A Formulation of Transversely Coupled Betatron Stochastic Cooling of Coasting Beams

A formulation of stochastic cooling with coupled degrees of freedom, with emphasis on the tensorial signal suppression phenomenon for transversely coupled betatron stochastic cooling of coasting beams, is provided. The relevant expressions for the damping and diffusion coefficients and the elements of the signal suppression tensor are given in terms of the general cooling interaction harmonics. The formulation is necessarily abstract in order to provide a general framework of quantitative analysis and demands exact knowledge of the nature of the coupling interaction for it to be useful in any particular case.