In partial fulfillment of the requirements for the degree of Doctor of Philosophy from Michigan State University.
The normal form coordinates have a very important advantage over the particle
optical coordinates: if the transformation can be carried out successfully (general
restrictions for that are not much stronger than the typical restrictions imposed on the
behavior of the particles in the accelerator) then the motion in the new coordinates has
a very clean representation allowing to extract more information about the dynamics
of particles, and they are very convenient for the purposes of visualization.
All the problem formulations include the derivation of the objective functions,
which are later used in the optimization process using various optimization algorithms.
Algorithms used to solve the problems are specific to collider rings, and applicable to
similar problems arising on other machines of the same type.
The details of the long-term behavior of the systems are studied to ensure the their stability for the desired number of turns. The algorithm of the normal form transformation is of great value for such problems as it gives much extra information about the disturbing factors. In addition to the fact that the dynamics of particles is represented in a way that is easy to understand, such important characteristics as the strengths of the resonances and the tune shifts with amplitude and various parameters of the system are calculated.
Each major section is supplied with the results of applying various numerical optimization methods to the problems stated. The emphasis is made on the efficiency comparison of various approaches and methods. The main simulation tool is the arbitrary order code COSY INFINITY written by M. Berz, K. Makino, et al. at Michigan State University. Also, the code MAD is utilized to design the 750x750 GeV Muon Collider storage ring baseline lattice.
The OptiM to COSY lattice converter is written specifically for the need of the studies included into the dissertation, and tested on the Tevatron accelerator lattice.
P. Snopok (2007)
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