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Nash, B.

Paper	Title	Page
MPPP008	Equilibrium Beam Invariants of an Electron Storage Ring with Linear x-y Coupling	1111
	J. Wu, A. Chao, B. Nash SLAC, Menlo Park, California
	Funding: Work is supported by the U.S. Department of Energy under contract DE-AC02-76SF00515. 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. *B. Nash, J. Wu, and A. Chao, work in progress.

Paper

Title

Page

MPPP008

Equilibrium Beam Invariants of an Electron Storage Ring with Linear x-y Coupling

1111

J. Wu, A. Chao, B. Nash
SLAC, Menlo Park, California

Funding: Work is supported by the U.S. Department of Energy under contract DE-AC02-76SF00515.

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.

*B. Nash, J. Wu, and A. Chao, work in progress.