Abstract
This work concerns the dynamics of a type of particle accelerator called a synchrotron, in which particles are made to move in nearly circular orbits of large radius. The stability of the transverse motion of such a rotating particle may be modeled as being governed by Mathieu’s equation. For a train of two such particles the equations of motion are coupled due to plasma interactions and resistive wall coupling effects.In this paper we study a system consisting of a train of two such particles which is modeled as two coupled nonlinear Mathieu equations with delay coupling. In particular we investigate the stability of two coupled parametrically forced linear normal modes.
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References
Morrison TM, Rand RH (2007) Resonance in the delayed nonlinear Mathieu equation. Nonlinear Dyn 341–352. doi:10.1007/s11071-006-9162-5
Rand RH (2012) Lecture notes in nonlinear vibrations. The Internet-First University Press, New York. http://www.ecommons.library.cornell.edu/handle/1813/28989
Acknowledgements
The authors wish to thank their colleagues J. Sethna, D. Rubin, D. Sagan and R. Meller for introducing us to the dynamics of the Synchrotron.
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© 2016 The Society for Experimental Mechanics, Inc.
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Bernstein, A., Rand, R. (2016). Coupled Parametrically Driven Modes in Synchrotron Dynamics. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15221-9_8
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DOI: https://doi.org/10.1007/978-3-319-15221-9_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15220-2
Online ISBN: 978-3-319-15221-9
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