# PS10 - Phys601/F11/Problem Set 10 Subject to upgrade note...

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Phys601/F11/Problem Set 10 Due November 23, 2011 Subject to upgrade; note new due date Midterm in class: Nov 16 Midterm take-home: ~ Nov 17-20 10.1H Geometric optics of MHD waves* This problem considers the geometric optics of an MHD wave about a magnetic X-point. “Magnetosonic waves” in a low pressure magneto-plasma satisfy the wave equation 2 2 2 t V ψ = . V is the Alfven velocity, here assumed varying slowly in position r = (x,y) as V = V ( r ), where V = B /( μ 0 ρ ) 1/2 , B is the magnetic field, μ 0 is μ 0 , and ρ is the mass density of the medium. Assume that ρ is a constant. For this problem, we are considering an ambient magnetic field which is an “X-point”. Assume that the magnetic field is derivable from a vector potential A z = Hxy. For normalization, set H 2 /( μ 0 ρ ) = 1. To be precise, V 2 = V.V . We are interested in ray trajectories about the X-point . Assume that the motion is 2-D only, ie, dz/dt = 0, k z = 0. Work in Cartesian coordinates to begin. Proceed as follows:

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PS10 - Phys601/F11/Problem Set 10 Subject to upgrade note...

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