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shock - 1 Shock Waves in the Solar Wind A shock wave is...

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Unformatted text preview: 1 Shock Waves in the Solar Wind A shock wave is loosely defined as a very strong pressure wave that propagates at speed in excess of the local sound speed. Material passing through a shock is slowed, compressed, and heated. Shock waves can be created for a variety of reasons, but in space is normally a consequence of two plasma populations moving at very different speeds. For example, variations in the solar wind speed can result in a high-speed stream of plasma overtaking a slower stream, resulting in the creation of a shock wave. At Earth orbit, the dipolar magnetic field acts as a obstacle to the solar wind, resulting in the creation of a stationary bow wave that acts to slow and divert the flow. In these notes we will consider the both the generation as well as the macroscopic properties of a hydrodynamic shock wave. We will conclude with some remarks about effect of a magnetic field. Shock Wave Generation A shock wave is generated when a high velocity fluid is rapidly slowed or diverted by an obstacle to the flow. An example is the solar wind and the Earth’s magnetosphere. Because the solar wind is moving at speed much greater than the local sound speed, a bow wave is formed around the magnetosphere that abruptly slows and heats the plasma. The process of shock formation can be illustrated by consideration of a uniform plasma plasma that is terminated at an initially stationary piston (see Figure 1A). For times t < 0, the plasma and the piston are at rest. If the pressure of the plasma is P , and the density is ρ , then it follows that the initial sound speed C s is C s ≡ p γP /ρ , and where γ is the ratio of specific heats (5 / 3 for an ideal three-dimensional compression). At time t = 0, the piston moves to the left at a speed U x = δU p 1 << C s (see Figure 1B). It follows that the plasma near the wall will likewise move at a speed δU p 1 . The information that the wall is now moving is transmitted into the plasma by a sound wave that moves with a speed Cs0. Put differently, the sound wave accelerates the plasma up to the speed δU p 1 as is required by the new boundary condition....
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shock - 1 Shock Waves in the Solar Wind A shock wave is...

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