Case of equilibrium beam distribution dependence on storage ring nonlinearity

In an electron storage ring, the emittances are determined by the beam energy and the linear lattice; the effects of lattice nonlinearity are usually negligible. In this study, we show a case where the vertical emittance has a strong quadratic dependence on the vertical chromaticity, a form of lattice nonlinearity. In this case, a crab cavity is present in the lattice, which couples the longitudinal and vertical motions of the beam. A theoretic analysis is conducted to derive the emittance dependence on chromaticity, using the normal form approach to decouple the longitudinal and vertical motion. Particle tracking simulations are performed to verify the analytic results and a good agreement is found. The dependence of equilibrium emittances on nonlinear lattice properties as demonstrated in this paper may provide new possibilities for design options and machine control.

Abstract licence: CC BY

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