Leontovich boundary condition

The Shchukin-Leontovich boundary condition is a boundary condition in classical electrodynamics that relates to the tangential components of the electric Et and magnetic Ht fields on the surface of well-conducting bodies.[1][2][3][4]

Definition

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As originally formulated by Soviet physicists Alexander Shchukin and Mikhail Leontovich, the boundary condition is given as

 

where   and   represent the tangential components of the electric and magnetic fields,   is the effective surface impedance, and   is a unit normal pointing into the conducting material.[1] This condition is accurate when the conductivity of the conductor is large, which is the case for most metals. More generally, for cases when the radii of curvature of the conducting surface is large with respect to the skin depth, the resulting fields on the interior can be well approximated by plane waves, thus giving rise to the Shchukin-Leontovitch condition.[1][5] A generalization of the Shchukin-Leontovich impedance boundary condition for a flat surface of a uniform half-space with an arbitrary dielectric constant, presented as a one-sided non-local relation, was formulated in.[6]

Applications

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The Shchukin-Leontovich boundary condition is useful in many scattering problems where one material is a metal with large (but finite) conductivity. As the condition provides a relationship between the electric and magnetic fields at the surface of the conductor, without knowledge of the fields within, the task of finding the total fields is considerably simplified.

References

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  1. ^ a b c Landau, L. D.; Lifshitz, E. M. (1984). Electrodynamics of Continuous Media, Volume 8 (2nd ed.). Pergamon. ISBN 978-0750626347.
  2. ^ A. N. Shchukin. Propagation of Radio Waves [title translated from Russian]. Moscow, USSR, Svyazizdat, 1940, pp. 48-51.
  3. ^ M. A. Leontovich, "On a method for solving problems of electromagnetic wave propagation along the Earth's surface" [title translated from Russian], Izv. Akad. Nauk SSSR, Ser. Fiz., vol. 8, no. 1, pp. 16-22, 1944.
  4. ^ M. A. Leontovich, "On the approximate boundary conditions for the electromagnetic field on the surface of well conducting bodies" [title translated from Russian]. In a book: B. A. Vvedensky, Ed. Investigations on Radio Wave Propagation. Pt. 2 [title translated from Russian]. Moscow, USSR: Izd. Akad. Nauk SSSR, 1948, pp. 1-12.
  5. ^ Senior, T. B. A. (1960). "Impedance boundary conditions for imperfectly conducting surfaces". Appl. Sci. Res. 8: 418.
  6. ^ F. G. Bass, "Boundary conditions for the electromagnetic field at the surface with arbitrary dielectric constant," Radio Eng. Electron., vol. 5, no. 3, pp. 49-53, 1960.