Wave solutions, including coupling, of ionospherically, reflected long radio waves for a particularE-region model

Abstract

This paper is concerned with the solution of the coupled wave equations which arise in the application of the wave theory to the problem of ionospheric wave propagation. It concerns an extension of previous work [see 1 of “References” at end of paper], which will henceforth be referred to as [1]. The method of “variation of parameters” is used to obtain approximate solutions to the coupled equation from the uncoupled solutions obtained in [1]. A diurnal and seasonal model representing the E-region of the ionosphere above State College, Pennsylvania, is considered. This model, as in [1], consists of a Chapman-like E-region whose maximum in electron density is at a constant height. Approximate 150 kc/sec wave solutions including coupling are obtained for this model. These wave solutions, of course, exhibit the well-known reflection condition corresponding to an electron density of around 3,000 electrons/cm3. It is shown that the effect of the coupling is to cause a wave traversing a coupling region to excite a new wave propagated in the direction of propagation of the incident wave and also a back-scattered wave propagated in the reverse direction. As indicated below, these coupling effects become important in our model below the “reflection” level. The back-scattered wave due to the initial upgoing wave will thus appear as a reflected wave originating in the coupling region. The forward-scattered wave due to the down-going wave from the upper “reflection” level also must be considered, particularly in calculating the polarization of ionospherically reflected waves. It is shown that, in the case of 150 kc/sec waves, the coupling effects occur in the neighborhood of N = 300 electrons/cm3, which corresponds to the “classical reflection” level for the “ordinary” wave. The coupling effects become greater as the collisional frequency, ν, associated with the coupling N value decreased toward the critical collisional frequency, νc [2], for the night-time models due to the increase in heights of the “bottom” of the layer at these times. This results in stronger split echoes and greater departure from circularity in the polarization ellipses. The results of computations utilizing the theory, in comparison with experimental results, indicate that the stratification observed in the height records may be explained as outlined above. The absorption and polarization experimental results, however, cannot be accounted for by the E-region model utilized alone. The consideration of an electronic D-region, however, readily accounts for all three experimental factors, as will be discussed in detail in a later paper.