Chirikov criterion - Alchetron, The Free Social Encyclopedia

The Chirikov criterion or Chirikov resonance-overlap criterion was established by the Russian physicist Boris Chirikov. Back in 1959, he published a seminal article (Atom. Energ. 6: 630 (1959)), where he introduced the very first physical criterion for the onset of chaotic motion in deterministic Hamiltonian systems. He then applied such a criterion to explain puzzling experimental results on plasma confinement in magnetic bottles obtained by Rodionov at the Kurchatov Institute. As in an old oriental tale, Boris Chirikov opened such a bottle, and freed the genie of chaos, which spread the world over.

Description

According to this criterion a deterministic trajectory will begin to move between two nonlinear resonances in a chaotic and unpredictable manner, in the parameter range

K ≈ S 2 = ( Δ ω r / Δ d ) 2 > 1.

Here K is the perturbation parameter, while S = Δ ω r / Δ d is the resonance-overlap parameter, given by the ratio of the unperturbed resonance width in frequency Δ ω r (often computed in the pendulum approximation and proportional to the square-root of perturbation), and the frequency difference Δ d between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.

References

Chirikov criterion Wikipedia

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