In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that...

The statistics of quiescent times ${\tau }_L$ between successive bursts of solar flares activity, performed using 20 years of data, displays a power law distribution with exponent $\alpha \simeq 2.4$. This is an indication of an underlying complex dynamics with long correlation times. The observed scaling behavior is in contradiction with the self-organized criticality models of solar flares which predict Poisson-like statistics. Chaotic models, including the destabilization of the laminar phases and subsequent restabilization due to nonlinear dynamics, are able to reproduce the power law for the quiescent times. A shell model of MHD turbulence correctly reproduces all the observed distributions.

Direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), is observed in the solar wind by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom’s law for MHD turbulence, a linear relation is indeed observed for the scaling of mixed third-order structure functions involving Elsässer variables. This experimental result firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.

Intermittency in fluid turbulence can be emphasized through the analysis of Probability Distribution Functions (PDF) for velocity fluctuations, which display a strong non‐gaussian behavior at small scales. Castaing et al. (1990) have introduced the idea that this behavior can be represented, in the framework of a multiplicative cascade model, by a convolution of gaussians whose variances is distributed according to a log‐normal distribution. In this letter we have tried to test this conjecture on the MHD solar wind turbulence by performing a fit of the PDF of the bulk speed and magnetic field intensity fluctuations calculated in the solar wind, with the model. This fit allows us to calculate a parameter λ² depending on the scale, which represents the width of the log‐normal distribution of the variances of the gaussians. The physical implications of the obtained values of the parameter as well as of its scaling law are finally discussed.

Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law $f^{-5/3}$ below the ion cyclotron frequency $f_{ci}$. Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dissipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum $\sim k^{-7/3+2\alpha}$, which depends on the degree of plasma compression $\alpha$.Comment: accepted for publication in The Astrophysical Journal the 1st of October 200