RF Gymnastics in Synchrotrons

The RF systems installed in synchrotrons can be used to change the longitudinal beam characteristics. "RF gymnastics" designates manipulations of the RF parameters aimed at providing such non-trivial changes. Some keep the number of bunches constant while changing bunch length, energy spread, emittance or distance between bunches. Others are used to change the number of bunches. After recalling the basics of longitudinal beam dynamics in a hadron synchrotron, this paper deals with the most commonly used gymnastics. Their principle is described as well as their performance and limitations.