Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the Sym PIC code, which is designed for highefficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state subsonic ion flow in the range of 10 km s~(-1), agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.     

Numerical studies on pair production in ultra-intense laser interaction with a thin solid-foil

A theoretical and numerical model of photon and electron–positron pair production in strong-field quantum electrodynamics(QED) is described. Two processes are contained in our QED theoretical model, one is photon emission in the interaction of ultra-intense laser with relativistic electron(or positron), and the other is pair production by a gamma-ray photon interacting with the laser field.This model has been included in a PIC/MCC simulation code named BUMBLEBEE 1 D, which is used to simulate the laser plasma interaction. Using this code, the evolutions of electron–positron pair and gamma-ray photon production in ultra-intense laser interaction with aluminum foil target are simulated and analyzed. The simulation results revealed that more positrons are moved in the opposite direction to the incident direction of the laser under the charge separation field.     

快点火物理及其对数值模拟的要求

快点火(fast ignition)是一种新的惯性约束聚交点火方式。实验和理论研究表明其点火环节是非常复杂和困难的问题。研究快点火需要深入地进行数值模拟。报告主要从分析物理出发,探讨快点火对数值模拟的要求,同时结合实际情况进行讨论。快点火主要包括三个过程,即内爆预压缩、超强激光在次临界等离子体中和在超临界密度等离子体中的传播(成道和打洞)、超热电子的产生及其在介质,特别是稠密介质中的传输和高温点火区的形成。研究认为:研究预压缩不仅需要一维、二维,而且需要三维激光靶耦合总体程序;超热电子需要包括电磁场的Fokker-Planck方程描述;点火过程的等离子体流体力学则需要考虑电子、离子双流运动方程,而且应包括电磁场。PIC程序可用来研究局部的细节,并提供上述方程所需要的参数。此外,报告还简述了近两年来的快点火实验和一些国家的未来的计划。     

离子初始速度对等离子体鞘层厚度的影响

本文从理论上研究了离子初始速度对等离子体鞘层厚度的影响,建立了理论计算公式和数值模拟方法,考察了离子初始速度对鞘层厚度的影响因子。在离子初始能量为3.2 eV情况下,用粒子模拟程序进行了数值模拟,模拟与理论计算得到的空间电场分布十分接近。     

Effects of electron temperature on the ion extraction characteristics in a decaying plasma confined between two parallel plates

In this paper, a one-dimension particle-in-cell (PIC) code (EDIPIC) is employed to simulate the parallel-plate ion extraction process under an externally applied electrostatic field, focusing on the analysis of the influence of the initial electron temperature on the extracted ion fluxes to the metal plates during the ion extraction process. Compared with previously published results, the plasma oscillations on a timescale of the electron plasma period, and the excitation of the ion acoustic rarefaction waves resulting from the plasma oscillations originating from both the negative and positive electrodes, are studied for the first time. The modeling results show that both the negative and positive extractors can collect ions due to the plasma oscillations and the propagation of the ion acoustic rarefaction waves. With the increase of the initial electron temperature achieved by keeping other parameters unchanged, on the one hand, both the ion speed and flux to the negative and positive plates increase, which leads to a significant decrease of the ion extraction time, while on the other hand, the ion flux to the positive plate after the formation of a Child–Langmuir sheath is much more sensitive to an increase of the initial electron temperature than that to the negative plate. The PIC simulation results provide a deeper physical understanding of the influence of the initial electron temperature on the characteristics of the entire ion extraction process in a decaying plasma.     

摇摆条件下典型通道间湍流的流动传热特性

利用Fluent软件分析了摇摆条件对典型四棒束间的湍流流体流动和传热特性的影响机理。摇摆运动会对棒束间流体的流动传热特性产生一定影响,但不会对绝热通道与加热通道内流体流动相似性产生影响。而当摇摆幅度较大时,径向附加力会使通道横截面上的参数分布发生显著的变化,进而影响流体的流动与传热特性。在摇摆条件下,随着P/D（棒间距/棒直径）的逐渐减小,尤其是小于1.1时,典型棒束间流体的流动传热特性发生明显变化。     

Numerical simulation program of multicomponent ion beam transport from ECR ion source

In order to research multi-component ion beam transport process and improve transport efficiency, a special simulating program for ECR beam is becoming more and more necessary. We have developed a program written by Visual Basic to be dedicated to numerical simulation of the highly charged ion beam and to optimization of beam dynamics in transport line. In the program the exchange of electrons between highly charged ions and low charged ions or neutral atoms (residual gas in transport line) is taken into account, adopting classical molecular over-barrier model and Monte Carlo method, so the code can easily give the change of charge state distribution along the transmission line. The main advantage of the code is the ability to simultaneously simulate a large quantity of ions with different masses and charge states, and particularly, to simulate the loss of highly charged ions and the increase of low charged ions due to electron exchange in the whole transport process. Some simulations have been done to study the transmission line of LECR3 which is an ECR ion source for highly charged ion beam at IMP. Compared with experimental results, the simulations are considered to be successful.     

Homogenized model for fluid-structure interaction of the pressurized water reactor core internals during blowdown

A method for the numerical simulation of the pressurized water reactor core internal's behaviour during a blowdown accident is described, by which the motion of the reactor core and the interaction of the fuel elements with the core barrel and the coolant medium is calculated. Furthermore, some simple models for the support columns, lower and upper core support and the grid plate are provided. In order to investigate the global core motion during the blowdown accident, the core model describes the coupled fluid-rod motion with Homogenization methods. The heterogeneous fluid-rod mixture thus is treated as a special continuum with anisotropic material properties. Furthermore, the core model considers elastical rod forces against bending and axial straining and the direct interaction of neighbouring fuel elements, which is a highly nonlinear process due to the finite gaps. Because this effect is very important, two simulation models have been developed and are compared. All these models have been implemented into the blowdown code FLUX-4. With the new code version FLUX-5 the PWR-blowdown is parametrically investigated.     

An integrated high-performance beam optics-nuclear processes framework with hybrid transfer map-Monte Carlo particle transport and optimization

An integrated beam optics-nuclear processes framework is essential for accurate simulation of fragment separator beam dynamics. The code COSY INFINITY provides powerful differential algebraic methods for modeling and beam dynamics simulations in absence of beam-material interactions. However, these interactions are key for accurately simulating the dynamics of heavy ion fragmentation and fission. We have developed an extended version of the code that includes these interactions, and a set of new tools that allow efficient and accurate particle transport: by transfer map in vacuum and by Monte Carlo methods in materials. The new framework is presented, along with several examples from a preliminary layout of a fragment separator for a facility for rare isotope beams.     

Development of the PARASOL Code and Full Particle Simulation of Tokamak Plasma with an Open-Field SOL-Divertor Region Using PARASOL

The PARASOL code and the simulation by using PARASOL are introduced briefly. The PARASOL code with particle-in-cell (PIC) method and binary collision model was developed in JAERI and JAEA. Simulations using PARASOL code were carried out in order to investigate the power and particle control with diveror system in fusion reactors. The one-dimensional (1D) version of PARASOL was adopted to investigate the Bohm criterion, the supersonic flow, the SOL heat conduction, and so on. The heat propagation due to edge localized mode (ELM) was studied with the 1D-dynamic PARASOL. The two-dimensional version of PARASOL for the whole tokamak plasma including scrape-off-layer (SOL)-divertor region was useful for simulating the SOL °ow pattern, the electric ¯eld formation etc. Based on PARASOL simulation results, improved physics modeling for the °uid simulation was built up.     

重离子和脉冲激光模拟单粒子翻转阈值等效性研究

根据重离子和脉冲激发诱发单粒子翻转机理,分析了重离子和脉冲激光模拟单粒子翻转阈值（激光能量与重离子线性能量转移（LET））等效方法，得出脉冲激光与重离子单粒子翻转阈值等效计算公式。应用实验室的激光模拟单粒子效应试验系统，开展了几种器件和集成电路的单粒子翻转实验研究。利用获得的计算公式计算激光等效LET阈值，并与国内外重离子实测数据进行比较。结果表明，脉冲激光能量等效LET阈值与重离子试验LET阈值较为一致。     

铀氢锆瞬态实验装置计算程序的研发

本文针对新型核反应堆电源系统物理特性研究的铀氢锆瞬态实验装置,结合点堆动力学方程、非稳态热传导方程和热弹性动力学方程,研发了专用于铀氢锆瞬态实验装置实验过程模拟的瞬态计算程序。以保健物理研究堆（HPRR）为例,利用研发的程序进行模拟,得到HPRR的功率、反应性、温度和径向位移随时间的变化。程序的计算结果与Fuchs-Hansen模型的结果较为一致,验证了该瞬态计算程序的正确性。     

Two-Dimensional Numerical Simulation of Ion Collection from Pulsed Laser Induced Plasma

Abstract

The process of ion collection from a plasma produced between parallel plates by pulsed lasers was simulated with a two-dimensional numerical code. The trajectories and velocities of ions in the electric field are calculated using Newton's equation of motion. Assuming the Boltzmann relation for electrons, the electric field is calculated by solving numerically the Poisson equation. The numerical results for the time development of the ion collection are shown to be in good agreement with experimental results.     

中子时空动力学直接模拟方法研究与程序研制

直接模拟方法(DSM)是一种新的用于求解三维瞬态中子输运问题的方法.该方法通过直接模拟瞬态过程中系统内中子和缓发中子先驱核的动态行为来求解核反应堆动力学问题.由于该方法取消了现有方法的各种近似,具有普适通用性.本文在详细研究该方法的基础上,开发了相应的瞬态分析程序TMCC,并进行了算例的验证.     

3×3棒束通道内蒸汽对流换热特性数值分析

采用计算流体力学(CFD)方法,建立3×3棒束模拟体的数值模型,进行蒸汽冷却条件下的对流传热特性分析。结果表明:棒束通道内周向的壁面热流密度不均匀性明显,体现出流固耦合方法相比于均匀热流方法对传热细节模拟的优越性。蒸汽速度场、温度场、热流密度、换热系数等热工参数分布规律受入口效应、壁面效应、热源分布、物性参数等因素影响。压力的升高及氢气的加入均能提升通道内的换热性能。加热段换热系数沿程变化趋势与文献[13]中Deissier的趋势一致,CFD的换热系数结果与WCOBRA/TRAC程序中的关系式吻合较好。本文模拟方法可行,其结果可为后续的实验模拟体设计提供技术支持。     

Analysis of LMFBR containment response using a multifield implicit continuous-fluid eulerian code (MICE)

An Eulerian computer code, MICE, for analyzing multifield-fluid flow problems in LMFBR containments is presented. The hydrodynamics of the MICE code is based upon the implicit multifield (IMF) method which includes the treatment of multifield fluids, the interpenetration of materials, the heat transfer, and the material phase changes. The finite-difference equations and the numerical techniques used in obtaining the equilibrium pressures and in calculating the fluid-structure interactions are described in detail. Sample problems are given to illustrate the capabilities of the code.     

CR39探测器的带电粒子能量响应研究

为在神光系列激光装置上开展惯性约束聚变(ICF)带电粒子诊断,通过0.7~10 MeV加速器质子源和241 Am放射性同位素α粒子源完成了CR39探测器的质子和α粒子能量响应实验研究,结合TRIM程序和半经验模型建立了CR39刻蚀动力学模拟程序,模拟分析了p、D、T和α粒子在正入射和斜入射条件下CR39的径迹形状与能量响应特征,对多种ICF带电粒子谱仪的CR39探测器单元的设计提出了优化方案。     

基于OpenFOAM的中子输运动力学求解器ntkFoam研究

由于中子输运模拟的复杂性及其与其他物理过程耦合的困难性，全堆芯精细中子输运-热工水力多物理计算是核工程领域的难点。本文基于有限体积C++开源软件OpenFOAM，采用有限体积法建立稳态和瞬态中子输运动力学方程数值求解模型，开发了中子输运动力学求解器ntkFoam。通过对多个基准问题进行模拟验证表明，本文建立的ntkFoam求解器能准确模拟中子输运动力学问题，并能很好地适应于不同维度及复杂几何条件；可实现中子输运、传热传质的精细耦合，为基于中子输运计算的全堆芯多物理模拟提供了一些精确耦合的思路与方法。      

中性束注入快离子初始分布的蒙特卡罗模拟

比较精确地模拟计算中性束注入（NBI）托卡马克等离子体的快离子初始分布是采用大规模数值模拟方法研究NBI快离子相关物理问题的首要任务。本文建立了NBI托卡马克等离子体的简化物理模型,采用蒙特卡罗方法自主开发了NBI应用程序。选取ASDEX Upgrade（AUG）托卡马克上切向注入和垂直注入两种情况为计算实例,分别模拟计算出NBI粒子被离子化的初始三维空间位置,并统计得出初始快离子的径向分布、极向角分布、环向角分布和投掷角分布,这些计算结果与国际上相关文献结果一致。