Graduate Thesis Or Dissertation
 

The propagation of waves and pulses in the presence of conical structures

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/794080689

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  • The electromagnetic field in a cone of arbitrary slant height with a symmetrically placed time harmonic ring source is studied. Through the use of the modified Helmholtz equation as an intermediate, we obtain the solution of the semi-infinite cone directly from the finite cone. To demonstrate the need for the modified Helmholtz equation a simple example is used in which the solution is known. The Green function is derived from a well known summation formula involving the eigenvalues and eigenfunctions, which are determined from the roots of certain Legendre and Bessel functions. The results obtained here for the semi-infinite cone are compared with those obtained by Buchholz [4], and the special case Ѳ0 = π/2 is compared with a double ring in free space. In both cases the results are in agreement. Once the results have been obtained for the time harmonic case, they are generalized by Laplace transform theory to arbitrary time dependency. This is accomplished by finding the field for a "Dirac" pulse at time t and integrating the product of the pulse function and the "Dirac" pulse field with respect to time.
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