Session GO8: Analystical and Computational Techniques, ICF and HED

A comparison of non-local electron transport models relevant to inertial confinement fusion

We compare the reduced non-local electron transport model developed by Schurtz et al. (Phys. Plasmas 7, 4238 (2000)) to Vlasov-Fokker-Planck simulations. Two new test cases are considered: the propagation of a heat wave through a high density region into a lower density gas, and a 1-dimensional hohlraum ablation problem. We find the reduced model reproduces the peak heat flux well in the ablation region but significantly over-predicts the coronal preheat. The suitability of the reduced model for computing non-local transport effects other than thermal conductivity is considered by comparing the computed distribution function to the Vlasov-Fokker-Planck distribution function. It is shown that even when the reduced model reproduces the correct heat flux, the distribution function is significantly different to the Vlasov-Fokker-Planck prediction. Two simple modifications are considered which improve agreement between models in the coronal region.   

Benchmark of nonlocal transport models against Vlasov-Fokker-Planck codes in situations of immediate relevance to ICF

Hydrodynamics simulations relevant to inertial confinement fusion require a detailed description of energy transport, in particular by electrons. This may be nonlocal if, as is commonly the case, the plasma is not in local thermodynamic equilibrium (i.e. if the electron mean free path is long compared to the temperature scale-length). In this case, a kinetic model of electron thermal transport is required. Some of the most successful approaches to nonlocal transport (SNB [1] \& M1 [2] models) are systematically compared [3] against Vlasov-Foker-Planck \& Particle-in-Cell codes, extending benchmarking beyond the 1D unmagnetized case and studying situations of immediate relevance to ICF. [1] Schurtz et al., Phys. Plasmas, 7 (10) 2000. [2] Del Sorbo et al., Phys. Plasmas, 22 (8) 2015. [3] Brodrick et al., Phys. Plasmas, arXiv preprint arXiv:1706.04153 (2017).   

Analytic insights into nonlocal electron thermal transport

Several theories of nonlocal electron thermal transport in laser target plasmas, based on a Krook model give rather different results. Sometimes these models show very little effect of fuel preheat on target gain, other calculations show enough preheat that the gain is substantially reduced. We find that there are errors in the theoretical models and very likely errors in some of their numerical implementation. Hence analytic insight is necessary. We derive approximate analytical solutions for the Krook model for nonlocal electron energy transport, ultimately finding a relatively simple formula to estimate for fuel preheat in terms of the laser and target plasma parameters. This analysis can be used as a check on the more complex fluid simulation. In addition to the Krook model being not correctly formulated, another consideration is that a Fokker Planck model gives a rather different solution for the preheat. We also derive a formula for the preheat based on a Fokker Planck model, a formula with is intuitively reasonable and predicts much less preheat than a Krook model. In either model, there can be broadening of the ablation layer which may have an effect on the Rayleigh Taylor instability growth rate.   

Plasma simulation with a multi-scale numerical method

Multi-scale effect is widely existed in plasma. Plasma will be deviated from ideal plasma assumption when it meets external field, in which parts of electrons will gain energy from the field and become runaway electrons. Ideal MHD method can't deal with the physical problems if the problems are closed related to those runaway electrons effect. To solve those problems, PIC (particle in cell simulation) method and hybrid fluid method were used traditionally. But those methods have their own limitations, PIC method needs a very long calculation time which limits time scale it can simulate, and hybrid method introduces some non-physical assumptions and requires dealing complex data exchange between different methods. In this paper, a muti-scale method is described, in which the evolution of plasma is referenced UGKS direct modeling method [1], and finite volume scheme is used to solve the multicomponent plasma BGK equations. And the time-varying Maxwell equations are deduced with the finite difference scheme, the magnetic field divergence is controlled by adopting the CT/CD method. This method does not require different calculation methods in calculation of different time scales. It will be degradation to kinetic scheme if the plasma average collision time is large and degradation to MHD scheme if the average plasma collision time is small automatically. The computational accuracy of this method is quite the same as that of the DSMC method, and the calculation time required is far less than that of the PIC method. The method can be applied to the simulation gas discharge plasma under extreme conditions and complex non-ideal completely ionized plasma.   

A Multifluid Numerical Algorithm for Interpenetrating Plasma Dynamics

Interpenetrating plasmas occur in situations including inertial confinement fusion experiments, where plasmas ablate off the hohlraum and capsule surfaces and interact with each other, and in high-energy density physics experiments that involve the collision of plasma streams ablating off discs irradiated by laser beams. Single-fluid, multi-species hydrodynamic models are not well-suited to study this interaction because they cannot support more than a single fluid velocity; this results in unphysical solutions. Though kinetic models yield accurate solutions for multi-fluid interactions, they are prohibitively expensive for at-scale three-dimensional (3D) simulations. In this study, we propose a multifluid approach where the compressible fluid equations are solved for each ion species and the electrons. Electrostatic forces and inter-species friction and thermal equilibration couple the species. A high-order finite-volume algorithm with explicit time integration is used to solve on a 3D Cartesian domain, and a high-order Poisson solver is used to compute the electrostatic potential. We present preliminary results for the interpenetration of two plasma streams in vacuum and in the presence of a gas fill.   

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect.   

Multiscale Molecular Dynamics Investigations of the Ablator/Fuel Interface during Early Stages of Inertial Confinement Fusion

At the National Ignition Facility, high-powered laser beams are used to compress a small target to generate fusion reactions. A critical issue in achieving this is the understanding of mix at the ablator/fuel interface. Mixing occurs at various length scales, ranging from atomic inter-species diffusion to hydrodynamic instabilities. Because the interface is preheated by energy from the incoming shock, it is important to understand the dynamics before the shock arrives. The interface is in the warm dense matter phase with a deuterium/tritium fuel mixture on one side and a plastic mixture on the other. We would like to understand various aspects of the evolution, including the state of the interface when the main shock arrives, the role of electric field generation at the interface, and the character and time scales for diffusion. We present a multiscale approach to model these processes, which combines molecular dynamics to simulate the ionic degrees of freedom with orbital-free density functional theory to calculate the electronic structure. Simulation results are presented and connections to hydrodynamic models are discussed.   

Investigation of thermal conductivity~of materials for inertial confinement fusion applications

Numerous inertial confinement fusion (ICF) capsule implosion experiments use different materials and their mixtures. To numerically simulate such experiments, one requires many plasma parameters beforehand for a wide range of temperatures and densities. Thermal conductivity is one of them, which determines the heat transport in plasma so that it plays a key role in the growth of hydrodynamic instabilities during the capsule implosion process. Analytic models such as, Spitzer model and Lee-More model have been extensively used to calculate thermal conductivity. But these models are usually not valid especially for warm dense plasma regime. Tabular EOS data, such as SESAME tables, are not available for all materials. In this talk, we investigate different analytic models, first principle calculation, tabular data to calculate thermal conductivity for most commonly used materials and their mixtures in ICF experiments such as Polystyrene (CH) and Deuterium-Tritium (DT).   

Development of Fast and Reliable Free-Energy Density Functional Methods for Simulations of Dense Plasmas from Cold- to Hot-Temperature Regimes

Free-energy density functional theory (DFT) is one of the standard tools in high-energy-density physics used to determine the fundamental properties of dense plasmas, especially in cold and warm regimes when quantum effects are essential. DFT is usually implemented via the orbital-dependent Kohn--Sham (KS) procedure. There are two challenges of conventional implementation: (1) KS computational cost becomes prohibitively expensive at high temperatures; and (2) ground-state exchange-correlation (XC) functionals do not take into account the XC thermal effects.\footnote{V.V. Karasiev, L. Calderin, and S.B. Trickey, Phys. Rev. E \textbf{93}, 063207 (2016).} This talk will address both challenges and report details of the formal development of new generalized gradient approximation (GGA) XC free-energy functional which bridges low-temperature (ground state) and high-temperature (plasma) limits.\footnote{V.V. Karasiev, J.W. Dufty, and S.B. Trickey, ``Non-Empirical Semi-Local Free-Energy Density Functional for Matter Under Extreme Conditions,'' submitted to Physical Review Letters.} Recent progress on development of functionals for orbital-free DFT as a way to address the second challenge will also be discussed. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.   

Density-Functional-Theory--Based Equation-of-State Table of Beryllium for Inertial Confinement Fusion Applications

Beryllium has been considered a superior ablator material for inertial confinement fusion target designs. Based on density-functional-theory calculations, we have established a wide-range beryllium equation-of-state (EOS) table of density $\rho =$ 0.001 to $\rho =$ 500 g/cm$^{\mathrm{3}}$ and temperature $T =$ 2000 to $10^{8}$ K. Our first-principles equation-of-state (FPEOS) table\footnote{Y. H. Ding and S. X. Hu, Phys. Plasmas \textbf{24}, 062702 (2017).} is in better agreement with widely used \textit{SESAME }EOS table (\textit{SESAME }2023) than the average-atom \textit{INFERNO }model and the \textit{Purgatorio }model. For the principal Hugoniot, our FPEOS prediction shows $\sim $10{\%} stiffer behavior than the last two models at maximum compression. Comparisons between FPEOS and \textit{SESAME }for off-Hugoniot conditions show that both the pressure and internal energy differences are within $\sim $20{\%} between two EOS tables. By implementing the FPEOS table into the 1-D radiation--hydrodynamics code \textit{LILAC}, we studied the EOS effects on beryllium target-shell implosions. The FPEOS simulation predicts up to an $\sim $15{\%} higher neutron yield compared to the simulation using the \textit{SESAME }2023 EOS table. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.   

Progress towards an {\it ab initio} real-time treatment of warm dense matter

Time-dependent density functional theory (TDDFT) provides an accurate description of equilibrium properties of warm dense matter, such as the dynamic structure factor (Baczewski, {\it et al.}, Phys. Rev. Lett., 116(11), 2016). While non-equilibrium properties, such as stopping power, have also been demonstrated to be within the grasp of TDDFT, the ultrafast isochoric heating of condensed matter into the warm dense state, enabled by recent advances in XFELs, remains beyond its capabilities. In this talk, we will describe the successes of and continuing challenges for TDDFT for warm dense matter, and present progress towards a more complete {\it ab initio} treatment of isochoric x-ray heating. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the DOE’s National Nuclear Security Administration under contract DE-NA0003525.   

``Green's function'' approach {\&} low-mode asymmetries}

Long wavelength, low mode asymmetries are believed to play a leading role in limiting the performance of current ICF implosions on NIF. These long wavelength modes are initiated and driven by asymmetries in the x-ray flux from the hohlraum; however, the underlying hydrodynamics of the implosion also act to amplify these asymmetries. The work presented here aim to deepen our understanding of the interplay of the drive asymmetries and the underlying implosion hydrodynamics in determining the final imploded configuration. This is accomplished through a synthesis of numerical modeling, analytic theory, and experimental data. In detail, we use a Green's function approach to connect the drive asymmetry seen by the capsule to the measured inflight and hot spot symmetries. The approach has been validated against a suite of numerical simulations. Ultimately, we hope this work will identify additional measurements to further constrain the asymmetries and increase hohlraum illumination design flexibility on the NIF. The technique and derivation of associated error bars will be presented.   

Multi-dimensional simulation package for ultrashort pulse laser-matter interactions

Advanced simulation models recently became a popular tool of investigation of ultrashort pulse lasers (USPLs) to enhance understanding of the physics and allow minimizing the experimental costs for optimization of laser and target parameters for various applications. Our research interest is focused on developing multi-dimensional simulation package FEMTO-2D to investigate the USPL-matter interactions and laser induced effects. The package is based on solution of two heat conduction equations for electron and lattice sub-systems - enhanced two temperature model (TTM). We have implemented theoretical approach based on the collision theory to define the thermal dependence of target material optical properties and thermodynamic parameters. Our approach allowed elimination of fitted parameters commonly used in TTM based simulations. FEMTO-2D is used to simulated the light absorption and interactions for several metallic targets as a function of wavelength and pulse duration for wide range of laser intensity. The package has capability to consider different angles of incidence and polarization. It has also been used to investigate the damage threshold of the gold coated optical components with the focus on the role of the film thickness and substrate heat sink effect.