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Based on the generalized Zakharov model, a numerical model of electromagnetic wave propagating in the ionosphere at different angles is established by combining the finite difference time domain (FDTD) method of obliquely incident plasma with the double hydrodynamics equation and through equivalently transforming the two-dimensional Maxwell equation into one-dimensional Maxwell equation and the plasma hydrodynamics equation. In this paper. the dominant equation of Z-wave in obliquely incident nonlinear ionospheric plasma having been analyzed and deduced, the FDTD algorithm suitable for calculating the propagation characteristics of ionospheric electromagnetic wave is deduced. The simulation results prove the accuracy and effectiveness of this method for the Langmuir disturbance caused by electromagnetic wave heating the ionosphere at a small inclination angle. The results show that under small angle incidence, the high-power high-frequency electromagnetic wave excites the Langmuir wave near the O-wave reflection point in the ionospheric plasma. At the same time, the wave particle interaction causes the O-wave to convert into Z-wave and propagate into the higher region of the ionosphere. In this work, the electromagnetic wave propagation characteristics are further studied based on ionospheric plasma, which is helpful in laying the foundation of numerical algorithm for comprehensively and in depth analyzing the influence of ionospheric Langmuir disturbance on ionospheric radio wave propagation characteristics.
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Keywords:
- finite difference time domain method /
- Zakharov equation /
- oblique incidence /
- Langmuir disturbance
[1] Perkins F W, Kaw P K 1971 J. Geophys. Res. 761 282
[2] Gurevich A V, Carlson H C, Medvedev Y V, Zybin K P 2004 J. Plasma Phys. Res. 30 995
Google Scholar
[3] Cannon P D, Honary F, Borisov N 2016 J. Geophys. Res. Space. Phys. 121 2755
Google Scholar
[4] Close R A, Bauer B S, Wong A Y, Langdon A B, Kruer W L, Mjølhus E 1990 Radio Sci. 25 1341
Google Scholar
[5] Eliasson B, Papadopoulos K 2016 J. Geophys. Res. Space Phys. 121 2727
Google Scholar
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Google Scholar
[7] Rietveld M T, Isham B, Grydeland T, Hoz C L, Hagfors T 2002 Adv. Space Res. 29 1363
Google Scholar
[8] Eliasson B, Thidé B 2008 J. Geophys. Res. 113 A02313
[9] Eliasson B, Stenflo L 2013 Mod. Phys. Lett. B 27 1330005
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Google Scholar
[11] Eliasson B, Thidé B 2007 J. Geophys. Res. Lett. 34 L06106
[12] Eliasson B, Shao X, Milikh G, Mishin E V, Papadopoulos K 2012 J. Geophys. Res. Space Phys. 117 A10321
[13] 刘默然, 周晨, 赵正予, 张援农 2016 电波科学学报 31 743
Google Scholar
Liu M R, Zhou C, Zhao Z Y, Zhang Y N 2016 Chin. J. Radio 31 743
Google Scholar
[14] 何昉, 赵正予, 倪彬彬, 张援农 2016 电波科学学报 21 525
Google Scholar
He F, Zhao Z Y, Ni B B, Zhang Y N 2016 Chin. J. Radio 21 525
Google Scholar
[15] Zhu T 2018 M. S. Thesis (Zhenjiang: Jiangsu University) (in Chinese)
[16] Eliasson B, Milikh G, Shao X, Mishin E V, Papadopoulos K 2015 J. Plasma Phys. 81 415810201
Google Scholar
[17] Zhang Y 2014 M. S. Thesis (Xi’an: Xidian University) (in Chinese)
[18] 樊永永 2013 硕士学位论文 (西安: 西安电子科技大学)
Fan Y Y 2013 M. S. Thesie (Xi’an: Xidian University) (in Chinese)
[19] 杨利霞, 谢应涛, 孔娃, 于萍萍, 王刚 2010 物理学报 59 6089
Google Scholar
Yang L X, Xie Y T, Kong W, Yu P P, Wang G 2010 Acta Phys, Sin. 59 6089
Google Scholar
[20] Taflove A, Hagness S C, Piket-May M 2005 Computational Electrodynamics: the Finite-difference Time-domain Method (Academic Press) pp629–669
[21] Mjølhus E, Helmersen E, DuBois D F 2003 Nonlinear Processes Geophys. 10 151
Google Scholar
[22] Robinson T R 1989 Phys. Res. 179 153
[23] Mishin E, Hagfors T, Kofman W 1997 J. Geophys. Res. Space Phys. 102 27265
Google Scholar
[24] Gondarenko N A, Guzdar P N, Ossakow S L, Bernhardt P A 2003 J. Geophys. Res. Space Phys. 108 1470
Google Scholar
[25] Gondarenko N A, Ossakow S L, Milikh G M 2006 Geophys. Res. Lett. 33 399
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Ge D B, Yan Y B 2011 The Finite-Difference Time-Domain Method (Xi’an: Xidian University Press) pp42–46 (in Chinese)
[27] 李定 2006 等离子体物理学 (北京: 高等教育出版社) 第88页
Li D 2006 Plasma Physics (Beijing: Higher Education Press) p88 (in Chinese)
[28] Benson R F, Webb P A, Green J L, Carpenter D L, Sonwalkar V S, James H G, Reinisch B W 2006 Ringberg Workshop on High Frequency Waves in Geospace, Ringberg, Germany, July 11–14, 2004 p687
[29] Zhang J, Hai Y F, Wayne S 2018 IEEE Trans. Plasma Sci. 46 2146
Google Scholar
[30] Chen J, Yan Y B, Li Q L, Yuan G, Li H Y, Hao S J, Che H Q 2018 12 th International Symposium on Antennas, Propagation and Electromagnetic Theory (ISAPE) Hangzhou, China, December 3–6, 2018 p650
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图 1 TEz波斜入射电离层等离子体的传播模型
Figure 1. Propagation model of TEz wave obliquely incident ionospheric plasma.
图 2 FDTD电磁场时域的逐步迭代流程图
Figure 2. Step by step iterative flow chart of FDTD electromagnetic field in time domain.
图 3 电磁波加热电离层传播模型
Figure 3. Ionospheric propagation model heated by electromagnetic wave.
图 4 O波与X波
Figure 4. O wave and X wave.
图 5 w-k色散曲线
Figure 5. w-k dispersion curve.
图 6 背景电子密度及t = 0.249 ms时刻电场
$ {E_x} $ 分量幅值分布Figure 6. Background electron density and amplitude distribution of electric field
${{E}_{x}}$ component at t = 0.249 ms.
图 7 背景电子密度及t = 0.821 ms时刻电场
$ {E_x} $ 和${{E}_{y}}$ 分量幅值分布Figure 7. Background electron density and distribution of electric field
$ {E_x} $ and${{E}_{y}}$ component amplitude at t = 0.821 ms.
图 8 背景电子密度及t = 0.90 ms时刻电场
$ {E_x} $ 和${{E}_{y}}$ 分量幅值分布Figure 8. Background electron density and distribution of electric field
$ {E_x} $ and${{E}_{y}}$ component amplitude at t = 0.90 ms.
图 9 背景电子密度及t = 1.03 ms时刻电场
$ {E_x} $ ,${{E}_{y}}$ 和${{E}_{z}}$ 分量幅值分布Figure 9. Background electron density and distribution of electric field
$ {E_x} $ ,$ {{E}_{y}} $ and${{E}_{z}}$ component amplitude at t = 1.03 ms.
图 10 背景电子密度及t = 1.27 ms时刻电场
${{E}_{x}}$ ,${{E}_{y}}$ 和$ {E_z} $ 分量幅值分布Figure 10. Background electron density and distribution of electric field
$ {E_x} $ ,$ {{E}_{y}} $ and${{E}_{z}}$ component amplitude at t = 1.27 ms.
图 11 O波转换区域的静电扰动及
$ {{n}_{\text{s}}} $ 扰动 (a) O波转换区域${\text{|}}{{E}_{z}}{\text{|}}$ 变化; (b) O波转换区域${\text{|}}{{n}_{\text{s}}}{\text{|}}$ 变化; (c) Z波转换区域${\text{|}}{{E}_{z}}{\text{|}}$ 变化; (d) Z波转换区域${\text{|}}{{n}_{\text{s}}}{\text{|}}$ 变化Figure 11. Electrostatic disturbance and
$ {{n}_{\text{s}}} $ disturbance in O-wave conversion region: (a) Variation of O-wave conversion region with respect to${\text{|}}{{E}_{z}}{\text{|}}$ ; (b) variation of O-wave conversion region with respect to${\text{|}}{{n}_{\text{s}}}{\text{|}}$ ; (c) variation of Z-wave conversion region with respect to${\text{|}}{{E}_{z}}{\text{|}}$ ; (d) variation of Z-wave conversion region with respect to${\text{|}}{{n}_{\text{s}}}{\text{|}}$ . -
[1] Perkins F W, Kaw P K 1971 J. Geophys. Res. 761 282
[2] Gurevich A V, Carlson H C, Medvedev Y V, Zybin K P 2004 J. Plasma Phys. Res. 30 995
Google Scholar
[3] Cannon P D, Honary F, Borisov N 2016 J. Geophys. Res. Space. Phys. 121 2755
Google Scholar
[4] Close R A, Bauer B S, Wong A Y, Langdon A B, Kruer W L, Mjølhus E 1990 Radio Sci. 25 1341
Google Scholar
[5] Eliasson B, Papadopoulos K 2016 J. Geophys. Res. Space Phys. 121 2727
Google Scholar
[6] Newman D L, Winglee R M, Robinson P A, Glanz J, Goldman M V 1990 Phys. Fluids B 2 2600
Google Scholar
[7] Rietveld M T, Isham B, Grydeland T, Hoz C L, Hagfors T 2002 Adv. Space Res. 29 1363
Google Scholar
[8] Eliasson B, Thidé B 2008 J. Geophys. Res. 113 A02313
[9] Eliasson B, Stenflo L 2013 Mod. Phys. Lett. B 27 1330005
[10] Mjølhus E, Hanssen A, DuBois D F 1995 J. Geophys. Res. 100 17527
Google Scholar
[11] Eliasson B, Thidé B 2007 J. Geophys. Res. Lett. 34 L06106
[12] Eliasson B, Shao X, Milikh G, Mishin E V, Papadopoulos K 2012 J. Geophys. Res. Space Phys. 117 A10321
[13] 刘默然, 周晨, 赵正予, 张援农 2016 电波科学学报 31 743
Google Scholar
Liu M R, Zhou C, Zhao Z Y, Zhang Y N 2016 Chin. J. Radio 31 743
Google Scholar
[14] 何昉, 赵正予, 倪彬彬, 张援农 2016 电波科学学报 21 525
Google Scholar
He F, Zhao Z Y, Ni B B, Zhang Y N 2016 Chin. J. Radio 21 525
Google Scholar
[15] Zhu T 2018 M. S. Thesis (Zhenjiang: Jiangsu University) (in Chinese)
[16] Eliasson B, Milikh G, Shao X, Mishin E V, Papadopoulos K 2015 J. Plasma Phys. 81 415810201
Google Scholar
[17] Zhang Y 2014 M. S. Thesis (Xi’an: Xidian University) (in Chinese)
[18] 樊永永 2013 硕士学位论文 (西安: 西安电子科技大学)
Fan Y Y 2013 M. S. Thesie (Xi’an: Xidian University) (in Chinese)
[19] 杨利霞, 谢应涛, 孔娃, 于萍萍, 王刚 2010 物理学报 59 6089
Google Scholar
Yang L X, Xie Y T, Kong W, Yu P P, Wang G 2010 Acta Phys, Sin. 59 6089
Google Scholar
[20] Taflove A, Hagness S C, Piket-May M 2005 Computational Electrodynamics: the Finite-difference Time-domain Method (Academic Press) pp629–669
[21] Mjølhus E, Helmersen E, DuBois D F 2003 Nonlinear Processes Geophys. 10 151
Google Scholar
[22] Robinson T R 1989 Phys. Res. 179 153
[23] Mishin E, Hagfors T, Kofman W 1997 J. Geophys. Res. Space Phys. 102 27265
Google Scholar
[24] Gondarenko N A, Guzdar P N, Ossakow S L, Bernhardt P A 2003 J. Geophys. Res. Space Phys. 108 1470
Google Scholar
[25] Gondarenko N A, Ossakow S L, Milikh G M 2006 Geophys. Res. Lett. 33 399
[26] 葛德彪, 闫玉波 2011 电磁波时域有限差分方法 (西安: 西安电子科技大学出版社) 第42—46页
Ge D B, Yan Y B 2011 The Finite-Difference Time-Domain Method (Xi’an: Xidian University Press) pp42–46 (in Chinese)
[27] 李定 2006 等离子体物理学 (北京: 高等教育出版社) 第88页
Li D 2006 Plasma Physics (Beijing: Higher Education Press) p88 (in Chinese)
[28] Benson R F, Webb P A, Green J L, Carpenter D L, Sonwalkar V S, James H G, Reinisch B W 2006 Ringberg Workshop on High Frequency Waves in Geospace, Ringberg, Germany, July 11–14, 2004 p687
[29] Zhang J, Hai Y F, Wayne S 2018 IEEE Trans. Plasma Sci. 46 2146
Google Scholar
[30] Chen J, Yan Y B, Li Q L, Yuan G, Li H Y, Hao S J, Che H Q 2018 12 th International Symposium on Antennas, Propagation and Electromagnetic Theory (ISAPE) Hangzhou, China, December 3–6, 2018 p650
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