Linear Oscillator Perturbed by Plane Electrostatic Waves

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A charged particle gyrating in a uniform magnetic field directed along the axis interacts with electrostatic waves, with equal wavenumbers and amplitudes but differing frequencies , propagating along the axis. Resonance occurs when (where is the cyclotron frequency). A stochastic web is then generated, as can be observed from its Poincaré map.

Contributed by: Enrique Zeleny (April 2013)
Open content licensed under CC BY-NC-SA


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The equation of motion is

,

where is the temporal frequency of the electrostatic wave. Thus we can derive the Hamiltonian, choosing :

.

References

[1] J. Meiss, "Hamiltonian Systems," Scholarpedia, 2(8): 1943, 2007. doi:10.4249/scholarpedia.1943.

[2] A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, 2nd ed., New York: Springer 1992 p. 238.

[3] J. Candy and W. Rozmus, "A Symplectic Integration Algorithm for Separable Hamiltonian Functions," Journal of Computational Physics 92, 1991 pp. 230–256. doi:10.1016/0021-9991(91)90299-Z.

[4] G. Zaslavsky, "Zaslavsky Web Map," Scholarpedia, 2(10): 3369, 2007. doi:10.4249/scholarpedia.3369.



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