半圆形隧道中导行波特征方程的近似求解

Approximation solution of characteristic equation of guide wave in a semicircle tunnel

当半圆形隧道中存在一根导线时,根据场的唯一性原理,该导线产生的场与圆形隧道中该导线与其镜象产生的场的叠加等效,虽然可用Newton法或抛物线法求其特征方程,但求解过于复杂,根据镜象电流的特点,推导了半圆形隧道导行波的简单算法。计算结果得到,在频率较高时,近似结果和精确结果基本相同。近似求解方法对矿井通信的研究有指导意义。

According to the unique principle, the fields produced by a conductor line located in a semicircle tunnel is equivalent to the fields produced by both oneself and its image line. The characteristic equation can be solved by Newton or parabola method, but the process is complexity. Based on the peculiarity of current in the image line, a simple algorithm is proposed in this paper. The calculation results show that at high frequency bands, the approximate solution is basically the same as that of precision solution. The approximate methods have a guidance meaning to mine communication.