Large-scale behavior of the tokamak density fluctuations

Abstract

An analysis of tokamak density fluctuations data permits the determination of two characteristic exponents. The exponents correspond to the powers of a power-law dependence of the distributions of the long-lasting monotonic change ͑''flight''͒ of the density and the time length of these changes. Speculation based on these results leads to construction of the fractional kinetic equation for the distribution function of the flights. The asymptotic transport properties of the particle density distribution function are directly connected with the exponents obtained from the density fluctuations data.

Multiscale behavior and fractional kinetics from the data of solar wind–magnetosphere coupling

“…This is the most reliable result and it confirms the fractal nature of the solar wind. Overall, the observed data suggest subdiffusive behavior, which is drastically different from the superdiffusive behavior demonstrated by the widely used anomalous diffusion models utilizing the concept of Levy flights [1,2,23].…”

“…The important role of kinetics was effectively demonstrated in [zaslavsky00, 2] where a new technique of data analysis was applied to the data of plasma density fluctuations in a tokamak. Assuming the presence of a Lévy-type multiscale process characterized by "flights", a special procedure was used to separate the flight events without a characteristic scale from the "noisy" events with a characteristic small scale.…”

“…Observing and analyzing different realizations of stochastic dynamical processes, one can classify them and apply the available techniques to the phenomena of which the details of the processes are not sufficiently known. A technique similar to the one used in the analysis of Lévy flights has been developed recently and has been applied to the plasma density fluctuations in the tokamak device [2]. Many studies of the solar wind -magnetosphere coupling have used the time series data to obtain the Hurst exponent characterizing the multiscale nature [3,4,5].…”

“…In this paper a specific form of Lévy flight analysis [2] to the data of the solar windmagnetosphere coupling. A correlated dataset [11] of the magnetospheric dynamics driven by the solar wind is used in this study.…”

Statistics of defect motion in spatiotemporal chaos in inclined layer convection

“…Similarly, the power spectrum S(ω) of the associated velocities will exhibit power law behavior as well. Some recent examples of such behavior in fluid dynamics include tokamak density fluctuations [24] and particle motion in two-dimensional rotating fluid flows [25]. Defect random walks have also been considered for models of intracellular Ca 2+ dynamics [8], in which subdiffusion was observed.…”