Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)



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

Author: L. D. Pustyl'nikov
Translated by: H. H. McFaden
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 65 (2004).
Journal: Trans. Moscow Math. Soc. 2004, 177-211
MSC (1991): Primary 34D20, 78A35; Secondary 37Kxx, 34C15, 70H08, 70H05, 70F10
Published electronically: October 1, 2004
MathSciNet review: 2193440
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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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Additional Information

L. D. Pustyl'nikov
Affiliation: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Pl. 4, Moscow 125047, Russia

Published electronically: October 1, 2004
Additional Notes: This work was carried out with the financial support of the Russian Foundation for Basic Research, grant no. 02–01–01067.
Dedicated: Dedicated to the memory of V.M. Alekseev
Article copyright: © Copyright 2004 American Mathematical Society