Analysis of Energy Processes in Inertial Confinement Fusion Plasmas Based on Quantum Simulations

1.惯性约束聚变过程中产生的等离子体是经典离子和至少半简并电子的混合物。模拟这些等离子体的困难主要来自于用具有连续空间自由度的波函数来描述电子的行为。还必须考虑到电子之间以及电子与离子之间的相互作用。有了最先进的计算资源，我们被迫将自己限制在对相当小的粒子系统的分析中。2.较小但不可忽略的困难也源于离子的运动。在惯性约束聚变过程中，离子之间的耦合是中等的，即使它们之间的耦合不是很强，离子-离子相互作用的影响在包括能量传输在内的许多方面都起着重要的作用。为了对离子和电子混合物进行可靠的模拟，以尽可能小的系统规模来模拟离子是必不可少的。3.基于上述考虑，我们在本研究项目中主要对等离子体量子模拟的两个重要方面进行了研究：(1)通过引入给定温度和压力下可变形的周期边界条件来模拟具有有限个小系统的扩展离子系统。(2)对于电子态的分析，我们提出了一种有用的方法。通过密度泛函方法建立了包含多体相互作用的有限元数值系统。(3)基于密度泛函理论中多体波函数的时间推进算符的泰勒展开式，我们发展了有效的方法来模拟电子的时间发展。

1.Plasmas produced in the process of inertial confinement fusion are mixtures of classical ions and at least half-degenerate electrons. The difficulty in simulating these plasmas comes mainly from the behavior of electrons described by wave functions with continuous degrees of freedom of space. It is also essential to take into account interactions between electrons and between electrons and ions. With the state-of-the-art computational resources, we are forced to limit ourselves within the analysis on rather small systems of particles.2.Smaller but not negligible difficulty also stems from motions of ions. In the process of inertial confinement fusion, the coupling between ions is intermediate and, even if they are not strongly coupled, the effect of ion-ion interaction in such regime plays important roles in many aspects including energy transport. In order to perform reliable simulations on the mixture of ions and electrons, it is indispensable to have efficient algorisms for simulating ions with smallest possible system size.3.Based on the above considerations, we have worked mainly on two important aspects of quantum simulation of plasmas in this research project :(1)We have developed useful methods to simulate extended ion systems coupled to electron liquid with finite smaller systems by introducing deformable periodic boundary conditions under given temperature and pressure.(2)For the analysis of electronic states, we have developed a numerical system based on the finite element method with inclusion of many-body interactions through the density functional approach.(3)We have also developed efficient methods to simulate the time development of electrons on the basis of the Taylor expansion of time-propelling operator of many-body wave function in the density functional theory.