I. Orbital Eigen-analysis for Electron Storage Rings

J.A. Ellison, U. New Mexico H. Mais, DESY G. Ripken, Deceased 2004 a. Basic problem A general 6-D formalism is presented for the calculation of the bunch parameters (e.g. 6-D stationary beam-envelope matrix) for electron storage rings including radiation damping and quantum excitation. The problem is formulated in terms of a stochastic differential equation (SDE) and basic to our approach is the orbital eigen-analysis first introduced in [1]. The latter gives a more general framework than that of Courant-Synder. An SDE approach was first introduced in [2] and developed further in [3]. At a later stage the work of [4] was incorporated and the starting point here is the SDE in Frenet-Serret coordinates with respect to a design orbit as described in [5]. The 6D-SDE is