Longitudinal Twiss parameters for tilted phase space ellipses

Abstract

The longitudinal emittance ϵ s is usually defined under the implicit assumption that the longitudinal phase space distribution is erect, an assumption that is significantly incorrect near transition. This note generalizes the definition of e, to include tilted distributions, by introducing longitudinal Twiss functions β a , α s and γ s that are analogous to transverse Twiss functions. The evolution of these longitudinal parameters through RHIC transition is presented, for a typical set of simulation data.