Crystalline Beams*
Alessandro G. Ruggiero
Brookhaven National Laboratory
Abstract: It is known that particle accelerators are subject to severe limitations that impede the attainment of very cold and dense beams of charged particles. These limitations are due to inter-particle Coulomb interaction: intrabeam scattering and space-charge effects.
There has been recent interest in the feasibility of producing a Crystalline Beam. This is a spatially ordered ensemble of particles having very small velocity fluctuations relative to each other. Such a state may be obtainable from an ordinary warm beam through the application of intense phase-space cooling (e.g., stochastic, electron, laser).
Crystalline Beams represent the ultimate in the control of space-charge effects. The study, and eventual demonstration of Crystalline Beams may lead to a variety of other applications, and will certainly provide a deeper insight into the fundamental limitations of storage rings and particle colliders.
The starting point is to understand the present limitations due to space-charge effects of ordinary "warm" beams of charged particles, notably in low-energy storage rings for light and heavy ions (including, of course, protons). The common case of interest is storage rings operating below the transition energy. Cooling techniques are the method to decrease the temperature and the density of the ion beam to a level where transient effects are noticeable, caused by the balance of the space charge forces, intrabeam scattering, and cooling. During the transition, the behavior of intrabeam scattering may at first sight be described as anomalous; but its complete understanding requires a refinement of the theory with a re-evaluation of the range of impact parameters. Space-charge forces themselves can no longer be described by a continuous charge distribution; but the corpuscular aspect of the beam has to be taken into account.
Finally, if the cooling rate is sufficiently high the beam may collapse toward an equilibrium configuration that would be the result of the particle-particle Coulomb repulsive forces balanced by the confinement forces of the storage ring. This configuration would yield Crystalline Beams; the shape and feasibility of which depend on the properties of the storage ring lattice, which is focussing and bending.
* Work performed under the auspices of the U.S. Department of Energy