EAD234B_Homework3_2010

EAD234B_Homework3_2010 - EAD 234B: E&M Homework #3 Due...

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EAD 234B: E&M Homework #3 Due Thursday, April 22, 2010 (1) We wish to consider the case of waveguides containing plasmas. To simplify the calculations, we will assume the waveguides are made from perfect conductors. (a) For simplicity, we consider the case of slow waves, which implies that Show that the resultant equation to be solved is then or subject to the appropriate boundary conditions. In the above, where we have made use of the cold plasma dielectric tensor in cylindrical coordinates, neglecting ion motion and have also assumed the magnetic field is aligned along the z- axis which we will subsequently take to be the axis of a perfectly conducting cylindrical waveguide. In addition, we will assume a homogeneous plasma. (b) Then, assuming wavelike solutions which are separable, show that this results in a Bessel equation for () ,,, rz t φθ . (c) We now look at a simple case and assume that the steady magnetic field is infinite. Show that the resultant dispersion relationship is where p n ν is the ν th zero of J n ( x ) = 0. Sketch this together with the standard empty waveguide
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This note was uploaded on 05/14/2010 for the course EAD 234 taught by Professor Ncl during the Spring '10 term at École Normale Supérieure.

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EAD234B_Homework3_2010 - EAD 234B: E&M Homework #3 Due...

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