Abstract
Two methods which have been proposed for increasing the synchrotron frequency spread and consequently stabilizing the longitudinal instability of a bunched beam in a synchrotron include the reduction of the amplitude of the accelerating field to a level ensuring almost complete filling of the separatrix by the bunch and the insertion of an additional accelerating system operating on the highest harmonic of the fundamental frequency of acceleration. In this paper the efficiencies of these methods are compared for the case when the impedance of the accelerator chamber is determined by a narrow-band resonator whose transmission bandwidth is much smaller than the bunch repetition frequency.
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