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Detection of the position of two beams with a common BPM

This paper proposes a method of detecting the position of two beams with a common BPM, the method which is useful even if the bunch time-spacing between the two beams is too small to separate each beam signal with fast switches. The method is based on the idea that unknown beam parameters can be estimated if the number of BPM electrodes is greater than that of the parameters, and if the signals are independent of each other. Since the number of unknown parameters of the two beams is 6, consisting of 4 positions and 2 intensities, an 8-electrode BPM, whose signals are detected in the frequency domain, is expected to play the role. The method is to be applied to measuring beam positions near the interaction paint of the two-ring collider KEKB, where the bunch spacing is only 2 ns in each ring. The independence of the signals is insured by a finite orbit separation at the common BPM.