The Efficiency of Acceleration by Phase Displacement in the Presence of RF Noise

During acceleration by phase displacement the particle synchrotron motion is non linear around the exterior of the RF bucket. Simultaneous numerical evaluation of this motion for a large number of ´particles´ allows calculation of relevant ´beam´ statistical parameters which can be used to define the relative efficiency of the acceleration technique. This procedure has been used in a computer program which calculates the reduction in efficiency of acceleration by phase displacement in the presence of RF noise and when the bucket parameters vary during the RF sweep. The results show that the variation of ¿t with ¿p/p produces a significant increase in the momentum blow-up per accelerating sweep. It is also shown that RF noise (frequency modulation) causes particles to penetrate the bucket separatrix and become decelerated within the bucket. This results in a significant reduction in the efficiency of acceleration and greatly contributes to the intensity losses. Extensive experimental results have confirmed the computed results.