Resolution and Systematics in Beam-Based Alignment of a Long, Periodic Beam Line(LCC-0006)

The beam-based alignment algorithm for the NLC main linac requires that the magnetic-electrical offset between the center of each BPM and the center of its quadrupole be determined with an absolute accuracy on the order of microns via quadrupole shunting; this allows the quads to be moved such that the beam is passing through the quad centers to this accuracy. In this note we consider the range over which each quadrupole must be shunted to achieve a 1 (micro) statistical resolution, given certain features of the lattice and assumptions about the shunting pattern and amount of data to be acquired. We give an expression for the amount that the quadrupole's center can shift during shunting if the systematic error on the determination of the center of the quad at its operating strength is to be held to 1 (micro). Finally we present a model of the expected quad center shifting due to unequal permeability of the 4 pole-pieces, and conclude that with some caution in the shunting technique the tolerance on this effect can be achieved