射线追踪变分方程及电离层传播问题应用

Variation equations of ray tracing and its applications in ionospheric wave propagation

从射线追踪的Haselgrove方程出发推导了射线变分方程,给出了变分方程中的所有二阶微分式的表达式。这组变分方程能实现传统的射线追踪所不具备的自导引功能和射线路径上的能量计算功能。基于这组射线变分方程,改进已有文献中的牛顿-差分自导引算法[8],提高了自导引计算的收敛速度。基于具有自导引和场强计算功能的射线追踪方法,研究了电离层行扰(TID)对高频传播的影响,这些影响主要表现为射距上能量的聚焦、固定接收机处相位的起伏和一跳跳距的变化等。显示出变分方程是对传统射线追踪方法的重要补充。

A set of ray tracing variation equations are derived from Haselgrove equations and all the 2nd order derivatives in the variation equations are given. Based on these, the automatic homing-in and field-strength calculations, which are not in- cluded in the traditional ray tracing programs（e, g. the Jones ray tracing programs）, can be realized. From these variation equations, the Newton-finite differences homing-in algorithm is improved so that the convergence rate are sped up. With our own ray tracing programs including homing-in and field-strength calculations, the impacts of traveling ionospheric disturbances on high frequency propagation are in- vestigated. These impacts appeared mainly as power focusing at different ranges, phase path fluctuations at a fixed receiver and the variations of one-hop skip distances. These results show that these variation equations are important supplements to the traditional ray tracing.