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a device in which beams of charged particles (elementary particles and ions) accelerated to high energies by an electric field collide head on (see). Such machines make it possible to study particle interactions and the production of new particles at the highest effective collision energies attainable under laboratory conditions. Machines with electron-electron (e–e–), electron-positron (e– e+), or proton-proton (pp) colliding beams are most common.
In conventional accelerators particle interactions are studied in the laboratory coordinate system: a beam of particles is accelerated to high energy and is made to collide with the particles of a stationary target. In accordance with the law of conservation of the total momentum of colliding particles, most of the energy of an incident particle goes to conserving the motion of the center of mass of the system of particles—that is, to imparting kinetic energy to the reaction-product particles. Only a small part of the energy is available as useful, or effective, collision energy—that is, as the interaction energy of the particles in their center-of-mass system. This useful energy may go, for example, to create new particles. For a collision of two particles of identical mass m0, one particle being at rest in the laboratory coordinate system and the other moving with a relativistic speed (close to the speed of light c), it can be shown that the energy in the center-of-mass system is , where E0 = m0c2 is the rest energy of the particle and E is the energy of the incident particle in the laboratory coordinate system. Thus, the larger the value of E, the smaller the fraction of E that determines the particle interaction energy.
Suppose, however, particles with momenta that are equal in magnitude and opposite in direction (that is, their total momentum is equal to zero) collide. The laboratory coordinate system then coincides with the center-of-mass system of the particles, and the effective collision energy is equal to the sum of the energies of the colliding particles. For particles of identical mass and identical energy E, we thus have Ecm = 2E. In other words, all the kinetic energy is available for interaction.
The use of colliding beams is especially favorable for studying interactions of such light particles as electrons and positrons, for which E0 = 0.5 million electron volts (MeV). If, for example, an electron of 1 gigaelectron volt (GeV) collides head on with another 1-GeV electron, Ecm = 2 GeV. To obtain the same effective collision energy with a stationary target electron, an incident electron energy E of Ge V would be required. For colliding beams of protons (E0 ≈ 1 GeV) having an energy E of, for example, 70 GeV (the proton energy of the Serpukhov accelerator is 76 GeV), Ecm = 140 GeV. By contrast, in a collision involving a proton at rest an effective collision energy of 140 GeV would be achieved only if the incident proton had an energy E of 10,000 GeV!
Colliding-beam machines are particularly important for studying elastic and inelastic processes involving the interaction of such stable particles as protons, antiprotons, electrons, and positrons. At very high energies conventional stationary-target accelerators cannot compete with colliding-beam machines.
A disadvantage of colliding-beam machines is the low density of the particle beams in comparison with the density of a stationary target. To increase particle density, charged particles are accumulated in special storage rings before the collision process in such a way that the circulating particle currents are at least a few tens of amperes (seeSTORAGE RINGS). Even at such currents, however, the intensity of beams of high-energy secondary particles (such as pions, kaons, and neutrinos) that are formed in the collisions is lower by several orders of magnitude than the intensity of beams of the same particles produced in conventional accelerators. Furthermore, since the energy of a secondary particle cannot exceed the energy of the colliding primary particles, traditional accelerators can produce secondary particles of higher energy than can colliding-beam machines. Colliding-beam machines can therefore supplement, but not replace, traditional accelerators. The development of both types of machines must proceed in parallel.
Accelerated charged particles enter the storage rings, which are annular vacuum chambers in a magnetic field, from a conventional accelerator. The magnetic field is usually generated by sector magnets separated by straight sections (without a magnetic field) for the beam intersection regions and the accelerating system. A colliding-beam machine may contain one or two storage rings. One ring is sufficient when the signs of the electric charges of the colliding particles are different, as in e– e+ or pp̄ beams, where p is an antiproton. Two rings, however, are needed when the signs are the same, as in e– e– or pp beams.
Before injection into the storage rings, the particles are accelerated in a strong- or weak-focusing proton or electron synchrotron or in a linear accelerator. Additional acceleration of the particles is possible in the storage rings after injection. Regardless of whether such additional acceleration is carried out, a colliding-beam storage ring must include an accelerating system to compensate for the energy lost by the charged particles owing to synchrotron radiation (for e– e+ beams) and to ionization of the residual gas in the chamber. The accelerating system also establishes the azimuthal dimensions of the beam (the number of particle bunches is equal to the frequency of the accelerating system divided by the particle orbit frequency). Typical schemes for e– e+ and pp colliding-beam machines are shown in Figures 1 and 2.
The principal quantity characterizing a colliding-beam machine is called the luminosity L; it determines the number N of events of the type being investigated per unit time. If an interaction with a cross section a is being studied, then N = Lσ. In the simplest case, the beam intersection angle is equal to zero, and L = R(N1N2/S)ω/2π. Here, N1 and N2 are the total numbers of particles in each beam in the rings, 5 is the cross-sectional area common to both beams, co is the angular frequency of the particles in a closed orbit, and R is the machine’s utilization factor, which is equal to the ratio of the length of the beam intersection sections to the orbital perimeter. In the more general case, R depends on the beam overlapping region, that is, on the angles of intersection and the relative dimensions of the beams.
For effective study of interaction processes with a cross section σ = 10–26–10–32 cm2, the luminosity must be 1028–1032 cm–2 · sec–1. To achieve such a value, the circulating current of the charged-particle beams is stored, and the beam cross sections are reduced by using special magnetic focusing in the straight sections and by employing electron or stochastic cooling to reduce the transverse component of the momentum of the colliding beams. The electron cooling method was proposed in 1966 by the Soviet physicist G. I. Budker for heavy particles (protons and antiprotons), for which automatic damping of the transverse oscillations of particles in the beam does not occur because of the virtual absence of synchrotron radiation. The method is based on the transfer of the thermal energy of a beam of heavy particles to an accompanying beam of electrons moving parallel to the path of the heavy particles and having a lower temperature. Experimental confirmation of this effect was first obtained at the Institute of Nuclear Physics of the Siberian Division of the Academy of Sciences of the USSR in 1974.
In order to carry out a continuous physical experiment with little variation in luminosity, the stored particle beams must have a long lifetime. The beam lifetime, which is the time in which beam intensity is reduced by a factor of 1/e (where e ≈ 2.7), depends on a number of effects, including single and multiple scattering of accelerated particles by atoms of the residual gas in the storage chamber. For electrons and positrons synchrotron radiation and quantum fluctuations also affect the beam lifetime. In addition, electron-electron (or positron-positron) scattering in the beam may also play a significant role. The experimental measure of beam lifetime is the relative magnitude of the loss of beam intensity in percent per hour. For the best machines now operating, the loss amounts to tenths of a percent per hour. For the Intersecting Storage Rings (ISR), a pp machine at the European Organization for Nuclear Research (CERN), the figure is 0.1 percent per hour at a current of 22 amperes (A). Such a long beam lifetime is achieved by using a high vacuum in the beam storage chambers: 10–11 mm Hg in the storage rings and 10–12 mm Hg in the beam intersection regions.
An essential element of an e– e+ colliding-beam machine is the electron-positron converter, which consists of a metal target with a thickness of about 1 radiation length; in Figure 1 the converter is shown on the straight beam. In the converter, electrons produce bremsstrahlung gamma quanta, which in turn produce electron-positron pairs. When the electron beam has an energy of hundreds of millions of electron volts, the conversion ratio—that
is, the ratio of the number of positrons injected into the storage device and the number of electrons extracted from the synchrotron—may reach a value of 10–4 for a positron beam with an energy approximately half as great as the electron energy.
Such a pp device as the ISR, which consists of two interlaced rings of magnets with strong focusing, has several intersection
|Table 1. Parameters of largest colliding-beam machines|
|Machine||Beam types||Energy (MeV)||Average radius of orbit (m)||Luminosity (cm–2·sec–1)||Date of first operation|
|VEPP-2 (Novosibirsk, USSR) ...............||e+ e–||2 × 700||1.9||~1029||1966|
|VEPP-4 (Novosibirsk, USSR) ...............||e+ e–||2 × 3,500||12.0||~1030||1978|
|SPEAR (Stanford USA) ...............||e+ e–||2 × 4,500||37.2||6 × 1030||1972|
|ACO (Orsay, France) ...............||e+ e–||2 × 540||3.5||1029||1966|
|ADONE (Frascati, Italy) ...............||e+ e–||2 × 1500||16.4||6 × 1029||1969|
|ISR (CERN, Geneva, Switzerland) ...............||pp||2 × 31,400||150||6.7 × 1030||1971|
|ISABELLE (Brookhaven, USA) ...............||2 × 200 × 103||428||under construction|
|PEP (Stanford, USA) ...............||e+ e–||2 × 15 × 103||350||1032||1980|
|SUPER ADONE (Frascati, Italy) ...............||e+ e–||2 × 12 × 103||136||1032||under construction|
points, where head-on collisions may be observed (Figure 2). This scheme makes it possible to conduct several physical experiments at the same time.
The parameters of the largest colliding-beam machines are given in Table 1.
Brief history of development. The development of machines for colliding-beam research began in many laboratories in the USSR and abroad in 1956, soon after the publication of a proposal by the American physicist D. W. Kerst. Between 1956 and 1966 colliding-beam devices were confined to the light stable particles electrons and positrons; for such particles very high relativistic speeds are reached at energies of hundreds of millions of electron volts. The proposal to build machines for colliding beams of electrons and positrons was due to Budker.
The first e–e– and e– e+ colliding-beam machines were constructed at the Institute of Nuclear Physics of the Siberian Division of the Academy of Sciences of the USSR (Budker, A. A. Naumov, and co-workers), the Stanford Linear Accelerator Center (W. K. Panofsky and co-workers, USA), the National Laboratories of the National Committee for Nuclear Energy (CNEN) at Frascati (S. Tasarri and co-workers, Italy), and the Linear Accelerator Laboratory at Orsay (P. Marin and co-workers, France).
The development of storage rings for colliding pp beams was made possible by the completion of a 28-GeV proton accelerator at CERN (Switzerland) in 1959 and of a 33-GeV proton accelerator at Brookhaven National Laboratory (USA) in 1961. The ISR at CERN began operation in 1971 (K. Jonsen and co-workers); it is capable of a beam energy of 31.4 GeV. The successful operation of the ISR at circulating proton currents of 22–25 A and a luminosity of 6.7 × 1030 cm–2 · sec–1 stimulated the further development of design work on high-energy pp, pp͂, and pe– storage devices. In addition to the machines listed in Table 1, six projects in the USSR, the USA, and Great Britain are in the design stage; completion of construction is expected to take place between 1980 and 1990.
REFERENCESKerst, D. W. “Properties of an Intersecting-beam Accelerating System.” CERN Symposium, vol. 1. Geneva, 1956. Page 36.
Budker, G. I., A. A. Naumov, et al. “Raboty po vstrechnym elek-tron-elektronnym, pozitron-elektronnym i proton-protonnym puchkam v Institute iadernoi fiziki SO AN SSSR.” In Trudy Mezh-dunarodnoi konferentsii po uskoriteliam: Dubna, 1963. Moscow, 1964. Pages 274–87.
Jonsen, K. [et al.]. “Some Problems Connected With the Use of Intersecting Proton Storage Rings.” In Trudy Mezhdunarodnoi konferentsii po uskoriteliam: Dubna, 1963. Moscow, 1964. Pages 312–25.
Budker, G. I. “Uskoriteli i vstrechnye puchki.” In Trudy VII Mezhdunarodnoi konferentsii po uskoriteliam zariazhennykh chastits vy-sokikh energii, vol. 1. Yerevan, 1970. Page 33.
Trudy IV Vsesoiuznogo soveshchaniia po uskoriteliam zariazhennykh chastits: Moscow, 1974, vol. 2. Moscow, 1975. Pages 300–18.
V. P. DMITRIEVSKII