set10-f7 - B . Given that requirement for B , argue whether...

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Astro 405/505, fall semester 2007 Homework, 10th set, return before Friday, November 16, 4pm. Don’t forget to give your name. Problem 19: The thickness of collisionless shocks Collisionless shocks have a thickness that is given by the mean free path for the interaction between the upstream and the downstream plasmas. For a homogeneous interstellar magnetic ±eld B 0 3 μ G, an ISM temperature T 10 4 K, one hydrogen atom per cc in the upstream medium, and a supernova remnant shock with V s 10 4 km/s calculate the sonic and the Alfv´ enic Mach numbers, M s and M A . Are we dealing with a strong shock, for which both numbers would be much larger than unity? Estimate the shock thickness as a function of the resonant ²uctuations in the magnetic ±eld, δB . To make the blastwave picture of supernova remnants viable, the shock thickness must be much smaller than the physical size of the remnant. Turn this into a requirement for
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Unformatted text preview: B . Given that requirement for B , argue whether or not the treatment of the uctuating magnetic eld as superposition of linear (small-amplitude) Alfv en waves may be justied. Problem 20: Wave-particle interactions We discussed in class that the electric-eld component of Alfv en waves vanishes, if one consid-ers them in a reference frame comoving with the wave, with velocity V A . In that case charged particles will be scattered without change in energy. a) Discuss what would happen if both forward and backward moving Alfv en waves existed. b) What would happen if the phase velocity of the waves was a function of k, as is the case for Whistler waves (a solution of the MHD equations for > g )?...
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