Average dielectric properties of discrete random media using multiple scattering theory

Abstract

Using rigorous multiple scattering theory in determining the average or bulk dielectric properties of discrete random media is the objective of this communication. The random medium is modeled as a random distribution of identical, spherical scatterers imbedded in an homogeneous unbounded background medium. At high scatterer concentration, the form of the radial distribution function becomes important; two forms are considered here, viz., virial series and the self-consistent form. The average loss tangent of the bulk medium is computed as a function of frequency and scatterer concentration, and compared with a frequently used mixture formula, e.g., Maxwell-Garnett. The results show that multiple scattering losses are significant at the higher concentrations and must be accounted for when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ka \gtrsim 0.05</tex> . The theory and the computational procedure can thus he used as a mixture formula for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ka</tex> in the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0 &lt; ka \lesssim 5.0</tex> and concentrations in the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.01 &lt; c \lesssim 0.40</tex> .