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Characterization of advanced vertical orbit excursion fixed-field accelerators: Application to the ISIS-II FETS vertical FFA

par Vanwelde, Marion
Président du jury Labeau, Pierre-Etienne
Promoteur Pauly, Nicolas
Co-Promoteur Hernalsteens, Cédric
Publication Non publié, 2023-10-13

Thèse de doctorat

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Résumé :

Vertical orbit excursion Fixed-Field Accelerators (vFFAs) have recently regained interest and are being considered for various applications. Their highly nonlinear magnetic field exponentially increases in the vertical direction, resulting in vertically stacked non-planar orbits. vFFAs feature strongly coupled linear optics due to the longitudinal and quadrupolar components of their magnetic field. The study of their beam dynamics requires appropriate simulation codes that allow for step-by-step particle tracking in complex magnetic fields. In addition, their linear beam dynamics study requires adequate coupling parametrization, while their nonlinear beam dynamics study must be performed in the full 4D phase space. This thesis aims to comprehensively characterize these aspects of vFFAs through numerical simulations and advanced analysis of their unique beam dynamics. First, numerical simulation codes for vFFA study have been developed, including methods for modeling the 3D magnetic field of scaling vFFAs that have been integrated in the ray-tracing code Zgoubi. These methods encompass field nonlinearities, fringe fields, and superposition of magnetic fields from neighboring magnets. Additionally, the modern Python 3 interface Zgoubidoo has been equipped with specific tools tailored for vFFAs, including the generation of 3D scaling vFFA field maps. Results from particle tracking in field maps and in the developed vFFA analytical model exhibit excellent agreement, enabling cross-validation of vFFA design studies with other simulation codes.Then, an in-depth study of the vFFA linear and nonlinear beam dynamics has been carried out. The main parametrization methods to describe linear coupled optics were reviewed in depth and implemented in Zgoubidoo, with a focus on clarifying their key physical interpretations. Comprehensive methods for characterizing the dynamic aperture in vFFA lattices have also been proposed, including the computation of 4D stability domain estimates and means to assess their operating performance and limitations.Finally, the simulation tools and methods developed throughout the thesis have been applied to the vFFA proton driver prototype designed under the ISIS-II upgrade project. The magnets of this vFFA ring exhibit slow magnetic field fall-offs, resulting in a significant influence of the neighboring cells on the optical lattice parameters, which has been taken into account by superposing field maps in Zgoubi. Peculiar beam dynamics phenomena have been highlighted in this lattice; a thorough investigation of the lattice linear coupling revealed the occurrence of forced mode flip conditions, and the investigation of the nonlinear beam dynamics has highlighted the emergence of fourth-order stability islands. Potential harmful high-order resonances have also been identified through a Frequency Map Analysis.This work paves the way for further experimental validation using 3D field maps, including possible magnetic field errors, and future vFFA-based solutions for various applications.