Abstract
IF an electromagnetic wave passes through a medium containing free electrons, which may make collisions with heavy particles, in the presence of a uniform magnetic field, the refractive index and absorption coefficient of the medium are given by the Appleton-Hartree equation1: 
where μ = refractive index; X = absorption coefficient; X = ƒ0
2/ƒ2; Y
T = (ƒH/ƒ) sin Θ; Y
L= (ƒH/ƒ) cos Θ; Z = v/2πƒ; ƒ = frequency of wave; ƒ0 = plasma frequency; ƒH= gyrofrequency; ν = frequency of collisions between electrons and neutral molecules; Θ = angle between wave normal and magnetic field.
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References
Ratcliffe, J. A., The Magneto-ionic Theory and its Application to the Ionosphere (Cambridge Univ. Press, 1959).
Booker, H. G., Proc. Roy. Soc., A, 150, 267 (1935).
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WALKER, A. The Quasi-Longitudinal Approximation to the Appleton-Hartree Equation. Nature 189, 742 (1961). https://doi.org/10.1038/189742a0
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DOI: https://doi.org/10.1038/189742a0
