Principle of Skew Quadrupole Modulation to Measure Betatron Coupling*

The measurement of the residual betatron coupling via skew quadrupole modulation is a new diagnostics technique that has been developed and tested at the Relativistic Heavy Ion Collider (RHIC) as a promising method for the linear decoupling on the ramp. By modulating the strengths of different skew quadrupole families the two eigentunes are precisely measured with the phase lock loop system. The projections of the residual coupling coefficient onto the skew quadrupole coupling modulation directions are determined. The residual linear coupling could be corrected according to the measurement. An analytical solution for skew quadrupole modulation based on the Hamiltonian perturbation theory is given, and simulation code using smooth accelerator model is also developed. Some issues concerning the practical applications of this technique are discussed.