Mode theory and the propagation of ELF radio waves

The mode Lheory of propagation of electromagnetic waves at extremely loll' frequen cies (ELF) (1.0 to 3,000 cycles per second) is treated ill this paper. StarLillg wiLh the representation of t he field as a sum of modes, approximate formulas arc presenLed for the attenuation and phase constants. Certain alternate representations of the individual modes arc mentioned. These are used as a basis for describing the physical behavior of the field at large distances from the source, particularly ncar the antipode of t he source. AL the ~horter distances, where the range is comparable to the \yavelength, the spherieal-earth mode series is besL trallsformed to a series involving cy li ndrical wave functions. This latter form is Llsed Lo evaluate the near field behavior of Lhe various field component. The effect of the earLh's magnetic field is also eV~Ll uated using a quasi-longiLudinal approximation. III general it is indicated t hat if the gyl"Ofrequency is less than t he effec tive value of the collision frequency, t he presence of the earth's magnetic field may be neglected for Ii;LF. When this condition is not met the attenuation may be increased somewhat. The influence of an inhomogencous ionosphere is also briefly considered and, finally, the propagation of E LF pulses is treated. It is suggested that certain observed characteristics of E LF waveforms may be attributed to t he inclination of the current challncl in t he lightning discharge.