激光能量沉积光路追踪法及其并行化
摘要
在激光驱动惯性约束聚变的数值模拟中,通常使用光路追踪法来计算激光能量沉积。它是把一束激光划分为大量的光线,然后根据每条光线通过物理求解域的路径和状态来计算能量沉积。本文讨论采用光路追踪法计算激光能量沉积的方法、实施过程中需要解决的实际问题。
首先介绍了光路追踪法的基本思想,给出了一般的光路方程、激光能量沉积公式、激光脉冲强度的时间和空间分布模型,分别讨论了二维直角坐标和二维柱坐标下的激光能量沉积计算。
其次,对已有光路追踪模块做了一些改进,如将计算节点电子数密度的插值方法改为双线性插值；增加了直线型的真空光路模型,给出了与双曲型模型的不同应用特点；为计算激光驱动产生X光激光的应用增加了线聚焦的计算模型。
在此基础上,我们编制了一个新的三维光路追踪程序,可以计算任意方向的光线通过网格的轨迹,能够更准确地模拟真实的激光光束在柱型腔靶中的三维散射,提高了数值精度和计算效率,并设计了数据输入输出、光线绘制的可视化接口以便于分析模拟结果。编制的程序模块已经用于研究工作,在应用中取得了良好的效果。
为了适应大规模、高置信度的数值模拟需要,本文还讨论了光路追踪法的并行策略,给出了一种分组流水线的光路追踪并行算法,并予以实施,结果表明它能够充分提高大量光线在区域分解网格下的并行性,使得大规模并行计算时的效率比未分组流水线方法提高百分之三十以上。
In order to simulate the energy deposition in inertial confinement fusion droved by laser, a geometric optics approximation called the ray-tracing algorithm was used in general without solving Maxwell's equations. In the algorithm, laser beams are discretized into a lot of rays, which are initialized with certain energy. Each ray is followed until it is absorbed or leaves the physical domain; energy of ray is transferred to the mesh by inverse bremsstrahlung. The practical problems applying the ray-tracing algorithm are discussed in this paper.
Firstly, the ray-tracing algorithm is presented, the key problems that need to be solved is analyzed, equations for ray trajectories, energy deposition and the power of laser pulse are described. Numerical calculation in 2-D Cartisien and 2-D cylindrical geometry is discussed.
Secondly, some improvement is realized in the module of laser deposition, for instance, the method to calculate density of electron number is changed to bilinear interpolation. A new model of ray trajectory in vacuum is added, which is consistent with trajectory in plasma. On the same time, for simulation of X-ray laser generated by laser, focus-line model is added as well.
With all work mentioned above, we have developed a new laser deposition module, which separate the complexities of the geometrical-optical ray-tracing problem from the basic physics modules. A 3D ray trajectory through a cell with an arbitrary direction is more accurately calculated and numerical precision is improved. When the interface about date I/O is designed, ray trajectories are rendered in 2-D and 3-D perspective with graphic tools that the result of numerical simulations is conveniently analyzed. The module has been used to the research and works well.
Because of the requirements of large scale and highly efficient simulation, the parallelization of ray-tracing algorithm is described. Ray-tracing computation combined with the existing decomposition of the domain is effectively dealt with by the group-pipeline strategy. The code was designed with the message passing programming environment, can significantly improve the parallel performance. The numerical results show that computing efficiency of large scale increased above 30 percent against the ungroup-pipeline strategy.
首先介绍了光路追踪法的基本思想,给出了一般的光路方程、激光能量沉积公式、激光脉冲强度的时间和空间分布模型,分别讨论了二维直角坐标和二维柱坐标下的激光能量沉积计算。
其次,对已有光路追踪模块做了一些改进,如将计算节点电子数密度的插值方法改为双线性插值；增加了直线型的真空光路模型,给出了与双曲型模型的不同应用特点；为计算激光驱动产生X光激光的应用增加了线聚焦的计算模型。
在此基础上,我们编制了一个新的三维光路追踪程序,可以计算任意方向的光线通过网格的轨迹,能够更准确地模拟真实的激光光束在柱型腔靶中的三维散射,提高了数值精度和计算效率,并设计了数据输入输出、光线绘制的可视化接口以便于分析模拟结果。编制的程序模块已经用于研究工作,在应用中取得了良好的效果。
为了适应大规模、高置信度的数值模拟需要,本文还讨论了光路追踪法的并行策略,给出了一种分组流水线的光路追踪并行算法,并予以实施,结果表明它能够充分提高大量光线在区域分解网格下的并行性,使得大规模并行计算时的效率比未分组流水线方法提高百分之三十以上。
In order to simulate the energy deposition in inertial confinement fusion droved by laser, a geometric optics approximation called the ray-tracing algorithm was used in general without solving Maxwell's equations. In the algorithm, laser beams are discretized into a lot of rays, which are initialized with certain energy. Each ray is followed until it is absorbed or leaves the physical domain; energy of ray is transferred to the mesh by inverse bremsstrahlung. The practical problems applying the ray-tracing algorithm are discussed in this paper.
Firstly, the ray-tracing algorithm is presented, the key problems that need to be solved is analyzed, equations for ray trajectories, energy deposition and the power of laser pulse are described. Numerical calculation in 2-D Cartisien and 2-D cylindrical geometry is discussed.
Secondly, some improvement is realized in the module of laser deposition, for instance, the method to calculate density of electron number is changed to bilinear interpolation. A new model of ray trajectory in vacuum is added, which is consistent with trajectory in plasma. On the same time, for simulation of X-ray laser generated by laser, focus-line model is added as well.
With all work mentioned above, we have developed a new laser deposition module, which separate the complexities of the geometrical-optical ray-tracing problem from the basic physics modules. A 3D ray trajectory through a cell with an arbitrary direction is more accurately calculated and numerical precision is improved. When the interface about date I/O is designed, ray trajectories are rendered in 2-D and 3-D perspective with graphic tools that the result of numerical simulations is conveniently analyzed. The module has been used to the research and works well.
Because of the requirements of large scale and highly efficient simulation, the parallelization of ray-tracing algorithm is described. Ray-tracing computation combined with the existing decomposition of the domain is effectively dealt with by the group-pipeline strategy. The code was designed with the message passing programming environment, can significantly improve the parallel performance. The numerical results show that computing efficiency of large scale increased above 30 percent against the ungroup-pipeline strategy.
引文
1.王淦昌、袁之尚著,惯性约束核聚变,原子能出版社,2005。
2.张钧、常铁强著,激光核聚变靶物理基础,国防工业出版社,2004。
3. Stefano Atzeni等著,沈百飞译,惯性聚变物理,科学出版社,2008。
4.裴文兵等,激光聚变中的科学计算,物理,38卷(2009年)8期,559-568。
5. W. Y. Zhang et al, Recent Progress and Future Prospects for IFE in China, Journal of Physics:Conference Series 112 (2008) 032001。
6. Brueckner K A,Jorna S. Laser-driven fusion. Rev. Mod. Phys.,1974,46(2):325。
7. Lindl J. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys.Plasmas,1995,2(11): 3933-4023。
8. S. H. Glenzer, Experiments and multiscale simulations of laser propagation through ignition-scale plasmas, Nature Physics 3,716-719 (2007) 。
9. J.A.Harte et al,LASNEX - a 2-D physics code for modeling ICF,Lawrence Livermore National Laboratory,UCRL-LR-105821-96-4,6:4 (1996),150-164。
10. A.I.Shestakov et al,the ICF3D code,Lawrence Livermore National Laboratory, UCRL-LR-105821-96-4,6:4 (1996),165-180。
11. A. Friedman,Three-Dimensional Laser Ray Tracing on an r-z Lagrangian Mesh, Laser Programs Annual Report, Lawrence Livermore National Laboratory, Livermore, UCRL-50021-83 (1983),3-51。
12.勇珩等,LARED-H程序中光路计算的并行化,数值计算与计算机应用,2003年04期,314-320。
13.莫则尧等,科学计算应用程序探讨,物理,38卷(2009年)8期,552-558。
14.常铁强等,激光等离子体相互作用与激光聚变,湖南科学技术出版社,1991,8-14。
15.段庆生等,激光辐照金(Au)圆盘靶的二维数值模拟,计算物理,19卷(2002)1期,57-61。
16.符尚武等,激光驱动内爆二维数值模拟方法及其程序(Lared-I)的研究,高技术通讯,1998年7月,51-54。
17. Shi-Bing Liu et al,Three-dimensional optical trajectory tracing and energy deposition of a laser beam in a laser-driven fusion, PHYSICAL REVIEW E, VOLUME 63, 036703.
18.朱少平等,激光靶耦合过程中的激光能量沉积方程,强激光与离子束,11卷(1999)6期,687-691。
19.张维岩等,一个三维激光光路追踪的新思路,804专题“1997年度工作报告”。
20.朱森昌等,黑腔靶激光能量沉积的数值模拟,强激光与粒子束,1989,1(2),145。
21.高耀明等,ICF内爆压缩X光成像过程数值模拟,强激光与粒子束,19卷(2007)11期。
22. T. B. Kaiser et al, Laser Energy Deposition Model for the ICF3D Code, American Physical Society, Division of Plasma Physics Meeting,1996APS..DPP..7S08K。
23. S Atzeni, Laser driven inertial fusion:the physical basis of current and recently proposed ignition experiments, Plasma Phys. Control. Fusion 51(2009)124029。
24. T. B. Kaiser et al, A Parallelized Object-Oriented 3D Laser/Heavy-Ion Driver for ICF Physics Modeling Codes, American Physical Society, Division of Plasma Physics Meeting,1997 APS.. DPPgTP224K。
25. R. J. Mason et al, A 3-D Ray-trace Model for RAGE, American Physical Society, 43rd Annual Meeting of the APS Division of Plasma Physics,2001APS.. DPPQP1154M。
26. R. J. Mason, A 3-D Ray-Trace Model for an AMR Code on Distributed Processors, American Physical Society,44th Annual Meeting of the Division of Plasma, 2002APS..DPPQP1103M。
27. D.C. Eder et al,Late-time simulation of National Ignition Facility Hohlraums, Lawrence Livermore National Laboratory, UCRL-JRNL-206693 (2004) 。
28.莫则尧等,二维三温流体力学数值模拟程序的并行化,计算物理,17卷(2000)6期,625-632。
29.袁国兴等,分区计算问题的并行设计,数值计算与计算机应用,2001年1期,22-28。
30.莫则尧等,多介质辐射流体力学数值模拟中的并行计算研究,自然科学进展,16卷(2006)3期,287-292。
31. Aleksei Shestakov et al,Parallelization of an Unstructured-grid,Laser Fusion Design Code, from SIAM News, Volume 32, Number 3 。
32.孟祥乾等,基于流水线负载平衡模型的并行爬虫研究,计算机工程,35卷(2009)2期,34-36。
33.刘杰,并行程序的优化与性能评价,计算机工程与科学,22卷(2000)5期,67-70。
34. Harry F.Jordan等著,迟利华等译,并行处理基本原理,清华大学出版社,2004。
35.张宝琳等,数值并行计算原理与方法,国防工业出版社,1999。
36.莫则尧等,消息传递并行编程环境,科学出版社,2001。
37.陈国良等,并行算法实践,高等教育出版社,2004。
38. Jack Dongarra等编著,莫则尧等译,并行计算综论,电子工业出版社,2005。
2.张钧、常铁强著,激光核聚变靶物理基础,国防工业出版社,2004。
3. Stefano Atzeni等著,沈百飞译,惯性聚变物理,科学出版社,2008。
4.裴文兵等,激光聚变中的科学计算,物理,38卷(2009年)8期,559-568。
5. W. Y. Zhang et al, Recent Progress and Future Prospects for IFE in China, Journal of Physics:Conference Series 112 (2008) 032001。
6. Brueckner K A,Jorna S. Laser-driven fusion. Rev. Mod. Phys.,1974,46(2):325。
7. Lindl J. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys.Plasmas,1995,2(11): 3933-4023。
8. S. H. Glenzer, Experiments and multiscale simulations of laser propagation through ignition-scale plasmas, Nature Physics 3,716-719 (2007) 。
9. J.A.Harte et al,LASNEX - a 2-D physics code for modeling ICF,Lawrence Livermore National Laboratory,UCRL-LR-105821-96-4,6:4 (1996),150-164。
10. A.I.Shestakov et al,the ICF3D code,Lawrence Livermore National Laboratory, UCRL-LR-105821-96-4,6:4 (1996),165-180。
11. A. Friedman,Three-Dimensional Laser Ray Tracing on an r-z Lagrangian Mesh, Laser Programs Annual Report, Lawrence Livermore National Laboratory, Livermore, UCRL-50021-83 (1983),3-51。
12.勇珩等,LARED-H程序中光路计算的并行化,数值计算与计算机应用,2003年04期,314-320。
13.莫则尧等,科学计算应用程序探讨,物理,38卷(2009年)8期,552-558。
14.常铁强等,激光等离子体相互作用与激光聚变,湖南科学技术出版社,1991,8-14。
15.段庆生等,激光辐照金(Au)圆盘靶的二维数值模拟,计算物理,19卷(2002)1期,57-61。
16.符尚武等,激光驱动内爆二维数值模拟方法及其程序(Lared-I)的研究,高技术通讯,1998年7月,51-54。
17. Shi-Bing Liu et al,Three-dimensional optical trajectory tracing and energy deposition of a laser beam in a laser-driven fusion, PHYSICAL REVIEW E, VOLUME 63, 036703.
18.朱少平等,激光靶耦合过程中的激光能量沉积方程,强激光与离子束,11卷(1999)6期,687-691。
19.张维岩等,一个三维激光光路追踪的新思路,804专题“1997年度工作报告”。
20.朱森昌等,黑腔靶激光能量沉积的数值模拟,强激光与粒子束,1989,1(2),145。
21.高耀明等,ICF内爆压缩X光成像过程数值模拟,强激光与粒子束,19卷(2007)11期。
22. T. B. Kaiser et al, Laser Energy Deposition Model for the ICF3D Code, American Physical Society, Division of Plasma Physics Meeting,1996APS..DPP..7S08K。
23. S Atzeni, Laser driven inertial fusion:the physical basis of current and recently proposed ignition experiments, Plasma Phys. Control. Fusion 51(2009)124029。
24. T. B. Kaiser et al, A Parallelized Object-Oriented 3D Laser/Heavy-Ion Driver for ICF Physics Modeling Codes, American Physical Society, Division of Plasma Physics Meeting,1997 APS.. DPPgTP224K。
25. R. J. Mason et al, A 3-D Ray-trace Model for RAGE, American Physical Society, 43rd Annual Meeting of the APS Division of Plasma Physics,2001APS.. DPPQP1154M。
26. R. J. Mason, A 3-D Ray-Trace Model for an AMR Code on Distributed Processors, American Physical Society,44th Annual Meeting of the Division of Plasma, 2002APS..DPPQP1103M。
27. D.C. Eder et al,Late-time simulation of National Ignition Facility Hohlraums, Lawrence Livermore National Laboratory, UCRL-JRNL-206693 (2004) 。
28.莫则尧等,二维三温流体力学数值模拟程序的并行化,计算物理,17卷(2000)6期,625-632。
29.袁国兴等,分区计算问题的并行设计,数值计算与计算机应用,2001年1期,22-28。
30.莫则尧等,多介质辐射流体力学数值模拟中的并行计算研究,自然科学进展,16卷(2006)3期,287-292。
31. Aleksei Shestakov et al,Parallelization of an Unstructured-grid,Laser Fusion Design Code, from SIAM News, Volume 32, Number 3 。
32.孟祥乾等,基于流水线负载平衡模型的并行爬虫研究,计算机工程,35卷(2009)2期,34-36。
33.刘杰,并行程序的优化与性能评价,计算机工程与科学,22卷(2000)5期,67-70。
34. Harry F.Jordan等著,迟利华等译,并行处理基本原理,清华大学出版社,2004。
35.张宝琳等,数值并行计算原理与方法,国防工业出版社,1999。
36.莫则尧等,消息传递并行编程环境,科学出版社,2001。
37.陈国良等,并行算法实践,高等教育出版社,2004。
38. Jack Dongarra等编著,莫则尧等译,并行计算综论,电子工业出版社,2005。