Some New Approaches to Solving Constrained Transfer Line Matching Problems

A common type of matching problem involves finding the strengths for four (4) quadrupoles in a transfer line, that will transport a particular beam at the entrance, to produce a beam at the exit of the line with a specified set of horizontal and vertical Twiss parameters. A number of optics programs may be used to find a solution to this type of problem, but the quadrupole strengths obtained are not always satisfactory or optimal with regard to other requirements. The non-uniqueness of the solutions (different solutions have different phase advances) offers the possibility that some of these other requirements could be used to differentiate between solutions. The constrained, nonlinear, optimization program NPSOL has been integrated into a software package that can use the outputs of various optics codes to formulate nonlinear constraints and objective (merit) functions. The package has been used to look for different solutions for the SLAC transfer lines between linac sectors 1 and 2 for three configurations involving (a) the electron damping ring, (b) the damping ring by-pass, and (c) the positron damping ring. The software is briefly described and a summary of selected results obtained to date is presented.