RadioScience, Volume 17,Number 5, pages 1321-1326,September-October 1982 Excitationof the earth-ionosphere waveguide by an ELF source in the ionosphere V. K. Tripathi, • C. L. Chang, and K. Papadopoulos • Science Applications, Inc., McLean, Virginia 22102 (Received August13, 1981;revised May 17, 1982;accepted May 17, 1982.) It is shown that for polar regions, where the conductivity is predominantly reactive, the wave functionsfor the transverse electromagnetic mode of the earth-ionosphere waveguideare Hankel functions of the first kind with real argument; therefore they extendup to large heights over the polar ionosphere. A Green's function for the excitation of the waveguide by extended current or field sources in the ionosphere is obtainedfor an exponential ionosphere. The potential of ELF waveguide exci- tation by wireless antennas is discussed. 1. INTRODUCTION There has beenconsiderable interestin the past in the excitation of the earth-ionosphere waveguideat ELF frequencies by satellite-bornecurrent sources located in the ionosphere. Galejs [1971], Einaudi and Wait [1971], Pappert [1973], and Kelly et al. [1974] studied this problem in considerable detail and demonstrated that the satellite-based antennas could be radiators at least as efficientas the ground-based dipoles. One important result of these investigations is that the principleof reciprocity holds individually for all modes of the waveguide and hencethe radi- ation fields on the surface of the earth due to a dipole sourcein the ionosphere could be deduced from the radiationpattern of a ground-based dipole. More recently, wireless ELF generation in the ionosphere has emerged as an alternative to antenna excitation.There are two main techniques in achiev- ing wireless ELF generation. The first relieson mod- ulating the electrojet currentin the lower ionosphere, using amplitude-modulatedHF from ground an- tennas [Davis and Willis, 1974; Stubbeand Kopka, 1977; Stubbe et al., 1981; Changet al., 1982]. The HF wavesheat the electrons and produce an oscillatory electron temperature at the modulation frequency; this produces a conductivity modulationand hence a current modulation. Stubbeet al. [1981] have actu- i Now at Department of Physics andAstronomy, University of Maryland, CollegePark, Maryland 20742. Copyright 1982 by the AmericanGeophysical Union. Paper number 2S0770. 0048-6604/82/0910-0770508.00 ally reported extremely encouraging experimental re- sults on ELF generationby modulating the polar electrojet current with a 4.04-MHz RF transmitter. The secondtechniquerelies on resonant nonlinear parametric excitation of an Alfven wave,by mixing two HF waves in the ionosphere[Papadopoulos et al., 1982]. In both cases the interaction region over which the ELF power is produced is comparable to the ELF wavelength in the ionosphere, and compu- tations based on the reciprocityprinciple cannot be applied. The excitation of the earth-ionosphere waveguide by extended sources requires knowledge of the mode structure of the continuation of the free spacetrans- verse electromagnetic (TEM) modein the ionosphere. Galejs [1971] has determined analytic expressions for the mode structure of the TEM mode, assuming a homogeneous ionosphere. Greifinger and Greifinger [1974] examined the inhomogeneous ionosphere case and determined the mode structure for the case of purely real conductivity increasing exponentially with height. While this modelgives good results for the equatorial zones, it is of very limited validity for higherlatitudes; in actual fact, it produces very de- ceptiveresults. This is caused by the fact that the ELF index of refractionis mainly real at higher lat- itudes,corresponding to reactive conductivity. As it will be seen later, this has the very profound effectof allowingthe mode to extendto much greateralti- tude.This can be physically seen asfollows: the hori- zontal component of the TEM propagation wave numberfi is close to co/c, which is several ordersof magnitude smaller than the propagation constant I k I in the ionosphere; this implies that k is predomi- nantly vertical. In the equatorial zones, k is perpen- 1321