Effects of Rf Stacking on Cooling Tail in the Fermilab Antiproton Accumulator

Abstract

The scheme has recently been proposed to produce a high-intensity antiproton beam in a stochastic cooling accelerator. This beam is to be bunched adiabatically, decelerated, and then allowed to debunch adiabatically. At this point the beam is ready for stochastic cooling. It is soon moved down in the stream by the tail cooling system in order to make room for the next stacked beam. There are in general two effects that RF stacking gives an already stacked beam or ''tail''. The first and larger is phase-displacement acceleration and the second is so-called dilution coming from a non-adiabatic change of RF parameters which is understood to be enhanced by the non-linearity of RF stacking dynamics. In this paper both effects are discussed from a phase dynamical point of view. The dynamics of tail cooling are then discussed with the help of the Fokker-Planck equation. From the tail cooling point of view, the effects of RF stacking can be regarded as the deformation of the tail occurring within a limited period, as tail cutting due to phase displacement, and as non-uniform dilution in the tail due to non-adiabatic diffusion. An easy method for estimating beam loss due to phase displacement is presentedmore » and used to obtain the criteria which should be imposed on the cooling system.« less