We study the time evolution of Solar Flares activity by looking at the statistics of quiescent times $\tau_{L}$ between successive bursts. The analysis of 20 years of data reveals a power law distribution with exponent $\alpha \simeq 2.4$ which is an indication of 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. In the case of the more realistic Shell Model of MHD turbulence we are able to reproduce all the observed distributions.Comment: 4 pages, 4 postscript figures. Submitted to Physical Review Letter

The solar-wind magnetohydrodynamic turbulence is observed to be mainly made of Alfvenic fluctuations propagating away from the sun. It is shown that such an asymmetric state is a general consequence of the evolution of developed magnetohydrodynamic turbulence, which, starting from an initial asymmetry between modes with cross helicity +1 and -1, tends, as a consequence of nonlinear interactions, towards a state where the only modes left are those initially prevailing (with either cross helicity +1 or -1).PACS numbers: 96.50.Dj, 96.60.Vg Theoretical investigations of strong hydromagnetic turbulence have always dealt so far with the isotropic case" and most often with the case where the average magnetic field is zero. '4 In the latter case, Kraichnan' has derived, using dimensional arguments, a 0 ' ' power law for the spectrum of the magnetic and kinetic energy densities of the fluctuations in the stationary state. The difference in the spectral index with respect to that of the Kolmogorov spectrum of isotropic hydrodynamic turbulence is due to the presence, in the smaller scales, of Alfvdn waves propagating in the magnetic field of the larger-scale eddies, thus impeding the energy transfer in this range of high wave numbers.Observations of incompressible magnetohydrodynamic (MHD) turbulence in the magnetized plasma of interplanetary space' ' indicate, however, ' that the existence of these Alfvd'n waves is not the only peculiar feature of MHD with respect to hydrodynamic turbulence.On the one hand, the spectral energy density of magnetic fluctuations E(k) defined by (5B')/4vp= f F(k) dk(1) (p being the plasma mass density) seems to follow a power law E(k)~k " with a spectral index v ranging from 1.2 to 2, for frequencies between 10 ' and 10 Hz. Although the scatter of the observed values of v precludes a definite identification with either a Kolmogorov or a Kraichnan spectrum, the observed power law is expected to result from a nonlinear energy cascade. 5v = + &B/(4 tt p) (2) the sign depending on the polarity of the average magnetic field and being such that only Alfvdnic fluctuations propagating away from the sun are observed. Notice that, in terms of the so-called cross helicity of hydromagnetic turbulence, " the observational result (2) implies that the MHD turbulence in the solar wind is either in a state characterized by the value +1 for the cross helicity, or in a -1 state.It is a simple matter to show that, if condition (2) is satisfied, there are no longer nonlinear interactions which is in apparent contrast with the presence of a spectrum. To see this, we write the equations for incompressible MHD fluctuations as" where 1 ( B ) (4) and C"=(B)/(4zp)~' is the Alfvenic speed in the average field (B). The above equations refer to Qn the other hand, in the same domain of wave vectors, and mainly in the trailing edges of fast solar-wind streams, one observes a striking correlation between the velocity 5v and magnetic fluctuations 6B which satisfy to a good degree the relation 144

Abstract.Intermittency in fluid turbulence can be emphasized through the analysis of Probability Distribution Functions (PDF) for velocity fluctuations, which display a

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Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law f À5/3 below the ion cyclotron frequency f ci . Above this frequency, the observed steeper power law is usually interpreted in two different ways, as 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 nonlinear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations rises. 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 $k À7/3þ2 , which depends on the degree of plasma compression .

Using direct numerical simulations of a hybrid Vlasov-Maxwell model, kinetic processes are investigated in a two-dimensional turbulent plasma. In the turbulent regime, kinetic effects manifest through a deformation of the ion distribution function. These patterns of non-Maxwellian features are concentrated in space nearby regions of strong magnetic activity: the distribution function is modulated by the magnetic topology, and can elongate along or across the local magnetic field. These results open a new path on the study of kinetic processes such as heating, particle acceleration, and temperature anisotropy, commonly observed in astrophysical and laboratory plasmas.

A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T⊥/T∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T⊥/T∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas

We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.Space flights have shown that the interplanetary medium is permeated by a supersonic, highly turbulent plasma flowing out from the solar corona, the so called solar wind [1,2]. The turbulent character of the flow, at frequencies below the ion gyrofrequency f ci ≃ 1Hz, has been invoked since the first Mariner mission [3]. In fact, velocity and magnetic fluctuations power spectra are close to the Kolmogorov's -5/3 law [2,6]. However, even if fields fluctuations are usually considered within the framework of magnetohydrodynamic (MHD) turbulence [2], a firm established proof of the existence of an energy cascade, namely the main characteristic of turbulence, remains a conjecture so far [4]. This apparent lack could be fulfilled through the evidence for the existence of the only exact and nontrivial result of turbulence [6], that is a relation between the third order moment of the longitudinal increments of the fields and the separation [5]. This observation would firmly put low frequency solar wind fluctuations within the framework of MHD turbulence. The importance of such question stands beyond the understanding of the basic physics of solar wind turbulence. For example, it is well known that turbulence is one of the main obstacles to the confinement of plasmas in the fusion devices [7,8]. The understanding of interplanetary turbulence and its effects on energetic particle transport is of great importance also for Space Weather research [9], which is a relevant issue for spacecrafts and communication satellites operations, and for the security of human beings. Finally, more theoretical problems are concerned, such as the puzzle of solar coronal heating due to the turbulent flux toward small scales [10].Incompressible MHD equations are more complicated than the standard neutral fluid mechanics equations because the velocity of the charged fluid is coupled with the magnetic field generated by the motion of the fluid itself. However, written in terms of the Elsässer variables defined as z ± = v ± (4πρ) −1/2 b (v and b are the velocity and magnetic field respectively and ρ the mass density), they have the same structure as the Navier-Stokes equations [4]where P is the total hydromagnetic pressure, while ν is the viscosity and κ the magnetic diffusivity. In particular, the nonlinear term appears as z ∓ · ∇z ± , suggesting the form of a transport process, in which Alfvé...