Exploratory Design Study Towards the First Plasma-Electron Screening Experiment

Daniel Casey | 18-FS-010


The enhancement of fusion reaction rates in a thermonuclear plasma by electron screening of the Coulomb barrier is an important plasma-nuclear effect that is present in stellar models, but has not been experimentally observed. Experiments using inertial-confinement fusion (ICF) implosions may provide a unique opportunity to observe this important plasma-nuclear effect. We demonstrated that prior National Ignition Facility (NIF) experiments approached the relevant physical regime with respect to density and temperature conditions, but the estimated screening magnitudes would need to be increased to obtain a measurement. We used these implosions as a starting point, and design calculations showed that practical target changes (such a adding high-Z gases) might be able to push these conditions to where plasma-screening effects may be measurable. Synthetic data exercises helped demonstrate where the anticipated experimental uncertainties will become important. Our research led to a proposal to conduct experiments at NIF performing initial assessments of the concepts demonstrated by this study. The science in question has applications in the fields of astrophysics, plasma physics, nuclear physics, and high-energy-density (HED) physics.

Background and Research Objectives

Despite widespread interest, the realization of a nuclear plasma screening experiment has been elusive because of several difficult challenges. First, extreme density and temperature conditions must be produced and diagnosed. Second, precise nuclear cross-section measurements must be made directly in the presence of strong density and temperature gradients. Finally, as the effect on fusion rates is often weak in the regimes that can be reproduced in the laboratory, care must be exercised to develop a test where the magnitude of the measurement is expected to exceed the experimental uncertainties. The first two challenges were recently overcome using gas-filled indirect-drive experiments at NIF (Casey et al. 2017). The objective of this feasibility study was to address the third challenge by assessing whether these ICF implosions can produce conditions where this screening effect is expected to be large enough to be measured.

For decades, research groups have identified plasma-electron screening as an important physical process worth pursuing in HED experiments. Ideas emerge periodically from the literature challenging the established models, exacerbated by the complete lack of experimental data. This screening process becomes important as nuclei undergo a fusion reaction when their kinetic energy overcomes the repulsive Coulomb force and exploits favorable binding energy. In many HED environments where these reactions occur (e.g., in stellar cores and ICF implosions), the nuclei are embedded in a plasma. The background electrons in this plasma can lower the Coulomb barrier, enhancing their reactivity. A similar screening effect occurs in particle accelerators that study nuclear reactions. In accelerator experiments, the bound electrons on the target screens the nucleus and enhances the reaction rate since the targets are not sufficiently hot to be plasmas. This effect differs from plasma screening and is removed to compute the bare nuclear cross-section. This effect is significant for low center-of-mass energy cross-sections and has in some cases been observed to be approximately 1.7 to 1.8 times larger than expected (Aliotta et al. 2001, Schröder et al. 1989).

This feasibility study assessed the issues related to plasma screening measurement and identified some credible solutions to long-standing challenges. The next step is to test these ideas experimentally, which has been proposed to the NIF Discovery Science program. We are considering a follow-up proposal to further develop the implosion platform for the NIF HED council. This project will define a new experimental platform on NIF that may be the first to observe plasma screening of nuclear reactions, addressing a fundamental question of HED physics.

Impact on Mission

This research supports the advancement of the science, technology, and engineering competencies that are the foundation of the NNSA mission. It also addresses Lawrence Livermore National Laboratory's research and development challenge in directed energy and enhances the Laboratory's core competencies in HED science and lasers and optical science and technology. By enabling new HED science experiments on NIF, this feasibility study helped establish a platform for measuring thermonuclear reaction rates directly in the environments where they occur and testing physics unique to those conditions. This research also helped initiate a unique cross-disciplinary collaboration between experts in plasma and nuclear physics to test a problem of shared interest.


The enhancement of fusion reaction rates in a thermonuclear plasma by electron screening of the Coulomb barrier is an important plasma-nuclear effect that is assumed in stellar models but has not been experimentally quantified. This project has shown that ICF implosions may provide a unique opportunity to observe this important plasma-nuclear effect. This research has been presented to the plasma, nuclear, and laboratory astrophysics communities, and publications are currently in preparation. It has directly led to a NIF Discovery Science proposal and may lead to other proposals. Observing plasma electron screening will have potential applications in several fields of research, including astrophysics, plasma and nuclear physics, and HED physics.


Aliotta, M., et al. 2001. "Electron Screening Effect in the Reactions 3 He(d, p) 4 He and d( 3 He, p) 4 He." Nuclear Physics A 690(4): 790–800. doi: 10.1016/s0375-9474(01)00366-9.

Casey, D. T., et al. 2017. "Thermonuclear Reactions Probed at Stellar-Core Conditions with Laser-Based Inertial-Confinement Fusion." Nature Physics 13: 1227. doi: 10.1038/nphys4220.

Schröder, U., et al. 1989. "Search for Electron Screening of Nuclear Reactions at Sub-Coulomb Energies." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 40-41(Part 1): 466–69. doi: 10.1016/0168-583x(89)91022-7.

Publications and Presentations

Casey, D. T., et al. 2018. "Thermonuclear Reactions Probed at Stellar Core Conditions with Laser-Based Inertial Fusion." Lawrence Berkeley National Laboratory Nuclear Physics Forum, Berkeley, CA, April 2018. LLNL-PRES-750481.

Weber, C., et al. 2018. "Stellar-Relevant Thermonuclear Reactivity Measurements at the National Ignition Facility." High Energy Density Laboratory Astrophysics, Kurashiki, Okayama, Japan, May 2018. LLNL-PRES-751698.

——— . 2018. "Stellar-Relevant Thermonuclear Reactivity Measurements at the National Ignition Facility." Nuclear Processes in Dense Plasmas Workshop, Livermore, CA, July 2018. LLNL-PRES-755746.