1996/07/09 by O. Meincke, Meincke, O.
Computer Science · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #acc-phys #physics.acc-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.acc-phys/9607001
64 pages, latex, 11 eps-figures appended as uuencoded file, german hyphenation corrected II
arxiv created 1996/07/09 · openalex publication_date 1996/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 closed-loop, similar to the feedback systems used to damp collective instabilities. These systems, which are able to act upon themselves, are potentially unstable. The self-consistent 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 Fokker-Planck 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 Fokker-Planck 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.