An improved transfer map approach to longitudinal beam dynamics

In this paper we present our transfer map approach for studying longitudinal beam dynamics. It combines synchrotron motion mapping equations with Differential Algebraic transfer map extraction. The novel approach can take into account a variety of effects, including non-relativistic effects, arbitrary changes to RF voltage and synchronous phase, as well as nonlinearities and coupling between transverse and longitudinal beam optics. All these are made possible efficiently and accurately, without the need for time consuming element-by-element 6D particle tracking. Moreover, longitudinal space charge effects can be readily treated too. The utility of this approach is demonstrated by applying it to the study of ion beam acceleration in a proposed pre-booster ring of the Medium Energy Electron Ion Collider (MEIC) facility at TJNAF.