Inner Triplet Quadrupole Fringe Fields in the High Luminosity Large Hadron Collider

Abstract

The High Luminosity Large Hadron Collider is an upgrade to the Large Hadron Collider which aims to produce more collisions over a single run of the accelerator. To do so, there is an effort to improve the peak luminosity of the existing machine by a factor of 5, and the total luminosity over time (integrated luminosity) by a factor of 10. To increase the luminosity of the machine, one crucial way is to reduce the size of the beam at the point of collision. To make a smaller beam, stronger focusing magnets are required. Furthermore, the beam would also need to reach greater extents in the inner triplet focusing magnets either side of the collision point. To facilitate the beam size in the inner triplet magnets, the magnets require larger distances between poles. However, larger distances between poles means that the tapering of the field at the end of the magnets is more pronounced. These tapering fields are known as fringe fields, and they have a nonlinear dynamical effect on the beam. This could mean a potentially disastrous effect on the beam performance. The goal of this thesis is to compare different fringe field models, and to observe the differences between them. An additional objective was to use a tracking code (SAMM) in a study of this kind. This would be to test its extensibility for new work, and for its GPU tracking abilities. The suitability of an analytic Enge field description for studies involving fringe fields was also an aim of this work. Though the results presented in this work show variations between the different models, it is still possible that the fringe fields would have a large impact on the beam stability. The result for the Enge field Taylor map showed a significant reduction in the stability of the beam compared to the no fringe model. On the other hand the numeric field Runge-Kutta fringe field model showed the opposite behaviour. Whereas the Enge field Runge-Kutta and the numeric field Taylor map were found to be in closer agreement to the no fringe model. The analysis was successfully carried out using SAMM. Through this work its functionality was extended to handle new field models and new integration routines. The GPU tracking allowed frequency map analysis to be run on a desktop computer within a reasonable timescale. The analytic Enge model was shown to be an alternative to a numeric model, but further work is required to find significant differences between them. The Enge model looks like it could be used as a faster alternative to the numeric model in future projects that require fringe field modelling.