Diffraction of a Dipole Field By a Unidirectionally Conducting Screen
Diffraction of a Dipole Field By a Unidirectionally Conducting Screen
James Joseph Radlow
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-V^/j5| log-g. (9U) Both of these functions are singular at x = 1 (or at ka/2n an integer) and they "behave near the singularity like (l-x)~ ' . A parametric plot of -k [y, (e ) + y (e )] is shown on Fig. 3, for the range < < rr.
Although more complicated procedares will give more accurate results, 00 in this paper y^ H^ (nka) will he approximated hy* n=l / (SHkar^/V'!/" *^'l^ " ''''^'[yiCe"") * y^C. "'')]. M. (89. ) kecome.. Then. AC~-2(^ )'/'(E [(-lAC-Dle'' " " ■'""' ii • ^(Hi)| by^)n^^^'-'^)] . (9, Finally, the right hand member of Eq. (ig) "becomes imd: -Ui Y: [j^(kH)/H^(kR)]e'°"'2 (96 -i m 2» ^. [(-1) *(-l)"Je-^/(+»)n/2-in02(J^/H^)(Jy/H^)(kR)[y^(e^^^)-Ky2(e^^^)] 1+ilL- yeFlki: [ J2 J^(kH)/H^(kR) e^''®2] n • The approximating function and the Hankel function series have the sajne first term in the asymptotic expansion.
- 8 - ^nx Fig. 3. A parametric plot of | [y^(e^®) + 72(6^®)] - 9 - At this point we may note that the quantity of particuler interest in (96) is the correction factor 2: [(-ir*(-l)^]e-^^^-^^^^/2-ine2 i, .
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