Chaos and Complex Systems
	Particle transport processes in astrophysical plasmas. The usual method to calculate the transport coefficients is based on the hypothesis of local thermodynamical equilibrium (LTE), i.e. the distribution function of particles is everywhere maxwellian. In general astrophysical but also laboratory plasmas are far from being in equilibrium, since Coulomb collisions, which represent the main mechanism of relaxation, are often negligible, due to low densities and high temperatures which are typical in such plasmas. Nevertheless mechanisms of relaxation different from Coulomb collisions might be at work: in particular plasmas are often characterized by the presence of wave turbulence. The interaction of this turbulence with plasma particles can provide a relaxation mechanism, which can replaces Coulomb collisions. In these cases transport is usually called anomalous and anomalous transport coefficients can be determined. The importance of a non collisional transport theory in astrophysical plasmas can be illustrated with a couple of examples: (a) The transport of particles the Earth's magnetotail represents a key problem both in laboratory devices and in astrophysical plasma. When Coulomb collisions are negligible, particle diffusion is attributed to wave-particle interactions. In particular, particle transport in a magnetic field reversal in the presence of turbulence driven by tearing instability represents an important issue both because this could control the particle loss in fusion machines, particularly in reversed field pinch experiments, and because magnetic field reversals, where most of the energy dissipation takes place, are an almost ubiquitous structure of astrophysical plasma.

(b) In planetary magnetospheres, a substantial fraction of plasma comes from the solar wind. The transport of this plasma across the magnetopause is scarcely understood, although it appears to happen where a high magnetic turbulence level is observed. Also in situations where transport is mainly due to Coulomb collisions, we can find plasmas which are far from equilibrium: a clear example in such regard is represented by solar transition region; it lies between the chromosphere and the solar corona. The name choromosphere derives from the colourful appearance which it presents during a solar eclipse (a reddish annulus around the rim of the photosphere, the result of strong H-alpha emission originating there); during a total eclipse, when the sun's disk is covered by the moon, a pearly halo extending to a distance of several solar radii from the solar surface, also appears; this extended atmosphere of the sun is called corona and it displays a temperature 200 times hotter than the underlying layers. Between the upper cromosphere and the corona, there is the transition region; in this part the temperature jumps from 25000 K in the upper cromosphere to 10^6 K in corona in only a few thousand kilometers, showing steep temperature and density gradients. The study of the solar transition region is interesting from the general point of view of the plasma physics, because it represents a match between a collision-dominated plasma (in cromosphere) and a collisionless one (in corona). While the description of the transport by Coulomb collisions is adequate for the lower part of the solar transition region, these collisions become neglegible in the higher part; this means that in such situations particle distribution functions could be far from being maxwellian and the classical transport theory does not hold. Then, a kinetic description is needed and new methods have to be set up to study these plasmas.