Near threshold anomalous transport in the standard map

White, R. B.; Benkadda, S.; Kassibrakis, Serge; Zaslavsky, G. M.

doi:10.1063/1.166361

Cited by 36 publications

(29 citation statements)

References 27 publications

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“…This analysis confirms early results obtained in RFX concerning field line dynamics [34], and the pioneering theory by Balescu [39]. Similar behavior is seen in the Chirikov-Taylor model [40]. Note that the radial diffusive behavior of the trapped particles (neoclassical banana regime of particles with λ = v /v 1 and (∆r) 2 ∝ t α , α ≈ 1) is not visible because of its very small magnitude.…”

Section: B Flightssupporting

confidence: 74%

Nonlocal Transport in the Reversed Field Pinch

Spizzo¹,

White²,

Cappello³

et al. 2009

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Several heuristic models for nonlocal transport in plasmas have been developed, but they have had a limited possibility of detailed comparision with experimental data. Nonlocal aspects introduced by the existence of a known spectrum of relatively stable saturated tearing modes in a low current reversed field pinch offers a unique possibility for such a study. A numerical modelling of the magnetic structure and associated particle transport is carried out for the reversed-field pinch experiment at the Consorzio RFX, Padova, Italy. A reproduction of the tearing mode spectrum with a guiding center code 1 reliably reproduces the observed soft X-ray tomography. Following particle trajectories in the stochastic magnetic field shows the transport across the unperturbed flux surfaces to be due to a spectrum of Lévy flights, with the details of the spectrum position dependent. The resulting transport is subdiffusive, and cannot be described by Rechester-Rosenbluth diffusion, which depends on a random phase approximation. If one attempts to fit the local transport phenomenologically, the subdiffusion can be fit with a combination of diffusion and inward pinch 2 . It is found that whereas passing particles explore the stochastic field and hence participate in Lévy flights, the trapped particles experience normal neoclassical diffusion.A two fluid nonlocal Montroll equation is used to model this transport, with a Lévy flight defined as the motion of an ion during the period that the pitch has one sign. The necessary input to the Montroll equation consists of a time distribution for the Lévy flights, given by the pitch angle scattering operator, and a distribution of the flight distances, determined numerically using a guiding center code. Results are compared to experiment. The relation of this formulation to fractional kinetics is also described.

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Section: B Flightssupporting

confidence: 74%

Nonlocal Transport in the Reversed Field Pinch

Spizzo¹,

White²,

Cappello³

et al. 2009

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“…Moreover, numerical investigations of the standard map suggest that in cases in which the structure of the phase space is highly intricate the numerical determination of the exponent might not even be a convergent process. 37 Due to these reasons, very few analytical results which relate the exponent to the structure of the phase space are known. However, for the particular case of self-similar hierarchies of resonant islands, by using a generalization of the Fokker-Planck-Kolmogorov ͑FPK͒ equation and renormalization group ͑RG͒ techniques, an analytical expression for the exponent as a function of two scaling parameters has been established in Ref.…”

Section: ͑10͒mentioning

confidence: 99%

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

Panoiu

2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.

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“…The standard map also serves as the usual test bed for the study of various transport phenomena and their quantifiers [14]. The study of impurity dynamics using the standard map as the base flow, can thus give us a handle on the way in which these phenomena affect the impurity dynamics.…”

Section: A the Embedded Standard Mapmentioning

confidence: 99%

Clustering, chaos, and crisis in a bailout embedding map

Thyagu

Gupte

2007

Phys. Rev. E

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We study the dynamics of inertial particles in two dimensional incompressible flows. The particle dynamics is modelled by four dimensional dissipative bailout embedding maps of the base flow which is represented by 2 − d area preserving maps. The phase diagram of the embedded map is rich and interesting both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The embedding map shows three types of dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus, the embedding map can target periodic orbits as well as chaotic structures in both the aerosol and bubble regimes at certain values of the dissipation parameter. The bifurcation diagram of the 4 − d map is useful for the identification of regimes where such structures can be found. An attractor merging and widening crisis is seen for a special region for the aerosols. At the crisis, two period-10 attractors merge and widen simultaneously into a single chaotic attractor. Crisis induced intermittency is seen at some points in the phase diagram. The characteristic times before bursts at the crisis show power law behaviour as functions of the dissipation parameter. Although the bifurcation diagram for the bubbles looks similar to that of aerosols, no such crisis regime is seen for the bubbles. Our results can have implications for the dynamics of impurities in diverse application contexts.

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Near threshold anomalous transport in the standard map

Cited by 36 publications

References 27 publications

Nonlocal Transport in the Reversed Field Pinch

Nonlocal Transport in the Reversed Field Pinch

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

Clustering, chaos, and crisis in a bailout embedding map

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