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建立了高空核爆炸X射线辐射能和碎片动能在大气层中沉积的计算模型, 利用该模型模拟了美国和苏联的4次大威力高空核爆炸试验(Checkmate, Starfish, K3, K4)的能量沉积情况, 分析了碎片动能在海拔100—200 km的沉积规律. 计算结果表明, 与X射线沉积区相比, 碎片动能沉积区范围较小, 能量密度较大; 碎片动能沉积在较短时间内(约0.5 s)完成, 在爆心附近和海拔115 km附近存在两个吸收峰; 动能沉积区在水平截面大体上为椭圆形, 爆炸纬度越高, 椭圆偏心率越小, 水平截面积随海拔高度的增加而增大, 随爆高的增大而减小; 距爆点较远、远离磁泡时, 动能沉积峰值点在穿过爆心的地磁场磁力线附近; 距爆点较近、磁泡内部的动能沉积峰值点在爆心投影点附近.An accumulation model of X-ray and debris in a high altitude nuclear explosion is built in this work. Using the established model, we simulate the energy accumulations of four large scale experiments (i.e. the Checkmate, Starfish, K3 and K4) conducted by the United States and the Soviet Union. The dynamics of the kinetic accumulation at 100–200 km altitude is analyzed. Our simulation results show that the kinetic patch spreads a relatively small spatial region and has a large energy density compared with the X-ray patch. The accumulation of the debris ions can be finished within around 0.5 s, and two absorption peaks (hence two kinetic patches) can be observed at an altitude of about 115 km and the burst point. The shape of the kinetic region projected onto the horizontal plane is roughly elliptical, the eccentricity will be smaller at higher latitudes, and the area will be larger at higher altitudes. Away from the bursting point, the maximum energy density of the kinetic patch is near the magnetic field line that crosses the bursting point. Within the magnetic bubble, the maximum energy density of the kinetic patch occurs near the bursting point.
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Google Scholar
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Google Scholar
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图 2
$ \lg ({\eta _{\text{X}}}) $ 等值线图 (a) Checkmate; (b) K4; (c) K3; (d) StarfishFig. 2. Contour of
$ \lg ({\eta _{\text{X}}}) $ : (a) Checkmate; (b) K4; (c) K3; (d) Starfish.
图 3 碎片动能沉积与X射线能量沉积的比值
$ {\eta _{{\text{DX}}}} $ 等值线云图 (a) Checkmate; (b) K4; (c) K3; (d) StarfishFig. 3. Contour of energy ratio
$ {\eta _{{\text{DX}}}} $ of the debris and X-ray: (a) Checkmate; (b) K4; (c) K3; (d) Starfish.
图 4 海拔高度115 km归一化碎片动能沉积线密度
$ {\delta _{\text{D}}} $ 随时间的变化Fig. 4. Time variation of the normalized debris kinetic energy line density
$ {\delta _{\text{D}}} $ at altitude 115 km.
图 5 爆后1 s归一化碎片动能沉积线密度
$ {\delta _{\text{D}}} $ 随海拔高度的变化Fig. 5. Altitude variation of the normalized line debris kinetic energy density
$ {\delta _{\text{D}}} $ at 1 s after detonation.
图 6 不同海拔的归一化碎片动能沉积云图, 图中, *为过爆点的背景地磁场磁力线在面内的位置, +为动能沉积密度最大的位置 (a) Checkmate, altitude = 105 km ; (b) Checkmate, altitude = 115 km; (c) Checkmate, 海拔高度为125 km; (d) Checkmate, 海拔高度为145 km; (e) K4, 海拔高度为105 km; (f) K4, 海拔高度为115 km; (g) K4, 海拔高度为125 km; (h) K4, 海拔高度为145 km; (i) K3, 海拔高度为105 km; (j) K3, 海拔高度为115 km; (k) K3, 海拔高度为125 km; (l) K3, 海拔高度为145 km; (m) Starfish, 海拔高度为105 km; (n) Starfish, 海拔高度为115 km; (o) Starfish, 海拔高度为125 km; (p) Starfish, 海拔高度为145 km
Fig. 6. Normalized debris energy accumulation at various altitudes, where, “*” denotes the magnetic field line which crosses the burst point, and “+” denotes the peak of the accumulated kinetic energy density: (a) Checkmate, altitude = 105 km; (b) Checkmate, altitude = 115 km; (c) Checkmate, altitude = 125 km; (d) Checkmate, altitude = 145 km; (e) K4, altitude = 105 km; (f) K4, altitude = 115 km; (g) K4, altitude = 125 km; (h) K4, altitude = 145 km; (i) K3, altitude = 105 km; (j) K3, altitude = 115 km; (k) K3, altitude = 125 km; (l) K3, altitude = 145 km; (m) Starfish, altitude = 105 km; (n) Starfish, altitude = 115 km; (o) Starfish, altitude = 125 km; (p) Starfish, altitude = 145 km.
表 1 高空核爆实验参数
Table 1. High-altitude nuclear tests parameters.
爆高/km 当量/kt 维度/(°) 质量/kg Checkmate 147 410 17 440 Starfish 400 1400 17 1500 K3 300 300 47 320 K4 150 300 47.6 320 
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[1] Dyal, P. 2006 J. Geophys. Res. 111 A12211
Google Scholar
[2] Gilbert J, Kappenman J, Radasky W, Savage E 2010 Meta-R-321
[3] Keith S, Earl W 2019 DTRA-TR-19-41
[4] Tesche F M, Barnes P R, Sakis A P 1992 DE92-010365
[5] 欧阳建明, 马燕云, 邵福球, 邹德滨, 刘建勋 2012 61 242801
Google Scholar
Ouyang J M, Ma Y Y, Shao F Q, Zou D B, Liu J X 2012 Acta Phys. Sin. 61 242801
Google Scholar
[6] 陶应龙 2010 博士学位论文 (北京: 清华大学)
Tao Y L 2010 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[7] 杨斌, 牛胜利, 朱金辉, 黄流兴 2012 61 202801
Google Scholar
Yang B, Niu S L, Zhu J H, Huang L X 2012 Acta Phys. Sin. 61 202801
Google Scholar
[8] 彭国良, 张俊杰 2021 70 180703
Google Scholar
Peng G Lg, Zhang J J 2021 Acta Phys. Sin. 70 180703
Google Scholar
[9] Peng G L, Zhang J J, Chen J N 2021 Phys. Fluids 33 076602
Google Scholar
[10] Winske D 1991 AD-A243198
[11] Thomas V A, Brecht S H 1986 Phys. Fluid 29 2444
Google Scholar
[12] Brecht S H, Thomas V A 1988 Comput. Phys. Commun. 48 135
Google Scholar
[13] Gladd N T, Brecht S H 1995 DNA-TR-94-161
[14] U. S. Standard Atmosphere 1976 ADA035728
[15] 王建国, 牛胜利, 张殿辉 2010 高空核爆炸效应参数手册 (北京: 原子能出版) 第35页
Wang J G, Niu S L, Zhang D H 2010 Parameter Handbook of High Attitude Nuclear Detonation Effects (Beijing: Atomic Energy Press) p35 (in Chinese)
[16] Douglas S H 1982 J. Comput. Phys. 47 452462
[17] Gargaté L, Bingham R, Fonseca R A, Silva L O 2007 Comput. Phys. Commun. 176 419
Google Scholar
[18] Lipatov A S 2002 The Hybrid Multiscale Simulation Technology (Berlin: Springer)
[19] Holland D H, Kaufman A M, O’Dell A A 1977 DNA-4501 F
[20] Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (Emp) Attack 2017 Vol. II: Recommended E3 HEMP Heave Electric Field Waveform for the Critical Infrastructures
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