Stable, coherent, longitudinal oscillations have been observed in several accelerators. Within the context of perturbation theory, the beam parameters and machine impedance often suggest these oscillations should be Landau damped. When nonlinear effects are included, long-lived, stable oscillations become possible for low intensity beams. In this paper we report observations of stable humps in bunched beams and present a theoretical framework for their description. Implications for bunched beam stochastic cooling are considered.

• Received 4 February 2004

DOI:https://doi.org/10.1103/PhysRevSTAB.7.044402

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.