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set10-f7

set10-f7 - δB Given that requirement for δB 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: δB . Given that requirement for δB , argue whether or not the treatment of the ²uctuating magnetic ±eld as superposition of linear (small-amplitude) Alfv´ en waves may be justi±ed. 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 ω > Ω g )?...
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