Simulating of electromagnetic scattering by a structure consisting of a perfectly conducting body and a thin wire

Using the method of auxiliary sources, we solve the problem of electromagnetic-wave scattering by a structure consisting of a perfectly conducting body and a thin wire. The gist of the method to be used is the following. We introduce an auxiliary surface S_e = K_eS inside perfectly conducting body D. Let S_e be homothetic to the surface S of the body D. The homothety (similarity) coefficient K_e characterizes the spacing of the auxiliary surface to the surface S. We specify a finite set of points {M_n }N₌₁ on auxiliary surface S_e . At each point M_n we locate a pair of independent auxiliary elementary electric dipoles with moments equal to p" = p" e" ,p" = p" e" · The dipoles are aligned with the unit vectors e^, e_x" , respectively, in a plane tangential to S_e at the point M„ and radiate in homogeneous medium with parameters s_e and ц_е. We also introduce a continuously distributed auxiliary current J on the axis of thin wire. Now we represent the unknown scattered field {E_e,H_e} in outer medium D_e as a sum of the fields from the introduced auxiliary dipoles and current: Г n _ n Е_е(М) = (И(йъ_е)\ E Vx(Vxn„) + Vx(VxII)k H_e(M)= £ УхП„+УхП , U=i J "=i п_и = ^_е{М,М„)Рг, П =\^x¥_e(M,M{)Jdl , T_e(M,M„) = exp(%^)/(4^^)_f i п„_д=ч>_е(мм_пЛ)К> ^ппл=^е(мм_пЛ)рГ, К=р1К⁺р"Л- Here ^ = e|i_e is the wave number in the outer medium D_e; R_MM is the distance from the point M_n on S_e to the point M in D_e; R_MMi is the distance from the point M_t on the wire axis to the same point M in D_e; p^, p^ (n = i, N) are unknown dipole moments and J is an unknown axis current. The integration is performed along the axis of the wire 1. The chosen representations of the field satisfy Maxwell's equations and radiation conditions. To satisfy boundary conditions on the surfaces of the body and wire, we should properly select the dipole moments and the axial-current J . Before making that, we introduce the piecewise-constant approximation for the axial current. We divide the line 1 in N_t small intervals in which the current can be considered constant. Then the formula for П can be represented in the following approximate form: N_t I, where is the current in the г'-th interval of the wire and e_i is the unit vector directed along the tangent to the central point of the considered interval. Within the framework of such an approach, the problem of determination of the unknown axial-current distribution is reduced to the problem of finding N_l current elements. To find the dipole moments and the current elements, we use perfectly conducting boundary conditions which are satisfied according to the collocation method. Let Mj , where j = 1, 2, ..., L, and M., where j = 1, 2, . . . , L , be the collocation points on the surfaces body and wire, respectively. Then the unknown dipole moments and the current elements can be found from the following system of linear algebraic equations: n^ x E^ - -n^ x E^, j = l,L, =-^eL, j = 1L, where n¹ is the normal vector and Ё{ and E^ are the vectors of electric-field components of scattered field and exciting field at the collocation point Mj; E^J el and Eji are the electric-field longitudinal components of scattered field and exciting field at the collocation point M . on the wire surface. Note that we neglected the azimuthal component of the wire surface current in comparison with longitudinal component. After solving the linear algebraic equations we determine the required parameters of the scattered field. Based on the method described above, we developed a computer code for calculating the scattered-field components. Using this code, we carried out a series of computational calculations aimed at estimation of influence of nearby perfectly conducting body on current distribution along thin wire. We investigated the influence of thin wire on scattering cross-sections of perfectly conducting body as well. We present some results in the paper.

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