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Power line harmonic radiation (PLHR), which specifically refers to the electromagnetic wave radiation observed in ionosphere or magnetosphere, is radiated by the transmission lines of power systems on the ground. PLHR is shown as a parallel spectrogram between 400 Hz and 5 kHz in frequency-time power spectrogram of electromagnetic field. And the frequency spacing of the parallel spectrogram is 50/100 Hz or 60/120 Hz. As an artificial pollution source in the near earth space, PLHR has attracted more and more attention. However, so far, there have been little proposed quantitative researches on the formation mechanism. This paper studies the propagation model for the electromagnetic waves generated by the electric dipole source above the non-ideal conductive ground in the stratified anisotropic ionosphere. Based on the method by Lehtinen(2008), a new full-wave finite element method is give to solve the problem. By recursively calculating reflection coefficients and mode amplitudes, the method contains no index increasing items. So it can effectively overcome the numerical overflow in programming calculations. In order to verify the correctness of the method, comparison are made between the existing analytical solutions and the solutions obtained from the proposed method, and they are in excellent agreement. Further more, using the present model, the new method and the associated parameters about practical power lines, ground and ionosphere, we have studied the effects of the frequency of dipole source, the bottom boundary height of ionosphere, the earth conductivity, and the geomagnetic field direction on PLHR propagation in the ionosphere. Results show that when the frequency of radiation source equals the cut off frequency of earth-ionosphere waveguide-guided wave modes, the strength of PLHR for penetrating into the ionosphere becomes larger. Keeping the harmonic current constant, a smaller ground conductivity would be accompanied by a larger power of PLHR. PLHR propagates along the direction of the geomagnetic field in the ionosphere. Therefore, it is much easier for a high-order harmonic radiation of transmission lines to penetrate into the ionosphere along the direction of the geomagnetic field in the areas with low ground conductivity under a certain condition. Results obtained in this paper may have important implications to explain the formation mechanism of PLHR.
[1] Bullough K 1995 Handbook of atmospheric electrodynamics (Vol. 2) (Boca Raton: Fla CRC Press) p291
[2] Simoes F, Pfaff R, Berthelier J J, Klenzing J 2012 Space. Sci. Rev. 168 551
[3] Parrot M, Němec F, Santolk O, Berthelier J J 2005 Ann. Geophys. 23 3301
[4] Němec F, Santolk O, Parrot M, Berthelier J J 2007 Adv. Space. Res. 40 398
[5] Němec F, Santolk O, Parrot M, Berthelier J J 2007 Adv. Space. Res. 40 398
[6] Němec F, Santolk O, Parrot M, Bortnik J 2010 J. Geophys. Res. 115 A11301
[7] Němec F, Parrot M, Santolk O 2010 J. Geophys. Res. 115 A11301
[8] Parrot M, Němec F, Santolk O 2014 Sci. Journal of Beijing University of Aeronautics and Astronautics 40 1672(in Chinese) [吴静, 张翀, 付静静, 马齐爽 2014 北京航空航天大学学报 40 1672]
[9] Wu J, Zhang C, Fu J J, Ma Q S 2014 Sci. Journal of Beijing University of Aeronautics and Astronautics 40 1672 (in Chinese) [吴静, 张翀, 付静静, 马齐爽2014 北京航空航天大学学报40 1672]
[10] Carson J R 1926 Bell Syst. Technol. J. 5 539
[11] Wedepohl L M, Efthymiadis A E 1983 J. Atmos. Terr. Phys. 45 409
[12] Yearby K H, Smith A J, Bullough K 1983 J. Atmos. Terr. Phys. 45 409
[13] Tatnall A R L, Matthews J P, Bullouth K, Kaiser T R 2008 Chin. Phys. B 17 3629
[14] Ni G Y, Yan L, Yuan N C 2008 Chin. Phys. B 17 3629
[15] Ando Y, Hayakawa M, Molchanov O A 2014 Chin. Phys. B 23 034102
[16] Wu J, Fu J J, Zhang C 2014 Chin. Phys. B 23 034102
[17] Budden K G 1985 The Propagation of Radio Waves:The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere (Cambridge: Cambridge Univ. Press) pp574-576
[18] Nagano I, Mambo M, Hutatsuishi G 1975 Radio. Sci. 10 611
[19] Xia M Y, Chen Z Y 1999 Sci. China Ser. E 29 163 (in Chinese) [夏明耀, 陈志雨 1999 中国科学(E辑) 29 163]
[20] Lehtinen N G, Inan U S 2008 J. Geophys. Res. 113 A06301
[21] Nabighian M N (translated by Zhao J X, Wang Y J) 1992 Electromagnetic Methods in Applied Geophysics (Vol. 1) (Beijing: Geological Publishing House) pp217-226 (in Chinese) [米萨克 N 纳比吉安著 (赵经祥, 王艳君译) 1992 勘查地球物理电磁法(第一卷)(北京: 地质出版社)第217226页]
[22] Fu C M, Di Q Y, Wang M Y 2010 Sci. Chinese J. Geophys-Ch. 53 177(in Chinese) [付长民, 底青云, 王妙月 2010 地球物理学报 53 177]
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[1] Bullough K 1995 Handbook of atmospheric electrodynamics (Vol. 2) (Boca Raton: Fla CRC Press) p291
[2] Simoes F, Pfaff R, Berthelier J J, Klenzing J 2012 Space. Sci. Rev. 168 551
[3] Parrot M, Němec F, Santolk O, Berthelier J J 2005 Ann. Geophys. 23 3301
[4] Němec F, Santolk O, Parrot M, Berthelier J J 2007 Adv. Space. Res. 40 398
[5] Němec F, Santolk O, Parrot M, Berthelier J J 2007 Adv. Space. Res. 40 398
[6] Němec F, Santolk O, Parrot M, Bortnik J 2010 J. Geophys. Res. 115 A11301
[7] Němec F, Parrot M, Santolk O 2010 J. Geophys. Res. 115 A11301
[8] Parrot M, Němec F, Santolk O 2014 Sci. Journal of Beijing University of Aeronautics and Astronautics 40 1672(in Chinese) [吴静, 张翀, 付静静, 马齐爽 2014 北京航空航天大学学报 40 1672]
[9] Wu J, Zhang C, Fu J J, Ma Q S 2014 Sci. Journal of Beijing University of Aeronautics and Astronautics 40 1672 (in Chinese) [吴静, 张翀, 付静静, 马齐爽2014 北京航空航天大学学报40 1672]
[10] Carson J R 1926 Bell Syst. Technol. J. 5 539
[11] Wedepohl L M, Efthymiadis A E 1983 J. Atmos. Terr. Phys. 45 409
[12] Yearby K H, Smith A J, Bullough K 1983 J. Atmos. Terr. Phys. 45 409
[13] Tatnall A R L, Matthews J P, Bullouth K, Kaiser T R 2008 Chin. Phys. B 17 3629
[14] Ni G Y, Yan L, Yuan N C 2008 Chin. Phys. B 17 3629
[15] Ando Y, Hayakawa M, Molchanov O A 2014 Chin. Phys. B 23 034102
[16] Wu J, Fu J J, Zhang C 2014 Chin. Phys. B 23 034102
[17] Budden K G 1985 The Propagation of Radio Waves:The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere (Cambridge: Cambridge Univ. Press) pp574-576
[18] Nagano I, Mambo M, Hutatsuishi G 1975 Radio. Sci. 10 611
[19] Xia M Y, Chen Z Y 1999 Sci. China Ser. E 29 163 (in Chinese) [夏明耀, 陈志雨 1999 中国科学(E辑) 29 163]
[20] Lehtinen N G, Inan U S 2008 J. Geophys. Res. 113 A06301
[21] Nabighian M N (translated by Zhao J X, Wang Y J) 1992 Electromagnetic Methods in Applied Geophysics (Vol. 1) (Beijing: Geological Publishing House) pp217-226 (in Chinese) [米萨克 N 纳比吉安著 (赵经祥, 王艳君译) 1992 勘查地球物理电磁法(第一卷)(北京: 地质出版社)第217226页]
[22] Fu C M, Di Q Y, Wang M Y 2010 Sci. Chinese J. Geophys-Ch. 53 177(in Chinese) [付长民, 底青云, 王妙月 2010 地球物理学报 53 177]
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