ON THE MAINTENANCE CONDITION OF A CRYSTALLINE BEAM

It has been often stated that the so-called “maintenance condition” must be satisfied to achieve beam crystallization in a cooler storage ring. The condition requires the ring lattice to have a betatron phase advance below about 127 degrees per single superperiod [1]. In the present work, we show that this condition is not sufficient in general situations. Systematic multi-particle simulations and analytic studies suggest that the phase advance per lattice period should be lower than 90 degrees in order to reach a crystalline state at an arbitrary line density.