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Generalized Randomly Amplified Linear System Driven by Gaussian Noises: Extreme Heavy Tail and Algebraic Correlation decay in Plasma Turbulence

par Steinbrecher, György;Weyssow, Boris
Référence Physical Review Letters, 92, page (125003)
Publication Publié, 2004

Article révisé par les pairs

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Résumé :

The extreme heavy tail and the power-law decay of the turbulent flux correlation observed in hot magnetically confined plasmas are modeled by a system of coupled Langevin equations describing a continuous time linear randomly amplified stochastic process where the amplification factor is driven by a superposition of colored noises which, in a suitable limit, generate a fractional Brownian motion. An exact analytical formula for the power-law tail exponent beta is derived. The extremely small value of the heavy tail exponent and the power-law distribution of laminar times also found experimentally are obtained, in a robust manner, for a wide range of input values, as a consequence of the (asymptotic) self-similarity property of the noise spectrum. As a by-product, a new representation of the persistent fractional Brownian motion is obtained.