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

Scaling in long term data sets of geomagnetic indices and solar wind ϵ as seen by WIND spacecraft

We study scaling in fluctuations of the geomagnetic indices (AE, AU, and AL) that provide a measure of magnetospheric activity and of the ε parameter which is a measure of the solar wind driver. Generalized structure function (GSF) analysis shows that fluctuations exhibit self-similar scaling up to about 1 hour for the AU index and about 2 hours for AL, AE and ε when the most extreme fluctuations over 10 standard deviations are excluded. The scaling exponents of the GSF are found to be similar for the three AE indices, and to differ significantly from that of ε. This is corroborated by direct comparison of their rescaled probability density functions

Self-similar signature of the active solar corona within the inertial range of solar-wind turbulence

We quantify the scaling of magnetic energy density in the inertial range of solar-wind turbulence seen in situ at 1 AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar minimum, when the coronal fields are more ordered, we find multifractality. This quantifies the solar-wind signature that is of direct coronal origin and distinguishes it from that of local MHD turbulence, with quantitative implications for coronal heating of the solar wind

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

Multi-Spacecraft Measurement of Turbulence within a Magnetic Reconnection Jet

The relationship between magnetic reconnection and plasma turbulence is investigated using multipoint in-situ measurements from the Cluster spacecraft within a high-speed reconnection jet in the terrestrial magnetotail. We show explicitly that work done by electromagnetic fields on the particles, $\mathbf{J}\cdot\mathbf{E}$, has a non-Gaussian distribution and is concentrated in regions of high electric current density. Hence, magnetic energy is converted to kinetic energy in an intermittent manner. Furthermore, we find the higher-order statistics of magnetic field fluctuations generated by reconnection are characterized by multifractal scaling on magnetofluid scales and non-Gaussian global scale invariance on kinetic scales. These observations suggest $\mathbf{J}\cdot\mathbf{E}$ within the reconnection jet has an analogue in fluid-like turbulence theory in that it proceeds via coherent structures generated by an intermittent cascade. This supports the hypothesis that turbulent dissipation is highly nonuniform, and thus these results could have far reaching implications for space and astrophysical plasmas.Comment: 5 pages, 3 figures, submitted to Physical Review Letter

Kinetic Signatures and Intermittent Turbulence in the Solar Wind Plasma

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 AU. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are non-uniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Scaling and a Fokker-Planck model for fluctuations in geomagnetic indices and comparison with solar wind as seen by Wind and ACE

The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or that may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short-term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum, along with the parameter that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the parameter at solar maximum. This self-similarity persists for fluctuations on timescales at least up to about 1–2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle, and the trend follows that found in the scaling of fluctuations in . The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle, as well as being distinct from those in the parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (Langevin equation) for time series of the geomagnetic indices