In general, the temperature of a charged particle beam travelling in an accelerator is very high. Seen from the rest frame of the beam, individual particles randomly oscillate about the reference orbit at high speed. This internal kinetic energy can, however, be removed by introducing dissipative interactions into the system. As a dissipative process advances, the beam becomes denser in phase space or, equivalently, the emittance is more diminished. Ideally, it is possible to reach a “zero-emittance” state where the beam is Coulomb crystallized. The space-charge repulsion of a crystalline beam just balances the external restoring force provided by artificial electromagnetic elements. This paper briefly reviews the dynamics of coasting and bunched crystalline beams circulating in a storage ring. Results of molecular dynamics simulations are presented to demonstrate the nature of various crystalline states. A practical method to approach such an ultimate state of matter is also discussed.
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