Resonant behaviour of head tail modes [synchrotrons]

Bunched beams in synchrotrons suffer from synchro-betatron resonances. They an produced by the coupling of the longitudinal motion into the transverse plane via dispersion and/or off-centre orbits in the accelerating cavities. These resonances are incoherent. The wake fields from bunches on central orbits, provoke head tail modes, which at a certain intensity will lead to the mode coupling instability. Besides head-tail modes, these wake fields create also new resonant conditions for coherent motion. In LEP, these coherent resonances, which are also present for central orbits, start to dominate the beam behaviour as of a certain bunch current and the mode coupling instability limit can only be reached for well defined betatron tunes