Measurement of Mutual Diffusion in Warm Dense Matter

Project Overview

This project has developed and conducted thermal conductivity measurements of materials at warm dense matter (WDM) conditions, that is at near solid densities and temperatures on order of 1 - 20 electronvolts (10,000 - 200,000 Kelvins). There is an abundance of published theoretical calculations, but their predictions differ significantly. This is because modeling matter in the WDM regime is particularly challenging; these systems often exhibit strong ion-ion correlations, as well as a distinct quantum behavior of the electrons. On the other hand, only very few experiments have attempted to measure transport properties in this plasma regime. Measurements of plasma transport properties like thermal conductivity and mutual diffusion are challenging because diffusion in particular is a slow process, occurring in WDM at a rate on the order of 0.1 micron per nanosecond. With the advent of the National Ignition Facility (NIF), such measurements, which require well-controlled and steady WDM conditions for durations of 10 ns and more, come within reach.

Our experimental measurements were enabled by developing x-ray Fresnel Refractive - Diffractive Radiography (FDR) for experiments at the Omega laser and the NIF. FDR is a novel diagnostic technique that allows following the slow diffusion-driven electron-density-gradient changes across the interface of two isochorically-heated samples with better than 1 micron spatial resolution, which is more than 5 times improved compared to previous experiments. Thermal conductivity is the ability to transport heat in response to temperature gradients. It is the basic microscopic quantity that governs the atomic level energy transport, and plays a vital role in several areas of contemporary WDM research, including modeling of astrophysical objects and understanding interface mixing in inertial confinement fusion (ICF) implosions. Our team has also developed an experimental platform for cylindrical implosion experiments of liquid deuterium samples for the NIF. This is of relevance for measuring the equation of state of deuterium, and paths the way for mutual diffusion (the measurement of ions due to particle density gradients) measurements in isochorically heated samples.

Mission Impact

Plasma transport properties like thermal conductivity and mutual diffusion are fundamental processes that govern the energy transport and hydrodynamic stability, respectively, in ICF implosion experiments and in nuclear weapons systems. Experimental measurements of thermal conductivity and diffusivity in Warm Dense Matter are of crucial importance to benchmark transport and mixing models and hence improve predictability in simulations for ICF and Stockpile Stewardship applications. They enhance the fundamental understanding of aging nuclear weapons systems, and therefore maintain and enhance the safety, security, and effectiveness of the U.S. nuclear weapons stockpile. Our NIF measurements have high visibility in the HED community and highlight Lawrence Livermore National Laboratory's leadership in HED science, and specifically the unique capabilities of the NIF for the HED community. Thanks to that, this project has helped attracting world-class scientists to work on scientific problems relevant for ICF and stockpile stewardship. The advancement in Refractive Enhanced Radiography (RER) through using smaller source sizes will also benefit efforts for Equation-of-State (EOS) measurements of low-Z materials, which is one of the mid-term priorities of the Plasma EOS program at Lawrence Livermore National Laboratory. 

Publications, Presentations, and Patents

C.H. Allen, M. Oliver, T.G. White, W. Theobald, A. Saunders, Y. Ping, O. Landen, L. Divol and T. Doeppner, "Developing x-ray Fresnel Diffractive-Refractive Radiography for Measuring Mutual Diffusion in Warm Dense Matter" (Presentation, 62nd Annual Meeting of the American Physical Society Division of Plasma Physics, Nov 2020). LLNL-PRES-817703

C.H. Allen, M. Oliver, T.G. White, W. Theobald, A. Saunders, Y. Ping, O. Landen, L. Divol and T. Doeppner, "Developing x-ray Fresnel Diffractive-Refractive Radiography for Measuring Mutual Diffusion in Warm Dense Matter" (Presentation, 23rd Topical Conference on High-Temperature Plasma Diagnostics (HTPD), Dec 2020). LLNL-PRES-817704

T.G. White, T. Doeppner, C.H. Allen, M. Oliver, L. Divol, A. Kemp, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, A. Saunders, D. Gericke, Z. Karmioal, and C. Spindloe, "New experimental techniques in warm dense matter research" (Presentation, Physics Colloquium at University of Rostock, Germany, 8 July 2021). IM# 1084239

C.H. Allen, M. Oliver, L. Divol, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T. Doeppner and T.G. White "Development of slit projection radiography with 1µm resolution at the Omega Laser Facility" (Presentation, OSA Imaging and Applied Optics Congress, Vancouver, BC, July 2021). LLNL-PRES-825433

C.H. Allen, M. Oliver, L. Divol, A. Kemp, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T. Doeppner and T.G. White, "Measuring Dynamic Density Gradients in Warm Dense Matter with 1 µm Spatial Resolution" (Presentation, OSA Imaging and Applied Optics Congress, South Lake Tahoe, CA, September 2021). LLNL-PRES-827034

T.G. White, T. Doeppner, C.H. Allen, M. Oliver, L. Divol, A. Kemp, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, A. Saunders, D. Gericke, Z. Karmioal, and C. Spindloe, "Fresnel Diffractive Radiography (FDR) at Omega and NIF" (Presentation, 16th International Conference on the Physics of Non-Ideal Plasmas, Dresden, Germany, Sept 2021). LLNL-PRES-827035

T.G. White, T. Doeppner, C.H. Allen, M. Oliver, L. Divol, A. Kemp, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, A. Saunders, D. Gericke, Z. Karmioal, and C. Spindloe "Measuring transport properties in warm dense matter: particle and thermal diffusion" (Presentation, Plasma Physics Colloquium at MIT, 28 October 2021). IM# 1084239

Allen, C.H., M. Oliver, L. Divol, O.L. Landen, Y. Ping, M. Schoelmerich, R. Wallace, R. Earley, W. Theobald, T.G. White, and T. Doeppner, "Toward an integrated platform for characterizing laser-driven, isochorically heated plasmas with 1 μm spatial resolution." Appl. Optics 61(8), 1987 (2022).

Oliver, M., C.H. Allen, L. Divol, Z. Karmiol, O.L. Landen, Y. Ping, R. Wallace, M. Schoelmerich, W. Theobald, T. Doeppner, and T.G. White. "Diffraction enhanced imaging utilizing a laser produced x-ray source." Rev. Scient. Instrum. 93, 093502 (2022). https://doi.org/10.1063/5.0091348.

Allen, C.H., M. Oliver, L. Divol, A. Kemp, O.L. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T. Doeppner, and T.G. White, "Developing x-ray Fresnel Diffractive-Refractive Radiography for Measuring Mutual Diffusion in Warm Dense Matter" (Presentation, 63rd Annual Meeting of the American Physical Society Division of Plasma Physics, Pittsburgh, PA, Nov 2021). LLNL-PRES-840561

M. Oliver, T. Doeppner, C. Allen, Y. Ping, L. Divol, A. Kemp, M. Schoelmerich, C. Spindloe, and T.G. White, "Scale Length Measurements in Warm Dense Matter" (Presentation, XFEL user group meeting, Hamburg, Germany, January 2022). LLNL-PRES- 841075. IM# 1061923

Allen, C.H., M. Oliver, L. Divol, A. Kemp, O.L. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T.G. White, and T. Doeppner, "Transport Property Experiments at OMEGA and NIF" (Presentation, NIF user group meeting, Livermore, CA, Feb 2022). LLNL-POST-840562

T.G. White, T. Doeppner, C.H. Allen, M. Oliver, L. Divol, A. Kemp, O. Landen, Y. Ping, M. Schoelmerich, W. Theobald, A. Saunders, D. Gericke, Z. Karmioal, and C. Spindloe, "Measuring transport properties in warm dense matter: particle and thermal diffusion" (Presentation, Physics Colloquium at GSI Darmstad, 12 April 2022). IM# 1084239

C.H. Allen, T.G. White, M. Oliver, L. Divol, A. Kemp, O.L. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T. Doeppner, "Fresnel Diffractive Radiography Measurements of Transport Properties in Warm Dense Matter" (Presentation, 49th IEEE International Conference on Plasma Science, Seattle, WA, May 2022). LLNL-PRES-840560

M.O. Schoelmerich, T. Doeppner, C. Allen, M. Biener, J. Delora-Ellefson, L. Divol, D.O Gericke, D. Haden, C. Heinbockel, D. Kalantar, A. Kemp, G. Kemp, O.L. Landen, M. Oliver, Y. Ping, W. Theobald, and T.G. White, " Developing a platform for Fresnel refractive-diffractive radiography with 1 μm spatial resolution at the National Ignition Facility" (Presentation, 24th Topical Conference on High Temperature Plasma Diagnostics, Rochester May 2022). LLNL-POST- 835686

Allen, C.H., M. Oliver, L. Divol, T. Griffin, A. Kemp, G.E. Kemp, O.L. Landen, Y. Ping, M. Schoelmerich, W. Theobald, T. Doeppner, and T.G. White "Developing x-ray Fresnel Diffractive Radiography for Measuring Thermal Conductivity in Warm Dense Matter." 64th Annual Meeting of the American Physical Society Division of Plasma Physics, Spokane, Oct 2022. LLNL-PRES-840561

Schoelmerich, M.O., T. Döppner, C. H. Allen, L. Divol, M. Oliver, D. Haden, M. Biener, J. Crippen, J. Delora-Ellefson, B. Ferguson, D.O Gericke, A. Goldman, A. Haid, C. Heinbockel, D. Kalantar, Z. Karmiol, G. Kemp, J. Kroll, O.L. Landen, N. Masters, Y. Ping, C. Spindloe, W. Theobald, and T.G. White. "Developing a platform for Fresnel refractive-diffractive radiography with 1 μm spatial resolution at the National Ignition Facility." Rev Sci Instrum. 2023 Jan 1;94(1):013104. doi: 10.1063/5.0101890.

Allen, C.H., M. Oliver, L. Divol, D. Gericke, D. Kalantar, A. Kemp, G.E. Kemp, J. Kroll, O.L. Landen, L. Morrison, Y. Ping, S. Shores, M. Schoelmerich, W. Theobald, R. Wallace, T. Doeppner, and T.G. White, "Fresnel Diffractive Radiography Experiments at Omega and NIF." (Presentation, NIF user group meeting, Livermore. CA, February 2023). LLNL-POST- 845549

C.H. Allen, "Experimentally Measuring Thermal Conductivity in Warm Dense Matter Using Fresnel Diffractive Radiography" (Presentation, PhD thesis, University Reno, NV, August 2023).

M. Oliver, T. White, T. Doeppner, B. Nagler, L. Morrison, C. Spindloe, E. Galtier, H.J. Lee, D. Khaghani, G. Dyer, C. Allen, D. Haden, M. Schoelmerich, Y. Ping, L. Divol, A. Kemp, and D. Gericke, "Experimental measurement of Thermal Conductivity in Warm dense matter" (Presentation, LCLS user group meeting, Stanford, CA, Sept 2023). IM# 1084385

T. Doeppner, C. H. Allen, D. Haden, S. Shores-Prins, T. Griffins, L. Morrison, T. White,M. Schoelmerich, L. Divol, Y. Ping, E. Kemp, O. Landen, R. Wallace, D. Kalantar, M. Oliver, C. Spindloe, D. Gericke, B. Earley, W. Theobald, "Measurement of Thermal Conductivity in Warm Dense Matter" (Presentation, 11th International Workshop of High Pressure, Planetary and Plasma Physics, Rostock, Germany, Sept 2023).  IM #1083802