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当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.When the vehicle is traveling at hypersonic speeds or during re-entry, the surface is enveloped 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 regulating the density of the plasma sheath. In this paper, 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 was investigated to obtain the plasma density distribution in space. The results show that the application of a traveling magnetic field is capable of generating a density reduction region with dimensions of 50$\times$ 100 mm at the rear end of the vehicle, reducing the density of the inhomogeneous plasma in the region by a maximum of 71% and providing sustained communication time. Meanwhile, the effects of initial density, collision frequency, traveling velocity and current magnitude on the plasma density distribution were investigated. The results show that with the increase of the initial density, the ability to regulate the plasma density is improved, but due to the large density base, the regulated plasma density is still higher than that of the low-density case; the increase of the collision frequency significantly reduces the regulation effect; the increase of the traveling velocity and the current are able to enhance the density regulation effect, but continuing to increase the traveling velocity on the basis of 800 m/s does not produce a more significant regulation effect. Based on the data from the RAM-C flight test, the effects of current magnitude and traveling velocity on the electromagnetic wave attenuation during the reentry process of the vehicle are investigated using the proposed model, and the mitigation effects of the traveling magnetic field on the electromagnetic wave attenuation are also compared with those of the applied static magnetic field. The results show that the applied traveling magnetic field can reduce the electromagnetic wave attenuation of the vehicle to less than 30dB in the X-band at 30.48km, as well as in the L-, S-, C- and X-bands at other altitudes. The comparison results of traveling magnetic field and static magnetic field show that the mitigation effect of traveling magnetic field on electromagnetic wave attenuation is significantly better than that of static magnetic field.
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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
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
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
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. 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)
图 9 四个时间点的电磁力大小和方向示意图
Fig. 9. Schematic representation of the magnitude and direction of the electromagnetic force at four points in time
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
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
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
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
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
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
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
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
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/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 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 21.34 4085 $ 5.03\times 10^{16} $ 23.00 5.3 
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