A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.

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.

Using statistical homogeneity, magnetic field fluctuations in the solar wind during Alfvénic periods are analyzed in terms of the two independent polarizations allowed for each wave vector k. It is shown that the energy spectra of the two polarizations can be related both to the correlation tensor and to the variance matrix, which is generally used to characterize the anisotropy of the turbulence. Assuming simple anisotropic power law models, the parameters defining the spectra of the two polarizations are determined by fitting the eigenvalues of the variance matrix on the corresponding eigenvalues evaluated by Bavassano et al. (1982) for Helios 2 data. Then the corresponding form of the correlation tensor is obtained. In particular, we found that the spectrum of polarization [1] fluctuations (corresponding, in a weak turbulence theory approach, to the Alfvén mode) is steeper than the polarization [2] spectrum (corresponding to the magnetosonic modes). While the former spectrum is dominated by wave vectors parallel to B0, the latter is strongly flattened on the plane containing the radial and the mean magnetic field B0 directions. A discussion of these results in connection with other observational and theoretical issues is outlined.

The description of the local turbulent energy transfer, and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission, together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at sub-ion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity and PACS numbers: 94.05.-a, 94.05.Lk, 95.30.Qd