Penetration depth in lossy materials: a closed-form expression for cylindrical phased array antennas

The purpose of the paper is to present a closed-form expression for the penetration depth associated with cylindrical phased array antennas. The model configuration is illustrated with respect to a cylindrical coordinate system (/spl rho/,/spl phi/,z). The model consists of an infinitely long cylinder with a radius a. The surface of the cylinder (/spl rho/=/spl rho//sub 0/) is divided into N apertures with the center of each aperture located at /spl phi//sub n/ =2/spl pi/n/N, n=0,1,...N-1. The width of an aperture is 2/spl phi//sub a/, so /spl phi//sub a/=/spl pi//N. The inside of the cylinder contains a homogeneous lossy material with conductivity /spl sigma/, permeability /spl mu/, and permittivity /spl epsiv/. The study is of interest in RF heating of the interiors of human bodies.<>