Oblique absorption effects of the D region during HF waves heating

With the development of heating research, the oblique heating effects of the D region are becoming increasingly important. For the vertical heating, the larger the beam width of heating wave is, the more evident the oblique effects are; For the oblique heating, the D region which also exhibits evident heating effects has received less attention than the F region in previous studies; Furthermore, the oblique heating effects of the D region should be considered for the studies on multi-beam modulation heating that has arisen recently. Therefore, the numerical model for oblique heating needs to be established to develop the heating study in the D region. In this paper, the classical model for vertical heating is improved by further considering the lossy characteristic of the D region. An added factor, the real part of the refractive index, is introduced to estimate the power density of heating wave. Based on this improved model, the oblique heating model is presented by applying the oblique extension of Wentzel-Kramers-Brillouin (WKB) method and “real pseudo ray” approximation. Considered that the D region presents horizontally discrete strata, oblique absorption effects are quantitatively studied by powerful high-frequency wave heating. Notably, the electron energy absorption occurs only along the vertical direction at the different incident angles due to the special spatial characteristic of the D region. Results show that with the increase of incident angle, the absorption index increases whereas the effective power density of oblique heating wave has a considerable reduction. Therefore, the larger the incident angle is, the less the electron temperature increases. Moreover, the electron temperature in the upper region is more sensitive to variations in incident angles than that in the lower region. In the upper D region, two additional factors severely restrict the enhancement of electron temperature. The self-absorption of the heating wave, well-known as one factor, decreases with the increase of incident angle. Another factor, the real part of refractive index which is neglected in past studies also restricts the increase of electron temperature in the upper D region.