Wave scattering by small bodies is of great interest in theory and for applications. An incomplete list of problems for which wave scattering by small bodies is of prime importance includes: radio wave scattering by rain and hail, light scattering by cosmic dust, light scattering in colloidal solutions, light propagation in muddy water, wave scattering by small inhomogeneities in a medium. We will show that the skin effect for thin wires and radiation from small holes are also dependent on wave scattering by small bodies. The number of examples is practically unlimited. The theory was originated by Rayleigh (1871) who contributed to this field until his death (1919). Rayleigh understood that the main term in the scattering amplitude in the problem of wave scattering by a small body with diameter much less than the wavelength of the exterior field can be described as dipole radiation. J. J. Thomson (1893) realized that for a small perfect conductor the magnetic dipole radiation is of the same order as the electric dipole radiation. Some efforts were made in order to develop an algorithm for finding the expansion of the scattered field in powers of ka, where k is the wave number and a is the characteristic dimension of the scatterer, ka ⋊ 1 (Stevenson [31], Kleinman [14]). Since in many cases the first term of this expansion already provides a good approximation we will only discuss this first approximation.


Small Body Wave Scattering Scattered Field Polarizability Tensor Initial Field 
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Copyright information

© Springer-Verlag New York, Inc. 1982

Authors and Affiliations

  • Alexander G. Ramm
    • 1
  1. 1.Department of MathematicsKansas State UniversityManhattanUSA

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