Localized PEPII Storage Ring Optics Measurements (SULI paper)

The current technique employed to determine the parameters which specify the betatron oscillation in the PEPII ring at SLAC is a global procedure in that the data from each BPM (Beam Position Monitor) is weighted equally. However for more accurate interaction point (IP) measurements it would be beneficial to weight the data from the BPMs closest to the IP much more heavily. Researchers are thus considering the possibility of developing a technique to determine the oscillation parameters near the IP using as few BPMs as possible. In this paper, allowing BPM gains and cross coupling, we show analytically that given data from N BPMs there remain 6N + 2 degrees of freedom in the matrices M{sub A,A}, M{sub B,A}, ..., M{sub N,N-1} unspecified by the observable data alone. From this we demonstrate that data from at least 3 BPMs is required to completely specify the system when the transfer maps between BPMs are assumed known, and that 4 BPMs may be more suitable