Intermittency, scaling and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft

The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. Here, we apply a model independent method of differencing and rescaling to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. Whereas the fluctuations of speed v and IMF magnitude B are multi-fractal, we find that the fluctuations in the ion density rho, energy densities B^2 and rho v^2 as well as MHD-approximated Poynting flux vB^2 are mono-scaling on the timescales up to ~26 hours. The single curve, which we find to describe the fluctuations PDF of all these quantities up to this timescale, is non-Gaussian. We model this PDF with two approaches-- Fokker-Planck, for which we derive the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade.Comment: 8 pages, 11 figures. APS format accepted to be published at PRE. Changes include the discussion of the functional form of tails for rescaled PDFs. Introductions has been modified as well. New figure 7 has been adde

The stability of charged-particle motion in sheared magnetic reversals

We consider the motion of charged particles in a static magnetic reversal with a shear component, which has application for the stability of current sheets, such as in the Earth's geotail and in solar flares. We examine how the topology of the phase space changes as a function of the shear component by. At zero by, the phase space may be characterized by regions of stochastic and regular orbits (KAM surfaces). Numerically, we find that as we vary by, the position of the periodic orbit at the centre of the KAM surfaces changes. We use multiple-timescale perturbation theory to predict this variation analytically. We also find that for some values of by, all the KAM surfaces are destroyed owing to a resonance effect between two timescales, making the phase space globally chaotic. By investigating the stability of the solutions in the vicinity of the fixed point, we are able to predict for what values of by this happens and when the KAM surfaces reappear

Comment on Bramwell et al, "Universal Fluctuations in Correlated Systems"

This is a comment on "Universal Fluctuations in Correlated Systems", by Bramwell et al, Phys. Rev. Lett., 84, 3744 (2000.Comment: To appear in Phys. Rev. Let

Signatures of dual scaling regimes in a simple avalanche model for magnetospheric activity

Recently, the paradigm that the dynamic magnetosphere displays sandpile-type phenomenology has been advanced, in which energy dissipation is by means of avalanches which do not have an intrinsic scale. This may in turn imply that the system is in a self-organised critical (SOC) state. Indicators of internal processes are consistent with this, examples are the power-law dependence of the power spectrum of auroral indices, and in situ magnetic field observations in the earth's geotail. However substorm statistics exhibit probability distributions with characteristic scales. In this paper we discuss a simple sandpile model which yields for energy discharges due to internal reorganisation a probability distribution that is a power-law, whereas systemwide discharges (flow of “sand” out of the system) form a distinct group whose probability distribution has a well defined mean. When the model is analysed over its full dynamic range, two regimes having different inverse power-law statistics emerge. These correspond to reconfigurations on two distinct length scales: short length scales sensitive to the discrete nature of the sandpile model, and long length scales up to the system size which correspond to the continuous limit of the model. The latter are anticipated to correspond to large-scale systems such as the magnetosphere. Since the energy inflow may be highly variable, the response of the sandpile model is examined under strong or variable loading and it is established that the power-law signature of the large-scale internal events persists. The interval distribution of these events is also discussed

Extremum statistics: a framework for data analysis

Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity (i.e. total energy dissipation, magnetization and so forth) that has been normalized to the first two moments follows a specific non-Gaussian curve. This curve follows a form suggested by extremum statistics, which is specified by a single parameter a (a = 1 corresponds to the Fisher-Tippett Type I (“Gumbel”) distribution). Here we present a framework for testing for extremal statistics in a global observable. In any given system, we wish to obtain a, in order to distinguish between the different Fisher-Tippett asymptotes, and to compare with the above work. The normalizations of the extremal curves are obtained as a function of a. We find that for realistic ranges of data, the various extremal distributions, when normalized to the first two moments, are difficult to distinguish. In addition, the convergence to the limiting extremal distributions for finite data sets is both slow and varies with the asymptote. However, when the third moment is expressed as a function of a, this is found to be a more sensitive method

Scaling collapse and structure functions: identifying self-affinity in finite length time series

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight