Betatron phase and nonlinear lattice correction

Betatron phase measured from excited oscillation can be used to correct the beta function and the nonlinear lattice. With an improved algorithm the measurement precision has achieved 1 mrad (rms), or equivalently, 0.3% of beta beat at NSLS-II. The beta beating can be corrected to 1% in less than half an hour. This precise technique can be applied to the nonlinear lattice correction as well. The betatron phase probed by an off-axis beam provides information on the sextupole strength. In comparison with the model the nominal strength can be restored. It was shown that the proposed scheme treated all the leading order resonance driving terms generated by sextupoles, as well as the detuning terms and the nonlinear chromaticity. At NSLS-II a half percent sextupole correction led to a 15% increase of the dynamic aperture.