On the turbulent energy cascade in anisotropic magnetohydrodynamic turbulence

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

Non-gaussian probability distribution functions in two dimensional Magnetohydrodynamic turbulence

Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field depend on the scale at hand, that is they are self-affine. The departure of the PDFs from a Gaussian function can be described through the scaling behavior of a single parameter lambda_r^2 obtained by fitting the PDFs with a given curve stemming from the analysis of a multiplicative model by Castaing et al. (1990). The scaling behavior of the parameter lambda_r^2 can be used to extract informations about the intermittency. A comparison of intermittency properties in different MHD turbulent flows is also performed.Comment: 7 pages, with 5 figure

On the probability distribution function of small scale interplanetary magnetic field fluctuations

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.Comment: 25pag, 20 jpg small size figures. In press on "ANnales Geophysicae" (September 2004

Methods for characterising microphysical processes in plasmas

Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres