Theoretical study of longitudinal beam splitting and related phenomena

Technical Report · Fri Oct 01 00:00:00 EDT 1993

DOI:https://doi.org/10.2172/105508· OSTI ID:105508

Ellison, J; Shih, H J ^[1]; Kummer, M ^[2]

---

1. Superconducting Super Collider Lab., Dallas, TX (United States)
2. University of Toledo, Toledo, OH (United States). Dept. of Mathematics

A recent experiment at the Indiana University Cyclotron Facility (IUCF) with electron cooling showed that rf phase modulation near 1:1 resonance leads to longitudinal beam splitting. Here we explain this by applying the method of averaging, a powerful tool from the study of dynamical systems, to the underlying equation of motion -- a pendulum equation with small damping and periodic forcing. The beam splitting is explained by showing that the associated Poincare map has two attracting fixed points, each with a well-defined basin of attraction. Our approach can be immediately applied to other accelerator physics problems governed by a similar equation.

• Research Organization: Superconducting Super Collider Lab., Dallas, TX (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC35-89ER40486
• OSTI ID: 105508
• Report Number(s): SSCL-Preprint-510; ON: DE95011220; TRN: 95:019188
• Resource Relation: Other Information: PBD: Oct 1993
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
SUPERCONDUCTING SUPER COLLIDER
BEAM SPLITTING
EQUATIONS OF MOTION
DAMPING
BEAM DYNAMICS
PHASE SPACE
MAPPING