Using multiple pickups for transverse feedback systems and optimal pickups–kicker placement for noise power minimization

We propose a new concept to use multiple pickups for estimating the beam displacement at the position 90° before the kicker is activated. The estimated values should be the driving feedback signal. The signals from the different pickups are delayed such that they correspond to the same bunch. Subsequently, a weighted sum of the delayed signals is suggested as an estimator of the feedback correction signal. The weighting coefficients are calculated in order to achieve an unbiased estimator, i.e., the output corresponds to the actual beam displacement at the position 90° before the kicker for non-noisy pickup signals. Furthermore, the estimator must provide the minimal noise power at the output among all linear unbiased estimators. This proposed concept is applied in our new approach to find optimal places for the pickups and the kicker around the accelerator ring such that the noise effect on the feedback quality is minimized. Finally, simulation results for the heavy ions synchrotrons SIS 18 at the GSI are shown.