Quantifying scaling in the velocity field of the anisotropic turbulent solar wind

Solar wind turbulence is dominated by Alfvénic fluctuations with power spectral exponents that somewhat surprisingly evolve toward the Kolmogorov value of −5/3, that of hydrodynamic turbulence. We analyze in situ satellite observations at 1AU and show that the turbulence decomposes linearly into two coexistent components perpendicular and parallel to the local average magnetic field and determine their distinct intermittency independent scaling exponents. The first of these is consistent with recent predictions for anisotropic MHD turbulence and the second is closer to Kolmogorov-like scaling

Solar cycle dependence of scaling in solar wind fluctuations

In this review we collate recent results for the statistical scaling properties of fluctuations in the solar wind with a view to synthesizing two descriptions: that of evolving MHD turbulence and that of a scaling signature of coronal origin that passively propagates with the solar wind. The scenario that emerges is that of coexistent signatures which map onto the well known "two component" picture of solar wind magnetic fluctuations. This highlights the need to consider quantities which track Alfvénic fluctuations, and energy and momentum flux densities to obtain a complete description of solar wind fluctuations

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

Modelling the measured local time evolution of strongly nonlinear heat pulses in the Large Helical Device

In some magnetically confined plasmas, an applied pulse of rapid edge cooling can trigger either a positive or negative excursion in the core electron temperature from its steady state value. We present a new model which captures the time evolution of the transient, non-diffusive local dynamics in the core plasma. We show quantitative agreement between this model and recent spatially localized measurements (Inagaki et al 2010 Plasma Phys. Control. Fusion 52 075002) of the local time-evolving temperature pulse in cold pulse propagation experiments in the Large Helical Device

Pseudo-nonstationarity in the scaling exponents of finite-interval time series

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as ~1/N as N for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and “real world” time series, and we find that in particular for heavy tailed processes, for realizable N, one is far from this ~1/N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some “real world” time series

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

AE, D ST and their SuperMAG Counterparts : the effect of improved spatial resolution in geomagnetic indices

For decades, geomagnetic indices have been used extensively to parameterize space weather events, as input to various models and as space weather specifications. The auroral electrojet (AE) index and disturbance storm time index (DST) are two such indices that span multiple solar cycles and have been widely studied. The production of improved spatial coverage analogs to AE and DST is now possible using the SuperMAG collaboration of ground‐based magnetometers. SME is an electrojet index that shares methodology with AE. SMR is a ring current index that shares methodology with DST. As the number of magnetometer stations in the SuperMAG network increases over time, so does the spatial resolution of SME and SMR. Our statistical comparison between the established indices and their new SuperMAG counterparts finds that, for large excursions in geomagnetic activity, AE systematically underestimates SME for later cycles. The difference between distributions of recorded AE and SME values for a single solar maximum can be of the same order as changes in activity seen from one solar cycle to the next. We demonstrate that DST and SMR track each other but are subject to an approximate linear shift as a result of the procedure used to map stations to the magnetic equator. We explain the observed differences between AE and SME with the assistance of a simple model, based on the construction methodology of the electrojet indices. We show that in the case of AE and SME, it is not possible to simply translate between the two indices

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

Detailed Structure and Dynamics in Particle-in-Cell Simulations of the Lunar Wake

The solar wind plasma from the Sun interacts with the Moon, generating a wake structure behind it, since the Moon is to a good approximation an insulator, has no intrinsic magnetic field and a very thin atmosphere. The lunar wake in simplified geometry has been simulated via a 1-1/2-D electromagnetic particle-in-cell code, with high resolution in order to resolve the full phase space dynamics of both electrons and ions. The simulation begins immediately downstream of the moon, before the solar wind has infilled the wake region, then evolves in the solar wind rest frame. An ambipolar electric field and a potential well are generated by the electrons, which subsequently create a counter-streaming beam distribution, causing a two-stream instability which confines the electrons. This also creates a number of electron phase space holes. Ion beams are accelerated into the wake by the ambipolar electric field, generating a two stream distribution with phase space mixing that is strongly influenced by the potentials created by the electron two-stream instability. The simulations compare favourably with WIND observations.Comment: 10 pages, 13 figures, to be published in Physics of Plasma

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