The Effect of Momentum Spread in Slow Extraction at an Integer Resonance - A Theoretical Study

Measurements of slow extraction efficiency at the CERN PS suggest that the loss during extraction is about three times that given by existing theory. In an attempt to explain this discrepancy, the effect of momentum spread in the circulating beam has been considered. Computations of the effect of momentum spread in an integer resonance extraction system have already been presented in an earlier study of the design of the CERN Intersecting Storage Rings (ISR) extraction system. The theory is, in general, applicable to any integer extraction system but in this paper we restrict our discussion to its implications for the particular case of the CERN Proton Synchrotron (CPS) extraction system. It seems that in an extraction system operating at an integer resonance, displacement of the unperturbed closed orbit from the axis of perturbing quadrupoles due to momentum spread, closed orbit distortion or deliberate misalignment, results in a considerable displacement of the unstable and stable fixed points. The perturbed closed orbits corresponding to these points oscillate about the unperturbed orbit with an amplitude which is several times greater than the unperturbed displacement. In this paper we first discuss a simple analytic model to illustrate the nature of the effect and then present the results of a computation for a more realistic model of the CPS.