Effects of kinematic correction on the dynamics in muon rings

Among many other challenges faced by muon accelerators and storage rings, the influence of nonlinear effects has to be studied carefully compared to conventional proton and electron machines. The short lifetime of muons as well as their production mechanism make the cooling of muon beams a necessity; however, in many scenarios still rather large transversal emittances persist, which makes nonlinear effects more pronounced than usual. There are a variety of sources for nonlinear effects besides deliberate and random nonlinear multipoles; particularly, there are nonlinear effects due to fringing fields, which have been known in the design of high-resolution spectrographs and recently have also been studied for storage rings [1]. Details of some first estimates of their effects are given in an accompanying paper [2]. In this paper we address another nonlinear effect that is directly connected to the presence of large emittances, namely the so-called kinematic correction, and report first results of the effects on some current muon storage ring designs