Excerpt from Field Strength Calculations for E. L. F. Radio Waves (Classic Reprint)
The mode theory of propagation of electromagnetic waves at extremely low frequencies (1. 0 to 3000 c/s)is briefly reviewed in this paper. Starting with the representation of the field as-a sum of modes, approximate formulas are presented for the attenuation and phase constants. At the shorter distances, where the range is comparable to the wavelength, the spheric-al-earth mode series is best transformed to a series involving cylindrical wave functions. This latter form is used to evaluate the near field behavior of the various field components. The effect of the earth's magnetic field is also evaluated using a quasi-longitudinal approximation which is particularly appropriate for propagation in the magnetic meridian. In general it is indicated that if the gyro frequency is comparable or greater than the effective value of the collision frequency, the presence of the earth's magnetic field may be important for E. L. F. In this case the attenuation may be increased somewhat. The in fluence of a purely transverse magnetic field is also considered.