Collective centroid oscillations as an emittance preservation diagnostic in linear collider linacs

Transverse bunch centroid oscillations, induced at operating beam currents at which transverse wakefields are substantial, and observed at Beam Position Monitors, are sensitive to the actual magnetic focusing, energy gain, and RF phase profiles in a linac, and are insensitive to misalignments and jitter sources. In the `pulse-stealing´ set-up implemented at the SLC, they thus allow the frequent monitoring of the stability of the in-place emittance growth inhibiting or mitigating measures-primarily the energy scaled magnetic lattice and the RF phases necessary for BNS damping-independent of the actual emittance growth as driven by misalignments and jitter. We have developed a physically based analysis technique to meaningfully reduce this data. Oscillation beta-beating is a primary indicator of beam energy errors; shifts in the `invariant´ amplitude reflect differential internal motion along the longitudinally extended bunch and thus are a sensitive indicator of the real rf phases in the machine; shifts in betatron phase advance contain corroborative information sensitive to both effects. Examples from initial SLC applications illustrate the method. Differential internal motion due to intra-bunch energy or amplitude spread, or bunch spatial extension which makes collective or multiparticle interactions possible, causes striking differences between the behavior of the centroid of a bunched beam, which is measured by a beam position monitor, and a single particle. Bunch inhomogeneities that respond differentially to the beamline environment engender decoherence, and possibly recoherence and echo phenomena; current dependent collective effects can strongly excite novel patterns of centroid motion. We first discuss general aspects of the difference between centroid and single particle mechanics in the context of developing a general parameterization scheme for the former; and then move to some more specific features of beam dynamics with transverse wakefields