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Rigorous Bounds on Survival Times in Circular Accelerators and Efficient Computation of Fringe-Field Transfer Maps

A Dissertation

In partial fulfillment of the requirements for the degree of Doctor of Philosophy from Michigan State University.


Analyzing stability of particle motion in storage rings contributes to the general field of stability analysis in weakly nonlinear motion. A method which we call pseudo invariant estimation (PIE) is used to compute lower bounds on the survival time in circular accelerators. The pseudo invariants needed for this approach are computed via nonlinear perturbative normal form theory and the required global maxima of the highly complicated multivariate functions could only be rigorously bound with an extension of interval arithmetic. The bounds on the survival times are large enough to be relevant; the same is true for the lower bounds on dynamical apertures, which can be computed. The PIE method can lead to novel design criteria with the objective of maximizing the survival time. A major effort in the direction of rigorous predictions only makes sense if accurate models of accelerators are available. Fringe fields often have a significant influence on optical properties, but the computation of fringe-field maps by DA based integration is slower by several orders of magnitude than DA evaluation of the propagator for main-field maps. A novel computation of fringe-field effects called symplectic scaling (SYSCA) is introduced. It exploits the advantages of Lie transformations, generating functions, and scaling properties and is extremely accurate. The computation of fringe-field maps is typically made nearly two orders of magnitude faster.

G. H. Hoffstätter (1994)


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