CERN Accelerating science

Article
Report number	SLAC-PUB-11277
Title	Equilibrium Beam Invariants of an Electron Storage Ring with Linear x-y Coupling
Author(s)	Wu, Juhao ; Chao, Alexander Wu ; Nash, Boaz
Affiliation	(SLAC)
Publication	2005
Imprint	14 Sep 2005
Number of pages	3
In:	21st IEEE Particle Accelerator Conference, Knoxville, TN, USA, 16 - 20 May 2005, pp.1111
Abstract	In accelerator systems, it is very common that the motion of the horizontal plane is coupled to that of the vertical plane. Such coupling will induce tune shifts and can cause instabilities. The damping and diffusion rates are also changed, which in turn will lead to a change in the equilibrium invariants. Following the perturbative approach which we developed for synchrobetatron coupling,* we study the x-y coupled case in this paper. Starting from the one turn map, we give explicit formulae for the tune shifts, damping and diffusion rates, and the equilibrium invariants. We focus on the cases where the system is near the integer or half integer, and sum or difference resonances where small coupling can cause a large change in the beam distribution.

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