BNL, Upton, Long Island, New York, USA
Most lattice correction algorithms, such as LOCO, rely on the amplitude of the BPM signals. However, these signals are a mixture of the BPM gain and beta-beat. Even though BPM gain can be fitted by analyzing the statistics of all the BPMs in a ring accelerator, we found the uncertainty is on the order of a few percent. On the other hand, the betatron phase advance, which is obtained from the correlation of two adjacent BPMs, is independent of the BPM gain and tilt error. It was found at NSLS-II that the measurement precision of the phase advance is typically 0.001 radian, which corresponds to about 0.2% of beta beat. The phase error can be corrected similarly using a response matrix, and at NSLS-II the phase error can be corrected to <0.005 radian (p-p) in less than half an hour. The same technique can be applied to the nonlinear lattice. By comparing the phase advance differences between the on- and off- orbit lattices, the sextupole strength error can be identified. Simulation and experimental results will be demonstrated in the paper.
BNL, Upton, Long Island, New York, USA
Performance, capabilities and limitations of various algorithms for linear magnet optics correction have been studied experimentally at NSLS-II. For the crosscheck, we have selected 4 algorithms based on turn-by-turn beam position analysis: weighted correction of betatron phase and amplitude, independent component analysis, model-independent analysis, and driving-terms-based linear optics characterization. A LOCO algorithm based on closed orbit measurement has been used as a reference. For the correction, either iterative solving of linear problem (matrix inversion with singular-value decomposition) or variational optimization has been used. For all the algorithms, accuracy limitations and convergence of linear lattice correction are discussed.