极低频垂直偶极子在地-电离层中场的数值积分算法

针对地-电离层空腔中极低频(ELF)场强问题,提出一种应用于任意复数角v的勒让德函数数值积分算法,并与已有渐近计算法、级数展开法进行比对,结果表明:该方法使用频率范围更广,计算精度、效率更高。利用此数值积分算法,计算了垂直偶极子激励的30Hz以下典型频点的场强分布,所得场强分布符合物理规律,无损耗条件下舒曼谐振频率与前人计算结果完全一致,印证了ELF垂直偶极子在地-电离层腔体中场的数值积分算法的正确性。

Numerical integral method for ELF fields excited by vertical electric dipole in asymmetric earth-ionosphere cavity

Extremely low frequency(ELF) propagation formulas for vertical electric dipole sources radiating in a spherical uniform earth-ionosphere cavity have been derived.These formulas have a range dependence characterized by either the Legendre function of the first kind of complex degree v and order zero or one of its first two derivatives.It is difficult to get the value of the Legendre function unless through appropriate approximations.In this paper,a new numerical integral method for the Legendre function is present.It is more efficient and accurate,and can be used in wider frequency band.The field excited vertical dipole at several frequencies are calculated through the numerical integral method.The fields calculated can image the physical phenomena of ELF propagation in earth-ionosphere cavity,and the frequencies of Schumem resonance is the same as previous researches.