Fokker-Planck analysis of transverse collective instabilities in electron storage rings

Journal Article · Thu Dec 01 00:00:00 EST 2016 · Physical Review Accelerators and Beams

DOI:https://doi.org/10.1103/PhysRevAccelBeams.19.124402· OSTI ID:1373908

Lindberg, Ryan R.

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We first expand on the work of T. Suzuki, Part. Accel. 12, 237 (1982) to derive the theoretical model including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. We reduce the problem to a linear matrix equation, whose eigenvalues and eigenvectors determine the collective stability of the beam. We then show that various predictions of the theory agree quite well with results from particle tracking simulations, including the threshold current for transverse instability and the profile of the unstable mode. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 1373908
• Journal Information: Physical Review Accelerators and Beams, Vol. 19, Issue 12; ISSN 2469-9888
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English