Shocks
Shocks are transition layers across which there is a transport of particles. There are three types of shocks in MHD: slow-mode, intermediate and fast-mode shocks.
Intermediate shocks are non-compressive (meaning that the plasma density does not change across the shock). A special case of the intermediate shock is referred to as a rotational discontinuity. They are isentropic. All thermodynamic quantities are continuous across the shock, but the tangential component of the magnetic field can "rotate". Intermediate shocks in general however, unlike rotational discontinuities, can have a discontinuity in the pressure.
Slow-mode and fast-mode shocks are compressive and are associated with an increase in entropy. Across slow-mode shock, the tangential component of the magnetic field decreases. Across fast-mode shock it increases.
The type of shocks depend on the relative magnitude of the upstream velocity in the frame moving with the shock with respect to some characteristic speed. Those characteristic speeds, the slow and fast magnetosonic speeds, are related to the Alfvén speed, and the sonic speed, as follows:
where is the Alfvén speed and is the angle between the incoming magnetic field and the shock normal vector.
The normal component of the slow shock propagates with velocity in the frame moving with the upstream plasma, that of the intermediate shock with velocity and that of the fast shock with velocity . The fast mode waves have higher phase velocities than the slow mode waves because the density and magnetic field are in phase, whereas the slow mode wave components are out of phase.
Read more about this topic: Shocks And Discontinuities (magnetohydrodynamics)
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