The asymptotic approach to the problem of high-frequency diffraction by elongated bodies is discussed in this work. The classical expansion is shown to require the frequencies to be too high for it to be applicable. Attempts to improve the approximating properties of the asymptotic methods are discussed. It is shown that effective approximations appear under the supposition that the squared transverse dimension of the body is proportional to its longitudinal size measured in wavelengths. This is referred to herein as the case of strongly elongated body and is examined in detail. It is assumed that the body has a rotational symmetry and can be well approximated by a spheroid. The cases of axial incidence and that of incidence at a grazing angle to the axis are considered. Both the asymptotics of the induced currents on the surface and of the far field amplitude are developed. Comparison with numerical results for a set of test problems shows that the leading terms of the new asymptotics provide good approximation in a uniform manner with respect to the rate of elongation. Some effects typical for scattering by elongated bodies are discussed.
Ivan Viktorovitch Andronov,
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