Investigation of radio ray-path and electron density slope of the ionosphere

The three dimensional ray-path equation considering the effect of the horizontal gradient of the ionospheric electron density is obtained. By integrating in upgoing and downgoing stage, the point on the raypath can be determined and the propagation channel in HF radio telecommunication may be recknoed and predicted. Considering the effect of the electron density slope the ray-path is asymmetric about the reflecting point, and the wave is no longer in the great circle determined by the original wave vector. The group path and the phase path can also be solved.