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Kildal, Design of hat fed reflector antennas using FDTD, Proc EMB 98Electromagnetic Computations for Analysis and Design of Complex Syst, Linkoping, Sweden, Nov. 1998. 1999 John Wiley & Sons, Inc. CCC 0895-247799 TRANSIENT SCATTERING BY CONDUCTING CYLINDERS IMPLICIT SOLUTION FOR THE TRANSVERSE ELECTRIC CASE Sadasiva M. Rao, 1 Douglas A. Vechinski, 1 and Tapan K. Sarkar 2 1 Department of Electrical Engineering Auburn University Auburn, Alabama 36849 2 Department of Electrical Engineering and Computer Science Syracuse University Syracuse, New York 13244-1240 Recei ed 26 September 1998 ABSTRACT: In this work, we present an implicit solution of the time-domain integral equation to calculate the induced current profile on ( ) infinite conducting cylinders illuminated by a trans erse electric TE incident pulse. A detailed description of the numerical procedure along with representati e results are presented for two types of integral equa- ) ( ) ) tions, iz. 1 the electric field integral equation EFIE , and 2 the ( ) magnetic field integral equation HFIE . 1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 129134, 1999. Key words: transient scattering; conducting cylinders; integral equations 1. INTRODUCTION Recently, a numerically efficient, implicit solution scheme was proposed to solve the time-domain integral equation arising in transient electromagnetic scattering problems. This approach was successfully applied to conducting cylinders Ž . transverse magnetic case 1 , arbitrary wires 2 , and arbi- trarily shaped conducting bodies 3 . Note that the implicit solution scheme provides a stable solution even at late times, which is one of the major advantages. In this work, we extend the implicit solution scheme to the transverse electric case of two-dimensional conducting cylin- ders. For the numerical solution, we consider both the elec- Ž . tric field integral equation EFIE and the magnetic field Ž . integral equation HFIE . The EFIE case is considered for the sake of completeness, whereas the HFIE solution is required to extend this technique to dielectric scatterers. Further, we note that the EFIE is applicable to both open and closed contours, whereas the HFIE is applicable to closed cylinders only. 2. INTEGRAL EQUATION FORMULATION The scattering geometry under consideration is shown in Figure 1. Let C denote the cross section of an open or closed Ž . perfectly electric conducting PEC cylinder parallel to the z-axis. At each point on C, let a represent an outward-di- n rected unit vector normal to the contour. The circumferential vector a is then obtained by a a a . z n The incident field is a plane wave with its magnetic field Ž . polarized in the z-direction TE incidence . The incident electromagnetic field, defined in the absence of the scatterer, Ž . induces a surface current Jr, t on the scatterer. The bound- ary conditions require that the total tangential electric field on the conducting surface be zero or s inc Ž. E J E 0 on C 1 tan s where E J is the scattered electric field due to the induced current J. The scattered field radiated by the current J may be written in terms of the magnetic vector and electric scalar potentials as A s Ž. E J 2 t where R J , t ž / c Ž . Ž. A , t dz dC 3 HH 4 R C z R q , t s ž / 1 c Ž . Ž. , t dz dC 4 HH 4 R C z 2 2 ' and R z , the distance from the field point Ž . Ž. Ž. to the source point , z . In 3 and 4, and are the permeability and permittivity of the surrounding medium, and c is the velocity of propagation of the electromagnetic wave. The electric surface charge density q is related to the s electric surface current density by the continuity equation q s Ž. J . 5 s t Ž. Ž. Combining 1 and 2 gives A inc Ž. E 6 tan t tan and represents the electric field integral equation formula- tion. We may also develop an integral equation that uses the boundary condition on the magnetic field. From boundary conditions, we obtain s Ž. inc Ž. J a H J H 7 n where H inc is the incident magnetic field, and H s is the scattered magnetic field due to the induced currents J. As before, the scattered field can be written in terms of the potential functions, and is given by 1 s Ž. Ž. H J A 8 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 2, April 20 1999 129