Theoretical group heights of reflection of 150kc/s radio waves vertically incident on the ionosphere

Abstract

This paper is concerned with the theoretical determination of the group heights of reflection of long radio waves vertically incident on the ionosphere. The theoretically expected group heights for 250 μsec Gaussian shaped pulses are determined utilizing: 1. (1) a wave theory treatment including coupling, 2. (2) a Chapman-like ionospheric model including all variables and their height variations and 3. (3) a fundamental radio frequency or carrier component of 150 kc/s. From the theoretical viewpoint the continuous wave (c.w.) results of Gibbons and Nertney [1], [2] are extended by including the dispersive characteristics of the above model. This is accomplished by determining the received pulse characteristics by means of a response function developed from a suitable Fourier-Hermite series which includes the frequency dependent effects of the model. It is found that the rapid changes in polarization near the lower edge of the E-region, called the “coupling region”, are very effective in generating reflected waves or pulses under suitable conditions, i.e. late night hours associated with low E-layer critical frequencies. However, the dispersive characteristics are small so that almost negligible group retardation is to be expected. At a higher level in the layer rapid variations in the index of refraction for one of the characteristic wave components occur in what is called the “reflection region”. Here the time-delays are large for low critical frequency models. Some geometrical discussion is included concerning polarization and coupling factors. If properly considered, the ordinary and extraordinary modes can be given a representation (in a certain complex space) as orthogonal principal directions. The above theory is compared with the experimentally observed group heights on a diurnal basis. Good agreement is obtained and is further strengthened by comparison with some recent measurements of R.E. Jones on the diurnal change in phase (c.w.) paths.