Designing linear lattices for round beam in electron storage rings using SLIM.

For some synchrotron light source beamline applications, a round beam is preferable to a flat one. A conventional method of obtaining round beam is to shift an electron storage ring's tune close to a linear difference resonance. Then 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.