The Universe is a great laboratory for studying natural plasmas. In the case of the solar system, the Sun is the source of the interplanetary plasma that spreads at a rate between 300 km/s and 1000 km/s. This plasma may encounter several obstacles during its trip: asteroids, comets, or planets. The most interesting obstacles for a physicist are the magnetized planets. With their magnetosphere, these planets significantly increase their cross-section and therefore their interaction with the solar wind; for example the Earth's magnetosphere is about 150 times larger than the Earth.

The system constituted by the solar wind plus the magnetosphere is naturally in a state of dynamic equilibrium, with a relatively thin interface between them which is called bow shock (see Figure 6.1). Behind this shock, there is a turbulent area called the magnetosheath which serves as a transition to the magnetosphere that is reached by crossing a discontinuity called the magnetopause. There is another type of interface for the solar wind: the terminal shock at the edge of the solar system (~100AU) when the wind speed becomes subsonic. Beyond the terminal shock, we have the heliosheath and then the heliopause (the interface where the solar wind is stopped by the interstellar medium). To understand the nature of these shocks and discontinuities, it is necessary to study the evolution of a thin interface in a plasma; that is the subject of this Chapter. To do this, we will use the macroscopic description of the standard compressible MHD.

Rankine–Hugoniot Conditions

The method generally used to get the conditions of a plasma around a discontinuity is to integrate the conservation laws – that we established in

Chapter 3 – around the discontinuity, in the ideal and inviscid limit. In this situation, we recall that, for standard MHD,

In the case of a thin discontinuity,2 in practice a surface S, the only measurable local changes in the plasma are perpendicular to the discontinuity, i.e. along the normal n of S.