Calculating IP tuning knobs for the PEP II high energy ring using singular value decomposition, response matrices and an adapted moore penrose method.

The PEP II lattices are unique in their detector solenoid field compensation scheme by utilizing a set of skew quadrupoles in the IR region and the adjacent arcs left and right of the IP. Additionally, the design orbit through this region is nonzero. This combined with the strong local coupling wave makes it very difficult to calculate IP tuning knobs which are orthogonal and closed. The usual approach results either in non-closure, not being orthogonal or the change in magnet strength being too big. To find a solution, the set of tuning quads had to be extended which resulted having more degrees of freedom than constraints. To find the optimal set of quadrupoles which creates a linear, orthogonal and closed knob and simultaneously minimizing the changes in magnet strength, the method using singular value decomposition, response matrices and an adapted Moore Penrose method had to be extended. The results of these simulations are discussed below and the results of first implementation in the machine are shown.