Showing How Plasma Electrons Can Enhance Fusion Reaction Rates

Fourth in a series of articles describing current National Ignition Facility Discovery Science experimental campaigns.

Part 1: “Using NIF to Study the Sluggish Pace of Star Formation”

Part 2: “NIF Takes a Quantum Leap into Elusive Metallic Hydrogen”

Part 3: “Putting the Squeeze on Helium”

Seven years ago, Lawrence Livermore National Laboratory (LLNL) researchers and their colleagues replicated the extreme conditions in the deep interiors of stars at LLNL’s National Ignition Facility (NIF). The work provided new insights into the nuclear fusion reactions that power the Sun and the stars, as well as nuclear weapons.

Now, in a follow-up NIF Discovery Science campaign, the researchers hope to use NIF’s unique capabilities to gain a better understanding of some of the factors affecting the rate of stellar nuclear reactions and how they could affect stellar nucleosynthesis—the creation of new materials inside stars.

Having achieved fusion ignition and burning plasmas on NIF, “we’re creating conditions that are unlike anywhere else on Earth,” says LLNL physicist Dan Casey, the principal investigator for the campaign. Those experiments are primarily designed to further NIF’s support for the National Nuclear Security Administration’s science-based Stockpile Stewardship Program.

Comparisons between NIF data and stellar calculations show that experimental conditions on NIF are very similar to those of stars during most of the stellar lifetime.

“There are specific questions that we’re interested in related to stars,” Casey says. “Stars are also big plasmas (freely moving ions and free electrons) undergoing thermonuclear burn. It is thought that some of the reactions that power stars are influenced by the plasma around them, but that has not been observed. We want to see this first-hand in the laboratory.”

The reaction rate of nuclear fusion, both in stars and in inertial confinement fusion (ICF) experiments like those on NIF, depends in part on the probability, or cross-section, that two atomic nuclei will undergo the quantum-mechanical process of “tunneling” through the Coulomb barrier—the electrostatic force that wants to keep particles with the same charge apart—and undergo a fusion reaction. Nearby electrons in high-energy-density plasma can enhance the tunneling probability and fusion reactivity by “screening,” or partially cancelling out, the electric field between the positively charged nuclei.

First postulated by the Dutch-American physicist Peter Debye in the 1920s, the screening effect works by “shielding the barrier that the nuclei have to cross in order to come together, and that reduces the energy they need in order to get over that barrier,” Casey says. The effect becomes more pronounced at higher energies, such as those in the center of stars and NIF ICF experiments.

While the 2017 NIF experiments were not the first thermonuclear measurements of nuclear reaction cross-sections, “the screening of nuclear reactions in a star due to dense plasma effects has never been measured,” Casey says. “That’s something that we might be able to measure here in the Laboratory. And that would be relevant for stars like our sun and also probably red dwarfs,” very low-mass stars that are the most abundant stars in the Milky Way.

Joining Casey on the campaign are other researchers from LLNL as well as the University of Notre Dame, the Massachusetts Institute of Technology (MIT), and Ohio University.

ICF implosions on NIF can access the temperatures and pressures found in the cores of stars, and the current Discovery Science experiments have developed a method for making relative cross-section measurements in these complex systems, Casey says. “These measurements are enabling more ambitious experiments in plasma nuclear science, like dense plasma screening,” relevant to the conditions in stellar cores for a range of types of stars.

Testing the Models

Data from experimental studies of plasma electron screening on NIF could test competing theoretical models of stellar plasma screening and help resolve long-standing disputes over their accuracy. The established models differ substantially from experimental results obtained by previous accelerator-based studies in which electrons are “bound” to the nuclei.

“Bound electrons will do the same thing that the plasma electrons do—they shield the Coulomb barrier and enhance the ability for the nuclei to react,” Casey says. “But these are fundamentally different from scenarios where the reactions occur in a thermal plasma environment, such as the conditions in stellar cores.”

The Discovery Science experiments to date, including a successful experiment in December, “show a plausible path to the plasma screening regime, and computer designs predict it can be pushed further—but conducting a nuclear plasma screening experiment faces several daunting challenges,” Casey says.

These include the production and diagnosis of extreme densities and temperatures, precise nuclear cross-section measurements, and development of an experiment in which the uncertainties of the measurements are smaller than the uncertainties in our understanding of nuclear reaction rates in dense, “cool” plasmas.

“Significant progress has recently been made in resolving the first two of these challenges by using gas-filled indirect-drive SymCap (symmetry capsule) experiments at NIF,” he says. “We have made multiple reaction-rate measurements and are working toward developing screening experiments.

“Thermonuclear cross-section measurements at stellar-like conditions for DD (deuterium-deuterium), DT (deuterium-tritium), and D³He (deuterium-helium-3) reactions demonstrate that nuclear physics and cross-section experiments can be conducted in the complex environments of ICF implosions, while also carefully diagnosing the plasma using nuclear diagnostic and neutron and x-ray imaging.”

Moving Forward

Casey said the researchers plan to address the third challenge by assessing whether ICF implosions can produce conditions in which the screening effect is large enough to be measured.

“There are clear design directions to increase the magnitude of the plasma screening effect by utilizing higher-Z (atomic number) reactions and higher-Z plasmas, reducing the plasma ion temperature, and increasing the plasma density,” Casey says.

“One of the reasons why (measuring screening) is so challenging is that to get into a strong screening regime, you have to get to somewhere where it’s very cold and it’s hard to make any reactions at all.”

The goal, he said, is to “get to a place in temperature-density space where things are very cold and very dense,” but not so cold that reactions cease entirely—all while ensuring the effect is strong enough to be measurable.

“At a (single) percent it’s probably not measurable,” Casey says, “but if we can get into the tens of percent, then that’s starting to get interesting.”

In the Dec. 20 experiment, 188 NIF laser beams delivered 877 kilojoules of energy onto a gas-filled, low-temperature SymCap target. The D³He plasma in the target was cooled with a substantial fraction of krypton (0.06 percent) to further lower the temperature and increase the density.

This was a big step toward raising the plasma electron screening and fusion reaction rates to potentially measurable levels, Casey says. “The experiment was quite successful in that it produced plenty of yield. We need more data to confirm this, but we think we got about halfway or a little further to where we want to get to.

“All indications are pretty encouraging that we may someday soon be able to test how the plasma electrons change the nuclear reaction rate with this experimental platform.”

The researchers are now preparing a proposal for the next series of experiments “to keep pushing this further and further into the screening regime until we get to where we think screening is measured,” Casey says.

“We’ve increased the krypton initial particle density and it went in the right direction, so we’ll probably increase the krypton even further and continue to push the development of the radiation chemistry technology for measuring the protons in this very dense, cool part of parameter space.”

Joining Casey on the experimental team are Chris Weber, Matthias Hohenberger, Charlie Cerjan, Ed Hartouni, Bruce Remington, and Dave Dearborn from LLNL; Maria Gatu Johnson from MIT; Michael Wiescher from Notre Dame; and Carl Brune from Ohio University. Former LLNL researcher Alex Zylstra also contributed to the campaign.