Researchers’ novel model captures detailed dynamics of splitting plutonium-240 nucleus
As plutonium-240 undergoes fission, it oscillates in ways that take energy away from the relative motion of the emerging daughter nuclei, a dynamic captured by a novel model called time-dependent superfluid local density approximation (TDSLDA), which has shown promise for capturing the real-time dynamics of nuclear evolution. (Image courtesy of the University of Washington)
While trying to fatten the atom in 1938, German chemist Otto Hahn accidentally split it instead. This surprising discovery put modern science on the fast track to the atomic age and to the realization of technologies with profound potential for great harm or great help.
Although scientific experts, thought leaders, and policy makers have worked to harness nuclear fission to benefit humanity, researchers have continued to struggle to understand the most fundamental aspects of this energy-releasing process. More than seven decades after Hahn’s breakthrough, a major question still looms: What exactly is taking place at the microscopic level during fission?
By recognizing the dual nature of fundamental matter, which can be described as both a particle and a wave, the Austrian physicist Erwin Schrodinger proposed an equation—quantum mechanics’ Schrodinger equation—capable of answering the question. The vast computational demands of solving such a problem for a heavy nucleus, however, would require an unfathomably powerful computer.
In an effort to create feasible nuclear fission models for current supercomputers, nuclear physicists had to devise shortcuts that often rely on approximations and constraints. The most successful of these approaches, density functional theory (DFT), describes nuclear dynamics by tracking changes in the density of the nucleus. To apply this method to fissile elements like uranium and plutonium, which contain more than 200 protons and neutrons, scientists need to extend the method to superfluid nuclei and then implement and validate DFT on leadership-class supercomputers.
A team led by Aurel Bulgac of the University of Washington is spearheading this effort by developing a novel theoretical approach that extends DFT to superfluid nuclei, which exhibit characteristics similar to other strongly interacting systems of many fermions, or particles with half-integer spin such as superconducting materials. The method, called time-dependent superfluid local density approximation (TDSLDA), has shown promise for capturing real-time dynamics of nuclear evolution without imposing the constraints that other models require.
In the first study of its kind, Bulgac’s team applied TDSLDA to a fissioning plutonium-240 nucleus using the Titan supercomputer at the US Department of Energy’s (DOE’s) Oak Ridge National Laboratory (ORNL). The simulation results achieved notable fidelity, and the predicted kinetic energy agreed with that produced by experiments. Additionally, the simulation suggested that the final stages of fission last about 10 times longer than previously calculated, a finding with wide ramifications for nuclear science and astrophysics.
Titan is the flagship supercomputer of the Oak Ridge Leadership Computing Facility (OLCF), a DOE Office of Science User Facility located at ORNL. Because of the size of the problem, Bulgac’s team needed access to Titan’s accelerated architecture to calculate tens of thousands of partial differential equations simultaneously.
“Our simulation shows the nucleus takes a longer route to scission, or split. It doesn’t simply break into two parts but oscillates in ways that take energy away from the relative motion of the emerging daughter nuclei,” Bulgac said. “It’s like hiking down a mountain. You can go straight down, or you can zigzag to the bottom. The second option takes much longer, but you end up at the same place.”
The results of this computational approach are an encouraging development for nuclear physics researchers who could benefit from an improved understanding of fission fragments’ excitation energies—the energy needed to boost a nucleus to a higher energy above its ground state. Currently, these properties are nearly impossible to glean from experiment. Better methods would benefit researchers who study nuclear fuel composition, nuclear forensics, and astrophysics, in which fission plays a role in producing the remnants of exploding stars.
Furthermore, the TDSLDA model indicates a pathway to a predictive microscopic framework of real-time fission dynamics without physical restrictions.
A Superfluid Split
When plutonium-239 captures a neutron, it undergoes fission about two-thirds of the time. This quality makes it a good candidate for the production of nuclear weapons and fuel for nuclear power plants. Because the isotope has been thoroughly studied, Bulgac’s team selected the heavy metal to help validate its model.
Conventional computational methods treat nuclear fission like a slightly squished drop of liquid. As the nucleus becomes more deformed, the number of directions the system moves—called degrees of freedom—increases. Typical nuclear simulations track the nucleus’s evolution in, at most, a five-dimensional space, a computationally demanding approach that still fails to capture all key properties.
Treating the nucleus like a superfluid within TDSLDA, in which the protons and neutrons pair up at low temperatures like electrons in a superconductor, simplifies the calculation and allows for the inclusion of all known collective degrees of freedom. Using this technique, Bulgac’s team observed that plutonium-240’s fission fragments remain in contact much longer than expected.
“The important point is that you need to know what is happening in your system,” Bulgac said. “What our simulations show is that the traditional DFT model needs to be extended to distinguish between the superfluid and normal states of the nucleus.”
Bulgac’s team applied its TDSLDA model under an allocation on Titan, a Cray XK7 capable of 27 petaflops (or 27 quadrillion calculations per second), awarded through the OLCF’s Director’s Discretionary program. The team conducted previous work on the model on an allocation awarded by DOE’s Office of Advanced Scientific Computing Research Leadership Computing Challenge (ALCC) program.
Calculating the plutonium-240 problem required more than 1,700 of Titan’s GPUs to solve around 56,000 partial differential equations. The simulation consisted of a plutonium-240 nucleus in a femtometer-size simulation box equivalent to a few quadrillionths of a meter in dimension. To shorten the time to scission, the simulation began with the nucleus on the cusp of splitting.
Prior to this particular study, Bulgac’s team undertook an extensive overhaul of its nuclear physics code to take advantage of Titan’s GPU accelerators. The effort resulted in a 10- to 25-fold performance improvement, depending on the size of the problem.
“The bigger the problem, the faster our code runs [compared to the CPU-only version],” Bulgac said. “Even though Titan has about 300,000 CPU cores and less than 19,000 GPUs, 90 percent of its speed lies in GPUs. The reason we succeeded in this effort is that we learned how to use Titan’s heterogeneous architecture.”
This year, Bulgac’s team is continuing to refine its model under a new ALCC allocation. The goal is to study nuclear fission properties under differing conditions. For example, the team plans to investigate the sensitivity of density functional parameters within known reasonable limits and to modify the incoming energy of the fission-inducing neutron.
“We don’t know the nuclear density functional sufficiently well enough,” Bulgac said. “We need to see how fission dynamics changes and how well our method agrees with reality when we change simulation parameters.”