Etude de la cinétique des particules dans les couches frontières de la magnétosphère terrestre

The magnetosphere

The Earth’s magnetosphere is a region in outer space, which is filled with free ions and electrons from both the solar wind and the Earth’s ionosphere. It is a complex system whose structure and behavior is controlled by two factors. The first is the terrestrial magnetic field, supposed to be generated via dynamo effect by currents flowing in the Earth’s core. Outside the Earth this field has the form of a dipole field in first approximation, aligned approximately with the Earth’s spin axis. The second factor is the solar wind, a fully ionized plasma that streams continuously outward from the Sun into the solar system at speeds of about 300–800 kilometers per second and carries a large-scale interplanetary magnetic field (IMF). The boundary of the magnetosphere on the dayside is ellipsoidal, at a distance of about 10-15 RE to the Earth; while on the night side it approaches roughly a cylinder with a radius 20-25 RE due to the compression of solar wind plasma. The tail region stretches well past 200 RE. A overall schematic view of the magnetosphere is shown in Fig 1.1 (Kivelson and Russell, 1995). 

The bow shock and the magnetosheath

 When an object or disturbance moves faster than the information about it can be propagated into the surrounding medium, medium near the disturbance cannot react or get out of the way before the disturbance arrives. Hence a compressed front forms and is called a shock. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an 20 extremely rapid rise in parameters of medium such as pressure, temperature and density. The solar wind plasma (Parker, 1958) travels usually at speeds up to 200-800km/s, which are faster than any fluid plasma wave relative to the magnetosphere. Therefore a standing shock wave forms around the magnetosphere. The standoff distance of the bow shock is about 15 RE on the dayside of the Earth. Fig.1.1 Three-dimensional schematic of the magnetosphere (Kivelson and Russell, 1995). In a viewpoint of magnetohydrodynamics, a shock is treated as a discontinuity, i.e., the thickness of its transition layer is regarded as zero. In this approximation, conservation of mass, momentum, and energy, together with the Maxwell equations lead to a set of relations between the upstream and the downstream quantities, known as the Rankine – Hugoniot jump relations. The magnetohydrodynamic problem is 21 more complicated than the corresponding gas dynamic problem because the magnetized plasma supports three independent magnetoacoustic wave modes: fast wave, slow wave and the intermediate wave. The bow shock is a fast shock. The properties of collisionless plasma shock waves depend primarily on two parameters. One is the Mach number of the shock wave, the ratio of upstream velocity to Alfvén speed, which is VA  B0 /  , where B0 is the magnetic field strength,  is the fluid density, and  is the magnetic permeability (in meter-kilogram-second units); for the terrestrial bow shock this is usually in the range from ~3 up to 10. The second is the propagation angle, or the angle between the upstream magnetic field and the normal to the shock surface. Across the surface of the bow shock, this angle ranges from 900 to 00 , i.e. from quasi-perpendicular to quasi-parallel. For a quasi-parallel shock, the particles escape upstream from the shock relatively easy, gyrating along the filed lines. The region of space upstream of the bow shock, magnetically connected to the shock and filled with particles backstreaming from the shock is known as the foreshock (Eastwood et al., 2005). It is not directly the solar wind plasma which constitutes the boundary of the magnetosphere but the strongly heated and compressed plasma behind the bow shock, which is called the magneosheath. The magnetosheath is formed mainly from decelerated and deflected solar wind, with a small contribution of plasma from the magnetosphere. Because the nature of the bow shock depends on the orientation of the interplanetary magnetic field with respect to the local bow shock normal, the properties of the magnetosheath plasma just behind the bow shock depend also on whether the shock is quasi-perpendicular or quasi-parallel. In general, the magnetosheath tends to be in a more turbulent state behind the spatially extended quasi-parallel bow shock than it is behind the quasiperpendicular shock. Inside the magnetosheath, the direction of the magnetic field changes from parallel with the IMF in the outer region to drape around the blunt inner boundary, which is called the.magnetopause. Meanwhile, the average flow direction deviates from the 22 direction along the Sun-Earth line such that the plasma flows around the magnetopause. The velocity downstream of the bow shock is subsonic; but it increases again to supersonic speeds around the magnetopause flanks. In addition, the magnetosheath plasma develops a pronounced temperature anisotropy behind the bow shock that increases toward the magnetopause and is more pronounced in the ions than in the electrons.

The magnetopause

 The existence of magnetopause (Chapman and Ferraro, 1931), the inner boundary of the magnetosheath, is a direct consequence of solar wind interaction with a magnetized planet. It is formed at a distance where the solar wind dynamic pressure equals the magnetic pressure of Earth’s field. At this location, typically around 8 – 11 RE away on the Earth – Sun line on the dayside, the Earth’s intrinsic dipolar magnetic field is separated from the ambient magnetosheath field. Ampere’s law then tells us that a sheet of electrical current, which is called the Chapman-Ferraro current, must develop to cancel the Earth’s field outside. The magnetopause is constantly in motion. Observations from ISEE spacecraft indicate that the velocity of magnetopause motion is quite variable ranging from about 3 to over 40 km/s and typically being about 20 km/s. The motion of the magnetopause seems to be driven by pressure fluctuations in the solar wind or the Kelvin- Helmholtz instability. Classical theory of interaction between the solar wind and the magnetosphere predicts the magnetopause to be an impenetrable boundary separating cold plasmas on magnetosheath magnetic field lines from hot tenuous plasmas on magnetospheric magnetic field lines. But in fact, observations indicate that a boundary layer of magnetosheath-like plasmas can be found just inside all regions of the magnetopause. These observations are evidence for the entry of magnetosheath plasma into the magnetosphere. A wide variety of processes, including magnetic reconnection, finite 23 Larmor radius effects, diffusion due to resonant interaction of ions with plasma waves, the Kelvin-Helmholtz instability and impulsive penetration, have been proposed to account for the transfer of solar wind mass into the magnetosphere, and the escape of magnetospheric particles into the magnetosheath.