Measurement of the Excitation of the Coupling Resonance Qh - Qv = 0

To take advantage of the large resonance-free regions close to the diagonal Qh = Qv in the tune diagram, the Intersecting Storage Rings (ISR) operate with nearly equal tunes. Thus, the excitation of the coupling resonance Qh - Qv = 0 is of importance and this has stimulated the study of its effects, the measurement of its excitation by axial and skew quadrupole fields and its compensation. A complex coupling coefficient C can be defined in terms of axial and skew quadrupole fields, and the unperturbed machine parameters. An electronic device has been built to measure |C| by kicking a small beam and analysing the coherent oscillation. By combining different coupling vectors, phase measurements are also possible. Examples are given of coupling vectors measured in the ISR for magnet tilts, skew quadrupoles and solenoids. The outlines of two methods for directly measuring both amplitude and phase are also given. Some ideas are extended to higher order resonances.