Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave

Itin, A. P.; Neishtadt, A. I.; Vasiliev, A. A.

doi:10.1016/s0167-2789(00)00039-7

Cited by 112 publications

(101 citation statements)

References 12 publications

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“…This approach was suggested in (Lifshitz, et al, 1962) for problems with separatrix crossings. Following (Arnol'd, 1963), see also (Neishtadt, 1999;Itin, 2000), let us determine the distribution of this random variable. Consider a point M far from the resonance such that trajectory passing through M intersects the resonance.…”

Section: Scattering On Resonancementioning

confidence: 99%

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Resonances and Particle Stochastization in Nonhomogeneous Electromagnetic Fields

Vainchtein

Rovinsky

Zelenyǐ

et al. 2004

Journal of Nonlinear Science

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In the present paper we investigate the resonant interaction between monochromatic electromagnetic waves and charged particles in configurations with magnetic field reversals (e.g. in the earth magnetotail). The smallness of certain physical parameters allows us to solve this problem using perturbation theory reducing the problem of resonant wave-particle interaction to the analysis of slow passages of a particle through a resonance.We discuss in details two of the most important resonant phenomena: capture into resonance and scattering on resonance. We show that these processes result in destruction of the adiabatic invariants, chaotization of particles, may lead to significant (almost free) acceleration of particles and govern transport in the phase space.We calculate the characteristic times of mixing due to resonant effects and separatrix crossings and discuss the relative importance of these phenomena.

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Section: Scattering On Resonancementioning

confidence: 99%

“…The problem of particle's motion in the field of electromagnetic or electrostatic waves is one of the classical problems of plasma physics (Sagdeev, 1983) and was well explored in the case of homogeneous external magnetic field (Karney, et al, 1989;Zaslavskii et al, 1989;Neishtadt et al, 1989;Chernikov et al, 1992;Itin et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

Resonances and Particle Stochastization in Nonhomogeneous Electromagnetic Fields

Vainchtein

Rovinsky

Zelenyǐ

et al. 2004

Journal of Nonlinear Science

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“…A conceptual phenomenon of classical adiabatic theory is destruction of adiabatic invariance at separatrix crossings which is encountered, in particular, in plasma physics and hydrodynamics, classical and celestial mechanics [10,11,12,13,14,15,16,17,18,19,20,21,22]. The phenomenon is very important for BEC physics: we consider here nonlinear two-mode models related to tunnelling between coupled BEC in a double well [23], nonlinear Landau-Zener tunnelling [24,25], Feshbach resonance passage in atom-molecule systems [26,27,28].…”

Section: Introductionmentioning

confidence: 99%

“…The asymptotic formula for this jump was obtained in [11,12,13]. Later, the general theory of adiabatic separatrix crossings was also developed for slow-fast Hamiltonian systems [10,17], and was applied to certain physical problems (see, for example, [16,18,19,20]). It was also noticed that nonlinear Landau-Zener (NLZ) tunnelling models constitute a particular case for which the general theory can be applied [27,28].…”

Section: Introductionmentioning

confidence: 99%

“…Rigorous definition of such probabilistic phenomena in dynamical systems was given in [48]. The probabilistic capture is important in problems of celestial mechanics [10], but it was also investigated in some problems of plasma physics and hydrodynamics [16], optics [18], classical billiards with slowly changing parameters and other classical models [19]. As shown in [47], the combination of the two phenomena leads to dephasing in dynamics of globally coupled oscillators modelling coupled Josephson junctions.…”

Section: Introductionmentioning

confidence: 99%

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Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Itin

Watanabe

2007

Phys. Rev. E

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We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a qualitatively new nonlinear phenomenon in a NLZ model which we propose to call separated adiabatic tunnelling (AT).

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Resonances and Mixing in Near‐Integrable Volume‐Preserving Systems

Vainchtein

2011

Transport and Mixing in Laminar Flows

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Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave

Cited by 112 publications

References 12 publications

Resonances and Particle Stochastization in Nonhomogeneous Electromagnetic Fields

Resonances and Particle Stochastization in Nonhomogeneous Electromagnetic Fields

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Resonances and Mixing in Near‐Integrable Volume‐Preserving Systems

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