Efficient modeling and mitigation of quadrupole errors in synchrotrons and their beam transfer lines

Abstract

This thesis investigates the problem of estimating quadrupole errors on synchrotrons as well as how to minimize the influence of quadrupole errors for beam transfer lines (beamlines). It emphasizes the importance to treat possible error sources in all parts of an accelerator in order to provide constantly high beam quality to the experimental stations. While the presented methods have been investigated by using the example of the SIS18 synchrotron and the HEST beamlines at GSI Helmholtz Centre for Heavy Ion Research, they are equally relevant for the future synchrotrons and beamlines of the Facility for Antiproton and Ion Research in Europe (FAIR). Part 1 discusses the problem of estimating quadrupole errors via orbit response measurements at synchrotrons. An emphasis is put on investigating the influence of the availability of steerer magnets and beam position monitors (BPMs) on the solvability of the inverse problem as well as on the propagation of measurement uncertainty for the estimation of quadrupole errors. The problem is approached via analytical considerations as well as via dedicated simulation studies. By developing an analytical expression for the Jacobian matrix, the theoretical boundaries for the solvability of the inverse problem are derived. Moreover, it is shown that the analytical expressions for the Jacobian matrix can be used during the fitting procedure to achieve a significant improvement in the computational efficiency by a factor $N_{steerers} \times N_{quadrupoles}$, where $N$ denotes the number of lattice elements of the respective type. The presented results are tested via dedicated measurements at the SIS18 synchrotron. Part 2 discusses – complementary to part 1 – the influence of quadrupole errors in beam transfer lines with respect to the beam quality requirements given by the experimental stations. A preventive approach is presented which allows to minimize the influence of possible quadrupole errors on the degradation of beam quality. By identifying and selecting robust quadrupole configurations, a stable operation of the beamline can be enabled and the time needed by operators to readjust the beamline parameters can be reduced. The concept of beamline robustness is developed and is studied with the help of dedicated simulations. The simulation results are used to identify certain properties that distinguish robust from nonrobust quadrupole configurations. Also, various methods for improving the computational process of identifying robust quadrupole configurations are presented. The methods and results are tested via dedicated measurements at two different beamlines at GSI Helmholtz Centre for Heavy Ion Research and at Forschungszentrum Jülich.