Problem 10 - To keep things simple you may assume(though...

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Phys761/F10/Hassam/Problem 10 10.1 Rederive the plasma wave from the 2-fluid equations as was done in class, except this time do not assume that the ions are relatively immobile; ie, keep the ion response. This will answer some of the questions that came up today; in particular, there was the question that even though the plasma wave as derived was self-consistent as A solution, there may be OTHER solutions that were missed. This is possible. Keeping all the terms will show (a) that the ion response is indeed negligible (for massive ions, but not for positrons) and (b) that there are no other modes.
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Unformatted text preview: To keep things simple, you may assume (though you don’t have to) that the pressure terms in the momentum equations can be ignored. It is also useful to treat the ions and electrons symmetrically and express each n ~ in terms of k.E ~ before plugging into Gauss’ Law. 10.2 Rederive the electromagnetic wave (transverse E x field) as was done in class by neglecting the ion u xi ~ motion. Having obtained the mode eigenvector and mode frequency by using this approximation, now prove self-consistently that |u xi ~ | << |u xe ~ |, for massive ions....
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