Levy flights on a comb and the plasma staircase

Alexander V. Milovanov, Jens Juul Rasmussen

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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
Issue number2
Number of pages11
Publication statusPublished - 2018


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