The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.

We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

In this paper, the Sun and its behavior are studied by means of complex networks. The complex network was built using the Visibility Graph algorithm. This method maps time series into graphs in which every element of the time series is considered as a node and a visibility criterion is defined in order to connect them. Using this method, we construct complex networks for magnetic field and sunspots time series encompassing four solar cycles, and various measures such as degree, clustering coefficient, mean path length, betweenness centrality, eigenvector centrality and decay exponents were calculated. In order to study the system in several time scales, we perform both a global, where the network contains information on the four solar cycles, and a local analysis, involving moving windows. Some metrics correlate with solar activity, while others do not. Interestingly, those metric which seem to respond to varying levels of solar activity in the global analysis, also do in the moving windows analysis. Our results suggest that complex networks can provide a useful way to follow solar activity, and reveal new features on solar cycles.

Wave–particle interactions are believed to be one of the most important kinetic processes regulating the heating and acceleration of solar wind plasma. One possible explanation for the observed preferential heating of alpha (He⁺²) ions relies on a process similar to a second-order Fermi acceleration mechanism. In this model, heavy ions are able to resonate with multiple counter-propagating ion-cyclotron waves, while protons can encounter only single resonances, resulting in the subsequent preferential energization of minor ions. In this work, we address and test this idea by calculating the number of plasma particles that are resonating with ion-cyclotron waves propagating parallel and antiparallel to an ambient magnetic field in a proton/alpha plasma with cold electrons. Resonances are calculated through the proper kinetic multispecies dispersion relation of Alfvén waves. We show that 100% of the alpha population can resonate with counter-propagating waves below a threshold in the differential streaming between protons and He⁺² ions, where U ₀ = −0.532, a = 1.211, β ₀ = 0.0275, and b =0.348 for isotropic ions. This threshold seems to match with constraints of the observed ΔU _αp in the solar wind for low values of the plasma beta (β _p ). Finally, it is also shown that this process is limited by the growth of plasma kinetic instabilities, a constraint that could explain alpha-to-proton temperature ratio observations in the solar wind at 1 au.

In this paper, we study solar magnetic activity by means of a complex network approach. A complex network was built based on information on the space and time evolution of sunspots provided by image recognition algorithms on solar magnetograms taken during the complete 23rd solar cycle. Both directed and undirected networks were built, and various measures such as degree distributions, clustering coefficient, average shortest path, various centrality measures, and Gini coefficients calculated for all them. We find that certain measures are correlated with solar activity and others are anticorrelated, while several measures are essentially constant along the solar cycle. Thus, we show that complex network analysis can yield useful information on the evolution of solar activity and reveal universal features valid at any stage of the solar cycle; the implications of this research for the prediction of solar maxima are discussed as well.