地-电离层中水平激发极低频场的勒让德展开算法
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摘要
地-电离层空腔中水平激励极低频(Extremely Low Frequency,ELF)场强可表示为勒让德函数及其导数的级数和,利用勒让德函数迭代公式,提出了极低频水平偶极子在地-电离层空腔中激励场的计算新算法.将该方法近区场的计算结果与半空间水平偶极子激励场计算结果对比,远场区结果与Bannister(dir.+ind.)公式计算结果对比,验证了新算法的正确性和精度.将本算法应用至几Hz以下,可获得特殊规律:远区电场、磁场水平分量与方位角无关,电场水平分量方向与偶极矩方向平行,磁场水平分量方向与之垂直.
Extremely low frequency(ELF)propagation formulas for horizontal electric dipole sources radiating in a spherical uniform earth-ionosphere cavity 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.Using the iterative formulas of Legendre function,A new method is presented in this paper.The resulting waves are expressed as a superposition of T M and T E modes.In the near-filed range,the method of images is expected to be similar to the near fields of a dipole located on a flat finitely conducting,the far field is same as the result of Bannister(dir.+ind.)formulas.This shows that the method is accurate.The result of frequencies under 1Hz show that the horizontal electric and magnetic components are independent of the azimuth,and the direction of horizontal electric components is parallel to the dipole axis in the isolines chart with distance,whereas,the direction of horizontal magnetic components is orthogonal to dipole axis.
Extremely low frequency(ELF)propagation formulas for horizontal electric dipole sources radiating in a spherical uniform earth-ionosphere cavity 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.Using the iterative formulas of Legendre function,A new method is presented in this paper.The resulting waves are expressed as a superposition of T M and T E modes.In the near-filed range,the method of images is expected to be similar to the near fields of a dipole located on a flat finitely conducting,the far field is same as the result of Bannister(dir.+ind.)formulas.This shows that the method is accurate.The result of frequencies under 1Hz show that the horizontal electric and magnetic components are independent of the azimuth,and the direction of horizontal electric components is parallel to the dipole axis in the isolines chart with distance,whereas,the direction of horizontal magnetic components is orthogonal to dipole axis.
引文
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[7]董慧,闫玉波,李清亮.FDTD模拟SLF/ELF水平电偶极子在非均匀地-电离层波导中的场[J].电波科学学报,2010,25(2):276-280.DONG Hui,YAN Yubo,LI Qingliang,FDTD analysis of fields excited by horizontal electric dipole in asymmetric earth-ionosphere cavity[J].Chinese Journal of Radio Science,2010,25(2):276-280.(in Chinese)
[8]彭怀云,陶伟,潘威炎,等.极低频垂直偶极子在地-电离层中场的数值积分算法[J].电波科学学报,2012,27(2):333-338.PENG Huaiyun,TAO Wei,PAN Weiyan,et al.Numerical integral method for elf fields excited by vertical electric dipole in asymmetric earth-ionosphere cavity[J].Chinese Journal of Radio Science,2012,27(2):333-338.(in Chinese)
[9]SHAMPINE L F.Vectorized adaptive quadrature in MATLAB[J].Journal of Computational and Applied Mathematics,2008,211(2):131-140.
[10]GRADSHTEYN I S,RYZHIK I M.Table of Integrals,Series,and Products[M].New York:Academic Press,1980.
[2]GALEJS J.Terrestrial Propagation of Long Electromagnetic Waves[M].Oxford:Pergamon Press,1972.
[3]BANNISTER P R.Simplified formulas for ELF propagation at shorter distances[J].Radio Science,1986,21(3):529-537.
[4]潘威炎.长波超长波极长波传播[M].成都:电子科技大学出版社,2004:333-368.
[5]BARRICK D E.Exact ULF/ELF Dipole field strengths in the earth-ionosphere cavity over the Schumann Resonance Region:idealized boundaries[J].Radio Science,1999,34(1):209-227.
[6]王元新,樊文生,潘威炎,等.垂直电偶极子在地-电离层波导中场的球谐级数解[J].电波科学学报,2007,22(2):204-211.WANG Yuanxin,FAN Wensheng,PAN Weiyan,et al.Spherical harmonic series solution of fields excited by vertical electric dipole in earth-ionosphere cavity[J.2007,22(2):204-211.(in Chinese)
[7]董慧,闫玉波,李清亮.FDTD模拟SLF/ELF水平电偶极子在非均匀地-电离层波导中的场[J].电波科学学报,2010,25(2):276-280.DONG Hui,YAN Yubo,LI Qingliang,FDTD analysis of fields excited by horizontal electric dipole in asymmetric earth-ionosphere cavity[J].Chinese Journal of Radio Science,2010,25(2):276-280.(in Chinese)
[8]彭怀云,陶伟,潘威炎,等.极低频垂直偶极子在地-电离层中场的数值积分算法[J].电波科学学报,2012,27(2):333-338.PENG Huaiyun,TAO Wei,PAN Weiyan,et al.Numerical integral method for elf fields excited by vertical electric dipole in asymmetric earth-ionosphere cavity[J].Chinese Journal of Radio Science,2012,27(2):333-338.(in Chinese)
[9]SHAMPINE L F.Vectorized adaptive quadrature in MATLAB[J].Journal of Computational and Applied Mathematics,2008,211(2):131-140.
[10]GRADSHTEYN I S,RYZHIK I M.Table of Integrals,Series,and Products[M].New York:Academic Press,1980.