Transverse damping systems in modern synchrotrons

Transverse feedback systems for suppression of transverse coherent beam oscillations are used in modern synchrotrons for preventing the development of transverse instabilities and damping residual beam oscillations after injection. Information on damper systems for the Large Hadron Collider (LHC; CERN, Geneva) and the accelerator complex FAIR (GSI, Darmstadt) is presented. The project for the LHC is being performed at the Laboratory of Particle Physics of the Joint Institute for Nuclear Research in collaboration with CERN. The information concerning the state of the project and the plans of its completion at the LHC is given. The results of the first design activity on transverse damping systems at the SIS100 and SIS300 synchrotrons, to be created in the framework of the new international project FAIR, are presented.