Abstract:
The problem of the occurrence of an energy cascade for Alfv\'enic turbulence in solar wind plasmas was hystorically addressed by using phenomenological arguments based to the weakness of nonlinear interactions and the anisotropy of the cascade in wave vectors space. Here, this paradox is reviewed through the formal derivation of a Yaglom relation from anisotropic Magnetohydrodynamic equation. The Yaglom relation involves a third-order moment calculated from velocity and magnetic fields and involving both Els\"asser vector fields, and is particularly useful to be used as far as spacecraft observations of turbulence are concerned.

Abstract:
We analyzed intermittency in the solar wind, as observed on the ecliptic plane, looking at magnetic field and velocity fluctuations between 0.3 and 1 AU, for both fast and slow wind and for compressive and directional fluctuations. Our analysis focused on the property that probability distribution functions of a fluctuating field affected by intermittency become more and more peaked at smaller and smaller scales. Since the peakedness of a distribution is measured by its flatness factor we studied the behavior of this parameter for different scales to estimate the degree of intermittency of our time series. We confirmed that both magnetic field and velocity fluctuations are rather intermittent and that compressive magnetic fluctuations are generally more intermittent than the corresponding velocity fluctuations. In addition, we observed that compressive fluctuations are always more intermittent than directional fluctuations and that while slow wind intermittency does not depend on the radial distance from the sun, fast wind intermittency of both magnetic field and velocity fluctuations clearly increases with the heliocentric distance....

Abstract:
In spite of a large number of papers dedicated to the study of MHD turbulence in the solar wind there are still some simple questions which have never been sufficiently addressed, such as: a) Do we really know how the magnetic field vector orientation fluctuates in space? b) What are the statistics followed by the orientation of the vector itself? c) Do the statistics change as the wind expands into the interplanetary space? A better understanding of these points can help us to better characterize the nature of interplanetary fluctuations and can provide useful hints to investigators who try to numerically simulate MHD turbulence. This work follows a recent paper presented by some of the authors which shows that these fluctuations might resemble a sort of random walk governed by Truncated Lévy Flight statistics. However, the limited statistics used in that paper did not allow for final conclusions but only speculative hypotheses. In this work we aim to address the same problem using more robust statistics which, on the one hand, forces us not to consider velocity fluctuations but, on the other hand, allows us to establish the nature of the governing statistics of magnetic fluctuations with more confidence. In addition, we show how features similar to those found in the present statistical analysis for the fast speed streams of solar wind are qualitatively recovered in numerical simulations of the parametric instability. This might offer an alternative viewpoint for interpreting the questions raised above. Full Article (PDF, 2723 KB) Citation: Bruno, R., Carbone, V., Primavera, L., Malara, F., Sorriso-Valvo, L., Bavassano, B., and Veltri, P.: On the probability distribution function of small-scale interplanetary magnetic field fluctuations, Ann. Geophys., 22, 3751-3769, doi:10.5194/angeo-22-3751-2004, 2004. Bibtex EndNote Reference Manager XML

Abstract:
In spite of a large number of papers dedicated to study MHD turbulence in the solar wind there are still some simple questions which have never been sufficiently addressed like: a)do we really know how the magnetic field vector orientation fluctuates in space? b) what is the statistics followed by the orientation of the vector itself? c) does the statistics change as the wind expands into the interplanetary space? A better understanding of these points can help us to better characterize the nature of interplanetary fluctuations and can provide useful hints to investigators who try to numerically simulate MHD turbulence. This work follows a recent paper presented by the same authors. This work follows a recent paper presented by some of the authors which shows that these fluctuations might resemble a sort of random walk governed by a Truncated Leevy Flight statistics. However, the limited statistics used in that paper did not allow final conclusions but only speculative hypotheses. In this work we aim to address the same problem using a more robust statistics which on one hand forces us not to consider velocity fluctuations but, on the other hand allows us to establish the nature of the governing statistics of magnetic fluctuations with more confidence. In addition, we show how features similar to those found in the present statistical analysis for the fast speed streams of solar wind, are qualitatively recovered in numerical simulations of the parametric instability. This might offer an alternative viewpoint for interpreting the questions raised above.

Abstract:
The intermittent behavior of solar wind turbulent fluctuations has often been investigated through the modeling of their probability distribution functions (PDFs). Among others, the Castaing model (Castaing et al. 1990) has successfully been used in the past. In this paper, the energy dissipation field of solar wind turbulence has been studied for fast, slow and polar wind samples recorded by Helios 2 and Ulysses spacecraft. The statistical description of the dissipation rate has then be used to remove intermittency through conditioning of the PDFs. Based on such observation, a self-consistent, parameter-free Castaing model is presented. The self-consistent model is tested against experimental PDFs, showing good agreement and supporting the picture of a multifractal energy cascade at the origin of solar wind intermittency.

Abstract:
Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of earthquakes. We show that this process strongly departs from a Poisson statistics for both catalogue and sequence data sets. This indicate the presence of correlations in the system probably related to the stressing perturbation characterizing the seismicity in the area under analysis. As shown by this analysis, the catalogues, at variance with sequences, show common statistical properties.

Abstract:
This study focuses on the role that magnetically dominated fluctuations have within the solar wind MHD turbulence. It is well known that, as the wind expands, magnetic energy starts to dominate over kinetic energy but we lack of a statistical study apt to estimate the relevance of these fluctuations depending on wind speed, radial distance from the sun and heliographic latitude. Our results suggest that this kind of fluctuations can be interpreted as non-propagating structures, advected by the wind during its expansion. In particular, observations performed in the ecliptic revealed a clear radial dependence of these magnetic structures within fast wind, but not within slow wind. At short heliocentric distances (~0.3 AU) the turbulent population is largely dominated by Alfvénic fluctuations characterized by high values of normalized cross-helicity and a remarkable level of energy equipartition. However, as the wind expands, a new-born population, characterized by lower values of Alfvénicity and a clear imbalance in favor of magnetic energy becomes visible and clearly distinguishable from the Alfvénic population largely characterized by an outward sense of propagation. We estimate that more than 20% of all the analyzed intervals of hourly scale within fast wind are characterized by normalized cross-helicity close to zero and magnetic energy largely dominating over kinetic energy. Most of these advected magnetic structures result to be non-compressive and might represent the crossing of the border between adjacent flux tubes forming, as suggested in literature, the advected background structure of the interplanetary magnetic field. On the other hand, their features are also well fitted by the Magnetic Field Directional Turnings paradigm as proposed in literature.

Abstract:
Statistics associated with the fluctuations in solar wind parameters show a remarkable dependence on the solar activity phase. In particular, we focus our attention on the waiting-time statistics governing the MHD fluctuations of the z-component of the interplanetary magnetic field, which are important within the framework of the Sun-Earth connections, and briefly discuss the preliminary results. Data from several spacecrafts, covering different phases of the solar cycle and different radial distances, are used. We found that propagating Alfvénic fluctuations and convected structures strongly influence the statistics which vary from quasi-Poissonian to power law.

Abstract:
Statistical properties of the temporal distribution of polarity reversals of the geomagnetic field are commonly assumed to be a realization of a renewal Poisson process with a variable rate. However, it has been recently shown that the polarity reversals strongly depart from a local Poisson statistics, because of temporal clustering. Such clustering arises from the presence of long-range correlations in the underlying dynamo process. Recently achieved laboratory dynamo also shows reversals. It is shown here that laboratory and paleomagnetic data are both characterized by the presence of long-range correlations.

Abstract:
Incompressible and isotropic magnetohydrodynamic turbulence in plasms can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfv\'enic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same dataset. Large scale density fluctuations, despite their low amplitude, play thus a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can moreover supply the energy dissipation needed to account for the local heating of the non-adiabatic solar wind.