First-Order Averaging Principles for Maps with Applications to Beam Dynamics in Particle Accelerators

Scott Dumas; James A. Ellison; Mathias Vogt

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First-Order Averaging Principles for Maps with Applications to Beam Dynamics in Particle Accelerators

Scott Dumas·James A. Ellison·Mathias Vogt

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Abstract

For slowly evolving, discrete-time-dependent systems of difference equations (iterated maps), we believe the simplest means of demonstrating the validity of the averaging method at first order is by way of a lemma that we call Besjes' inequality. In this paper, we develop the Besjes inequality for identity maps with perturbations that are (i) at low-order resonance (periodic with short period) and (ii) far from low-order resonance in the discrete time. We use these inequalities to prove corresponding first-order averaging principles, together with a principle of adiabatic invariance on extended timescales; and we generalize and apply these mathematical results to model problems in accelerator beam dynamics, and to the Henon map.

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Scott Dumas, James A. Ellison, Mathias Vogt. 2003-11-13. First-Order Averaging Principles for Maps with Applications to Beam Dynamics in Particle Accelerators. https://arxiv.org/abs/physics/0311058

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