Charged-particle transport in high energy density plasmas

Charged-particle transport processes, which are influenced by the electronic and ionic conductivity, viscosity, diffusion, and stopping power, govern the evolution of diverse plasma systems, from stars and giant planets to inertial confinement fusion (ICF) capsules. To model these systems over the pertinent time and length scales, researchers often employ hydrodynamic codes that require knowledge of the coefficients quantifying these transport processes over a wide range of material conditions. Since precision measurements of transport properties in hot and warm dense matter are challenging, benchmark experimental data are rare. Thus, hydrodynamic codes that require transport coefficients as closures rely on analytic models or computational approaches for transport coefficients.

There are multiple theoretical and computational approaches to calculating transport coefficients in high energy density (HED) plasmas, ranging from roughly parameterized analytic expressions to computationally intensive simulation methods based on density functional theory (DFT). Comparing calculations of transport coefficients at specified conditions from multiple approaches, as has been done in two code-comparison workshops,^1,2 is one step toward quantifying the uncertainties or errors associated with a given approach. That understanding, in turn, can help improve calculations, inform sensitivity studies in simulations, and stimulate focused experimental efforts.

This collection of articles covers recent work on charged-particle transport from the HED physics community. It includes context for the importance of transport coefficients to ICF, surveys and comparisons of theoretical and computational approaches, and in-depth analyses of calculational and experimental techniques.

This collection is anchored by two overviews of how transport coefficients and their uncertainties inform radiation-hydrodynamic simulations. Haines³ describes the sensitivities of ICF simulations to transport coefficients and explores how uncertainties in the treatment of transport in mixtures can improve understanding of persistent discrepancies between simulation predictions and laser-indirect-drive ICF measurements. Hu et al.⁴ provide an overview of how transport processes are currently treated in simulations of laser-direct-drive ICF experiments, as well as an outlook for addressing current challenges for improvements in the reliability of fusion target design for inertial fusion energy and high-gain ICF.

Stanek et al.² present a summary of the results of the 2023 charged-particle transport coefficient code-comparison workshop, which studied multiple approaches to both electronic and ionic transport calculations in a variety of materials and conditions. They also propose cases for the next workshop. Several other papers in this collection present details of these modeling approaches and comparisons: Shaffer et al.⁵ focus on electronic conductivities, reviewing and comparing three approaches: quantum kinetic theory, Kubo–Greenwood applied to DFT-molecular dynamics, and time-dependent DFT. They also explore the effects of dynamic screening and variation in exchange-correlation approximations. Johnson et al.⁶ show how output from average-atom models can inform electronic and ionic transport models based on both kinetic theory and molecular dynamics; they compare their results with DFT-based approaches and analytic models.

The collection includes several in-depth analyses of calculations of various transport coefficients based on state-of-the-art multi-center DFT models, which often serve as benchmarks for the modeling community. Melton et al.⁷ provide a detailed and comprehensive description of the methods used to produce their contributions of electronic and ionic transport coefficients to the 2023 code comparison workshop, including convergence studies, extrapolation techniques, and ensemble selection in the code Vienna Ab-initio Simulation Package (VASP).^8–10 Blanchet et al.¹¹ provide a similarly comprehensive description of the methodology used to produce transport data for the workshop with the code Abinit.^12–14 White et al.¹⁵ investigate transport and optical response properties of carbon-hydrogen mixtures, exploring options for mixing methods. Kononov et al.¹⁶ describe a multi-lab effort exploring the reproducibility and sensitivities of stopping power calculations from several independent time-dependent DFT codes and offer strategies for controlling finite-size effects.

Finally, the collection includes several forward-looking contributions and explorations that underscore the rich connections of charged-particle transport to other fields and advanced experimental capabilities. Röpke¹⁷ uses quantum statistical methods to produce benchmark values for the electrical conductivity in hydrogen including electron–electron collisions. Shashikant et al.¹⁸ apply methods from machine learning to generate force fields that can be coupled to molecular dynamics to generate ionic transport coefficients. Kinney et al.¹⁹ explore the high- and low-frequency limits of bremsstrahlung radiation in strongly coupled plasmas, comparing theory and simulations. The low-frequency limit of these optical properties is closely related to the electrical conductivity, and Ofori-Okai et al.²⁰ describe a new experimental approach to measuring this low-frequency behavior, combining THz spectroscopy with the x-ray free-electron laser at the Linac Coherent Light Source (LCLS).

Charged-particle transport plays a critical role in hydrodynamic modeling of HED plasmas, and there is a vibrant community of researchers studying experimental, theoretical, and computational methods to provide high-quality data. Each contributed article in this issue offers a glimpse into one or more of the many corners of modern physics that inform—and are informed by—the charged-particle transport properties of materials at extreme conditions. Many of the collected articles offer new or improved methods or strategies for computation or analysis that will be useful to other researchers working in this field. Many of the articles conclude by looking ahead: charting the needs, opportunities, and methods that will draw in new researchers to drive this field into the future.

We sincerely thank all the participants in the APS-DPP mini-conference and the charged-particle transport coefficient code comparison workshops for their presentations, calculations, measurements, and insights during discussions, with special thanks to those who contributed articles to this collection. We are very grateful to the editors and staff of Physics of Plasmas, who made this effort painless for the guest editors of this collection. Sandia National Laboratories is a multi-mission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for DOE's National Nuclear Security Administration (Contract No. DE-NA0003525). This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (Contract No. DE-AC52-07NA27344). The Los Alamos National Laboratory is managed by the Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy (Contract No. 89233218CNA000001). This material is based upon work supported by the Department of Energy (the National Nuclear Security Administration), as part of the University of Rochester's “National Inertial Confinement Fusion Program” (Award No. DE-NA0004144). This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

The authors have no conflicts to disclose.

Stephanie B. Hansen: Conceptualization (equal); Writing – original draft (lead); Writing – review & editing (lead). Lucas J. Stanek: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Brian M. Haines: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). S. X. Hu: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Patrick F. Knapp: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Michael S. Murillo: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Liam G. Stanton: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Heather D. Whitley: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.