Implementation of one-turn maps in SSCTRK using ZLIB

The particle tracking code SSCTRK is currently being adapted to operational simulation and beam-beam effect studies for the Collider rings of the SSC. During beam-beam effect studies, the lattice content of the bending arcs is normally not varied, making fast truncated Taylor map tracking through the arcs an attractive option. The implementation of SSCTRK as a truncated Taylor map tracking program has been carried out using the differential algebra library ZLIB, which simplified the task to that of straightforward translation of SSCTRK kick and drift arithmetic operations to calls to the corresponding polynomial operation subroutines of ZLIB. The accuracy and speed (relative to normal SSCTRK tracking) of truncated Taylor map tracking at 2mm betatron oscillation amplitude was studied in various orders of the map. The seventh order map was found to be in agreement with the normal SSCTRK to about eight significant figures on the first turn, and to a fraction of 1% on the 100,000th turn, for a typical 5cm magnet aperture lattice, and could be made to track at ten times the speed of the normal SSCTRK kick-drift tracking on a scalar architecture (Sun) workstation. (The map tracking subroutines of ZLIB are optimized for vector and parallel architecture supercomputers, and typically achieve even faster relative performance on these, but operational simulation studies will be more conveniently carried out on dedicated workstations which have the incoming generation of superscalar'' CPUs)