METHOD TO EXTRACT TRANSFER MAPS IN THE PRESENCE OF SPACE CHARGE IN CHARGED PARTICLE BEAMS

Taylor transfer maps have been standard tools to study accelerator lattices for the last two decades. Taylor transfer maps for static fields, and in the absence of space charge effects, have been derived with different approaches in recent times [1]. However, the derivation of Taylor transfer maps in the presence of space charge is a challenging problem that has no solutions yet. In this paper we present a method for calculating quantities of interest such as tunes, dispersion and resonances from the Taylor map of the system, with an accurate approximation of space charge effects on the beam. The space charge calculation involves a novel numerical integration technique to efficiently evaluate the Taylor expansion of a potential around a singular point. This will allow for an accurate computation of space charge induced tune shifts and resonances, as well as allowing for experimental setups to discriminate between space charge caused issues, and lattice caused issues. The beam optics code COSY Infinity was used to implement the new method. The effects of space charge are added to the map using Strang splitting.