三维行波磁场对等离子体鞘套密度的调控作用

徐子原; 周辉; 刘光翰; 高中亮; 丁丽; 雷凡

doi:10.7498/aps.73.20240877

摘要

飞行器以高超音速飞行或再入过程中, 表面会被等离子体鞘套包覆. 等离子体鞘套会阻碍电磁波传播, 造成飞行器无线电信号衰减甚至中断, 即通信黑障. 行波磁场是一种能够通过调控等离子体鞘套密度来缓解通信黑障的磁场. 本文针对一维行波磁场无法准确描述空间内等离子体密度分布的问题, 建立了三维行波磁场产生模型和三维等离子体密度分布模型. 通过研究行波磁场与等离子体相互作用的机理, 得到了空间内等离子体的密度分布. 研究结果表明, 在行波磁场的作用下, 等离子体会往飞行器前端汇聚, 从而在后端形成尺寸为50$\times$100 mm的密度降低区域, 使该区域内的等离子体密度最大降低71%, 且提供持续的通信时间. 基于RAM-C飞行试验的数据, 利用所提出的模型研究了电流大小和行波速度对飞行器再入过程中电磁波衰减的影响, 同时对比了行波磁场与外加静磁场对电磁波衰减的抑制效果. 结果表明, 施加行波磁场能够使飞行器在30.48 km处的X波段以及其他高度处的L波段、S波段、C波段和X波段的电磁波衰减降低到30 dB以下. 行波磁场和静磁场的对比结果表明, 行波磁场对电磁波衰减的抑制效果明显优于静磁场.

关键词:

Abstract

When the vehicle travels at a hypersonic speed or during re-entry, the surface is covered by a plasma sheath. Plasma sheath can impede electromagnetic wave propagation, causing vehicle radio signals to be attenuated or even interrupted, which is communication blackout. The traveling magnetic field is a kind of magnetic field that can mitigate the communication blackout by adjusting the density of the plasma sheath. In this work, a three-dimensional traveling magnetic field generation model and a three-dimensional plasma density distribution model are established for the problem that the one-dimensional traveling magnetic field cannot accurately describe the plasma density distribution in space. The mechanism of the interaction between the traveling magnetic field and the plasma is investigated to obtain the plasma density distribution in space. The results show that applying a traveling magnetic field can generate a density reduction region of 50$\times$100 mm at the rear of the vehicle, resulting in a maximum decrease of 71% in plasma density in the region and providing continuous communication time. Meanwhile, the effects of initial density, collision frequency, traveling velocity and current magnitude on the plasma density distribution are investigated. The results show that with the increase of the initial density, the ability to regulate the plasma density is improved. However, due to the large density base, the adjusted plasma density is still higher than the plasma density of the low-density case. The increase of the collision frequency can significantly reduce the regulation effect. Increasing the traveling velocity and current can enhance the density-adjusting effect. However, further increasing the traveling velocity to above 800 m/s does not yield a more significant adjustment effect. Based on the data from the RAM-C flight test, the proposed model is used to study the effects of current magnitude and traveling velocity on the electromagnetic wave attenuation during aircraft reentry. The mitigation effect of the traveling magnetic field on electromagnetic wave attenuation is also compared with the effect of applying a static magnetic field. The results show that the applied traveling magnetic field can reduce the electromagnetic wave attenuation of the vehicle to below 30 dB in the X-band at an altitude of 30.48km, as well as in the L-, S-, C- and X-bands at other altitudes. The comparison between traveling magnetic field and static magnetic field demonstrates that the traveling magnetic field significantly outperforms the static magnetic field in mitigating electromagnetic wave attenuation.

Keywords:

作者及机构信息

1.
山东理工大学电气与电子工程学院, 淄博　255000

2.
陕西科技大学电气与控制工程学院, 西安　710016

通信作者: 周辉, zhouh@sdut.edu.cn

基金项目: 国家自然科学基金(批准号: 62101310, 62304125)和陕西省青年自然科学基金(批准号: 2023-JC-QN-0051)资助的课题.

Authors and contacts

1.
School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255000, China

2.
School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi’an 710016, China

Corresponding author: Zhou Hui, zhouh@sdut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62101310, 62304125) and the Young Scientists Fund of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2023-JC-QN-0051).

文章全文 : translate this paragraph

参考文献

[1]	Bai B, Liu Y M, Li X P, Yao B, Shi L 2018 Phys. Plasmas 25 062101 Google Scholar
[2]	Zhao Q, Xing X J, Xuan Y L, Liu S Z 2014 Plasma Sci. Technol. 16 614 Google Scholar
[3]	Lemmer K M, Gallimore A D, Smith T B, Davis C N, Peterson P 2009 J. Spacecr. Rockets 46 1100 Google Scholar
[4]	Kundrapu M, Loverich J, Beckwith K, Stoltz P, Shashurin A, Keidar M, Ketsdever A 2015 J. Spacecr. Rockets 52 853 Google Scholar
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[10]	Takahashi Y, Enoki N, Takasawa H, Oshima N 2020 J. Phys. D: Appl. Phys. 53 235203 Google Scholar
[11]	Miyashita T, Takasawa H, Takahashi Y, Steffens L, Gülhan A 2024 AIAA J. 62 437 Google Scholar
[12]	Miyashita T, Sugihara Y, Takahashi Y, Nagata Y, Kihara, H 2024 J. Phys. D: Appl. Phys. 57 325206 Google Scholar
[13]	Ouyang W C, Liu Q, Wu Z W 2023 Chin. J. Aeronaut. 36 137
[14]	Zhou H, Li X P, Xie K, Liu Y M, Yu Y Y 2017 AIP Advances 7 025114 Google Scholar
[15]	Keidar M, Kim M, Boyd I D 2008 J. Spacecr. Rockets 45 445 Google Scholar
[16]	Kim M, Keidar M, Boyd I D 2008 IEEE Trans. Plasma Sci. 36 1198 Google Scholar
[17]	Guo S S, Xie K, Xu H, Fu M X, Niu Y Y 2023 Plasma Sci. Technol. 25 065401 Google Scholar
[18]	Stenzel R L, Urrutia J M 2013 J. Appl. Phys. 113 103303 Google Scholar
[19]	Liu D, Li X, Liu Y, Xu J, Lei F, Chen X 2018 AIP Advances 8 085020 Google Scholar
[20]	Xu J H, Li X P, Liu D L, Wang Y 2021 Plasma Sci. Technol. 23 075301 Google Scholar
[21]	Han M Y, Li Z M, Zhou H, Li Z Y, Liu G H, Xu Z Y, Liu Z 2024 IEEE Trans. Plasma Sci. 52 259 Google Scholar
[22]	Guo S S, Xie K, Sun B, Liu S W 2020 Plasma Sci. Technol. 22 125301 Google Scholar
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[24]	Liu D L, Li X P, Liu Y M, Xu J H, Lei F, Chen X 2018 AIP Advances 8 085803
[25]	Kim M 2009 Ph.D. Dissertation (Ann Arbor: University of Michigan
[26]	Zhou H, Li X P, Xie K, Liu Y M, Yao B, Ai W 2017 AIP Advances 7 105314 Google Scholar
[27]	Xu J H, Li X P, Liu D L, Xu C, Qin Y Q 2021 Phys. Plasmas 28 042509 Google Scholar
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施引文献

图 1 TMF调控等离子体密度的三维模型示意图

Fig. 1. Schematic of the three-dimensional model of the plasma density regulated by TMF

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图 2 TMF产生装置结构图

Fig. 2. Structural diagram of TMF generator

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图 3 矩形线圈的空间直角坐标系

Fig. 3. Spatial cartesian coordinate system for rectangular coil

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图 4 仿真模型示意图

Fig. 4. Schematic diagram of the simulation model

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图 5 初始等离子体密度分布　(a)等离子体密度沿Z轴的一维分布; (b)等离子体密度在空间中的三维分布

Fig. 5. Initial plasma density distribution: (a) One-dimensional distribution of plasma density along the Z-axis; (b) three-dimensional distribution of plasma density in space

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图 6 磁通密度大小与分布　(a)磁通密度随电流变化的曲线; (b)磁通密度最大值与距离飞行器表面的高度的关系

Fig. 6. Magnitude and distribution of magnetic flux density: (a) Curve of flux density as a function of current; (b) flux density maximum as a function of height from the surface of the vehicle

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图 7 磁通密度在空间中的分布　(a) XOY截面; (b) XOZ截面; (c) (175, 50, 25)处磁通密度随时间变化的曲线

Fig. 7. The distribution of magnetic flux density in space: (a) XOY section; (b) XOZ section; (c) curve of magnetic flux density as a function of time at (175, 50, 25)

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图 8 电磁力随时间变化的曲线

Fig. 8. Curve of electromagnetic force as a function of time

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图 9 4个时间点的电磁力大小和方向示意图　(a) $1\times10^{-6} \;{\mathrm{s}}$; (b)$3\times10^{-5} \;{\mathrm{s}} $; (c)$5\times10^{-5} \;{\mathrm{s}} $; (d)$1.2\times10^{-4} \;{\mathrm{s}} $

Fig. 9. Schematic representation of the magnitude and direction of the electromagnetic force at four points in time: (a)$1\times10^{-6} \;{\mathrm{s}} $; (b)$3\times10^{-5} \;{\mathrm{s}} $; (c)$ 5\times10^{-5} \;{\mathrm{s}} $; (d)$1.2\times10^{-4} \;{\mathrm{s}} $

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图 10 等离子体密度随时间的变化趋势

Fig. 10. Trends in plasma density over time

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图 11 等离子体密度沿不同方向的取值示意图和变化曲线　(a)等离子体密度取值示意图; (b)沿X轴取值; (c)沿Y轴取值; (d)沿Z轴取值

Fig. 11. Schematic diagram of plasma density values along different directions: (a) Schematic diagram of plasma density taking values; (b) values along the X-axis; (c) values along the Y-axis; (d) values along the Z-axis

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图 12 初始密度对等离子密度削弱的影响

Fig. 12. Effect of initial density on plasma density reduction

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图 13 碰撞频率对等离子体密度削弱的影响

Fig. 13. Effect of collision frequency on plasma density reduction

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图 14 行波速度对等离子体密度削弱的影响

Fig. 14. Effect of traveling velocity on plasma density reduction

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图 15 电流对等离子体密度削弱的影响

Fig. 15. Effect of current on plasma density reduction

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图 16 阶段1施加TMF对电磁波衰减的影响　(a)电流对电磁波衰减的影响; (b)行波速度对电磁波衰减的影响

Fig. 16. Effect of applying TMF on EM wave attenuation in phase 1: (a) Effect of current on the attenuation of EM waves; (b) effect of traveling velocity on the attenuation of EM waves

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图 17 阶段2施加TMF对电磁波衰减的影响　(a)电流对电磁波衰减的影响; (b)行波速度对电磁波衰减的影响

Fig. 17. Effect of applying TMF on EM wave attenuation in phase 2: (a) Effect of current on the attenuation of EM waves; (b) effect of traveling velocity on the attenuation of EM waves

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图 18 阶段3施加TMF对电磁波衰减的影响　(a)电流对电磁波衰减的影响; (b)行波速度对电磁波衰减的影响

Fig. 18. Effect of applying TMF on EM wave attenuation in phase 3: (a) Effect of current on the attenuation of EM waves; (b) effect of traveling velocity on the attenuation of EM waves

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图 19 阶段4施加TMF对电磁波衰减的影响　(a)电流对电磁波衰减的影响; (b)行波速度对电磁波衰减的影响

Fig. 19. Effect of applying TMF on EM wave attenuation in phase 4: (a) Effect of current on the attenuation of EM waves; (b) effect of traveling velocity on the attenuation of EM waves

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图 20 TMF与外加静磁场的效果对比　(a) L波段; (b) S波段; (b) C波段; (b) X波段

Fig. 20. Comparison of the effect of TMF with applied static magnetic field: (a) L-band; (b) S-band; (b) C-band; (b) X-band

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表 1 RAM-C飞行试验中不同高度下的等离子体鞘套参数

Table 1. Plasma sheath parameters at different altitudes in the RAM-C flight test

再入过程	海拔/km	气压/Pa	等离子体密度/$ {\mathrm{m}}^{-3} $	碰撞频率/GHz	等离子体鞘套厚度/cm
阶段1	76.2	2	$ 4.02\times 10^{16} $	0.005	14.0
阶段1	71.02	17	$ 1\times 10^{17} $	0.012	11.2
阶段2	61.57	25	$ 4.037\times 10^{17} $	0.050	7.8
	53.34	55	$ 6.86\times 10^{17} $	0.175	7.0
	47.55	288	$ 1.02\times 10^{18} $	0.420	5.8
阶段3	30.48	1197	$ 1\times 10^{19} $	5.710	6.8
阶段4	25.01	2094	$ 5\times 10^{18} $	13.18	5.4
阶段4	21.34	4085	$ 5.03\times 10^{16} $	23.00	5.3

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map

[1]	Bai B, Liu Y M, Li X P, Yao B, Shi L 2018 Phys. Plasmas 25 062101 Google Scholar
[2]	Zhao Q, Xing X J, Xuan Y L, Liu S Z 2014 Plasma Sci. Technol. 16 614 Google Scholar
[3]	Lemmer K M, Gallimore A D, Smith T B, Davis C N, Peterson P 2009 J. Spacecr. Rockets 46 1100 Google Scholar
[4]	Kundrapu M, Loverich J, Beckwith K, Stoltz P, Shashurin A, Keidar M, Ketsdever A 2015 J. Spacecr. Rockets 52 853 Google Scholar
[5]	Cheng J J, Jin K, Kou Y, Hu R F, Zheng X J 2017 J. Appl. Phys. 121 093301 Google Scholar
[6]	Xiong J, Yuan K, Tang R, Mao M, Deng X 2023 Phys. Plasmas 30 090701 Google Scholar
[7]	刘祥群, 刘宇, 凌艺铭, 雷久侯, 曹金祥, 李瑾, 钟育民, 谌明, 李艳华 2022 71 145202 Google Scholar Liu X Q, Liu Y, Ling Y M, Lei J H, Cao J X, Li J, Zhong Y M, Chen M, Li Y H 2022 Acta Phys. Sin. 71 145202 Google Scholar
[8]	Yang M, Li X P, Xie K, Liu Y M 2015 Phys. Plasmas 22 022120 Google Scholar
[9]	Belov I F, Borovoy V Y, Gorelov V A, Kireev A Y, Korolev A S, Stepanov E A 2001 J. Spacecr. Rockets 38 249 Google Scholar
[10]	Takahashi Y, Enoki N, Takasawa H, Oshima N 2020 J. Phys. D: Appl. Phys. 53 235203 Google Scholar
[11]	Miyashita T, Takasawa H, Takahashi Y, Steffens L, Gülhan A 2024 AIAA J. 62 437 Google Scholar
[12]	Miyashita T, Sugihara Y, Takahashi Y, Nagata Y, Kihara, H 2024 J. Phys. D: Appl. Phys. 57 325206 Google Scholar
[13]	Ouyang W C, Liu Q, Wu Z W 2023 Chin. J. Aeronaut. 36 137
[14]	Zhou H, Li X P, Xie K, Liu Y M, Yu Y Y 2017 AIP Advances 7 025114 Google Scholar
[15]	Keidar M, Kim M, Boyd I D 2008 J. Spacecr. Rockets 45 445 Google Scholar
[16]	Kim M, Keidar M, Boyd I D 2008 IEEE Trans. Plasma Sci. 36 1198 Google Scholar
[17]	Guo S S, Xie K, Xu H, Fu M X, Niu Y Y 2023 Plasma Sci. Technol. 25 065401 Google Scholar
[18]	Stenzel R L, Urrutia J M 2013 J. Appl. Phys. 113 103303 Google Scholar
[19]	Liu D, Li X, Liu Y, Xu J, Lei F, Chen X 2018 AIP Advances 8 085020 Google Scholar
[20]	Xu J H, Li X P, Liu D L, Wang Y 2021 Plasma Sci. Technol. 23 075301 Google Scholar
[21]	Han M Y, Li Z M, Zhou H, Li Z Y, Liu G H, Xu Z Y, Liu Z 2024 IEEE Trans. Plasma Sci. 52 259 Google Scholar
[22]	Guo S S, Xie K, Sun B, Liu S W 2020 Plasma Sci. Technol. 22 125301 Google Scholar
[23]	Soliman E A, Helaly A, Megahed A A 2007 Prog. Electromagn. Res. 67 25 Google Scholar
[24]	Liu D L, Li X P, Liu Y M, Xu J H, Lei F, Chen X 2018 AIP Advances 8 085803
[25]	Kim M 2009 Ph.D. Dissertation (Ann Arbor: University of Michigan
[26]	Zhou H, Li X P, Xie K, Liu Y M, Yao B, Ai W 2017 AIP Advances 7 105314 Google Scholar
[27]	Xu J H, Li X P, Liu D L, Xu C, Qin Y Q 2021 Phys. Plasmas 28 042509 Google Scholar
[28]	Rawhouser R 1970 Overview of the AF Avionics Laboratory Reentry Electromagnetics Program Hampton, VA, October 13, 1970 p3
[29]	Ouyang W C, Ding C B, Liu Q, Lu Q M, Wu Z W 2023 Results Phys. 53 106983 Google Scholar
[30]	Wu X, Zhang J H, Dong G X, Shi L 2024 Chin. Phys. B 33 055201 Google Scholar
[31]	杨敏, 王佳明, 齐凯旋, 李小平, 谢楷, 张琼杰, 刘浩岩, 董鹏 2022 71 235201 Google Scholar Yang M, Wang J M, Qi K X, Li X P, Xie K, Zhang Q J, Liu H Y, Dong P 2022 Acta Phys. Sin. 71 235201 Google Scholar

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