Betatron phase advance measurement at SPEAR

There are many reasons to determine the betatron phase advance between two azimuthal positions in a circular accelerator or storage ring. The authors measured the betatron phase advance between various pairs of azimuthal points in the SPEAR Storage Ring by two different methods. The first method is to excite a steady state coherent betatron oscillation with a network analyzer. The second method is to excite a free coherent betatron oscillation with an impulse kick, and to digitally sample the transverse position of the beam at the pickup stations. The results of these digital samples are Fourier analyzed with a computer to obtain the phase advance. The second method is discussed, and the experimental results compared to theory