Rigorous Bounds on Survival Times in Circular Accelerators and Efficient Computation of Fringe-Field Transfer Maps
In partial fulfillment of the requirements for the degree of Doctor
of Philosophy from Michigan State University.
AbstractAnalyzing 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)
DownloadClick on the icon to download the corresponding file.
Download Adobe PDF version (4334735 Bytes).
Go Back to the reprint server.
Go Back to the home page.
This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.