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IEEE Transactions on Antennas and Propagation
Volume 48 Number 5, May 2000

Table of Contents for this issue

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Matched Asymptotic Expansion for the Low-Frequency Scattering by a Semi-Circular Trough in a Ground Plane

Robert W. Scharstein and Anthony M. J. Davis

Page 801.

Abstract:

Plane wave scattering by an electrically small circular trough cut in an infinite ground plane is solved analytically for both the TM and TE polarizations. A quasi-static solution for the inner field based upon a transformation to bipolar coordinates exploits the failure of the narrow trough to react to the detailed wave nature of the incident field and forms the starting point for the method of matched asymptotic expansions. The distant behavior of the inner field must agree with the near behavior of the outer field, which is a radiative solution of the Helmholtz equation. In addition to yielding several analytic terms of the solution in low-order powers and the logarithm of the trough wave size $ka$ the matching process provides an account of the interplay between all of the physical parameters.

References

  1. B. K. Sachdeva and R. A. Hurd, "Scattering by a dielectric-loaded trough in a conducting plane", J. Appl. Phys., vol. 48, pp.  1473-1476, 1977.
  2. M. A. Kolbehdari, H. A. Auda and A. Z. Elsherbeni, "Scattering from a dielectric cylinder partially embedded in a perfectly conducting ground plane", J. Electromagn. Waves Applicat., vol. 3, pp.  531-554, 1989.
  3. M. K. Hinders and A. D. Yaghjian, "Dual-series solution to scattering from a semicircular channel in a ground plane", IEEE Microwave Guided Wave Lett., vol. 1, pp.  239-242, Sept.  1991.
  4. T. J. Park, H. J. Eom, Y. Yamaguchi, W.-M. Boerner and S. Kozaki, "TE-plane wave scattering from a dielectric-loaded semi-circular trough in a conducting plane", J. Electromagn. Waves Applicat., vol. 7, pp.  235-245, 1993.
  5. A. M. J. Davis and F. G. Leppington, "Scattering of long surface waves by circular cylinders or spheres", Q. J. Mech. Appl. Math., vol. 38, pp.  411-432, 1985.
  6. P. M. Morse and H. Feshbach, Methods of Theoretical Physics-Part II, New York: McGraw-Hill, 1953, p.  1210. 
  7. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed.   New York: Academic, 1994, p.  27.