Levy flights on a comb and the plasma staircase

Alexander V. Milovanov, Jens Juul Rasmussen

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Abstract

We formulate the problem of confined Levy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V (x) α |Δx|n within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Levy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n > 4 - μ where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ = 1), n > 3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.
Original languageEnglish
Article number022208
JournalPhysical Review E
Volume98
Issue number2
Number of pages11
ISSN2470-0045
DOIs
Publication statusPublished - 2018

Cite this

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title = "Levy flights on a comb and the plasma staircase",
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Levy flights on a comb and the plasma staircase. / Milovanov, Alexander V.; Rasmussen, Jens Juul.

In: Physical Review E, Vol. 98, No. 2, 022208, 2018.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Levy flights on a comb and the plasma staircase

AU - Milovanov, Alexander V.

AU - Rasmussen, Jens Juul

PY - 2018

Y1 - 2018

N2 - We formulate the problem of confined Levy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V (x) α |Δx|n within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Levy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n > 4 - μ where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ = 1), n > 3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.

AB - We formulate the problem of confined Levy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V (x) α |Δx|n within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Levy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n > 4 - μ where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ = 1), n > 3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.

U2 - 10.1103/PhysRevE.98.022208

DO - 10.1103/PhysRevE.98.022208

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JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

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