The uniformity of a slow-extracted beam from a synchrotron is degraded by ripples from the power converters of the magnetic elements. This effect can be reduced by making the beam particles cross more quickly from the stable to the unstable region. Among the various methods that have been proposed for this purpose, RF bucket channelling seems to be a good candidate for compensating low frequency ripples in spills of the order of one second. The method is based on the technique of RF phase displacement acceleration. In the configuration studied, a coasting beam is accelerated slowly into a third-order resonance by a betatron core. The acceleration rate set by the betatron core determines the spill length. Empty buckets are then created at the resonance frequency and adjusted with a phase angle that would decelerate any trapped beam by an equal and opposite amount. The main RF system can be used for this purpose. The empty buckets cause an obstruction in phase space and the beam particles are forced to channel around the buckets. The particle speed is thus increased as the particle crosses into the resonance region, making the extraction less sensitive to ripple. The energy at which the particles enter in the unstable region is not fixed, but depends on their momentum and betatron amplitude. An improvement factor is obtained for all momenta and betatron amplitudes, provided that the bucket is properly positioned and that its half height is greater than the energy spread engaged in the resonance. The existing theory is extended to show that particles entering at different energies get different improvement factors, and how the improvement in the spill depends on the frequency and amplitude of the ripple
