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Extension to perpendicular incidence
Line source excitation
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amplitude angle of incidence approximation assumed asymptotic expansion atmosphere attenuation rates axis Bessel functions boundary conditions Bremmer Budden Chapter complex contour correction factor corresponding curves dielectric constant discussed distance earth electric field electromagnetic waves electrons exponential expressed field components finite formula Furthermore given by Eq ground half space half-space Hankel function height Hertz vector homogeneous horizontal dipole integrand interface ionosphere kc/s layer line source linear low frequencies magnetic field Maxwell's equations modal equation mode theory numerical obtained phase integral phase velocity Phys plane wave plasma poles problem Proc quantity radiation radio waves reflection coefficient refractive index region saddle point shown in Figs solution Sommerfeld spherical stratified medium surface impedance surface wave tanh troposphere two-layer unity v.l.f. propagation valid values vertical electric dipole vertical polarization Wait wave propagation waveguide written Zenneck zero