• Kelvin-Helmholtz instability
• magnetic reconnection
• magnetosphere
• solar wind

The plasma state is usually referred as the fourth state of matter. In practice it is a collection of a very large number of charged particles, globally neutral, dominated by the electromagnetic forces where binary interactions are very weak. The matter in the Sun-Earth environment is in a plasma state. Thus space plasmas with direct in-situ measurments by space-craft constitute a natural laboratory for plasma physics. Around the 1970s data provided by satellites showed evident injection of hot solar wind particles into the magnetosphere, the magnetized structure surrounding our planet. In principle the magnetosphere should protect the Earth from outer particles. However this injection exists and it is made possible by magnetic reconnection, the only plasma instability able to change connections between magnetic field lines and to modify the magnetic field large scale topology. When magnetic reconnection takes place, it breaks an important plasma theorem called frozen-in law which has as main consequence that regions of plasma initially not connected will remain unconnected forever. During the periods in which the magnetic field associated to the solar wind is directed more or less northward, the role of a classical hydrodynamic instability, namely the Kelvin-Helmholtz instability, has been in past decades deeply investigated in order to understand its possible role in enhancing the process of plasma mixing. Kelvin-Helmholtz instability, leading to the formation of fully rolled-up vortices, is of hydrodynamic nature and it develops in the presence of a velocity variation (shear) across the interface between two types of fluids. A general way to modelize a plasma consists in treating it as a fluid (under appropriate conditions), and from knowledge of hydrodynamics we expect the developing of the KH instability at the flanks of the Earth’s magnetosphere because of such a shear velocity between the solar wind plasma and the magnetospheric one at rest. In the last years satellites have confirmed these expectations giving clear evidences of Kelvin-Helmholtz vortices at the flanks of the magnetosphere. Thus researchers, encouraged by the possibility to compare their results with satellite data, have started to improve numerical codes able to simulate the complex dynamics of the system. The numerical tool is essential for this problem because of its strong non-linearities, number of scales and frequencies involved, which prevent the development of fully analytical models.

Our work focuses on the study of the interaction between the solar wind and the magnetosphere at the Earth magnetospheric flanks. In particular it consists in the analysis of the results of a 3D simulation aimed at reproducing the dynamics of the system. The velocity, magnetic field and density have been chosen in order to reproduce at best the large scale configuration recorded by satellites. It is worth to notice that the 3D configuration is able to reproduce with a higher degree of realism the system of interest as well as to introduce effects not reproducible with a simpler 2D study, such as the high-latitudes stabilization of Kelvin-Helmholtz instability (with respect to the equatorial plane of the Earth magnetosphere). The first part of our analysis focuses on the understanding of the effects of this high-latitudes stabilization. In particular we find that the wavefronts of the Kelvin-Helmholtz instability tilt with respect to the equatorial plane (this behavior cannot emerge from 2D studies). Then, we focus on the reconnection events, aiming in particular at individuating their latitudinal distribution. We find magnetic field lines which change connections two or more times. Double-reconnected lines are particularly relevant because they are able to mix the two different types of plasma (magnetospheric and solar wind one) efficiently.

The thesis work is organized as follows. In Chapter 1 we give an introduction to the subject. In Chapter 2 we discuss the basic concepts of plasma physics. In Chapter 3 we deal with the process responsible for the injection of solar wind particles into the magnetosphere, the magnetic reconnection instability, while in Chapter 4 we introduce the classical theory of the magnetized Kelvin-Helmholtz instability. In Chapter 5 we give an overview of the system that we want to simulate. In Chapeter 6 we introduce the code used and we present the results of the analysis. Finally in Chapter 7 we summarize the results obtained and discuss about future perspectives.