New Method for Inverting the Closed Orbit Distortion Problem

A certain class of magnet misalignments in storage rings and other accelerators produces closed orbit distortions (CODs). Quite often the CODs are measured at a fewer number of locations (N) than the number of misalignment parameters (M). There is a linear relation between COD measurements, u(j), j= l, ..., N and the misalignment parameters e(k), k= l, ..., M. Hence the c(k)' s are underdetermined. If M < 2N, one can obtain an overdetermined set of equations by measuring the COD at two quadrupole settings. There are several ways of inverting the COD measurements to get the misalignment parameters that are fairly insensitive to errors in the measured CODs. A computer program called CODINV has been written to test some of these schemes. Two schemes give fairly good results when applied to the lattice of the Los Alamos Proton Storage Ring (PSR). The first scheme requires measurements at two nearby tunes and the use of singularvalue decomposition methods. The second scheme requires measurements of the CODs in the FODO and DOFO cell arrangements but is easier mathematically.