Stable oscillating motions in a model of a charged-particle accelerator

Pustyl′nikov, L.

doi:10.1090/S0077-1554-04-00141-4

Stable oscillating motions in a model of a charged-particle accelerator
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by L. D. Pustyl′nikov
Translated by: H. H. McFaden

Trans. Moscow Math. Soc. 2004, 177-211

DOI: https://doi.org/10.1090/S0077-1554-04-00141-4

Published electronically: October 1, 2004

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Abstract:

This paper is devoted to a qualitative study of oscillating motions in Hamiltonian systems with five-dimensional phase space that depend periodically on the independent variable. It is proved that in the phase space there exists an open set of initial data giving rise to oscillating motions that are Lyapunov stable. The main example of such systems is the classical model of an accelerator of charged particles moving in a variable periodic electric field and a constant magnetic field, and the resulting oscillating motions lead to unbounded growth of the energy of the particles. It is established that the property of stability of the solutions is preserved under a small change in the Hamiltonian function.

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