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Reflection and Transmission of Electromagnetic Waves at Electron Density Gradients
1.H. A. Lorentz, The Theory of Electrons (B. G. Teubner, Leipzig, Germany, 1909), p. 306 ff.
2.H. Margenau, Phys. Rev. 69, 508 (1946);
2.H. Margenau, 109, 6 (1958)., Phys. Rev.
3.S. Chapman and T. G. Cowling, The Mathematical Theory of Non‐Uniform Gases (Cambridge University Press, New York, 1952), Chap. 18.
4.J. A. Stratton, Electromagnetic Theory (McGraw‐Hill Book Company, Inc., New York, 1941), p. 268 ff.
5.P. M. Woodward and A. M. Woodward, TRE Rept. T 1800, Telegraphy Research Establishment, Malvern, England.
6.The solutions could be written equally well in terms of Bessel functions of order and or as J. Wallot [Ann. Physik 60, 734 (1919)] has done for a pure dielectric problem (or see Stratton, p. 580 of work cited in footnote 4), in terms of Hankel Functions. The Airy formulation was chosen because appropriate tables for complex arguments were more readily available.
7.Wallot’s treatment (see footnote 6) of the similar problem for more general profiles of permittivity, is not transcribable to a variable conductivity, since the concomitant variation of imposed by Eq. (2) would need be complex. P. Poincelot [Compt. rend. 244, 2031, 2298 (1957)] considers more general profiles of that extend to infinity, and hence lack the second boundary essential to the problem under study here.
8.J. A. Stratton, p. 511 ff. of work cited in footnote 4.
9.A. Erdélyi, Asymptotic Expansions (Dover Publications, New York, 1956), p. 94 ff.
10.F. A. Albini and R. G. Jahn, Tech. Rept. No. 3, Guggenheim Jet Propulsion Center, California Institute of Technology, Pasadena, California, 1960.
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12.H. G. Haddenhorst, Z. angew. Phys. 8, 264 (1956).
13.E. Greene and D. Hornig, J. Chem. Phys. 21, 617 (1953).
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