Three-Dimensional Laser Cooling of Stored and Circulating Ion Beams by Means of a Coupling Cavity

It is shown theoretically that a coupling cavity (namely, an rf cavity operating in the ${\mathrm{TM}}_{210}$ mode) inserted into a storage ring will enhance the coupling between longitudinal and transverse degrees of freedom. As a result, the demonstrated very effective laser cooling of the longitudinal motion can now be extended to transverse motion; i.e., employed to cool a beam in all three directions.