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Unformatted text preview: Astro 405/505, fall semester 2007 Homework, 7th set, solutions Problem 13: Collisionless shocks a) Neutral gas can interact only by neutral-neutral collisions, which are also required to col- lisionally ionize it. Ionized gas has more ways of interaction, by Coulomb collisions and collectively through electromagnetic fields. Ionized gas will therefore adapt more quickly, and therefore the shock thickness will be smaller. b) Electrons suffer a much larger acceleration in electromagnetic fields, and so their mean free path is smaller. The different mean free paths of electrons and ions leads to a certain charge separation and currents, and hence to electric and magnetic fields that mediate the shock transition. Problem 14: Fourier transformation If the sound speed depends on the frequency ω or wavenumber k , I can not write the solution as a Fourier integral depending on y = x ± c s t , because y now depends on k . However, individual waves are still partial solutions to the wave equation,...
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