Relazione su invito
Plasma turbulence: a beautiful and complex mathematical problem with a wide spectrum of physical applications.
Plasma represents 99.9% of the matter in the universe. According to the local plasma parameters either a fluid description or a kinetic one can account for the dynamical evolution of the plasma. Also when a fluid description is possibly used, almost always Reynolds and Lundquist numbers are so high that the plasma is in a turbulent state. Moreover in a lot of situations, due to its extremely low collisionality, the plasma is far from thermodynamic equilibrium and only a kinetic description can account for the plasma properties. Also in these cases, due to the intrinsic nonlinearity of the equations which model the plasma behaviour, a lot of beautiful mathematical problems arise. Apart from the wide spectrum of astrophysical applications, understanding non linear plasma physics is of primary interest in the perspective of achieving laboratory nuclear fusion both through magnetic field confinement and through inertial plasma confinement. Space experiments have given us the possibility to perform $in situ$ observations in Solar Wind, which have furnished physical tests to Mathematical models for plasma turbulence which should not be realised in earth laboratories. Solar Wind is now used as a space Wind tunnel, where plasma turbulence can be studied both from the point of view of fluid description and from the point of view of kinetic collisionless description. In the talk some of the more relevant results obtained in the theory of plasma turbulence, using both advanced techniques of analysis of space data and high-performance computer simulations will be presented and discussed.