Simulation of graded cooling for ordered beams in storage rings

Ordered structures in beams survive the bending in dipole magnets of a stor age ring, provided that the ring is smooth: the dispersion must be nearly c onstant around the ring, so that the transversal velocity profile of the pa rticles in the beam remains undisturbed. Conventional laser cooling affects the ions in the beam independently of their transversal position, so that the velocity profile is disturbed and the order is destroyed. We show with the help of molecular dynamics computer simulations that order can be prese rved if the cooling force depends on the transversal position of the partic les in such a manner that the dispersion and the transversal velocity profi le remain constant (graded cooling).