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Title: Modelling curvilinear beamline effects on beam- and spin-dynamics in the Fermilab Muon g-2 storage ring
Author: Herrod, Alexander
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2019
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A model of the Fermilab Muon g-2 Experiment storage ring is developed with the BMAD simulation library for beam- and spin-dynamics studies. Particular focus is given to the electrostatic quadrupoles, the plates of which follow the curvature of the particle design trajectory of the magnetically uniform storage ring. To model these, standard electric multipoles and a novel method based on cylindrical harmonics are investigated and found to accurately match the electric field maps produced for the bulk and fringe regions of the curved quadrupoles respectively, despite these methods being specifically for straight beamlines. The toroidal multipole description is then developed, to include curvature and longitudinal field variations (to model the fringe field regions). Various combinations of the different descriptions (including use of the field maps) are used for the bulk and fringe fields of the quadrupoles, and the toroidal multipoles are found to provide the best agreement with the measured tunes of the storage ring. Two integrators are also developed, based on the method of Wu, Forest and Robin. The first of these describes motion in a uniform magnetic dipole field with arbitrary electric field, and produces results comparable to those of the adaptive-step fourth-order Runge--Kutta integrator implemented in BMAD, suitable for tracking over thousands of turns. The second is a generalisation of the first to arbitrary magnetic vector potentials superimposed on that of the uniform dipole, with arbitrary electric fields, and was also found to agree with the Runge--Kutta integrator. Simulations of antimuon storage for 2000 turns of the storage ring were performed, where losses were studied along with the evolution of beam polarisation. The storage losses, important for reducing the systematic error in the measurement of the muon g-2, were found to be largely due to collimator shape. The correlation between momentum and spin precession frequency reflect the effects expected from the electric field correction in the T-BMT equation, on the order of 10^-6. Particle injection was also studied, for various injection angles, quadrupole strengths and strengths of injection kick, and in the cases where experimental data was provided, the model was found to be consistent with the experiment.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral