Methods of orbit correction system optimization

Extracting optimal performance out of an orbit correction system is an important component of accelerator design and evaluation. The question of effectiveness vs. economy, however, is not always easily tractable. This is especially true in cases where betatron function magnitude and phase advance do not have smooth or periodic dependencies on the physical distance. In this report a program is presented using linear algebraic techniques to address this problem. A systematic recipe is given, supported with quantitative criteria, for arriving at an orbit correction system design with the optimal balance between performance and economy. The orbit referred to in this context can be generalized to include angle, path length, orbit effects on the optical transfer matrix, and simultaneous effects on multiple pass orbits