Shock Waves in Plasmas; Magnetic Field Effects

We have noted the existence of three types of waves in plasma with magnetic fields. These waves propagate as a fluid wave and may possibly steepen to form shock waves as in OFM. In the plasma medium with magnetic fields present we need to determine the following: (1) What are the speeds of (propagation or flow speeds where there is formation of) shock waves and (2) What are the changes in properties that occur across the shock waves in plasmas. In the following basic considerations, for simplicity we will assume one-dimensional flow: f(x)  0, but f(y) = f(z) = 0.
1. Hydromagnetic shock equations
We consider the following orthogonal coordinate situation (Figure 8.14) with incoming flow in the x-direction ...

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