回旋加速器非线性强流空间电荷效应仿真研究
摘要
回旋加速器不仅广泛应用于国防基础科学研究,而且在同位素生产以及医学诊断、质子治疗等应用领域也得到广泛的应用。引入虚拟样机技术,用虚拟方法进行低能加速器的设计、制造、安装、调试和运行仿真,有助于降低制造成本和工程风险。
在粒子加速器中,束流自身的非线性空间电荷场将直接导致束流发射度的增长。粒子的能量较低时,空间电荷力更加显著,使得这一效应更加明显。空间电荷主导的束流行为的一个普遍特征是,一个初始非线性截面束在传输过程中将变得更加均匀,这个过程同时伴随着束流发射度的大幅度增长和束晕的出现。因此,对其束流动力学的模拟仿真是必要的,非线性束流仿真系统将作为虚拟样机集成平台的一个重要组成部分。
本文详细地讨论了带空间电荷效应的非线性束流仿真系统的研究情况及其实现方法。首先基于边界元理论,推导出自由空间电荷场的计算公式,然后对相关模块进行了理论分析与详细设计,最后搭建集成仿真平台,主要包括相空间粒子分布的产生、分布测试、模型前处理、模拟计算和后处理五个部分。
为验证程序设计的正确性,本文根据层流流体理论和高斯理论推导出特殊情况下的束流运动方程,并求解出初始截面为K-V分布和高斯分布两种情况下的近似解析解,将其结果与该仿真系统的模拟结果进行比对,结果相当吻合。最后给出一条注入线的模拟计算结果,并与ORBIT、TRACE 3-D的计算结果进行比对,结果表明:该程序所采用数值方法的计算结果与ORBIT、TRACE 3-D的计算结果有较好的一致性。该程序可用于直线加速器及回旋加速器中的空间电荷效应模拟。
Cyclotrons are not only widely used in fundamental researches in national defense, but also widely employed in isotopes production, medical diagnosis and proton therapy. By employing VP technology, we applied virtual method in design, production, installation, and simulation of low energy cyclotrons, which conduces to reducing cost and risks.
The nonlinear space-charge field of a beam is a serious concern for beam emittance growth in particle accelerators. This effect is most pronounced when particles are slow and space-charge forces are significant. The general property of space-charge dominated beam behavior is that a beam with an initial nonlinear profile tends to become more uniform and this process is associated with strong emittance growth and the appearance of beam halo, therefore, describing the behavior of the beam with space charge effect is necessary, non-linear beam simulation system will be as an important component of the VP platform.
This paper discusses the research and implementation of the non-linear beam simulation system with space charge effect. First of all, based on the Boundary Element. Method (BEM) theory, we obtain the computational expressions of space charge field in free space. Then, the analysis and design modules are introduced in details. Finally, the simulation platform is developed including five parts, namely, Beam distribution generator in phase space, pre-processing, distribution testing, simulation and post-processing.
For validating the accuracy of the design, according to laminar flow, we obtained the formula of beam dynamics from specific cases and computed the approximate solution with initially K-V beam and Gaussian beam. The calculation shows good agreement between theory and numeric results. Finally, the simulation result of an injection beam line is presented. The computation results are compared with ORBIT and TRACE 3-D, which shows good agreement. This code can be used to study beam dynamics in linacs and high intensity cyclotrons.
在粒子加速器中,束流自身的非线性空间电荷场将直接导致束流发射度的增长。粒子的能量较低时,空间电荷力更加显著,使得这一效应更加明显。空间电荷主导的束流行为的一个普遍特征是,一个初始非线性截面束在传输过程中将变得更加均匀,这个过程同时伴随着束流发射度的大幅度增长和束晕的出现。因此,对其束流动力学的模拟仿真是必要的,非线性束流仿真系统将作为虚拟样机集成平台的一个重要组成部分。
本文详细地讨论了带空间电荷效应的非线性束流仿真系统的研究情况及其实现方法。首先基于边界元理论,推导出自由空间电荷场的计算公式,然后对相关模块进行了理论分析与详细设计,最后搭建集成仿真平台,主要包括相空间粒子分布的产生、分布测试、模型前处理、模拟计算和后处理五个部分。
为验证程序设计的正确性,本文根据层流流体理论和高斯理论推导出特殊情况下的束流运动方程,并求解出初始截面为K-V分布和高斯分布两种情况下的近似解析解,将其结果与该仿真系统的模拟结果进行比对,结果相当吻合。最后给出一条注入线的模拟计算结果,并与ORBIT、TRACE 3-D的计算结果进行比对,结果表明:该程序所采用数值方法的计算结果与ORBIT、TRACE 3-D的计算结果有较好的一致性。该程序可用于直线加速器及回旋加速器中的空间电荷效应模拟。
Cyclotrons are not only widely used in fundamental researches in national defense, but also widely employed in isotopes production, medical diagnosis and proton therapy. By employing VP technology, we applied virtual method in design, production, installation, and simulation of low energy cyclotrons, which conduces to reducing cost and risks.
The nonlinear space-charge field of a beam is a serious concern for beam emittance growth in particle accelerators. This effect is most pronounced when particles are slow and space-charge forces are significant. The general property of space-charge dominated beam behavior is that a beam with an initial nonlinear profile tends to become more uniform and this process is associated with strong emittance growth and the appearance of beam halo, therefore, describing the behavior of the beam with space charge effect is necessary, non-linear beam simulation system will be as an important component of the VP platform.
This paper discusses the research and implementation of the non-linear beam simulation system with space charge effect. First of all, based on the Boundary Element. Method (BEM) theory, we obtain the computational expressions of space charge field in free space. Then, the analysis and design modules are introduced in details. Finally, the simulation platform is developed including five parts, namely, Beam distribution generator in phase space, pre-processing, distribution testing, simulation and post-processing.
For validating the accuracy of the design, according to laminar flow, we obtained the formula of beam dynamics from specific cases and computed the approximate solution with initially K-V beam and Gaussian beam. The calculation shows good agreement between theory and numeric results. Finally, the simulation result of an injection beam line is presented. The computation results are compared with ORBIT and TRACE 3-D, which shows good agreement. This code can be used to study beam dynamics in linacs and high intensity cyclotrons.
引文
[1]方守贤.我国粒子加速器的现状和发展[J].物理, 1999, 28(9): 557~566.
[2]樊明武,张兴治,李振国,等.Measurement and adjustment of CIAE medical cyclotron magnet.IEEE Proceedings of the 1993 Particle Accelerator Conference (PAC), Vol. 2: 2841-2843.
[3]夏慧琴,刘纯亮.束流传输原理.西安:西安交通大学出版社,1991.
[4]肖美琴,张天爵,樊明武. CYCIAE型回旋加速器轴向注入系统概念设计.原子能科学技术. 1996. Vol.30, No.5. 392~398.
[5] Kanaya Noriichi. Virtual accelerator and fundamental guidelines towards sharable software for accelerator control systems[J]. Nuclear Instruments & Methods in Physics Research, 1994, Elsevier Science B V: 497～500.
[6] Yamamoto Nobore. Use of a virtual accelerator for a development of an accelerator control system [A]. Proceedings of the IEEE Particle Accelerator Conference[C]. May 12-May 16, 1997, 2: 2455～2457.
[7]樊明武,秦斌,陈德智等.回旋加速器虚拟样机技术.湖北科学技术出版社.
[8]秦斌,虚拟样机环境下的紧凑型回旋加速器物理设计:[博士学位论文].华中科技大学,2007.
[9] Valery A, Sami G. Simulation of currents in X-band accelerator structures using 2D and 3D particle-in-cell code. SLAC-PUB-8866, 2002.
[10] J.Wang, J.Anderson, J.Polk. Three-Dimensional Particle Simulations of Ion Optics Plasma Flow. Jet Propulsion Laboratory, California Institute of Technology.
[11]刘大刚,祝大军,周俊等,三维电磁粒子模拟程序设计.强激光与粒子束. 2006. Vol.18, No.1.
[12] D.F.Gordon, A.Ting, T.Jones et al. Particle-in-cell Simulation of optical injectors for plasma accelerators. Proceedings of the 2003 Particle Accelerator Conference.
[13]邢庆子,林郁正,傅世年.PIC方法在FRQ加速器z-code和t-code模拟程序中的应用研究.NUCLEAR TECHNIQUES, 2005, Vol. 28, No.5.
[14] J. Galambos et al. ORBIT-a ring injection code with space charge, Proc. of PAC99, 3143-3145.
[15] J. Beebe-Wang et al. Space charge simulation methods incorporated in some multi-particle tracking codes and their results comparison, Proc. of PAC2002, 1329-1331.
[16] J.Qiang, R.D.Ryne, et al. An Object-Oriented Parallel Particle-In-Cell Code for Beam Dynamics Simulation in Linear Accelerators. J.Comput. Phys. 2000,163, 434-451.
[17] Cheng Shi-Hong, Numerical Simulation technology,National Changhua University of Education.
[18] Christlieb A.J., R. Krasny and J.P. Verboncoeur,“Efficient Particle Simulation of a Virtual Cathode using a Grid-Free Tree code Poisson Solver”, IEEE Transactions on Plasma Science-Special Issue, 2004, Volume 32, Num. 2, 384.
[19] J.H.Walther, An influence matrix particle-particle, particle-mesh algorithm with exact particle-particle correction, Journal of computational physics, 2003.
[20] F.H. Harlow,“The Particle-in-cell Computing Method in Fluid Dynamics”, Methods Comput. Phys, 1964, 3, 319.
[21] R.W. Hockney and J.W. Eastwood, Computer Simulation Using Particles, Institute of Physics, 1988.
[22] F. GRESCHIK and H.-J. KULL, Two-dimensional PIC simulation of atomic clusters in intense laser fields, Laser and Particle Beams, 2004, 22, 137–145.
[23] Alfredo U.Luccio, Numerical simulation of particle Accelerators, Parallel Computing. 2001, 163-177.
[24] L.G.Vorobiev, R.C.York, Beam dynamics modeling by sub three dimensional particle-in-cell code, Proceedings of the 2001 Particle Accelerator Conference, 3072.
[25] Leonid G.Vorobiev and Richard C.York, Space charg calculations for sub threedimensional particle-in-cell code, physical review special topics-accelerators and beams, 2000, volume 3, 114201.
[26] Yuri K. Batygin, Accuracy and efficiency of 2D and 3D fast poison's solvers for space charge field calculation of intense beam, The Institute of Physical and Chemical Research (RIKEN), Saitama 351-01, Japan.
[27] G.P¨oplau and U. van Rienen,“Multigrid Solvers for Poisson’s Equation in Computational Electromagnetics”, in:Scientific Computing in Electrical Engineering (U. van Rienen, M. G¨unther, D. Hecht, eds.), LNCSE 18, Springer–Verlag, Berlin, 2001, 169– 176.
[28] G. P¨oplau, U. van Rienen, M.J. de Loos, and S.B. van der Geer,“A Fast 3D Multigrid Based Space Charge Routine in the GPT Code”, Proceedings of EPAC 2002 (Paris), 1658– 1668.
[29]杨德全,赵忠生,边界元理论及应用,北京理工大学出版社,2002.
[30] Yuri K.Batygin, Particle-in-cell code BEAMPATH for beam dynamics simulations in linear accelerators and beamlines, Nuclear Instruments and Method in Physics Research A 539 (2005) 462-466.
[31] Wu Jiankang, Introduction to Computational Fluid Dynamics, Huazhong University of Science & Technology, 2004, 66-68.
[32]刘正林,面向对象程序设计,华中科技大学出版社,2002.
[33] Bruce Eckel, Thinking in C++ (Second Edition),机械工业出版社,2002.
[34]王清辉,王彪,Visual C++ CAD应用程序开发技术,机械工业出版社,2003.
[35]张兆顺,崔桂香.流体力学,清华大学出版社,2006, 244-294.
[36]流体力学,赵汉中,华中科技大学力学系.2004, 117-153.
[37] D.Bruhwiler,Yuri K.Batygin, Beam Transport for Uniform Irradiation: Nonlinear Space Charge and Effect of Boundary Conditions , Proceedings of PAC95, Dallas, 1995, 3254-3256.
[38] Yuri K.Batygin, Beam intensity redistribution in a nonlinear optics channel, NuclearInstruments and Method in Physics Research B, 79 (1993), 455-489.
[39] Yuri K.Batygin, Test problems for validation of space charge codes, Proceedings of the 1999 Particle Accelerator Conference, New York, 1999.1740-1742.
[40] Y.K.Batygin, Proceedings of PAC93, 50-52.
[41] Andrew J. Jason and Barbara Blind, Klaus Halbach, Beam expansion with specified final distributions, IEEE, 1998, 2728-2730.
[42]杨建俊等,基于PIC方法的二维束流动力学模拟程序及其初步应用,高能物理与核物理,2007, Vol.31, No.8.
[2]樊明武,张兴治,李振国,等.Measurement and adjustment of CIAE medical cyclotron magnet.IEEE Proceedings of the 1993 Particle Accelerator Conference (PAC), Vol. 2: 2841-2843.
[3]夏慧琴,刘纯亮.束流传输原理.西安:西安交通大学出版社,1991.
[4]肖美琴,张天爵,樊明武. CYCIAE型回旋加速器轴向注入系统概念设计.原子能科学技术. 1996. Vol.30, No.5. 392~398.
[5] Kanaya Noriichi. Virtual accelerator and fundamental guidelines towards sharable software for accelerator control systems[J]. Nuclear Instruments & Methods in Physics Research, 1994, Elsevier Science B V: 497～500.
[6] Yamamoto Nobore. Use of a virtual accelerator for a development of an accelerator control system [A]. Proceedings of the IEEE Particle Accelerator Conference[C]. May 12-May 16, 1997, 2: 2455～2457.
[7]樊明武,秦斌,陈德智等.回旋加速器虚拟样机技术.湖北科学技术出版社.
[8]秦斌,虚拟样机环境下的紧凑型回旋加速器物理设计:[博士学位论文].华中科技大学,2007.
[9] Valery A, Sami G. Simulation of currents in X-band accelerator structures using 2D and 3D particle-in-cell code. SLAC-PUB-8866, 2002.
[10] J.Wang, J.Anderson, J.Polk. Three-Dimensional Particle Simulations of Ion Optics Plasma Flow. Jet Propulsion Laboratory, California Institute of Technology.
[11]刘大刚,祝大军,周俊等,三维电磁粒子模拟程序设计.强激光与粒子束. 2006. Vol.18, No.1.
[12] D.F.Gordon, A.Ting, T.Jones et al. Particle-in-cell Simulation of optical injectors for plasma accelerators. Proceedings of the 2003 Particle Accelerator Conference.
[13]邢庆子,林郁正,傅世年.PIC方法在FRQ加速器z-code和t-code模拟程序中的应用研究.NUCLEAR TECHNIQUES, 2005, Vol. 28, No.5.
[14] J. Galambos et al. ORBIT-a ring injection code with space charge, Proc. of PAC99, 3143-3145.
[15] J. Beebe-Wang et al. Space charge simulation methods incorporated in some multi-particle tracking codes and their results comparison, Proc. of PAC2002, 1329-1331.
[16] J.Qiang, R.D.Ryne, et al. An Object-Oriented Parallel Particle-In-Cell Code for Beam Dynamics Simulation in Linear Accelerators. J.Comput. Phys. 2000,163, 434-451.
[17] Cheng Shi-Hong, Numerical Simulation technology,National Changhua University of Education.
[18] Christlieb A.J., R. Krasny and J.P. Verboncoeur,“Efficient Particle Simulation of a Virtual Cathode using a Grid-Free Tree code Poisson Solver”, IEEE Transactions on Plasma Science-Special Issue, 2004, Volume 32, Num. 2, 384.
[19] J.H.Walther, An influence matrix particle-particle, particle-mesh algorithm with exact particle-particle correction, Journal of computational physics, 2003.
[20] F.H. Harlow,“The Particle-in-cell Computing Method in Fluid Dynamics”, Methods Comput. Phys, 1964, 3, 319.
[21] R.W. Hockney and J.W. Eastwood, Computer Simulation Using Particles, Institute of Physics, 1988.
[22] F. GRESCHIK and H.-J. KULL, Two-dimensional PIC simulation of atomic clusters in intense laser fields, Laser and Particle Beams, 2004, 22, 137–145.
[23] Alfredo U.Luccio, Numerical simulation of particle Accelerators, Parallel Computing. 2001, 163-177.
[24] L.G.Vorobiev, R.C.York, Beam dynamics modeling by sub three dimensional particle-in-cell code, Proceedings of the 2001 Particle Accelerator Conference, 3072.
[25] Leonid G.Vorobiev and Richard C.York, Space charg calculations for sub threedimensional particle-in-cell code, physical review special topics-accelerators and beams, 2000, volume 3, 114201.
[26] Yuri K. Batygin, Accuracy and efficiency of 2D and 3D fast poison's solvers for space charge field calculation of intense beam, The Institute of Physical and Chemical Research (RIKEN), Saitama 351-01, Japan.
[27] G.P¨oplau and U. van Rienen,“Multigrid Solvers for Poisson’s Equation in Computational Electromagnetics”, in:Scientific Computing in Electrical Engineering (U. van Rienen, M. G¨unther, D. Hecht, eds.), LNCSE 18, Springer–Verlag, Berlin, 2001, 169– 176.
[28] G. P¨oplau, U. van Rienen, M.J. de Loos, and S.B. van der Geer,“A Fast 3D Multigrid Based Space Charge Routine in the GPT Code”, Proceedings of EPAC 2002 (Paris), 1658– 1668.
[29]杨德全,赵忠生,边界元理论及应用,北京理工大学出版社,2002.
[30] Yuri K.Batygin, Particle-in-cell code BEAMPATH for beam dynamics simulations in linear accelerators and beamlines, Nuclear Instruments and Method in Physics Research A 539 (2005) 462-466.
[31] Wu Jiankang, Introduction to Computational Fluid Dynamics, Huazhong University of Science & Technology, 2004, 66-68.
[32]刘正林,面向对象程序设计,华中科技大学出版社,2002.
[33] Bruce Eckel, Thinking in C++ (Second Edition),机械工业出版社,2002.
[34]王清辉,王彪,Visual C++ CAD应用程序开发技术,机械工业出版社,2003.
[35]张兆顺,崔桂香.流体力学,清华大学出版社,2006, 244-294.
[36]流体力学,赵汉中,华中科技大学力学系.2004, 117-153.
[37] D.Bruhwiler,Yuri K.Batygin, Beam Transport for Uniform Irradiation: Nonlinear Space Charge and Effect of Boundary Conditions , Proceedings of PAC95, Dallas, 1995, 3254-3256.
[38] Yuri K.Batygin, Beam intensity redistribution in a nonlinear optics channel, NuclearInstruments and Method in Physics Research B, 79 (1993), 455-489.
[39] Yuri K.Batygin, Test problems for validation of space charge codes, Proceedings of the 1999 Particle Accelerator Conference, New York, 1999.1740-1742.
[40] Y.K.Batygin, Proceedings of PAC93, 50-52.
[41] Andrew J. Jason and Barbara Blind, Klaus Halbach, Beam expansion with specified final distributions, IEEE, 1998, 2728-2730.
[42]杨建俊等,基于PIC方法的二维束流动力学模拟程序及其初步应用,高能物理与核物理,2007, Vol.31, No.8.