Precise determination of the amplitude functions in collider insertions with an application to LEP

The authors review two methods often used to establish β* at the collision point, appraise their performances (with numerical applications to the Large Electron Positron Collider), and propose an additional procedure to get results that are 10 times more accurate. The first method relies on measuring the amplitude of coherent oscillations at a nearby monitor and gives good results in the defocusing plane only. In the second procedure, the Q-shift which results from a known variation of strength in one of the insertion quads is measured. The accuracy of this well-known method is severely limited for practical reasons. A refined procedure, involving antisymmetric perturbations of both insertion quads, is shown to lead to far more accurate values for β_z* (focusing plane)