Rigorous Lower Bounds on the Survival Time in Particle Accelerators
AbstractAnalyzing stability of particle motion in storage rings is an interesting question in 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. Differential Algebraic (DA) techniques are
essential to manipulate the Taylor expansions required in this theory. Using the new
method of differential Algebra with Remainder (RDA), the remainder terms in Taylor
expansions can be bounded rigorously during numerical calculations, which will ultimately
lead to a rigorous bound on the survival time. The lower bounds on the survival times
are large enough to be relevant; the same is true for the lower bound on the dynamic
aperture of a storage ring, which can also be computed.
Keywords: Long-term stability; nonlinear dynamics; Nekhoroshev; Ljapunov; RDA; interval
arithmetic; global optimization.
G. Hoffstätter, M. Berz, Particle Accelerators 54 (1996) 193-202
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