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Rigorous Lower Bounds on the Survival Time in Particle Accelerators


Analyzing 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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