Measurement of beta-function and phase using the response matrix

A new method for extracting the beta-function and phase for the beam position monitors (BPMs) and the corrector magnets from the measured response matrix is presented. The response matrix relates beam motion at the BPM locations to changes in corrector magnet strengths. Using the model beta and phase as the initial values, new values are obtained by iteration. The accuracy of beta and phase thus calculated is limited by the accuracy of response matrix measurement and calibration of BPMs and correctors. The scaling ambiguity in the beta-function is resolved by matching the beta product and phase advance across a drift region. A by-product of this technique is an accurate determination of the betatron tune, and in principle, quadrupole strengths can be calculated from the betas and phases. This method is applied to data obtained from the X-ray ring at the National Synchrotron Light Source at Brookhaven. The possibility of applying the results to lattice-debugging will also be discussed