Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin-resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi-Tosi-Land-Sjölander scheme with the QMC data to remove finite-size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110 , 146405 (2013)] and configuration path integral Monte Carlo/permutation-blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117 , 115701 (2016)].     

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, and matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor S(q, ω) and the plasmon dispersion ω(q) . Recently, the first ab initio results for S(q, ω) of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations (Dornheim et al., Phys. Rev. Lett., 121, 255001, 2018). Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random-phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeroes of the dielectric function can solve this problem for WDM conditions.     

用于温密物质研究的强流电子束加载技术

能量20 MeV、流强2.5 kA的电子束脉冲可以在数十ns的时间内将靶材料加载至温密物质状态,进而可以开展材料状态方程、电导率以及不透明度等的实验研究工作。介绍了在神龙一号加速器上开展温密物质实验研究的束靶作用方式以及相应的测试技术。对电子束在直径0.3 mm、长1 mm的金属靶丝内的能量沉积和流体动力学响应进行了数值模拟。结果表明:靶丝的温度随着靶材料原子序数的增加而上升,而靶丝内温度分布的均匀性随着原子序数的增加而降低;在电子束加载后40 ns时刻Ta丝内的最高温度可以达到约1.6 eV。     

Wave packet molecular dynamics–density functional theory method for non‐ideal plasma and warm dense matter simulations

A new wave packet molecular dynamics–density functional theory (WPMD‐DFT) method is proposed for atomistic simulations of non‐ideal plasma and warm dense matter. The method is based on the WPMD approach, where the electronic exchange and correlation effects are treated using an additional energy term taken from DFT. This term is calculated by integration over the mesh values of the wave packet density. The local density approximation is implemented so far. WPMD‐DFT is meant as a replacement for the anti‐symmetrized WPMD (AWPMD) method which is more time consuming and lacks electron correlation. In this paper, we compare the results obtained by WPMD‐DFT, WPMD, AWPMD, classical molecular dynamics, and path integral Monte Carlo methods for the internal energy of the hydrogen plasma in the temperature range 10–50 kK and electron number density from 10²⁰ to 10²⁴ cm^?3. We also demonstrate the ability to handle the simultaneous dynamics of electrons and ions by calculating the electron–ion temperature relaxation. The scalability of the WPMD‐DFT method with the number of electrons is shown for implementations in central processing unit and graphical processing unit.     

X射线汤姆孙散射在温稠密物质研究中的应用

温稠密物质(warm dense matter,WDM)是近年来兴起的一个前沿研究领域,它处于传统的凝聚态与等离子体状态之间的过渡状态.此状态下的物质广泛存在于宇宙和实验室中,如巨行星的内核、惯性约束聚变的内爆燃料等.然而人们对温稠密物质又是陌生的,因为传统的凝聚态和等离子体物理的理论和实验方法难以用于研究这样的物质状态.近几年,随着高功率激光装置以及诊断技术的发展,人们发展出X射线汤姆孙散射方法,对温稠密态物质开展了深入的研究,获得了重要的实验结果.     

温稠密铝等离子体物态方程及其电离平衡研究

温稠密物质的物性参数在惯性约束聚变能源、Z箍缩等高能量密度物理领域的实验结果分析和物理过程数值模拟等方面有着重要的应用价值.本文应用部分电离等离子体模型,在理想自由能的基础上考虑了库仑相互作用、排斥体积作用和极化作用等非理想特性,开展了温稠密等离子体物态方程和电离平衡的研究.计算了温稠密铝等离子体的压强等物态方程数据和在密度为1.0×10^-4-3.0 g/cm^3,温度为1.0×10^4-3.0×10^4 K范围内的粒子组分.计算结果显示,铝等离子体的平均电离度在临界密度区域内随着密度的增加而突然增大.根据非理想Saha方程中有效电离能这一关键参数,分析了铝等离子体平均电离度在临界密度区域内随密度迅速增大的现象.     

强粒子束产生温稠密物质热力学状态估计

基于能量平衡原理,结合SRIM统计方法,以铝靶为例,对重离子束和强电子束产生高温高密度物质所需的束流参数进行估计,分析各自产生温稠密物质的优缺点。结果显示,从电子辐射能损和束流利用观点来看,1~10MeV电子束产生温稠密物质具有较好的均匀性和较高的利用率;而重离子束加载可以获得较宽区域的温稠密物质。     

Density functional theory for dielectric properties of warm dense matter

ABSTRACT

Density functional theory (DFT) is applied for the calculation of the dielectric function (DF), reflectivity, conductivity, plasma frequency and effective free electron density of warm dense matter (WDM). Shock-compressed xenon plasma and warm dense hydrogen are considered. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the DF. The real part of the DF is calculated by means of the Kramers–Kronig transformation. Sum rule within the framework of the DFT is used for determination of the plasma frequency and effective free electron density. Corrections to the reflectivity are considered, which allow for the finite width of the transient layer (wave front) at the WDM border.     

温稠密物质中不同价态离子分布对X-射线弹性散射光谱计算的影响

在天体物理和惯性约束聚变研究中涉及到的温稠密物质通常包含多种元素的混合,并且每种元素还被电离成多种离子价态,不同价态离子结构及其丰度将直接影响温稠密物质的诊断及其物理性质.同时,从电子结构计算出发来研究宏观物理性质时,还需要考虑温度、密度效应对离子结构的影响.本文从不同价态离子的电子结构计算出发,采用考虑了离子间相互作...     

激光产生温稠密物质的微观动力学过程及状态诊断

随着大型激光装置的建立和精密测量技术的发展,强激光与固体相互作用成为实验室产生温稠密物质的一个重要手段。温稠密物质的结构复杂性、瞬态性和非平衡性给理论建模和实验测量带来了巨大挑战。本文系统介绍了激光产生温稠密物质的实验手段和理论模拟方法方面的重要进展,分析了其中的电子激发动力学、电子-离子能量弛豫过程、离子动力学等物理过程,总结了温稠密物质状态诊断的实验技术和理论方法,并论述了激光产生温稠密物质的发展趋势。     

Ionization dynamics of dense matter generated by intense ultrashort X‐ray pulses

We investigate a pump‐probe X‐ray Thomson scattering (XRTS) experiment that might be carried out at a free electron laser facility to study warm‐to‐hot states of dense matter. Ultrashort and intense X‐ray pulses with different energies (1,560–1,830 eV) heat a 1 µm thick Al target isochorically and create homogeneous and uncompressed warm‐to‐hot states of dense matter. A second pulse with variable delay probes this heated state via XRTS. The X‐ray laser–target interaction is modelled within radiation‐hydrodynamic simulations applying the HELIOS‐CR code. The HELIOS‐CR results qualitatively agree with Monte‐Carlo simulations, where the laser pulse absorption is simulated based on a uniform random sequence of events. The electron feature in the simultaneously observed X‐ray scattering spectrum is a function of the degree of ionization and the target temperature. Therefore, the temporal evolution of the plasmon peak measures the ionization dynamics on ultra‐short time scales. The XRTS spectrum is calculated based on the Chihara formula utilizing the Born‐Mermin approximation for the free electron dynamic structure factor. The proposed experiment will reveal important details of the ionization dynamics on ultra‐short time scales as well as of the relaxation on ps time scales.     

Equation‐of‐state studies of high‐energy‐density matter using intense ion beams at the Facility for Antiprotons and Ion Research

This paper describes an experiment design based on numerical simulations to measure the equation‐of‐state properties of high‐energy‐density (HED) matter using intense particle beams. The simulations are performed using a 2D hydrodynamic computer code, BIG2, while the beam parameters are considered to match the Facility for Antiprotons and Ion Research beam. This study has shown that in such experiments one can generate different phases of HED lead. Similar calculations are planned for other materials.     

Permutation blocking path integral Monte Carlo simulations of degenerate electrons at finite temperature

We analyse the simulation of strongly degenerate electrons at finite temperature using the recently introduced permutation blocking path integral Monte Carlo (PB‐PIMC) method [T. Dornheim et al., New J. Phys. 17 , 073017 (2015)]. As a representative example, we consider electrons in a harmonic confinement and carry out simulations for up to P = 2000 so‐called imaginary‐time propagators – an important convergence parameter within the PIMC formalism. This allows us to study the P‐dependence of different observables of the configuration space in the Monte Carlo simulations and of the fermion sign problem. We find a surprisingly persisting effect of the permutation blocking for large P, which is explained by comparing different length scales. Finally, we touch upon the uniform electron gas in the warm dense matter regime.     

Investigation of warm dense matter using time-resolved X-ray absorption spectroscopy with third- and fourth- generation light sources

The advent of high-power lasers has provided insights into laboratory high energy density (>10¹¹ J/m³) physics. In particular, the properties of warm dense matter (WDM) with temperatures of 10⁴–10⁶ K and near-solid densities is a research area that has garnered significant interest recently. However, owing to the high temperatures and pressures associated with WDM, the measurement of fundamental properties is difficult, and insufficient data has been a significant setback in WDM research. Herein, we review recent developments in time-resolved X-ray absorption spectroscopy with synchrotron and X-ray free electron lasers for WDM research. Various physical properties, such as atomic bonding, electronic structures, electron–phonon coupling, and thermal conductivity of various elements in WDM conditions are investigated via this noble X-ray technique at various time scales from 100 ps to 100 fs.     

固体氢的压缩行为

 同时考虑分子的平动与转动自由度，用等温等压系综的路径积分蒙特卡罗方法研究了固体氢的状态方程。在有实验数据的区域，计算结果同实验结果符合很好，在无实验数据的超高压区域，计算结果同实验的外推结果符合。为了定量研究零点运动，还计算了体系的能量。     

Application of intense ion beams to planetary physics research at the Facility for Antiprotons and Ion Research facility

This paper presents detailed 2D hydrodynamic simulations of implosion of a multi‐layered cylindrical target that is driven by an intense uranium beam. The target is comprised of a thick, high‐Z, high‐ρ cylindrical shell that encloses a sample material (Fe in the present case). Two options have been used for the focal spot geometry: an annular form and a circular form. The purpose of this work is to show that an intense heavy‐ion beam can induce the extreme physical conditions in the sample material similar to those that exist in the planetary cores. In this study, we use parameters of the beam that will be generated at the Facility for Antiprotons and Ion Research (FAIR), Darmstadt, in a few years' time. Production of these high‐energy‐density (HED) samples will allow us to study planetary physics in the laboratory. It is to be noted that planetary physics research is an important part of the FAIR HED physics program. A dedicated experiment named LAboratory PLAnetary Sciences (LAPLAS) has been proposed for this purpose. These simulations show that in such experiments an Fe sample can be imploded to the Earth's core conditions and to those in more massive rocky planets called Super‐Earths. Similarly, implosion of hydrogen and water samples will generate the core conditions of solar and extrasolar hydrogen‐rich gas giants and water‐rich icy planets, respectively. The LAPLAS experiments will thus provide very valuable information on the equation of state and transport properties of matter under extreme physical conditions, which will help scientists understand the structure and evolution of the planets in our solar system as well as of the extrasolar planets.     

高密核物质中核子的运动对于K介子的等效质量和能量的影响

本文对比分析了目前用于研究K介子产生与演化的不同动力学模型中,高温高密核物质中K⁺介子和K^-介子的等效质量和它所感受到的平均场.所得结果显示:在关于K介子的一般的平均场理论中,所定义的K⁺介子的等效质量随着核物质密度的增大而增加, K^-介子的等效质量随着核物质密度的增大而减小;但在K介子演化的协变动力学模型中,所采用的K⁺介子和K^-介子等效质量是随着核物质密度的增大都是减小的 关键词： 高密核物质 K介子 等效质量 核子运动     

初始溅射粒子密度对烧蚀粒子密度和速度分布的影响

采用蒙特-卡罗(Monte Carlo)模拟方法,研究了初始溅射粒子密度对其传输中的密度和速度分布以及环境气体密度分布的影响.结果表明,随着初始溅射粒子密度增大,烧蚀粒子和环境气体高密度峰的交叠区离开靶的最大距离减小,被衬底反弹后,距靶的最小距离减小,烧蚀粒子的速度分布随初始溅射粒子密度增大而变宽,当初始溅射粒子密度大于8.33×10²⁵ m^-3时,出现速度劈裂现象.所得结论为进一步定量研究纳米晶粒的成核机理提供了基础. 关键词： Monte Carlo模拟 烧蚀粒子 密度分布 速度分布     

强流重离子束驱动的高能量密度物理研究进展

强流高能离子束可以准等容加热任何高密度样品,制备出尺度大、状态均匀、内部无冲击波的高能量密度物质,为实验室研究高能量密度物理提供了一种独特的新手段。介绍了国内外典型的强流重离子加速器装置及其与高能量密度物理相关的关键参数设计和研究规划;展示了基于粒子和流体模拟的离子束驱动高能量密度物质产生和状态演化规律进展;介绍了一套兼具高时空分辨和高穿透力的高能电子成像诊断技术;分析了中低能区离子束与等离子体相互作用过程中的碰撞和电荷交换微观机制,以及激光加速超短超强离子束在等离子体中的非线性输运和欧姆能损机制。