Assessment of numerical methods for particle tracking in field maps

Particle tracking in accelerators elements requires accurate and efficient numerical methods. The aim of this thesis is to study and test methods which guarantee the conservation of particle motion properties when crossing non-linear elements. Two techniques for the reconstruction and post-processing of realistic vector potentials, aiming to preserve the divergence free property of the magnetic field, have been implemented and compared with more classical interpolation methods. Various integration techniques for the determination of particle motion have been compared. Moreover, the impact of different interpolation methods on the numerical integration process was observed. The idea for this thesis work started during an internship at CERN (European Organization for Nuclear Research, Geneva, Switzerland), from September 2017 to November 2018. There, my work was coordinated by Dr. Andrea Latina, in the “Beam Department” (BE), “Accelerators and Beam Physics” (ABP) group. At the end of the time spent at CERN, this work was continued and completed at Politecnico di Milano. This thesis presents the results achieved independently in both the experiences, analysing the process of particle tracking from two complementary view points.