Measurement of Xy Coupling Using Turn-by-turn Bpm at Kekb

We have measured xy coupling of the interaction point(I.P.) at KEKB. When a normal mode is excited by a shaker with tune frequency, the horizontal or vertical betatron oscillations can be measured by a turn-by-turn BPM in the laboratory coordinate system. A harmonic analysis has been performed to extract the xy coupling parameters at I.P. from the detected betatron oscillations. 1 IDEA AND FORMALISM The transformation from the physical coordinate, (x, px, y, py) to the normal(xy decoupled) coordinate, (u, pu, v, pv) at a position is written by   u pu v pv   = C   x px y py   , (1) where the 4× 4 matrix C is defined by C = ( μI JRJ R μI ) , (2) and the relation between μ and R is μ + det R = 1. The submatrices are I = ( 1 0 0 1 ) , J = ( 0 1 −1 0 ) , (3)