Nonlinear damping of coherent transverse oscillations of a beam in hadron cyclic accelerators and colliders

The correlation between the requirements for the quality of a beam and parameters of systems of damping of transverse coherent oscillations for modern hadron accelerators and colliders is considered. Special attention is directed to systems in which the signal in the kicker is not proportional to the signal of the pickup. It is shown that a nonlinear mode of suppression can provide a greater damping rate. Limiting beam blow-up at injection and accumulation is made possible by an appropriate choice of the discrimination level of the pickup signal.