Anomalous three-dimensional symmetries of solar-wind plasma

Annales Geophysicae, 2011

Using the four Cluster spacecraft, we have determined the three-dimensional wave-vector spectra of fluctuating magnetic fields in the solar wind. Three different solar wind intervals of Cluster data are investigated for this purpose, representing three different spatial scales: 10 000 km, 1000 km, and 100 km. The spectra are determined using the wave telescope technique (k-filtering technique) without assuming the validity of Taylor's frozen-inflow hypothesis nor are any assumptions made as to the symmetry properties of the fluctuations. We find that the spectra are anisotropic on all the three scales and the power is extended primarily in the directions perpendicular to the mean magnetic field, as might be expected of two-dimensional turbulence, however, the analyzed fluctuations are not axisymmetric. The lack of axisymmetry invalidates some earlier techniques using single spacecraft observations that were used to estimate the percentage of magnetic energy residing in quasitwo-dimensional power. However, the dominance of twodimensional turbulence is consistent with the relatively long mean free paths of cosmic rays in observed in the heliosphere. On the other hand, the spectra also exhibit secondary extended structures oblique from the mean magnetic field direction. We discuss possible origins of anisotropy and asymmetry of solar wind turbulence spectra.

Physical Review Letters, 2011

A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, non-axisymmetry across the inertial and dissipation ranges is quantified using in-situ observations from Cluster. The observed inertial range non-axisymmetry is reproduced by a 'fly through' sampling of a Direct Numerical Simulation of MHD turbulence. Furthermore, 'fly through' sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in non-axisymmetry with power spectral exponent. The observed non-axisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.

Universe

The statistical properties of fast Alfvénic solar wind turbulence have been analyzed by means of empirical mode decomposition and the associated Hilbert spectral analysis. The stringent criteria employed for the data selection in the Wind spacecraft database, has made possible to sample multiple k‖ field-aligned intervals of the three magnetic field components. The results suggest that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, whereas a Kolmogorov-like scaling (E(k‖)∼k−5/3) and a weak or absent level of intermittency are robust characteristics of the Alfvénic slab component of solar wind turbulence.

Monthly Notices of the Royal Astronomical Society, 2019

We analyse velocity fluctuations in the solar wind at magneto-fluid scales in two data sets, extracted from Wind data in the period 2005-2015, that are characterized by strong or weak expansion. Expansion affects measurements of anisotropy because it breaks axisymmetry around the mean magnetic field. Indeed, the small-scale three-dimensional local anisotropy of magnetic fluctuations (δB) as measured by structure functions (SF B) is consistent with tube-like structures for strong expansion. When passing to weak expansion, structures become ribbon-like because of the flattening of SF B along one of the two perpendicular directions. The power-law index that is consistent with a spectral slope −5/3 for strong expansion now becomes closer to −3/2. This index is also characteristic of velocity fluctuations in the solar wind. We study velocity fluctuations (δV) to understand if the anisotropy of their structure functions (SF V) also changes with the strength of expansion and if the difference with the magnetic spectral index is washed out once anisotropy is accounted for. We find that SF V is generally flatter than SF B. When expansion passes from strong to weak, a further flattening of the perpendicular SF V occurs and the small-scale anisotropy switches from tube-like to ribbon-like structures. These two types of anisotropy, common to SF V and SF B , are associated with distinct large-scale variance anisotropies of δB in the strong-and weak-expansion data sets. We conclude that SF V show anisotropic three-dimensional scaling similar to SF B , with however systematic flatter scalings, reflecting the difference between global spectral slopes.

Physics of Plasmas, 2004

The solar wind plasma is a natural laboratory for studies of plasma turbulence. Long, evenly sampled satellite data sets are natural candidates for statistical studies and these are often performed in the context of magnetohydrodynamic ͑MHD͒ turbulence. In this paper, scaling properties of solar wind bulk plasma parameters are discussed. Low order probability density function ͑PDF͒ asymmetry analysis is applied to data that combines slow and fast solar wind. Results are compared to those obtained using a PDF rescaling technique. A break in scaling, identified by the rescaling method, is confirmed to occur at a temporal scale of ϳ26 hours. Low asymmetry levels of the fluctuations PDF are identified for the quantities that also exhibit self-similar statistics. A generalized structure function analysis is then applied to the kinetic energy density obtained from slow and fast solar wind streams. The applicability of a Fokker-Planck model for slow and fast wind v 2 fluctuations is investigated.

Physical Review Letters, 2012

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly 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.

The Astrophysical Journal, 2018

We study the anisotropy with respect to the local magnetic field of turbulent magnetic fluctuations at magnetofluid scales in the solar wind. Previous measurements in the fast solar wind obtained axisymmetric anisotropy, despite that the analysis method allows nonaxisymmetric structures. These results are probably contaminated by the wind expansion that introduces another symmetry axis, namely, the radial direction, as indicated by recent numerical simulations. These simulations also show that while the expansion is strong, the principal fluctuations are in the plane perpendicular to the radial direction. Using this property, we separate 11 yr of Wind spacecraft data into two subsets characterized by strong and weak expansion and determine the corresponding turbulence anisotropy. Under strong expansion, the small-scale anisotropy is consistent with the Goldreich & Sridhar critical balance. As in previous works, when the radial symmetry axis is not eliminated, the turbulent structures are field-aligned tubes. Under weak expansion, we find 3D anisotropy predicted by the Boldyrev model, that is, turbulent structures are ribbons and not tubes. However, the very basis of the Boldyrev phenomenology, namely, a cross-helicity increasing at small scales, is not observed in the solar wind: the origin of the ribbon formation is unknown.

Advances in Space Research, 2007

Sharp (<10 min) and large (>20%) solar wind ion flux changes are common phenomena in turbulent solar wind plasma. These changes are the boundaries of small-and middle-scale solar wind plasma structures which can have a significant influence on Earth's magnetosphere. These solar wind ion flux changes are typically accompanied by only a small change in the bulk solar wind velocity, hence, the flux changes are driven mainly by plasma density variations. We show that these events occur more frequently in high-density solar wind. A characteristic of solar wind turbulence, intermittency, is determined for time periods with and without these flux changes. The probability distribution functions (PDF) of solar wind ion flux variations for different time scales are calculated for each of these periods and compared. For large time scales, the PDFs are Gaussian for both data sets. For small time scales, the PDFs from both data set are more flat than Gaussian, but the degree of flatness is much larger for the data near the sharp flux change boundaries.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015

The Astrophysical Journal, 2012

The description of the turbulent spectrum of magnetic fluctuations in the solar wind in the kinetic range of scales is not yet completely established. Here, we perform a statistical study of 100 spectra measured by the STAFF instrument on the Cluster mission, which allows to resolve turbulent fluctuations from ion scales down to a fraction of electron scales, i.e. from ∼ 10 2 km to ∼ 300 m. We show that for k ⊥ ρ e ∈ [0.03, 3] (that corresponds approximately to the frequency in the spacecraft frame f ∈ [3, 300] Hz), all the observed spectra can be described by a general law E(k ⊥) ∝ k −8/3 ⊥ exp (−k ⊥ ρ e), where k ⊥ is the wave-vector component normal to the background magnetic field and ρ e the electron Larmor radius. This exponential tail found in the solar wind seems compatible with the Landau damping of magnetic fluctuations onto electrons.