CHAPTER 4 - WAVES IN A SPHERICAL GUIDE

Abstract

The waveguide is excited by vertical or horizontal electric or magnetic dipole sources, and its boundaries are characterized by surface impedances. The resulting waves are expressed as a superposition of T.M. and T.E. modes. The wave numbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase-velocity estimates, but other propagation parameters are of restricted validity in the V.L.F. range, where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances; and for an elevated source, the horizontal fields are essentially omnidirectional also in the V.L.F. range. Near fields of vertical and horizontal electric dipoles are expressed as a summation of waveguide modes. At the antipode the horizontal field components vanish for a vertical electric dipole, and the vertical electric field vanishes for a horizontal electric dipole.