Orbit and Optics Improvement by Evaluating the Nonlinear BPM Response in CESR

We present an improved system for orbit and betatron phase measurement utilizing nonlinear models of beam position monitor (BPM) pickup response. We first describe the calculation of the BPM pickup signals as nonlinear functions of beam position using Greens reciprocity theorem with a two-dimensional formalism. We then describe the incorporation of these calculations into our beam position measurements by inverting the nonlinear functions, giving us beam position as a function of the pickup signals, and how this is also used to improve our calculation of the betatron phase advance. Measurements are presented comparing this system with the linearized pickup response used historically at CESR.