On the ionospheric parameters which govern high-latitude ELF propagation in the earth-ionosphere waveguide

An approximate wave solution is obtained for the propagating ELF mode at high latitudes in the earth-ionosphere waveguide. A simple approximate expression for the complex propagation constant emerges from the solution. The propagation constant depends on four parameters, two altitudes and a scale height associated with each altitude. The lower altitude is the height at which the conduction current parallel to the magnetic field becomes equal to the displacement current. The associated scale height is the local scale height of the parallel conductivity. Under daytime ionospheric conditions, the upper altitude is the height at which the local wave number becomes equal to the reciprocal of the local scale height of the refractive index. The associated scale height is the local scale height of the refractive index. Under the simplest nighttime conditions, the second set of parameters is replaced by the altitude of the E-region bottom and the local wave number just inside the E region. The relative phase velocity depends, in first approximation, only on the ratio of the two altitudes. The attenuation rate depends on the other two parameters as well. The two principal attenuation mechanisms are Joule heating by longitudinal currents in the vicinity of the lower altitude and energy leakage of the whistler component of the ELF wave at the upper altitude.