Confinement and stability of crystalline beams in storage rings

We present a fully analytical approach to the study of the confinement and stability of open-quote open-quote Crystalline Beams close-quote close-quote in storage rings, in terms of such fundamental accelerator concepts as tune shift and stopband. We consider a open-quote open-quote Crystalline Beam close-quote close-quote consisting of substrings, arranged symmetrically around the reference trajectory, and we examine the motion of a slightly perturbed test particle on one of them. Our approach quite naturally leads to the conclusion, that (a) storage rings need to be operated below the transition energy, and (b) the open-quote open-quote Crystalline Beam close-quote close-quote has the same periodicity as the storage ring. Each open-quote open-quote Crystalline Beam close-quote close-quote has an upper and lower limit of the spacing between the ions. The upper limit is determined by condition (b), and the lower limit is set by the stability of the test particle motion around the equilibrium. copyright 1995 American Institute of Physics