvantage of neutrino beams is that massive targets are required (perhaps 1,000 tons) to produce reasonable interaction rates. Neutrino beams have been used to establish the nature of the weak interaction and to measure the distribution of quarks in the nucleus.

The decays of mesons can also be used to produce beams of muons. Muon beams have been used to study the distribution of quarks in nuclei, and static properties of the muon, such as its magnetic moment, have also been measured. Low-energy muon beams can be brought to rest in an absorber. Stopped muons have proven to be a sensitive way to search for rare decays.

Polarized Beams and Ion Beams

Polarized beams must be produced by a special ion source. There is no practical method for developing polarization of nuclei after they leave the ion source, so the polarization must be meticulously preserved as the beam is accelerated. Proton beams are polarized most often, but sources have been developed to polarize other nuclei. Polarized beams have been used in conjunction with polarized targets to determine the spin-dependent properties of proton-proton interactions.

Ion beams are also produced by special sources, but in general, the ions are not polarized. Before acceleration to high energy, ions invariably have all their electrons stripped off the nucleus although some electrons are typically present at intermediate stages between the source and the first circular accelerator. Ion beams are mainly used to study nucleus-nucleus interactions.

See also:Accelerator; Beam transport; Extraction Systems; Injector System

Bibliography

Lee, S. Y. Accelerator Physics (World Scientific, Singapore, 1999).

Wilson, R.R. "The Batavia Accelerator." Scientific American 230 (2), 72–83 (1974).

John Marriner