volume | PIER Journals

2010-10-22

Electromagnetic Wave Scattering by Many Small Particles and Creating Materials with a Desired Permeability

Alexander G. Ramm

Professor Alexander G. Ramm

Mathematics Department

Kansas State University

USA

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Progress In Electromagnetics Research M, Vol. 14, 193-206, 2010

doi:10.2528/PIERM10091603 | Google Scholar

Abstract

Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a → 0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium. While the initial medium has a constant permeability μ0, the limiting medium, obtained as a result of embedding many small particles with prescribed boundary impedances, has a non-homogeneous permeability which is expressed analytically in terms of the density of the distribution of the small particles and their boundary impedances. Therefore, a new physical phenomenon is predicted theoretically, namely, appearance of a spatially inhomogeneous permeability as a result of embedding of many small particles whose physical properties are described by their boundary impedances.

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Alexander G. Ramm, "Electromagnetic Wave Scattering by Many Small Particles and Creating Materials with a Desired Permeability," Progress In Electromagnetics Research M, Vol. 14, 193-206, 2010.
doi:10.2528/PIERM10091603

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