Practical method for measurement and compensation of linear coupling driving term

Abstract

We demonstrated a method with practical value for the measurement and global compensation of a complex coupling driving term C of linear difference resonance, using a turn-by-turn beam position monitor (BPM) at the SPring-8 storage ring. The method is based on the perturbation theory with the single-resonance approximation. The accurate complex C was obtained from coefficients of the eigenmode expansion of the coupled betatron oscillation observed near a target linear difference resonance. The global compensation for the measured C was successfully carried out by determining optimal strengths of the two independent correcting skew quadrupoles for generating a counterterm -C without using empirical methods. Meanwhile, we then confirmed that the determined optimal strengths gave a minimum vertical beam size by scanning the strength of the correcting skew quadrupole field. To demonstrate the validity of our method, C was also measured while varying the strengths of the correcting magnets around the optimal values to generate deliberate skew quadrupole error fields. We confirmed that the measured values of C agreed with those coming from the deliberate error fields.