Statistical Signal Processing Techniques for Coherent Transversal Beam Dynamics in Synchrotrons

Transversal coherent beam oscillations can occur in synchrotrons directly after injection due to errors in position and angle, which stem from inaccurate injection kicker reactions. Furthermore, the demand for higher beam intensities is always increasing in particle accelerators. The wake fields generated by the traveling particles will be increased by increasing the beam intensity. This leads to a stronger interaction between the beam and the different accelerator components, which increases the potential of coherent instabilities. Thus, undesired beam oscillations will occur when the natural damping is not enough to attenuate the oscillations generated by the coherent beamaccelerator interactions. The instabilities and oscillations can be either in transversal or longitudinal direction. In this work we are concerned with transversal beam oscillations only. In normal operation, transversal beam oscillations are undesired since they lead to beam quality deterioration and emittance blow up caused by the decoherence of the oscillating beam. This decoherence is caused by the tune spread of the beam particles. The emittance blow up reduces the luminosity of the beam, and thus the collision quality [1,2]. Therefore, beam oscillations must be suppressed in order to maintain high beam quality during acceleration. A powerful way to mitigate coherent instabilities is to employ a feedback system. A Transversal Feedback System (TFS) senses instabilities of the beam by means of Pickups (PUs), and acts back on the beam through actuators, called kickers [3, 4]. In this thesis, a novel concept to use multiple PUs for estimating the beam displacement at the position with 90◦ phase advance before the kicker is proposed. The estimated values should be the driving feedback signal. The signals from the different PUs 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 with 90◦ phase advance before the kicker for non-noisy PU 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 PUs and the kicker around the accelerator ring such that the noise effect on the feedback quality is minimized. A new TFS design for the heavy ions synchrotrons SIS 18 and SIS 100 at the GSI has been developed and implemented using FPGA. The correction signal of transverse feedback system is usually calculated according to the transfer matrices between the pickups and the kickers. However, errors due to magnetic field imperfections and magnets misalignment lead to deviations in the transfer matrices from their nominal values. Therefore, using the nominal values of the transfer optics with uncertainties leads to feedback quality degradation, and thus beam disturbances. Therefore, we address a novel concept for feedback systems that are robust against optics errors or uncertainties. One kicker and multiple pickups are assumed to be used for each transversal direction. We introduce perturbation terms to the transfer matrices between the kicker and the pickups. Subsequently, the Extended Kalman Filter is used to estimate the feedback signal and the perturbation terms using the measurements from the pickups. Moreover, we propose a method for measuring the phase advances and amplitude scaling between the positions of the kicker and the Beam Position Monitors (BPMs). Directly after applying a kick on the beam by means of the kicker, we record the BPM signals. Subsequently, we use the Second-Order Blind Identification (SOBI) algorithm to decompose the recorded noised signals into independent sources mixture [5, 6]. Finally, we determine the required optics parameters by identifying and analyzing the betatron oscillation sourced from the kick based on its mixing and temporal patterns. The accelerator magnets can generate unwanted spurious linear and non-linear fields [7] due to fabrication errors or aging. These error fields in the magnets can excite undesired resonances leading together with the space charge tune spread to long term beam losses and reducing dynamic aperture [8–10]. Therefore, the knowledge of the linear and non-linear magnets errors in circular accelerator optics is very crucial for controlling and compensating resonances and their consequent beam losses and beam quality deterioration. This is indispensable, especially for high beam intensity machines. Fortunately, the relationship between the beam offset oscillation signals recorded at the BPMs is a manifestation of the accelerator optics, and can therefore be exploited in the determination of the optics linear and non-linear components. Thus, beam transversal oscillations can be excited deliberately for purposes of dignostics operation of particle accelerators. In this thesis, we propose a novel method for detecting and estimating the optics lattice non-linear components located in-between the locations of two BPMs by analyzing the beam offset oscillation signals of a BPMs-triple containing these two BPMs. Depending on the non-linear components in-between the locations of the BPMs-triple, the relationship between the beam offsets follows a multivariate polynomial accordingly. After calculating the covariance matrix of the polynomial terms, the Generalized Total Least Squares method is used to find the model parameters, and thus the non-linear components. A bootstrap technique is used to detect the existing polynomial model orders by means of multiple hypothesis testing, and determine confidence intervals for the model parameters