Electromagnetic Wave Propagation through Slowly Varying Plasma

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Abstract
We solve the second-order linear inhomogeneous wave equation by the WKB method. Then a sequence of successive substitutions are developed, by the help of which solutions correct up to any higher order are reduced to the WKB solution of an equation like the original equation. This procedure is adopted to study propagation of electromagnetic wave obliquely through slowly but continuously varying plasma layers. Across a plane where N (the equilibrium plasma concentration) is continuous, but its first- and second-order space rate of variation along the normal are discontinuous, we have solved the boundary value problems for wave propagation. The characteristics of the reflected and transmitted fields depend on these derivatives of N such that the reflected wave vanishes in the limit of constancy of N. We find that the direction of flow of electromagnetic energy is deviated from its straight course in the uniform region. Expressions for relative shift of the wave vector along and perpendicular to the direction in the uniform medium, with respect to the distance of wave advancement in that medium in a given time, have been deduced. The deviation of the direction of propagation is slightly more for the field of transverse magnetic (TM) polarization than for the transverse electric (TE) polarization, but both these directions lie in the plane of incidence and are opposite to one another with respect to the direction in the uniform medium, where by transverse polarizations are meant those with respect to the plane of incidence. Hence, the original wave is split into two waves. Deflection is increased and, consequently, speed of propagation decreased for the TM field, whereas deflection is decreased and speed of propagation increased for the TE component if the wave propagates into a plasma of increasing concentrations; consequently, the TM field will be reflected back earlier than the TE part. Besides these results, it is hoped that our treatment may help in attacking problems of coupling of different types of plasma waves due to slow variation of equilibrium parameters occuring from more complete set of equations describing plasma behavior.