Positioning Tolerances of Beam Line Magnets

The positioning tolerances of magnets are an important consideration in the design and installation of a beam line. A misaligned magnet can both shift the beam centroid and affect the beam line transmission characteristics. To first order and without misalignments, the coordinates at any point of a beam particle are given as a transfer matrix times the initial coordinates. To this we add a term linear in the misalignment parameters giving the beam centroid shift, and a term bilinear in the initial particle coordinates and the misalignment parameters giving the effect on the beam focal properties. This formalism has been incorporated into the computer program TRANSPORT. The effect of either a known misalignment or an uncertainty in position may be exhibited. In a single run, up to ten magnets may be separately misaligned, and their separate effects on the beam coordinates printed in a table.