Transverse Laser Cooling of a Fast Stored Ion Beam through Dispersive Coupling
To understand how a longitudinally acting force can affect the horizontal betatron motion consider a stored ion resonantly absorbing photons from a collinearly merged laser beam. In combination with an appropriate mechanism counteracting the light pressure [11], the momentum change in the cooling region can be approximated by Dp . 2fzsp 2 p0d 1 Kxzx with the momentum deviation jp 2 p0 j? p 0. The friction coefficient fz determines the longitudinal cooling rate and reflects the momentum dependence of the light force resulting from the Doppler effect. The horizontal-longitudinal coupling coefficient Kxz stems from the intensity gradient along the horizontal direction x of the Gaussian laser beam [12].