Stability and Signal Suppression of Schottky Signals from Stochastically Cooled Beams

Abstract

Several thorough treatments of stochastic cooling now exist which go far beyond the original conceptual picture of ''removing fluctuations from the Schottky noise''. The trend has been to replace this statistical picture with ensemble evolution equations amenable to continuum treatment. High performance antiproton accumulation systems attempt operation at the limits of system feedback gain as dictated by instability thresholds and signal suppression degradation. The many admitted and implicit assumptions associated with the current models are most questionable near the high gain limit. This paper first highlights a few of these assumptions and points out inconsistencies to which they lead. In particular it reveals a fundamental difference between transverse (including Palmer) cooling and filter cooling. It then points out an alternative for a refined cooling approach called the ''renormalization group'' (RG). Instability thresholds may be viewed as phase transitions. The unique success of the RG approach in describing the behavior of systems near phase transitions is well known in other branches of physics. In this paper the author limits himself to making this approach plausible and sketching out its methodology but argues also for a re-examination of a statistical approach to stochastic cooling.