Longitudinal instability of a bunched beam resulting from current loading of the accelerating system in an ultrahigh-energy proton synchrotron

Collective effects in the acceleration and storage of particles have recently attracted considerable interest. The authors discuss the theory of the longitudinal multipole instabilities of coupled modes of a bunched beam. Up to now, there has been no electrodynamic calculation of the excitation of the resonant elements around the beam, so that only impedances of a simple resonator type are used (the variations in the longitudinal component of the electric field on the resonator axis are not taken into account). Furthermore, and particularly significantly, elements of a waveguide nature have been ignored (the accelerating systems of the CERN SPS synchrotron in the working frequency band are examples of such elements). The authors' intention is to correct these deficiencies of the theory. (7 refs).