Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

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

Fourier-Hermite decomposition of the collisional Vlasov-Maxwell system: implications for the velocity space cascade

Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulence, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associated with inter-particle correlations, are derived in the above cases. The implications of introducing collisions on the phase space cascade are finally discussed.Comment: Special issue featuring the invited talks from the International Congress on Plasma Physics (ICPP) in Vancouver, Canada 4-8 June 201

Superdiffusive and Subdiffusive Transport of Energetic Particles in Solar Wind Anisotropic Magnetic Turbulence

The transport of energetic particles in a mean magnetic field and the presence of anisotropic magnetic turbulence are studied numerically, for parameter values relevant to the solar wind. A numerical realization of magnetic turbulence is set up in which we can vary the type of anisotropy by changing the correlation lengths lx, ly, lz. We find that for lx, ly lz, transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. Decreasing the lx/lz ratio down to 0.3, Gaussian diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Implications for energetic particle propagation in the solar wind and for diffusive shock acceleration are discussed

Large-Amplitude Velocity Fluctuations in Coronal Loops: Flare Drivers?

Recent space observations of coronal lines broadening during a flare occurrence suggest that unresolved nonthermal velocity rises well above the background level before the start of the flare, defined as the start of hard X-ray emission. Using a new shell model to describe the Alfvenic turbulence inside a coronal loop, it is shown that the occurrence of high values (of the order of 100 km s-1) of the large-scale fluctuating velocity can represent an efficient trigger to a nonlinear intermittent turbulent cascade and then to the generation of a burst of dissipated energy. The numerical results of the model furnish a well-supported physical explanation for the reason why large velocity fluctuations represent the flare trigger rather than the result of the later energy deposition

A SHELL MODEL TURBULENT DYNAMO

Turbulent dynamo phenomena, observed almost everywhere in astrophysical objects and also in the laboratory in the recent VKS2 experiment, are investigated using a shell model technique to describe magnetohydrodynamic turbulence. Detailed numerical simulations at very high Rossby numbers (α2 dynamo) show that as the magnetic Reynolds number increases, the dynamo action starts working and different regimes are observed. The model, which displays different large-scale coherent behaviors corresponding to different regimes, is able to reproduce the magnetic field reversals observed both in a geomagnetic dynamo and in the VKS2 experiment. While rough quantitative estimates of typical times associated with the reversal phenomenon are consistent with paleomagnetic data, the analysis of the transition from oscillating intermittent through reversal and finally to stationary behavior shows that the nature of the reversals we observe is typical of α2 dynamos and completely different from VKS2 reversals. Finally, the model shows that coherent behaviors can also be naturally generated inside the many-mode dynamical chaotic model, which reproduces the complexity of fluid turbulence, as described by the shell technique

SHORT-WAVELENGTH ELECTROSTATIC FLUCTUATIONS IN THE SOLAR WIND

Hybrid Vlasov-Maxwell simulations have been used recently to investigate the dynamics of the solar-wind plasma in the tail at short wavelengths of the energy cascade. These simulations have shown that a significant level of electrostatic activity is detected at wavelengths smaller than the proton inertial scale in the longitudinal direction with respect to the ambient magnetic field. In this paper, we describe the results of a new series of hybrid Vlasov-Maxwell simulations that allow us to investigate in more detail the generation process of these electrostatic fluctuations in terms of the electron-to-proton temperature ratio Te /Tp . This analysis gives evidence for the first time that even in the case of cold electrons, Te Tp (the appropriate condition for solar-wind plasmas), the resonant interaction of protons with large-scale left-hand polarized ion-cyclotron waves is responsible for the excitation of short-scale electrostatic fluctuations with an acoustic dispersion relation. Moreover, through our numerical results we propose a physical mechanism to explain the generation of longitudinal proton-beam distributions in typical conditions of the solar-wind environment

THE ROLE OF ALPHA PARTICLES IN THE EVOLUTION OF THE SOLAR-WIND TURBULENCE TOWARD SHORT SPATIAL SCALES

We present a numerical study of the kinetic dynamics of protons and alpha particles during the evolution of the solar-wind turbulent cascade, in which the energy injected in large-scale slab-type Alfvenic fluctuations is transferred toward short spatial scale lengths, across the proton skin depth. We make use of a hybrid Vlasov-Maxwell code that integrates numerically the Vlasov equation for both the ion species, while the electrons are considered as a fluid. The system evolution is investigated in terms of different values of the electron to proton and alpha particle to proton temperature ratios. The numerical results show that the previously studied kinetic dynamics of protons is not strongly affected by the presence of alpha particles, at least when they are present in low concentration. Our simulations not only provide a physical explanation for the generation of beams of accelerated particles along the direction of the ambient magnetic field for both protons and alpha particles, but also show that this mechanism is more efficient for protons than for alpha particles, in agreement with recent solar-wind data analyses

Where Does Fluid-like Turbulence Break Down in the Solar Wind?

Power spectra of the magnetic field in solar wind display a Kolmogorov law f –5/3 at intermediate range of frequencies f, say within the inertial range. Two spectral breaks are also observed: one separating the inertial range from an f –1 spectrum at lower frequencies, and another one between the inertial range and an f –7/3 spectrum at higher frequencies. The breaking of fluid-like turbulence at high frequencies has been attributed to either the occurrence of kinetic Alfven wave fluctuations above the ion-cyclotron frequency or to whistler turbulence above the frequency corresponding to the proton gyroradius. Using solar wind data, we show that the observed high-frequency spectral break seems to be independent of the distance from the Sun, and then of both the ion-cyclotron frequency and the proton gyroradius. We suppose that the observed high-frequency break could be either caused by a combination of different physical processes or associated with a remnant signature of coronal turbulence

Model for the spatio-temporal intermittency of the energy dissipation in turbulent flows

Modeling the intermittent behavior of turbulent energy dissipation processes both in space and time is often a relevant problem when dealing with phenomena occurring in high Reynolds number flows, especially in astrophysical and space fluids. In this paper, a dynamical model is proposed to describe the spatio-temporal intermittency of energy dissipation rate in a turbulent system. This is done by using a shell model to simulate the turbulent cascade and introducing some heuristic rules, partly inspired by the well known $p$-model, to construct a spatial structure of the energy dissipation rate. In order to validate the model and to study its spatially intermittency properties, a series of numerical simulations have been performed. These show that the level of spatial intermittency of the system can be simply tuned by varying a single parameter of the model and that scaling laws in agreement with those obtained from experiments on fully turbulent hydrodynamic flows can be recovered. It is finally suggested that the model could represent a useful tool to simulate the spatio-temporal intermittency of turbulent energy dissipation in those high Reynolds number astrophysical fluids where impulsive energy release processes can be associated to the dynamics of the turbulent cascade.Comment: 22 pages, 9 figure