Stochastic wave equations are derived to describe electromagnetic wave propagation in an isotropic medium in which the electric permittivity and the magnetic permeability are weaklyrandom functions of time. Approximate analytical solutions are obtained using separation of variables and the WKB method for some configurations that can be used to model the electromagnetic field in the ionosphere. The form of the initial and boundary conditions determines whether the solution takes a form representing a direct current electric field or continuous pulsation electromagnetic waves. The temporal variation of the calculated induced electromotive force (EMF) is in agreement with observations.

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Journal Progress In Electromagnetics Research B
Nijimbere, V. (Victor), & Campbell, L. (2019). Electromagnetic field solutions in an isotropic medium with weakly-random fluctuations in time and some applications in the electrodynamics of the ionosphere. Progress In Electromagnetics Research B, 83(2019), 77–92. doi:10.2528/PIERB18102003