Lie Algebraic Methods for Treating Lattice Parameter Errors in Particle Accelerators

Liam Michael Healy
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...
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