Laser cooling and crystalline beams in storage rings

We discuss problems of beams with high phase-space densities and an eventual crystalline ordering. In particular, we address ourselves to the effect of laser cooling in connection with an accelerator design devoted to crystalline beams. We find that standard longitudinal laser cooling becomes inefficient for temperatures above the transition to crystalline order because a conflict with the accelerator dispersion function develops towards lower temperatures. We demonstrate that the obstacle can be overcome by using graded laser cooling which is designed to match with the dispersion function of the given accelerator.