1.College of Mechanical and Electrical Engineering, Beijing Institute of Technology, Beijing 100081, China 2.Northwest Institute of Nuclear Technology, Xi’an 710024, China
Abstract:A Hydro-Magneto-PIC (particle-in-cell) hybrid model is proposed to describe the motion of the fission debris in high altitude nuclear explosions (HANEs). Compared with the state-of-art numerical models, our model is able to stably compute the motion of the fission debris in a broader spatial region. In a real HANE, the physical process contains many spatial scales. The upward moving debris particles manifest kinetic properties due to the fact that the dilute ambient atmosphere and the downward expanding particles manifest a fluid-like pattern and can be approximated by the usual hydro-dynamical models. Meanwhile, the debris particles receive electromagnetic forces from both the geomagnetic fields and the charged particles at all frequencies. This broad scale of frequencies can induce large- and small-scale instabilities, which cannot be solved by the usual hydrodynamic equations. Considering the motions of the debris and the different properties of the high temperature ions, the low temperature ions and the neutral atmosphere, we consistently combine three models for completely describing the debris expansion. The high temperature ions are described by the PIC model for their intrinsic kinetic behaviors, the low temperature ions are described by the magneto-hydrodynamic model for their fluid property, and fluid equations are applied to the neutral particles with no electromagnetic force. The corresponding interactions among the three components are added into the equations as the source terms. With the combination of the three models, our algorithm can stably calculate the regions that are a few thousand kilometers in altitude. Our proposed model contains both the kinetic and fluid properties, and is stable in numerical implementations. Finally, we calculate the debris motion in the Starfish experiment. The results confirm a consistency of our proposed model with the observations. The spatial scale of our simulation results is consistent with the result in the Starfish experiment. In addition, we also plot the distribution of the debris with different projection angles at various snapshots. These results give us an intuition to understand the influence of the various factors, such as the friction of atmosphere, the magnetic pressure, flute instability and the Hall currents. Our model provides a tool for implementing the HANE simulation in a broader scheme, and can also be utilized in other plasma systems. Keywords:high altitude nuclear explosion/ Hydro-Magneto-PIC hybrid model/ debris
3.分析与讨论为验证计算模型, 以高空核爆炸试验数据最完整的Starfish试验为例进行计算. Starfish试验爆炸地点为北纬17°, 西经170°, 高度为400 km, 当量1.4 Mt. 初始条件的选取参考文献[17, 18], 即初始碎片质量取1000 kg, 碎片动能占总爆炸能量的20%, 碎片原子质量数取铁原子的质量数56, 电荷数取1, 地磁场取爆点的偶极子磁场. 计算区域取西东方向为X方向, 计算范围为[–800 km, 800 km], 网格数240; 南北方向为Y方向, 计算范围为[–800 km, 800 km], 网格数240; 沿高度方向为Z方向, 计算范围为[100 km, 800 km], 网格数120; 爆心坐标为[0, 0, 400 km]. 图1为试验拍摄到的爆炸场景照片[18], 计算得到的碎片密度在子午面上的投影面密度云图如图2所示, 沿磁力线方向的投影二维面密度云图如图3所示, 沿高度方向的投影二维面密度云图如图4所示. 文献[18]中给出的试验观测数据在爆后0.1 s左右时碎片云水平扩展半径约200 km, 碎片云底部约在220 km高度附近. 由图2(a)和图4(a)可知, 本文的计算结果在0.1 s时碎片云在南北方向的半径略大于200 km, 碎片云底部略大于250 km, 与试验结果基本一致. X射线火球在80 km高度附近, 会遮挡试验光学观测结果, 但碎片缓发β射线在海拔70 km左右的沉积区形状与爆炸区沿磁力线方向的投影较为相似, 利用这个特点可以通过观测沉积区形状反推碎片云形状. 观测数据表明0.2 s时碎片云南北方向水平半径小于500 km, 下边界在180 km附近. 由图2(b)和图4(b)可知, 在0.2 s时本文计算的碎片云在南北方向的半径大约为400 km, 碎片云底部的半径大约为150 km, 与试验结果基本一致. 图 1 Starfish试验照片: 爆后4 s β射线沉积区图像 Figure1. Photos of Starfish: β patch photo after burst time 4 s
图 2 不同时刻Starfish试验模拟计算的三维碎片云密度沿子午面方向的投影面密度云图 (a) 0.1 s; (b) 0.2 s; (c) 0.5 s; (d) 1 s Figure2. Contour plot of three-dimensional debris density in the geomagnetic meridian plane in Starfish experiment at different time: (a) 0.1 s; (b) 0.2 s; (c) 0.5 s; (d) 1 s.
图 3 不同时刻Starfish试验模拟计算的三维碎片云密度沿磁力线方向的投影面密度云图 (a) 0.1 s; (b) 0.2 s; (c) 0.5 s; (d) 1 s Figure3. Contour plot of three-dimensional debris density in the XOY plane (perpendicular to the geomagnetic fields) in Starfish experiment at different time: (a) 0.1 s; (b) 0.2 s;(c) 0.5 s;(d) 1 s.
图 4 不同时刻Starfish试验模拟计算的三维碎片云密度沿高度方向的投影面密度云图 (a) 0.1 s; (b) 0.2 s; (c) 0.5 s; (d) 1 s Figure4. Contour plot of three-dimensional debris density in the XOY plane (perpendicular to altitude direction) in Starfish experiment at different time: (a) 0.1 s; (b) 0.2 s; (c) 0.5 s; (d) 1 s.
可见, 当霍尔速度相对离子速度不可忽略时, 等效速度不再具有对称性, 进而导致电场、磁场、速度场等不再具备对称性. 图5给出了爆后0.2 s时子午面上x0方向离子速度与霍尔速度的分布, 可以看到离子速度较大的地方霍尔速度也较大, 且霍尔速度略小于离子速度, 但其影响不可忽略. 这表明在高空核爆炸中必须考虑霍尔效应, 在霍尔效应作用下各场量空间对称性被破坏. 图 5 爆后0.2 s子午面上的x0方向速度分布: (a)离子速度; (b)霍尔速度 Figure5. Velocity distributions in the x0 direction in meridian plane at t = 0.2 s: (a) Ion velocity; (b) Hall velocity.