sol10-f7 - small at least at the wavenumbers or wavelengths...

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Astro 405/505, fall semester 2007 Homework, 10th set, solutions Problem 19: Collisionless shocks I frst calculate the sound speed and the AlFv´ en velocity. c s 11 . 7 km / s v A 6 . 5 km / s The shock velocity is about 3 orders oF magnitude higher than these two, so we have a strong shock. The shock thickness should be oF the order oF the mean Free path For scattering on magnetic turbulence. δ r g ± B 0 δB ² 2 = V Ω g ± B 0 δB ² 2 = m e,p c V B 0 e ( δB ) 2 where V ( V s ) is the velocity oF SN particle that run into the ambient medium. The pro- tons and other ions apparently determine the shock thickness. The typical size oF supernova remnants is about 10 pc in radius, as given by the charateristic sizes at which the blast wave turns in and out oF the Sedov phase. The shock thickness should be a small Fraction oF that, e.g. down by a Factor 0.001. Then 3 · 10 16 cm = m p c V B 0 e ( δB ) 2 δB 0 . 003 μ G The magnetic ±uctuations are at a level oF one per mille oF the homogeneous feld and thus
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Unformatted text preview: small, at least at the wavenumbers or wavelengths in resonance with the particles. The energy density oF the waves is about 10-6 times that oF the background feld, making linear AlFv´ en waves are good approximation. However, we have only probed the ±uctuations at the wavelength λ ≈ 2 · 10 12 cm. Problem 20: Wave-particle interactions In both cases there is no single reFerence Frame that is comoving with the waves, essentially because di²erent waves have di²erent velocities. In all Frames oF reFerence the particles will thereFore see electric felds, so their energy changes. Typically the direction oF change is random, so some particles lose by running against an electric feld, and others gain by running along the electric feld. The change in energy is thereFore largely di²usive....
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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