Capture into Resonance: A Method for Efficient Control

Dmitri Vainchtein and Igor Mezić
Phys. Rev. Lett. 93, 084301 – Published 20 August 2004

Abstract

To achieve large changes in adiabatic invariants using small control input, a conservative dynamical system must possess an internal resonance. Capture into resonance is an inherently probabilistic process. We propose a control method to make it more structured. We study the motion of charged particles in an electromagnetic field as an example of such a system. When the nominal dynamics brings particles close to a resonance surface, a short control pulse forces the capture of a particle into the resonance with the wave. A captured particle is transported by the wave across the energy levels. The second pulse releases a particle from the resonance when the desired energy level is achieved. We discuss the distribution of energy achieved by the method.

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  • Received 16 March 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.084301

©2004 American Physical Society

Authors & Affiliations

Dmitri Vainchtein* and Igor Mezić

  • Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, California 93106, USA

  • *Electronic address: dmitri@engineering.ucsb.edu
  • Electronic address: mezic@engineering.ucsb.edu

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Issue

Vol. 93, Iss. 8 — 20 August 2004

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