Optical properties of wigglers with high field-to-energy ratio

One of the options to bring electron cooling to high energies is to employ an electron storage ring, which utilizes damping wigglers to counteract emittance growth of electron bunches used to cool hadrons. An example of such a cooler is the Ring Electron Cooler (REC) that can find potential future applications in Electron Ion Collider. The REC is designed to operate at 150 MeV and requires wigglers with peak field of 2.4 T. This unique combination a strong field wiggler operated at a relatively low energy results in unusual optical properties. In this paper we derive analytic formulas for focusing and chromaticity of different wiggler options and compare analytic and beam tracking results. While our analysis was used to optimize chromaticity in the REC, the derived formulas have a general applicability to wigglers with a high field-to-energy ratio.