Centroid and emittance of a kicked beam in rings

Abstract

We generalize the existing decoherence theory of a kicked beam to linearly uncoupled 4D transverse phase space. Analytical results for the beam centroid motion as well as beam emittance (i.e., 1st and 2nd order beam moments) are given. We formulate the problem in the language of one-turn map and normal form theory in order to emphasize the approximations used and facilitate further generalizations. We will not discuss the chromaticity decoherence factor, which can be found in the references.