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The plasma sheath is produced by high-temperature heating during the reentry of a hypersonic vehicle to the Earth atmosphere. Temperature around the vehicle rises rapidly because of severe friction with air. The vehicle temperature behind friction is high enough to excite various real gas effects including chemical reactions of air, which contains ablation particles of vehicle, free electrons, and ions. The plasma sheath greatly affects the transmission of electromagnetic waves and has very strong interference on the communication signals, which results in interrupt between the target and the ground station, namely, blackout. The electron density of plasma sheath surrounding the aircraft is inhomogeneous and varies with time. Temperature and pressure will also change at different altitudes. Therefore, it is meaningful to investigate the propagation characteristics of electromagnetic waves in temporally and spatially inhomogeneous plasma sheath. The temporally and spatially inhomogeneous plasma sheath model is introduced and the electron density data of the National Aeronautics and Space Administration (NASA) reentry vehicle is employed. The relationships among temperature, pressure, and collision frequency are obtained with the empirical formula of collision frequency. Then, the reflection coefficient and transmission coefficient of time-varying single layer plasma are calculated with the shift operator finite-difference time-domain (SO-FDTD) method. These results are compared to verify the correctness of the proposed method. Finally, the LTJEC-FDTD method is used to calculate the reflection coefficient, transmission coefficient and absorptivity at different relaxation time, temperature, and pressure in the terahertz (THz) band. The results show that the higher temperature and pressure will enable the electromagnetic wave to penetrate the plasma sheath at high relaxation time of electron density. If the incident wave frequency is lower than the cut-off frequency of plasma, the reflection of electromagnetic wave will be more obvious. However, when the incident wave frequency is in the THz band, the effects of temperature and pressure on the propagation of electromagnetic wave are obviously weakened. The absorption of electromagnetic wave by plasma will be more obvious when the relaxation time, temperature, and pressure decrease. If the relaxation time of electron density is shorter than or equal to the period of THz wave, more energy of electromagnetic wave will be absorbed by the plasma sheath. Contrarily, if the relaxation time of electron density is much longer than the period of THz wave, the absorption of electromagnetic energy will decrease. This study gives some insight into the temporally and spatially inhomogeneous plasma sheath, and provides a theoretical basis for solving the blackout problem.
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Keywords:
- temporally and spatially inhomogeneous plasma /
- plasma sheath /
- terahertz wave /
- finite-difference time-domain method
[1] Bo Y, Zhao Q, Luo X G, Liu Y, Chen Y X, Liu J W 2016 Acta Phys. Sin. 65 035201 (in Chinese) [薄勇, 赵青, 罗先刚, 刘颖, 陈禹旭, 刘建卫 2016 65 035201]
[2] Sang C F, Dai S Y, Sun J Z, Bonnin X, Xu Q, Ding F, Wang D Z 2014 Chin. Phys. B 23 115201
[3] Li Y R, Ma J X, Zheng Y B, Zhang W G 2010 Chin. Phys. B 19 085201
[4] Yu D R, Qing S W, Yan G J, Duan P 2011 Chin. Phys. B 20 065204
[5] Yang L X, Shen D H, Shi W D 2013 Acta Phys. Sin. 62 104101 (in Chinese) [杨利霞, 沈丹华, 施卫东 2013 62 104101]
[6] Cui P Y, Dou Q, Gao A 2014 J. Astr. 35 1 (in Chinese) [催平远, 窦强, 高艾 2014 宇航学报 35 1]
[7] Fang T Z, Jiang N, Wang L 2005 Chin. Phys. B 14 2256
[8] Wang J L, Zhang J L, Liu Y F, Wang Y N, Liu C Z, Yang S Z 2004 Chin. Phys. B 13 0065
[9] Gnoffo P A, Gupta R N, Shinn J L 1989 Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium (Hampton: Langley Research Center) NASA-TP-2867
[10] Dunn M G, Kang S W 1973 Theoretical and Experimental Studies of Reentry Plasmas (Washington: National Aeronautics and Space Administration) NASA-CR-2232
[11] Jones W L, Cross A E 1972 Electrostatic-Probe Measurements of Plasma Parameters for Two Reentry Flight Experiments at 25000 Feet Per Second (Hampton: Langley Research Center) NASA-TN-D-6617
[12] Stenzel R L, Urrutia J M 2013 J. Appl. Phys. 113 103303
[13] Rybak J P, Churchill R J 1971 IEEE Trans. Aerospace Electron. Syst. 7 879
[14] Keidar M, Kim M, Boyd I D 2008 J. Spacecraft Rockets 45 445
[15] Yuan C X, Zhou Z X, Xiang X L, Sun H G, Pu S Z 2010 Phys. Plasmas 17 1133044
[16] Li S T, Li J, Zhu Z B, Cui W Z 2015 J. Terahertz Sci. Electron. Informat. Techn. 13 203 (in Chinese) [李拴涛, 李军, 朱忠博, 崔万照 2015 太赫兹科学与电子信息学报 13 203]
[17] Chen W B, Gong X Y, Deng X J, Feng J, Huang G Y 2014 Acta Phys. Sin. 63 194101 (in Chinese) [陈文波, 龚学余, 邓贤君, 冯军, 黄国玉 2014 63 194101]
[18] Zheng L 2013 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [郑灵 2013 博士学位论文 (成都: 电子科技大学)]
[19] Chen W, Guo L X, Li J T, Liu S H 2016 IEEE Trans. Plasma Sci. 44 3235
[20] Lee J H, Kalluri D K 1999 IEEE Trans. Antennas Propag. 47 1146
[21] Wang M Y, Yu M X, Xu Z T, Li G P, Jiang B J, Xu J 2010 IEEE Trans. Plasma Sci. 43 4182
[22] Ge D B, Yan Y B 2011 Finite-Difference Time-Domain Method for Electromagnetic Waves (3rd Ed.) (Xi'an: Xidian University Press) p259 (in Chinese) [葛德彪, 闫玉波 2011 电磁波时域有限差分方法 (第三版) (西安: 西安电子科技大学出版社) 第259页]
[23] Yu P P 2012 M. S. Thesis (Zhenjiang: Jiangsu University) (in Chinese) [于萍萍 2012 硕士学位论文 (镇江: 江苏大学)]
[24] Jin S S 2011 M. S. Thesis (Xi'an: Xidian University) (in Chinese) [金莎莎 2011 硕士学位论文 (西安: 西安电子科技大学)]
[25] Liu Z W, Bao W M, Li X P, Liu D L 2014 Acta Phys. Sin. 23 235201 (in Chinese) [刘智惟, 包为民, 李小平, 刘东林 2014 23 235201]
[26] Potter D L 2006 37th AIAA Plasmadynamics and Lasers Conference San Francisco, USA, June 5-8, 2006 p3239
[27] Liu S B 2004 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [刘少斌 2004 博士学位论文 (长沙: 国防科学技术大学)]
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[1] Bo Y, Zhao Q, Luo X G, Liu Y, Chen Y X, Liu J W 2016 Acta Phys. Sin. 65 035201 (in Chinese) [薄勇, 赵青, 罗先刚, 刘颖, 陈禹旭, 刘建卫 2016 65 035201]
[2] Sang C F, Dai S Y, Sun J Z, Bonnin X, Xu Q, Ding F, Wang D Z 2014 Chin. Phys. B 23 115201
[3] Li Y R, Ma J X, Zheng Y B, Zhang W G 2010 Chin. Phys. B 19 085201
[4] Yu D R, Qing S W, Yan G J, Duan P 2011 Chin. Phys. B 20 065204
[5] Yang L X, Shen D H, Shi W D 2013 Acta Phys. Sin. 62 104101 (in Chinese) [杨利霞, 沈丹华, 施卫东 2013 62 104101]
[6] Cui P Y, Dou Q, Gao A 2014 J. Astr. 35 1 (in Chinese) [催平远, 窦强, 高艾 2014 宇航学报 35 1]
[7] Fang T Z, Jiang N, Wang L 2005 Chin. Phys. B 14 2256
[8] Wang J L, Zhang J L, Liu Y F, Wang Y N, Liu C Z, Yang S Z 2004 Chin. Phys. B 13 0065
[9] Gnoffo P A, Gupta R N, Shinn J L 1989 Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium (Hampton: Langley Research Center) NASA-TP-2867
[10] Dunn M G, Kang S W 1973 Theoretical and Experimental Studies of Reentry Plasmas (Washington: National Aeronautics and Space Administration) NASA-CR-2232
[11] Jones W L, Cross A E 1972 Electrostatic-Probe Measurements of Plasma Parameters for Two Reentry Flight Experiments at 25000 Feet Per Second (Hampton: Langley Research Center) NASA-TN-D-6617
[12] Stenzel R L, Urrutia J M 2013 J. Appl. Phys. 113 103303
[13] Rybak J P, Churchill R J 1971 IEEE Trans. Aerospace Electron. Syst. 7 879
[14] Keidar M, Kim M, Boyd I D 2008 J. Spacecraft Rockets 45 445
[15] Yuan C X, Zhou Z X, Xiang X L, Sun H G, Pu S Z 2010 Phys. Plasmas 17 1133044
[16] Li S T, Li J, Zhu Z B, Cui W Z 2015 J. Terahertz Sci. Electron. Informat. Techn. 13 203 (in Chinese) [李拴涛, 李军, 朱忠博, 崔万照 2015 太赫兹科学与电子信息学报 13 203]
[17] Chen W B, Gong X Y, Deng X J, Feng J, Huang G Y 2014 Acta Phys. Sin. 63 194101 (in Chinese) [陈文波, 龚学余, 邓贤君, 冯军, 黄国玉 2014 63 194101]
[18] Zheng L 2013 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [郑灵 2013 博士学位论文 (成都: 电子科技大学)]
[19] Chen W, Guo L X, Li J T, Liu S H 2016 IEEE Trans. Plasma Sci. 44 3235
[20] Lee J H, Kalluri D K 1999 IEEE Trans. Antennas Propag. 47 1146
[21] Wang M Y, Yu M X, Xu Z T, Li G P, Jiang B J, Xu J 2010 IEEE Trans. Plasma Sci. 43 4182
[22] Ge D B, Yan Y B 2011 Finite-Difference Time-Domain Method for Electromagnetic Waves (3rd Ed.) (Xi'an: Xidian University Press) p259 (in Chinese) [葛德彪, 闫玉波 2011 电磁波时域有限差分方法 (第三版) (西安: 西安电子科技大学出版社) 第259页]
[23] Yu P P 2012 M. S. Thesis (Zhenjiang: Jiangsu University) (in Chinese) [于萍萍 2012 硕士学位论文 (镇江: 江苏大学)]
[24] Jin S S 2011 M. S. Thesis (Xi'an: Xidian University) (in Chinese) [金莎莎 2011 硕士学位论文 (西安: 西安电子科技大学)]
[25] Liu Z W, Bao W M, Li X P, Liu D L 2014 Acta Phys. Sin. 23 235201 (in Chinese) [刘智惟, 包为民, 李小平, 刘东林 2014 23 235201]
[26] Potter D L 2006 37th AIAA Plasmadynamics and Lasers Conference San Francisco, USA, June 5-8, 2006 p3239
[27] Liu S B 2004 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [刘少斌 2004 博士学位论文 (长沙: 国防科学技术大学)]
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