The Effect of Radiation Damping and Noise on the Transverse Mode Coupling Instability Due to Localized Structures

The transverse mode coupling instability due to localized structures of a storage ring, like RF-cavities, is investigated in presence of radiation damping and quantum excitation for both synchrotron and betatron oscillations. Replacing the Vlasov equation by the Fokker-Planck equation, the longitudinal dynamics can only be described in terms of transition probabilities, whereas the transverse motion of the bunch barycenter remains deterministic. By a numerical solution of the associated integral equation, we obtain better estimates of the instability growth rates and we show the disappearence of the stop-bands associated with very high order dipole modes, which turn out to be damped proportionally to their mode number.