In a particle accelerator or storage ring, particle motion consists of oscillations around the nominal orbit. Normally, the amplitude of the oscillations is constant in time. However, special techniques, known collectively as "beam cooling," can be used to reduce the average oscillation amplitudes of beam particles. A cooled beam will have a reduced momentum spread, a smaller physical size, a reduced angular divergence, or some combination of these characteristics. Beam cooling is conceptually similar to cooling of ordinary matter, which involves a reduction in the amplitude of the random motion of the constituent atoms.
Beam cooling techniques have proven essential for achieving high interaction rates at electron-positron and proton-antiproton colliding beam facilities, largely because of the need to create a dense beam of anti-particles. Beam cooling is not required for the Large Hadron Collider (LHC) project, a proton-proton colliding beam facility currently under construction at the European Laboratory for Particle Physics (CERN) in Geneva, Switzerland.
Electron cooling occurs when a beam particle, say a proton, moves slowly through a beam of electrons of uniform velocity. As it bumps into the electrons, the proton loses energy until it is at rest relative to the electrons. Thus, protons slower than the electron beam speed up and protons faster than the electron beam slow down. The motion of particles transverse to the electron velocity is decreased for the same reason. The process results in the transfer of energy from the hot proton beam to the cold electron beam. The electron beam is normally generated continuously and discarded after a single interaction with the hot beam.
Electron cooling has been implemented at several accelerator facilities. A typical application involves the creation of a dense, low-energy, low-momentum spread beam that can be used for high-precision spectroscopy experiments. The applicability of the method has been restricted to low energies because the cooling rates tend to be slower at high energy and because it is difficult to produce a high-energy electron beam that is sufficiently uniform in electron velocity.
Synchrotron Radiation Damping
Synchrotron radiation is the spontaneous radiation of charged particles subjected to a strong magnetic field. The radiation is proportional to the fourth power of the energy to mass ratio, (E/m )4, and, as a consequence, is important mainly for electrons at high energy. The radiation makes it difficult to accelerate or store electrons at high energy in circular accelerators and is a dominant consideration in the design of these accelerators. Special rings, known as synchrotron light sources, utilize synchrotron radiation to produce intense light beams that are scattered from a variety of experimental samples. Synchrotron radiation also produces beam cooling effects that are utilized in electron-positron colliding beam accelerators and special storage rings known as damping rings.
Synchrotron radiation cooling works primarily by providing a braking force antiparallel to the particle velocity. The reduction of the transverse component of the beam momentum results in smaller transverse oscillation amplitudes, but the loss of longitudinal momentum does not significantly change the momentum spread, as is required for cooling. Momentum cooling is achieved primarily by exploiting the coupling between the longitudinal and horizontal particle oscillations. Proper design of the focusing properties of the storage ring can result in a beam that is cooled in all three dimensions. The rapid loss of longitudinal beam momentum invariably requires that it be restored by electromagnetic fields, which are created in high-power, radio frequency cavities.
A number of circular electron-positron colliding beam machines have been designed and built to take advantage of the cooling properties of synchrotron radiation. Damping rings have been used to cool electrons and positrons at the Stanford Linear Collider (SLC), the only linear colliding beam facility that has been built. A linear accelerator avoids the copious synchrotron radiation associated with the magnetic fields required to bend the particles in a circle but requires damping rings utilizing synchrotron radiation to cool the beam to a small size to produce a high particle collision rate.
Ionization or Muon Cooling
Ionization cooling is similar to electron cooling except that the electrons are part of a medium (usually liquid hydrogen). The energy loss creates a braking force (similar to synchrotron radiation) resulting in transverse cooling and the need to replace the average longitudinal momentum that is lost in the medium. The strong momentum cooling effect present in electron cooling is not present in ionization cooling because the beam velocity is necessarily higher than that of the electrons in the medium, which are at rest.
This technique is practical only for muons: proton beams are too severely disrupted by nuclear interactions in the medium, and electron beams are disrupted by electromagnetic interactions. Muon beams are subject to electromagnetic interactions, but the magnitude is greatly reduced because the muon mass is larger than the electron mass. Ionization cooling has not been utilized nor even demonstrated in a practical system but has been extensively studied for possible future use in neutrino sources based on muon beams and for muon colliding beam facilities.
Stochastic cooling is a technique that requires the ability to measure fluctuations in the average beam motion about the nominal orbit. If it were possible to measure each particle individually, its motion could be corrected to coincide with the nominal orbit. In practice, only large groups of particles can be measured and corrected as a group. In any sample of particles, some have a position that is, say, lower than the nominal orbit and some have a higher position. The average position is close to the nominal orbit, but sometimes there are more high particles and sometimes there are more low particles. If the motion of the beam sample is corrected according to its average, the individual particle oscillation amplitudes are reduced after many sample positions are measured and corrected. The effectiveness of the technique requires the samples to consist of a continuously changing population of particles. Stochastic cooling systems are normally designed to cool one beam coordinate at a time, but multiple systems can be used to achieve cooling in three dimensions.
Stochastic cooling has been used most notably to cool antiproton beams. Antiprotons are produced in high-energy collisions but with a very low density compared to particle accelerator beams. Antiprotons are collected and transported into a storage ring where they are cooled in a succession of steps. The transverse oscillations are reduced about five-fold, but the main goal is to increase the beam intensity without increasing the momentum spread. In this process, known as "stochastic stacking," a pulse of antiprotons is added to an existing stack by placing it at a slightly higher momentum than the previously stacked beam. The cooling system then reduces the momentum spread to the size of the previously stacked beam and a new pulse is added. The cycle can be repeated thousands of times to produce a high intensity antiproton beam.
Other Cooling Techniques
Other cooling techniques are available to cool ion beams, very low energy particles (captured in particle traps), and atoms stored in traps. These techniques are not used for high-energy particle physics.
See also:Accelerator; Accelerators, Colliding Beam: Electron-Positron; Accelerators, Colliding Beam: Electron-Proton; Accelerators, Colliding Beam: Hadron; Accelerators, Early; Accelerators, Fixed-Target: Electron; Accelerators: Fixed-Target: Proton; Beam Transport; Extraction Systems; Injector System
Poth, H. "Electron Cooling: Theory, Experiment, Application." Physics Reports196 , 135–297 (1990).
van der Meer, S. "Stochastic Cooling and the Accumulation of Antiprotons." Reviews of Modern Physics57 (3), 689(1985).