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.

The waiting time distribution for solar flares has been considered. Using Geostationary Operational Environmental Satellite X-ray data, we show that a local Poisson hypothesis for solar flares is not consistent with observations, while the observed distribution is well reproduced by a Le ´vy function, which displays asymptotically a power-law tail. The origin of the observed waiting time distribution is then attributed to the fact that the physical process underlying solar flares is statistically self-similar in time and is characterized by a certain amount of "memory."

On the basis of observations of solar granulation obtained with the New Solar Telescope of Big Bear Solar Observatory, we explored proper motion of bright points (BPs) in a quiet-sun area, a coronal hole, and an active region plage. We automatically detected and traced BPs and derived their mean-squared displacements as a function of time (starting from the appearance of each BP) for all available time intervals. In all three magnetic environments, we found the presence of a super-diffusion regime, which is the most pronounced inside the time interval of 10-300 s. Super-diffusion, measured via the spectral index, γ, which is the slope of the mean-squared displacement spectrum, increases from the plage area (γ = 1.48) to the quiet-sun area (γ = 1.53) to the coronal hole (γ = 1.67). We also found that the coefficient of turbulent diffusion changes in direct proportion to both temporal and spatial scales. For the minimum spatial scale (22 km) and minimum time scale (10 s), it is 22 and 19 km² s^–1 for the coronal hole and the quiet-sun area, respectively, whereas for the plage area it is about 12 km² s^–1 for the minimum time scale of 15 s. We applied our BP tracking code to three-dimensional MHD model data of solar convection and found the super-diffusion with γ = 1.45. An expression for the turbulent diffusion coefficient as a function of scales and γ is obtained.

We study the acceleration of electrons and protons interacting with localized, multiple, small-scale dissipation regions inside an evolving, turbulent active region. The dissipation regions are Unstable Current Sheets (UCS), and in their ensemble they form a complex, fractal, evolving network of acceleration centers. Acceleration and energy dissipation are thus assumed to be fragmented. A large-scale magnetic topology provides the connectivity between the UCS and determines in this way the degree of possible multiple acceleration. The particles travel along the magnetic field freely without loosing or gaining energy, till they reach a UCS. In a UCS, a variety of acceleration mechanisms are active, with the end-result that the particles depart with a new momentum. The stochastic acceleration process is represented in the form of Continuous Time Random Walk (CTRW), which allows to estimate the evolution of the energy distribution of the particles. It is found that under certain conditions electrons are heated and accelerated to energies above 1 MeV in much less than a second. Hard X-ray (HXR) and microwave spectra are calculated from the electrons' energy distributions, and they are found to be compatible with the observations. Ions (protons) are also heated and accelerated, reaching energies up to 10 MeV almost simultaneously with the electrons. The diffusion of the particles inside the active region is extremely fast (anomalous super-diffusion). Although our approach does not provide insight into the details of the specific acceleration mechanisms involved, its benefits are that it relates acceleration to the energy release, and it well describes the stochastic nature of the acceleration process.Comment: 37 pages, 10 figures, one of them in color; in press at ApJ (2004