A Study of the Second-Difference Method for Radial Magnet Alignment

Abstract

Preliminary estimates indicate that the cost of surveying the main ring of the proposed 300-BeV cascade synchrotron will be quite high, because of the large diameter (~ 1-1/2 miles) and small tolerances (~ 0.005 inch). Courant and Sands have suggested replacing conventional surveying techniques by a scheme in which the only measurements to be made are local, relating each magnet to its neighbors. In principle, these measurements would enable one to determine the magnet positions (to within an overall translation and/or rotation) much more simply than by conventional techniques. Furthermore, the procedure of measurement and adjustment could be carried out completely automatically, if desired. The principle difficulty with the method lies in the accumulation of errors from the large number of observations. In order to study this phenomenon, we have considered in some detail a model scheme of this type. In Section II we describe the scheme, in Section III we outline the solution in the absence of measurement errors, and in Section IV we consider the effect of such errors.