Pattern Recognition: The Importance of Dispersion in Crystal Collimation

Abstract

One aspect of the upcoming CRYSTAL experiment is to study the dynamics of single protons circulating the SPS in the presence of a crystal. Under some circumstances (for example under crystal channeling) a proton may hit the crystal and the neighboring silicon strip position detectors only once, before extraction from the SPS. In general (at most crystal rotation angles) it is expected that single protons will hit the crystal many times, with many accelerator turns between each hit, before escaping. Intermediate regimes are also possible (for example under volume reflection) in which a proton hits the crystal only a few times over many turns before being lost. It is crucial that the data analysis of each single proton data set be able to distinguish between these different dynamical phases, and to be able to convincingly demonstrate that the fundamental processes at play in each phase are well understood. Distinguishing between dynamical phases depends crucially on the ability to perform pattern recognition--at least visually, but preferably quantitatively--on the single proton data sets. This note shows that synchrotron oscillations significantly affect the hit pattern of a proton on the crystal. (By hit pattern we mean either the measurement vector of turn numbermore » and penetration depth, for each proton, or a vector that can be directly derived from the measurement vector, such as the vector of inferred synchrotron phase and penetration depth.) The analysis is (deliberately) as rudimentary as possible, using an elementary linear calculation which neither includes any higher order effects in the accelerator, nor any dynamical interactions between the test proton and the crystal or the silicon detectors. Single particle simulation studies need to be carried out for CRYSTAL, exploring realistic effects besides dispersion, such as multiple scattering, dead zones, energy loss, dispersion slope, and linear coupling. Only after analysis software becomes available to interpret the output of such studies will it be possible to predict with any confidence that it will be possible to distinguish all single proton dynamical phases in the CRYSTAL experiment. Then reality will prevail.« less