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When a hypersonic vehicle is flying in the near space region, the strong friction between the vehicle and the air can cause the air to ionize. As a result, the plasma sheath around the vehicle and the wake flow field behind it are formed, significantly affecting the electromagnetic (EM) scattering characteristics of the vehicle and resulting in the communication blackout. Therefore, the investigation of electron density distribution of the plasma sheath and wake flow field is of the great significance in the detection, communication, etc. of the hypersonic target. In order to meet the requirements for on-ground electron density distribution measurement of the transient plasma flow fields, the feasibility of measuring electron density profile with seven-channel microwave interferometer measurement system is demonstrated in this work. The wake plasma is modeled as a non-uniform multilayer medium, and the full-wave simulation software FEKO is used to calculate the phase-shift information of EM wave transmitting through non-uniform single-layered dielectric plate, uniform and non-uniform multi-layered dielectric plates. According to the simulation results, the dielectric constant of the substrate is retrieved and compared with the preset result. The retrieved results show that it is feasible that the dielectric constant distribution of non-uniform multi-layered dielectric plate is measured by utilizing the proposed microwave interferometer system with one transmission port and seven receptions. The amplitude-phase dynamic range analysis of the proposed Ka-band microwave measurement system is also carried out. The key technologies including large instantaneous amplitude-phase dynamic range and ray tracking inversion algorithm for two-dimensional (2-D) electron density distribution are also developed. Finally, the complete scheme of Ka-band seven-channel microwave interferometer measurement system is introduced. The system includes one lens antenna to generate the required plane wave and seven open-ended waveguide receiving antennas which are asymmetrically arranged to improve the lateral spatial resolution of the system. The system exhibits the amplitude dynamic range and the phase dynamic range of over 65 dB and 180° under 1 MHz IF bandwidth respectively. The plasma electron density distributions are measured by utilizing the proposed seven-channel microwave interferometer system in the ballistic range and multi-functional shock tube. The response time of the system is smaller than 1μs, satisfying the requirement for the two-dimensional distribution measurement of the transient plasma flow field generated by the ballistic range and multi-functional shock tube. The differences between experimental and numerical results are less than 0.5 order of magnitude, and the variations in transient plasma generated in both ballistic target and shock tube equipments are well detected. The measurement range of plasma electron density is 1010－1013 cm–3 and the spatial resolution is better than 15mm. In addition, the proposed ray tracing method is also used to invert the two-dimensional (2D) electron density distributions of both square layered model and cylindrical layered model under identical experimental state. The results are in consistent with each other, indicating that the proposed ray tracing method can be used in the inversion of 2D electron density distribution of plasma with different shapes.
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Keywords:
- hypervelocity flow field /
- plasma /
- microwave interferometer /
- electron density /
- distribution measurement
[1] 于哲峰, 孙良奎, 马平, 杨益兼, 张志成, 黄洁 2017 红外 38 39
Google Scholar
Yu Z F, Sun L K, Ma P, Yang Y J, Zhang Z C, Huang J 2017 Infrared 38 39
Google Scholar
[2] John W, Marini M 1967 NASA TM X-55824 pp2-8
[3] 韦笑, 彭世鏐, 殷红成, 印国泰 2011 系统工程与电子技术 33 506
Google Scholar
Wei X, Peng S L, Yin H C, Yin G T 2011 Syst. Eng. Electron. 33 506
Google Scholar
[4] 杨利霞, 沈丹华, 施卫东 2013 物理学报 62 104101
Google Scholar
Yang L X, Shen D H, Shi W D 2013 Acta Phys. Sin. 62 104101
Google Scholar
[5] 黄勇, 陈宗胜, 徐记伟 2008 舰船电子对抗 31 18
Google Scholar
Huang Y, Chen Z S, Xu J W 2008 SEC 31 18
Google Scholar
[6] 吴建明, 高本庆 1997 电波科学学报 12 26
Wu J, Gao B Q 1997 Chin. J. Radio Sci. 12 26
[7] 朱方, 吕琼之 2008 现代雷达 30 14
Google Scholar
Zhu F, Lv Q Z 2008 Mod. Radar 30 14
Google Scholar
[8] 周超, 张小宽, 张晨新 2014 现代雷达 36 83
Google Scholar
Zhou C, Zhang X K, Z hang C X 2014 Mod. Radar 36 83
Google Scholar
[9] 李勇 2014 硕士学位论文(南京: 南京邮电大学)
Li Y 2014 M. S. Thesis (Nanjing: Nan-jing University of Posts and Telecommunications
[10] Hayami R A 1992 AIAA 17th Aerospace Ground Testing Conference Nashville, TN, U. S. A, July, 1992 p3998
[11] Landrum D B, Hayami R A 1994 AIAA 25th Plasmadynamics and Lasers Conference, Colorado Springs, CO, U. S. A, June, 1994 p2598
[12] Keidar M, Kim M, Boyd I D 2008 J. Spacecraft Rockets 45 445
Google Scholar
[13] Savino R, Paterna D, De Stefano Fumo M, D’Elia M 2010 Open Aerospace Eng. J. 3 76
Google Scholar
[14] Chadwick K M, Boyer D W, Andre S N 1996 ADA317594 (New York: Calspan Corp Buffalo
[15] Geist T, Wursching E, Hartfuss H J 1997 Rev. Sci. Instrum. 68 1162
Google Scholar
[16] Yoshikawa M, Negishi S, Shima Y, Hojo H, Mase A, Kogi Y, Imai T 2010 Rev. Sci. Instrum. 81 10D514
Google Scholar
[17] Kawamori E, Lin Y H, Mase A, Nishida Y, Cheng C Z 2014 Rev. Sci. Instrum. 85 023507
Google Scholar
[18] Shi P W, Shi Z B, Chen W, Zhong W L, Yang Z C, Jiang M, Zhang B Y, Li Y G, Yu L M, Liu Z T, Ding X T 2016 Plasma Sci. Technol. 18 708
Google Scholar
[19] 任冬梅 2005 硕士学位论文(成都: 电子科技大学)
Ren D M 2005 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[20] 朱佩涛 2006 硕士学位论文(成都: 电子科技大学)
Zhu P T 2006 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[21] 谢楷 2014 博士学位论文(西安: 西安电子科技大学)
Xie K 2014 Ph. D. Dissertation (Xi’ an: XiDian University
[22] 曾彬 2021 硕士学位论文(成都: 电子科技大学)
Zeng B 2021 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[23] 吴明兴, 田得阳, 唐璞, 田径, 何子远, 马平 2022 物理学报 70 115202
Google Scholar
Wu M X, Tian D Y, Tang P, Tian J, He Z Y, Ma P 2022 Acta Phys. Sin. 70 115202
Google Scholar
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图 1 Abel变换示意图
Figure 1. Diagram of Abel transform.
图 2 七通道微波干涉仪测量示意图
Figure 2. Schematic of seven-channel microwave interferometer measurement.
图 3 弹道靶模型尾迹离子体分层模型
Figure 3. The multi-layered model of plasma wake in ballistic range.
图 4 七通道微波干涉法测试分区域介质板仿真结构图
Figure 4. Simulation of multi-channel microwave interferometry with non-uniform dielectric plate.
图 5 近场扫描与开口波导天线接收相位结果反推分区域介质板的介电常数对比图
Figure 5. Comparison of dielectric constant distributions of the dielectric plate achieved with near-field scanning and open waveguide antenna.
图 6 分层介质板平面波激励近场扫描仿真结构示意图
Figure 6. Schematic of plane wave incident on uniform multi-layered dielectric plate.
图 7 开口波导天线接收相位结果反推分区域介质板的介电常数与理论值对比图
Figure 7. Comparison between the theoretical dielectric constant and that deduced from the phase information results received by open waveguide antennas.
图 8 分层分区域介质平板仿真结构示意图
Figure 8. Simulation model of non-uniform multi-layered dielectric plate.
图 9 分层分区域介质板介电常数仿真结果与理论值对比图
Figure 9. Comparison between simulation and theoretical results of the dielectric constant of non-uniform multi-layered dielectric plate.
图 10 七通道Ka波段微波干涉仪测量系统工作原理图
Figure 10. Schematic of the seven-channel Ka-band microwave interferometer measurement system.
图 11 宽度100 mm的空间分布接收天线阵示意图(尺寸单位: mm)
Figure 11. Diagram of the receiving antenna array with a width of 100 mm (The dimensions in the figure are in mm).
图 12 Al2O3球模型尾迹处电子密度径向二维分布 (a) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 10ϕ; (b) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 50ϕ; (c) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 100ϕ
Figure 12. Two-dimensional radial electron density distribution of plasma wake generated by spherical Al2O3 models: (a) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 10ϕ; (b) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 50ϕ; (c) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 100ϕ.
图 13 Al2O3球超高速等离子体流场驻点线上各化学反应的组元生成率曲线图 (a) $ {{\text{O}}_{2}} + {{\text{M}}_{1}} \Leftrightarrow {\text{2O + }}{{\text{M}}_{1}} $; (b) $ \text{N}_2+\text{M}_2\Leftrightarrow\text{2N + }\text{M}_2 $; (c) $ {\text{NO}} + {{\text{M}}_{3}} \Leftrightarrow {\text{N + O + }}{{\text{M}}_{3}} $; (d) $ {\text{NO}} + {\text{O}} \Leftrightarrow {{\text{O}}_{2}}{\text{ + N}} $; (e) $ {{\text{N}}_{2}} + {\text{O}} \Leftrightarrow {\text{NO + N}} $; (f) $ {\text{N}} + {\text{O}} \Leftrightarrow {\text{N}}{{\text{O}}^{+}}{+}{{\text{e}}^{{ - }}} $
Figure 13. Reaction rates vs. distance along wall from stagnation point of plasma flow field of supersonic spherical Al2O3 model: (a) $ \text{O}_2+\text{M}_1\Leftrightarrow\text{2O + }\text{M}_1 $; (b) $ \text{N}_2+\text{M}_2\Leftrightarrow\text{2N + }\text{M}_2 $; (c) $ {\text{NO}} + {{\text{M}}_{3}} \Leftrightarrow {\text{N + O + }}{{\text{M}}_{3}} $; (d) $ {\text{NO}} + {\text{O}} \Leftrightarrow {{\text{O}}_{2}}{\text{ + N}} $; (e) $ {{\text{N}}_{2}} + {\text{O}} \Leftrightarrow {\text{NO + N}} $; (f) $ {\text{N}} + {\text{O}} \Leftrightarrow {\text{N}}{{\text{O}}^{+}}{+}{{\text{e}}^{{ - }}} $.
图 14 方形等离子体分层模型
Figure 14. Model of layered square plasma.
图 15 激波管等离子体电子密度不同反演方法对比图 (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s
Figure 15. Comparison of plasma electron density in shock tube achieved with various methods: (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s.
图 16 激波管等离子体不同分层模型反演结果对比 (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s
Figure 16. Comparison of inversion results of shock tube plasma achieved with various models: (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s.
表 1 PMMA实测测试结果
Table 1. PMMA test results.
工作频率/
GHz$ {\varepsilon _{\text{r}}} $ $ \Delta {\varepsilon _{\text{r}}} $/% 开口波导法 微波干涉仪法 8.0 2.73 2.84 3.87 8.5 2.87 2.76 3.99 9.0 2.60 2.71 4.06 9.5 2.57 2.65 3.01 10.0 2.58 2.62 1.53 10.5 2.58 2.59 0.39 11.0 2.52 2.56 1.56 11.5 2.45 2.52 2.78 12.0 2.47 2.49 0.80 
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表 2 在工作频率为35 GHz下理想等离子体层电子密度测试范围
Table 2. Electron density test range of plasma at 35 GHz.
碰撞频率/
GHz等离子体
厚度/cm等离子体密度
下限/(1010 cm–3)等离子体密度
上限/(1010 cm–3)5 1 306.2 1120.1 2 162.2 612.1 8 42.27 163.5 20 16.98 64.5 40 8.511 32.4 60 5.072 22.1 10 1 171.4 1121.3 2 88.31 653.5 8 22.49 173.1 20 9.036 70.0 40 4.529 35.3 60 3.02 23.5
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[1] 于哲峰, 孙良奎, 马平, 杨益兼, 张志成, 黄洁 2017 红外 38 39
Google Scholar
Yu Z F, Sun L K, Ma P, Yang Y J, Zhang Z C, Huang J 2017 Infrared 38 39
Google Scholar
[2] John W, Marini M 1967 NASA TM X-55824 pp2-8
[3] 韦笑, 彭世鏐, 殷红成, 印国泰 2011 系统工程与电子技术 33 506
Google Scholar
Wei X, Peng S L, Yin H C, Yin G T 2011 Syst. Eng. Electron. 33 506
Google Scholar
[4] 杨利霞, 沈丹华, 施卫东 2013 物理学报 62 104101
Google Scholar
Yang L X, Shen D H, Shi W D 2013 Acta Phys. Sin. 62 104101
Google Scholar
[5] 黄勇, 陈宗胜, 徐记伟 2008 舰船电子对抗 31 18
Google Scholar
Huang Y, Chen Z S, Xu J W 2008 SEC 31 18
Google Scholar
[6] 吴建明, 高本庆 1997 电波科学学报 12 26
Wu J, Gao B Q 1997 Chin. J. Radio Sci. 12 26
[7] 朱方, 吕琼之 2008 现代雷达 30 14
Google Scholar
Zhu F, Lv Q Z 2008 Mod. Radar 30 14
Google Scholar
[8] 周超, 张小宽, 张晨新 2014 现代雷达 36 83
Google Scholar
Zhou C, Zhang X K, Z hang C X 2014 Mod. Radar 36 83
Google Scholar
[9] 李勇 2014 硕士学位论文(南京: 南京邮电大学)
Li Y 2014 M. S. Thesis (Nanjing: Nan-jing University of Posts and Telecommunications
[10] Hayami R A 1992 AIAA 17th Aerospace Ground Testing Conference Nashville, TN, U. S. A, July, 1992 p3998
[11] Landrum D B, Hayami R A 1994 AIAA 25th Plasmadynamics and Lasers Conference, Colorado Springs, CO, U. S. A, June, 1994 p2598
[12] Keidar M, Kim M, Boyd I D 2008 J. Spacecraft Rockets 45 445
Google Scholar
[13] Savino R, Paterna D, De Stefano Fumo M, D’Elia M 2010 Open Aerospace Eng. J. 3 76
Google Scholar
[14] Chadwick K M, Boyer D W, Andre S N 1996 ADA317594 (New York: Calspan Corp Buffalo
[15] Geist T, Wursching E, Hartfuss H J 1997 Rev. Sci. Instrum. 68 1162
Google Scholar
[16] Yoshikawa M, Negishi S, Shima Y, Hojo H, Mase A, Kogi Y, Imai T 2010 Rev. Sci. Instrum. 81 10D514
Google Scholar
[17] Kawamori E, Lin Y H, Mase A, Nishida Y, Cheng C Z 2014 Rev. Sci. Instrum. 85 023507
Google Scholar
[18] Shi P W, Shi Z B, Chen W, Zhong W L, Yang Z C, Jiang M, Zhang B Y, Li Y G, Yu L M, Liu Z T, Ding X T 2016 Plasma Sci. Technol. 18 708
Google Scholar
[19] 任冬梅 2005 硕士学位论文(成都: 电子科技大学)
Ren D M 2005 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[20] 朱佩涛 2006 硕士学位论文(成都: 电子科技大学)
Zhu P T 2006 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[21] 谢楷 2014 博士学位论文(西安: 西安电子科技大学)
Xie K 2014 Ph. D. Dissertation (Xi’ an: XiDian University
[22] 曾彬 2021 硕士学位论文(成都: 电子科技大学)
Zeng B 2021 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China
[23] 吴明兴, 田得阳, 唐璞, 田径, 何子远, 马平 2022 物理学报 70 115202
Google Scholar
Wu M X, Tian D Y, Tang P, Tian J, He Z Y, Ma P 2022 Acta Phys. Sin. 70 115202
Google Scholar
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