Measuring beta function and phase advance in RHIC with an AC dipole

High energy hadron collider operation requires accurate measurements of the beta functions and phase advances, to check the linear optics and to locate gradient errors. During the RHIC 2003 run, two AC dipoles with vertical and horizontal magnetic field were used to measure the linear optics at storage and at injection energies. The two AC dipoles are set up to adiabatically induce sizable coherent oscillations at a frequency close to the betatron frequencies. The beta functions and phase advances are then calculated from the 1024 turn-by-turn measurements available from all the RHIC BPMs (beam position monitors). Because the coherent excitation is adiabatic, the beam emittance is preserved after the measurement. The algorithm is discussed in this paper, and experimental results are presented.