An Investigation of Stochastic Cooling in the Framework of Control Theory
Abstract
This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling system must be considered as a closedloop, similar to the feedback systems used to damp collective instabilities. These systems, which are able to act upon themselves, are potentially unstable. The selfconsistent solution for the beam motion is derived by means of a mode analysis of the collective beam motion. This solution yields a criterion for the stability of each collective mode. The expressions also allow for overlapping frequency bands in the beam spectrum and thus are valid over the entire frequency range. Having established the boundaries of stability in this way, the FokkerPlanck equation is used to describe the cooling process. This description does not include collective effects and thus a stable beam must be assumed. Hence the predictions about the cooling process following from the FokkerPlanck equation only make physical sense within the boundaries of beam stability. Finally it is verified that the parameters of the cooling system which give the best cooling results are compatible with the stability of the beam.
 Publication:

arXiv eprints
 Pub Date:
 July 1996
 arXiv:
 arXiv:accphys/9607001
 Bibcode:
 1996acc.phys..7001M
 Keywords:

 Physics  Accelerator Physics
 EPrint:
 64 pages, latex, 11 epsfigures appended as uuencoded file, german hyphenation corrected II