Controlling chaos in wave-particle interaction

Details Controlling chaos in wave-particle interaction Controlling chaos in wave-particle interaction

2011-10-09

arxiv.org/abs/1110.1871v2

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 figures. Article to be submitted to Physical Review E

Scientific paper

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists in the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos to spread to large regions and make the controlled dynamics more regular. We show numerically that the control term obtained just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.

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