Designing linear lattices for round beam in electron storage rings using the solution by linear matrices analysis

TL;DR

This paper introduces the SLIM analysis method to precisely design round beam lattices in electron storage rings, overcoming limitations of perturbation theories and enabling exact beam size calculations for various coupling sources.

Contribution

It applies the SLIM analysis to design and analyze linearly coupled lattices for round beams, including effects of different coupling sources and specific magnet models.

Findings

SLIM provides exact beam size calculations in coupled lattices.

Both on- and off-resonance schemes for round beams are demonstrated.

SLIM formalism is extended to common magnet models like combined-function magnets and wigglers.

Abstract

For some synchrotron light source beamline applications, a round beam is preferable to a flat one. A conventional method of obtaining round beam in an electron storage ring is to shift its tune close to a linear difference resonance. The linearly coupled beam dynamics is analyzed with perturbation theories, which have certain limitations. In this paper, we adopt the Solution by LInear Matrices (SLIM) analysis to calculate exact beam sizes to design round beam lattices. The SLIM analysis can deal with a generally linearly coupled accelerator lattice. The effects of various coupling sources on beam emittances and sizes can be studied within a self-consistent frame. Both the on- and off-resonance schemes to obtain round beams are explained with examples. The SLIM formalism for two widely used magnet models: combined-function bending magnets, and planar wigglers and undulators, is also derived.