Lie-algebraic methods for treating lattice parameter errors in particle accelerators

Orbital dynamics in particle accelerators and ray tracing in light optics, are examples of Hamiltonian systems. The transformation from initial to final phase space coordinates in such systems is a symplectic map. Lie algebraic techniques have been used with great success in the case of idealized systems to represent symplectic maps by Lie transformations. These techniques allow rapid computation in tracking particles while maintaining complete symplecticity, and easy extraction of analytical quantities such as chromaticities and aberrations. Real accelerators differ from ideal ones in a number of ways. Magnetic or electric devices, designed to guide and focus the beam, may be in the wrong place or have the wrong orientation, and they may not have the intended field strengths. The purpose of this dissertation is to extend the Lie algebraic techniques to treat these misplacement, misalignment, and mispowering errors. Sympletic maps describing accelerators with errors typically have first-order terms. There are two major aspects to creating a Lie algebraic theory of accelerator errors: creation of appropriate maps and their subsequent manipulation and use