Skew Quadrupole Modulation to Measure Global Betatron Coupling

Abstract

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. In the second half of this note, We report the results from the dedicated beam studies carried on at the RHIC injection, store and on the ramp. A capability of measuring coupling on the ramp opens possibility of continuous coupling corrections during acceleration.