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给出了喷气Z箍缩动力学过程在二维柱坐标系下的等离子体粒子模拟物理模型，编写了相应的程序. 对低电流驱动下的稀薄喷气Z箍缩动力学过程进行了验证性的等离子体粒子模拟，得到了许多微观的Z箍缩物理信息，如负载中的电流（密度）、电磁场、粒子位置和密度的时空演化，以及总的Z箍缩拖尾质量和拖尾电流等信息. 发现在Z箍缩过程中，模拟得到的等离子体电流随时间的变化反映出了等离子体箍缩到心和反弹的过程特征，磁场随径向的变化与长直导线电流给出的磁场很接近；电子所受到的电场力和磁场力（洛伦兹力）是相当的，而离子所受到的力主要是电场力；电子首先在z方向加速，然后在自身运动产生电流的磁场的作用下向轴心箍缩，而离子是在电子和离子电荷分离所产生的电场力的作用下向轴心运动；在压缩到轴心附近时，电子首先因静电排斥而飞散，而离子则在惯性的作用下继续向轴心箍缩，而后滞止飞散. Z箍缩等离子体的拖尾质量在20%左右，拖尾电流最大时在7%左右.In this paper the physical model and numerical algorithm of particle-in-cell (PIC) simulation for gas-puff Z-pinch in two-dimensional cylindrical coordinates are briefly introduced. The code is also developed according to the model and algorithm. The rarefied gas-puff Z-pinch driven by a low current is simulated through the code, and some reasonable results are obtained. The results include the spatiotemporal distributions of current, electromagnetic field, particle positions and density, as well as the trailing mass and current. It is found that the simulated current reflects the plasma Z-pinch characteristics, i.e., the plasma current arrives at a minimum when the plasma enters into stagnation, and it begins to increase after the plasma has moved outwards. The simulated magnetic field agrees well with the theoretic value. The electric field force and magnetic field force experienced by electron are almost the same in magnitude, while the force acting on ion is mainly the electric field force. Firstly the electron is accelerated in the z direction and reaches a velocity, then it moves inward the axis in the same time by the Lorentz force. That causes the separation between electron and ion, and a strong electric field is produced. The produced electric field attracts the ion inward the electron. When the electrons arrive at the axis, they move inversely due to the static repellency among them, while the ions continue to move initially inwards, and later enter into stagnation, and finally collapse. The trailing mass is about 20% of the total Z-pinch plasma, and the maximum trailing current is about 7% of the driven current. In the future the code needs to develop further and realize parallel computation in order to simulate the practical Z-pinch processes by PIC simulation.
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Keywords:
- gas-puff Z-pinch /
- 2D electromagnetic PIC simulation /
- forces of particle /
- trailing plasma
[1] Matzen M K 1997 Phys. Plasmas 4 1519
[2] Dan J K, Ren X D, Huang X B, Zhang S Q, Zhou S T, Duan S C, Ouyang K, Cai H C, Wei B, Ji C, He A, Xia M H, Feng S P, Wang M, Xie W P 2013 Acta Phys. Sin. 62 245201(in Chinese)[但加坤, 任晓东, 黄显宾, 张思群, 周少彤, 段书超, 欧阳凯, 蔡红春, 卫兵, 计策, 何安, 夏明鹤, 丰树平, 王勐, 谢卫平 2013 物理学报 62 245201]
[3] Sheng L, Li Y, Yuan Y, Peng B D, Li M, Zhang M, Zhao J Z, Wei F L, Wang L P, Hei D W, Qiu A C 2014 Acta Phys. Sin. 63 055201(in Chinese)[盛亮, 李阳, 袁媛, 彭博栋, 李沫, 张美, 赵吉祯, 魏福利, 王亮平, 黑东炜, 邱爱慈 2014 物理学报 63 055201]
[4] Huang X B, Yang L B, Li J, Zhou S T, Ren X D, Zhang S Q, Dan J K, Cai H C, Duan S C, Chen G H, Zhang Z W, Ouyang K, Li J, Zhang Z H, Zhou R G, Wang G L 2012 Chin. Phys. B 21 055206
[5] Wu G, Qiu A C, Wang L P, L M, Qiu M T, Cong P T 2011 Acta Phys. Sin. 60 015203(in Chinese)[吴刚, 邱爱慈, 王亮平, 吕敏, 邱孟通, 丛培天 2011 物理学报 60 015203]
[6] Deeney C, Nash T J, Spielman R B, Seaman J F, Chandler G C, Struve K W, Porter J L, Stygar W A, McGum J S, Jobe D O, Gilliland T L, Torres J A, Vargas M F, Ruggles L E, Breeze S, Mock R C, Douglas M R, Fehl D L, McDaniel D H, Matzen M K, Peterson D L, Matuska W, Roderick N F, MacFarlane J J 1997 Phys. Rev. E 56 5945
[7] Spielman R B, Deeney C, Chandler G A, Douglas M R, Fehl D L, Matzen M K, McDaniel D H, Nash T J, Porter J L, Sanford T W L, Seaman J F, Stygar W A, Struve K W, Breeze S P, McGurn J S, Torres J A, Zagar D M, Gilliland T L, Jobe D O, McKenney J L, Mock R C, Vargas M, Wangoner T, Peterson D L 1998 Phys. Plasmas 5 2105
[8] Stygar W A, Ives H C, Fehl D L, Fehl D L, Cuneo M E, Mazarakis M G, Bailey J E, Bennett G R, Bliss D E, Chandler G A, Leeper R J, Matzen M K, McDaniel D H, McGurn J S, McKenney J L, Mix L P, Muron D J, Porter J L, Ramirez J S, Ruggles L E, Seamen J F, Simpson W W, Speas C S, Spielman R B, Struve K W, Torres J A, Vesey R A 2004 Phys. Rev. E 69 046403
[9] Commisso R J, Apruzese J P, Black D C, Boller J R, Moosman B, Mosher D, Stephanakis S J, Weber B V, Young F C 1998 IEEE Trans. Plasma Sci. 26 1068
[10] Shiloh J A, Fisher A, Rostoker N 1978 Phys. Rev. Lett. 40 515
[11] Jiang S Q, Chen F X, Xia G X, Ning J M, Xue F B, Li L B, Ye F, Yang J L, Pan Y J 2013 High Power Laser and Particle Beams 25 3069(in Chinese)[蒋树庆, 陈法新, 夏广新, 甯家敏, 薛飞彪, 李林波, 叶繁, 杨建伦, 潘英俊 2013 强激光与粒子束 25 3069]
[12] Coverdale C A, Deeney C, Velikovich A L, Clark R W, Chong Y K, Davis J, Chittenden J, Ruiz C L, Cooper G W, Nelson A J, Franklin J, LePell P D, Apruzese J P, Levine J, Banister J, Qi N 2007 Phys. Plasmas 14 022706
[13] Duan Y Y, Guo Y H, Wang W S, Qiu A C 2004 Acta Phys. Sin. 53 2654(in Chinese)[段耀勇, 郭永辉, 王文生, 邱爱慈 2004 物理学报 53 2654]
[14] Ning C, Ding N, Liu Q, Yang Z H 2006 Acta Phys. Sin. 55 3488(in Chinese)[宁成, 丁宁, 刘全, 杨振华 2006 物理学报 55 3488]
[15] Ning C, Yang Z H, Ding N 2003 Acta Phys. Sin. 52 1650(in Chinese)[宁成, 杨震华, 丁宁 2003 物理学报 52 1650]
[16] Welch D R, Rose D V, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2009 Phys. Rev. Lett. 103 255002
[17] Welch D R, Rose D V, Thoma C, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2010 Phys. Plasmas 17 072702
[18] Welch D R, Rose D V, Thoma C, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2011 Phys. Plasmas 18 056303
[19] Zhuo H B 2002 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)[卓红斌 2002 博士学位论文 (长沙: 国防科技大学)]
[20] Langdon A B, Birdsall C K 1970 Phys. Fluids 13 2115
[21] Birdsall C K 1985 Plasma Physics via Computer Simulation (New York: McGraw-Hill Book Company) pp365-366
[22] Villasenor J, Buneman O 1992 Comput. Phys. Commum. 69 306
[23] Yin Y, Chang W W, Xu H, Zhuo H B, Ma Y Y 2007 CJCP 24 655(in Chinese)[银燕, 常文蔚, 徐涵, 卓红斌, 马燕云 2007 计算物理 24 655]
[24] Ning C 2001 Nuclear Fusion and Plasma Physics 21 43(in Chinese)[宁成 2001 核聚变与等离子体物理 21 43]
[25] Yang Z H, Liu Q, Ding N 2004 High Power Laser and Particle Beams 16 469(in Chinese)[杨震华, 刘全, 丁宁 2004 强激光与粒子束 16 469]
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[1] Matzen M K 1997 Phys. Plasmas 4 1519
[2] Dan J K, Ren X D, Huang X B, Zhang S Q, Zhou S T, Duan S C, Ouyang K, Cai H C, Wei B, Ji C, He A, Xia M H, Feng S P, Wang M, Xie W P 2013 Acta Phys. Sin. 62 245201(in Chinese)[但加坤, 任晓东, 黄显宾, 张思群, 周少彤, 段书超, 欧阳凯, 蔡红春, 卫兵, 计策, 何安, 夏明鹤, 丰树平, 王勐, 谢卫平 2013 物理学报 62 245201]
[3] Sheng L, Li Y, Yuan Y, Peng B D, Li M, Zhang M, Zhao J Z, Wei F L, Wang L P, Hei D W, Qiu A C 2014 Acta Phys. Sin. 63 055201(in Chinese)[盛亮, 李阳, 袁媛, 彭博栋, 李沫, 张美, 赵吉祯, 魏福利, 王亮平, 黑东炜, 邱爱慈 2014 物理学报 63 055201]
[4] Huang X B, Yang L B, Li J, Zhou S T, Ren X D, Zhang S Q, Dan J K, Cai H C, Duan S C, Chen G H, Zhang Z W, Ouyang K, Li J, Zhang Z H, Zhou R G, Wang G L 2012 Chin. Phys. B 21 055206
[5] Wu G, Qiu A C, Wang L P, L M, Qiu M T, Cong P T 2011 Acta Phys. Sin. 60 015203(in Chinese)[吴刚, 邱爱慈, 王亮平, 吕敏, 邱孟通, 丛培天 2011 物理学报 60 015203]
[6] Deeney C, Nash T J, Spielman R B, Seaman J F, Chandler G C, Struve K W, Porter J L, Stygar W A, McGum J S, Jobe D O, Gilliland T L, Torres J A, Vargas M F, Ruggles L E, Breeze S, Mock R C, Douglas M R, Fehl D L, McDaniel D H, Matzen M K, Peterson D L, Matuska W, Roderick N F, MacFarlane J J 1997 Phys. Rev. E 56 5945
[7] Spielman R B, Deeney C, Chandler G A, Douglas M R, Fehl D L, Matzen M K, McDaniel D H, Nash T J, Porter J L, Sanford T W L, Seaman J F, Stygar W A, Struve K W, Breeze S P, McGurn J S, Torres J A, Zagar D M, Gilliland T L, Jobe D O, McKenney J L, Mock R C, Vargas M, Wangoner T, Peterson D L 1998 Phys. Plasmas 5 2105
[8] Stygar W A, Ives H C, Fehl D L, Fehl D L, Cuneo M E, Mazarakis M G, Bailey J E, Bennett G R, Bliss D E, Chandler G A, Leeper R J, Matzen M K, McDaniel D H, McGurn J S, McKenney J L, Mix L P, Muron D J, Porter J L, Ramirez J S, Ruggles L E, Seamen J F, Simpson W W, Speas C S, Spielman R B, Struve K W, Torres J A, Vesey R A 2004 Phys. Rev. E 69 046403
[9] Commisso R J, Apruzese J P, Black D C, Boller J R, Moosman B, Mosher D, Stephanakis S J, Weber B V, Young F C 1998 IEEE Trans. Plasma Sci. 26 1068
[10] Shiloh J A, Fisher A, Rostoker N 1978 Phys. Rev. Lett. 40 515
[11] Jiang S Q, Chen F X, Xia G X, Ning J M, Xue F B, Li L B, Ye F, Yang J L, Pan Y J 2013 High Power Laser and Particle Beams 25 3069(in Chinese)[蒋树庆, 陈法新, 夏广新, 甯家敏, 薛飞彪, 李林波, 叶繁, 杨建伦, 潘英俊 2013 强激光与粒子束 25 3069]
[12] Coverdale C A, Deeney C, Velikovich A L, Clark R W, Chong Y K, Davis J, Chittenden J, Ruiz C L, Cooper G W, Nelson A J, Franklin J, LePell P D, Apruzese J P, Levine J, Banister J, Qi N 2007 Phys. Plasmas 14 022706
[13] Duan Y Y, Guo Y H, Wang W S, Qiu A C 2004 Acta Phys. Sin. 53 2654(in Chinese)[段耀勇, 郭永辉, 王文生, 邱爱慈 2004 物理学报 53 2654]
[14] Ning C, Ding N, Liu Q, Yang Z H 2006 Acta Phys. Sin. 55 3488(in Chinese)[宁成, 丁宁, 刘全, 杨振华 2006 物理学报 55 3488]
[15] Ning C, Yang Z H, Ding N 2003 Acta Phys. Sin. 52 1650(in Chinese)[宁成, 杨震华, 丁宁 2003 物理学报 52 1650]
[16] Welch D R, Rose D V, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2009 Phys. Rev. Lett. 103 255002
[17] Welch D R, Rose D V, Thoma C, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2010 Phys. Plasmas 17 072702
[18] Welch D R, Rose D V, Thoma C, Clark R E, Mostrom C B, Stygar W A, Leeper R J 2011 Phys. Plasmas 18 056303
[19] Zhuo H B 2002 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)[卓红斌 2002 博士学位论文 (长沙: 国防科技大学)]
[20] Langdon A B, Birdsall C K 1970 Phys. Fluids 13 2115
[21] Birdsall C K 1985 Plasma Physics via Computer Simulation (New York: McGraw-Hill Book Company) pp365-366
[22] Villasenor J, Buneman O 1992 Comput. Phys. Commum. 69 306
[23] Yin Y, Chang W W, Xu H, Zhuo H B, Ma Y Y 2007 CJCP 24 655(in Chinese)[银燕, 常文蔚, 徐涵, 卓红斌, 马燕云 2007 计算物理 24 655]
[24] Ning C 2001 Nuclear Fusion and Plasma Physics 21 43(in Chinese)[宁成 2001 核聚变与等离子体物理 21 43]
[25] Yang Z H, Liu Q, Ding N 2004 High Power Laser and Particle Beams 16 469(in Chinese)[杨震华, 刘全, 丁宁 2004 强激光与粒子束 16 469]
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