Delay-Coupled Mathieu Equations in Synchrotron Dynamics

Abstract

This paper investigates the dynamics of two couplecd Mathieu equations. The coupling functions involve both delayed and nondelay terms. We use a perturbation method to obtain a slow flow which is then studied using Routh-Hurwitz stability criterion. Analytic results are shown to compare favorably with numerical integration. The numerical integrator, DDE23, is shown to inadvertently add damping. It is found that the nondelayed coupling parameter plays a significant role in the system dynamics. We note that our interest in this problem comes from an application to the design of nuclear accelerators.

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Showing 1-10 of 11 references

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1 Excerpt

On a restricted class of coupled Hill's equations and some applications

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1 Excerpt

A treatise on the stability of a given state of motion, particularly steady motion

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CLASSE: CESR. 2014 Cornell Laboratory for Accelerator-based Sciences and Education <http

  • Cornell Electron, Storage Ring

Figure 4.4: The left graph is the result of the numerical integration. The right graph is Fig

Figure 4.5: The left graph is the result of the numerical integration with an adjusted µ value of µ = −0.0375. The right graph is Fig

MATLAB's reference on dde23. http://www.mathworks.com/help/matlab/ref/dde23.html µ = 0