Shock is a nonlinear plasma wave generated by plasma flow (Burgess, 1995). This wave is irreversible (entropyincr= easing), and it causes a transition from supersonic (upstream, Mach number = M>1) to subsonic (M<1) flow. Shocks are thus places where plasma and = field go through dramatic changes in density, temperature, field strength, = and/or flow speed. If there is no plasma flow through the surface (Un <&= gt; 0) or there is no dissipation and compression across it, we talk about = discontinuity only, not shock.
=20The problem with space plasma is that there are several "typical&qu= ot; information speeds: for example, there are three different MHD wave types: fast, inte= rmediate, and slow. Furthermore, space plasmas are collisionless, which complicates things even more. The following table lists the p= ossible discontinuities and shocks under ideal MHD. The oblique shocks, div= ided into three categories, corresponds to the MHD waves listed above.
= =20Possible types of discontinuities in ideal M= HD 



Contact discontinuity  Un =3D 0, Bn <> 0  Density jump arbitrary, but pressure and all= other quantities are continuous 
Tangential discontinuity  Un =3D 0, Bn =3D 0  Plasma pressure and field change, maintainin= g static pressure balance 
Rotational discontinuity  Un =3D Bn/sqrt(mu x ro)  Largeamplitude intermediate wave; in isotro= pic plasma, field and flow change direction, but not magnitude 
Shock waves  Un <> 0  Flow crosses surface of discontinuity accomp= anied by compression and dissipation 
Parallel shock  Bt =3D 0  Magnetic field unchanged by shock 
Perpendicular shock  Bn =3D 0  Plasma pressure and field strength increase = at shock 
Oblique shocks  Bt <> 0, Bn <> 0  Fast shock 
U =3D flow velocity, B =3D magnetic field; n= , t refer to normal and tangential directions, respectively 
Many solar win= d discontinuities are tangential. In the absense of reconnection, magnetopause and crosstail current are also= tangential discontinuities. Of the shocks, fast shocks are the most typica= l in solar system plasmas. = For example, Earth's bow shock is a fast shock, as are also most= interplanetary shocks in the sol= ar wind.
=20An important factor influencing the shock behavior is the shock geometry=
, i.e., direction of the upstream magnetic field. It is measured using an a=
ngle T between the field and the shock normal. T =3D 0&de=
g; gives parallel shock, and T =3D 90°
Shock strength tells the amount of energy processed by the shock. It is = measured with the Mach number. Higher Mach number shocks are called supercr= itical as opposed to subcritical shocks. Bow shock is an example of the for= mer type (Alfven Mach number 1.510), while interplanetary shocks are of th= e latter type.
=20In all shock formations there is, by definition, irreversible dissipatio= n that transforms the ram energy of the plasma flow into thermal energy. Fo= r subcritical shocks this can happen because of effective, or anomalous, re= sistivity and viscosity due to waves (as opposed to collisions). The waves = grow due to some instability, which will be driven by departure from equili= brium of the particle distribution function.
=20However, in supercritical shocks anomalous resistivity cannot provide th= e required dissipation. Furthermore, ions are heated much more than electro= ns, which cannot be explained by the currentdriven instabilies invoked for= anomalous effects. It has been shown that reflection of ions from = the shock are important in these cases. In quasiperpendicular sho= cks, the shock field spreads out the ion distribution function, which will = provide free energy for ion instabilities downstream.
=20Planetary bow shock have upstream regions called foreshocks, created by = energetic particles that travel upstream from the bow shock. These regions = are full of interesting waves and particles.
=20Particle acceleration processes are typical at shocks.
=20