Researchers at the U.S. Department of Energys (DOE) Princeton Plasma Physics Laboratory have created an effective computer algorithm to model the crazy-quilt motion of free electrons during experimental efforts to harness the combination power that drives the sun and stars. The technique fixes a tough equation, permitting for better control of the fast-moving and unpredictable electrons in the fuel for fusion energy.
Fusion produces massive energy by integrating light aspects in the form of plasma– the hot, charged gas made from free electrons and atomic nuclei, or ions, that comprises 99 percent of the visible universe. Scientists all around the world are working to replicate the fusion process in order to produce a safe, tidy, and abundant power source for producing electrical power.
Resolving the formula
A crucial difficulty for scientists establishing blend on doughnut-shaped gadgets called tokamaks, which confine the plasma in electromagnetic fields, has actually been resolving the equation that describes the movement of free-wheeling electrons as they clash and bounce around. Standard approaches for imitating this motion, technically called pitch-angle scattering, have shown unsuccessful due to the complexity of the equation.
A successful set of computational rules, or algorithm, would fix the equation while saving the energy of the speeding particles. “Solving the stochastic differential equation provides the probability of every course the scattered electrons can take,” stated Yichen Fu, a college student in the Princeton Program in Plasma Physics at PPPL and lead author of a paper in the Journal of Computational Physics that proposes an option. Such equations yield a pattern that can be evaluated statistically but not identified exactly.
Yichen Fu, center, lead author of the path-setting paper with co-authors Laura Xing Zhang and Hong Qin. Credit: Photos of Fu and Qin by Elle Starkman/Office of Communications; collage by Kiran Sudarsanan.
The precise solution explains the trajectories of the electrons being spread. “However, the trajectories are probabilistic and we do not know exactly where the electrons would go since there are lots of possible paths,” Fu stated. “But by resolving the trajectories we can understand the possibility of electrons picking every path, and knowing that allows more precise simulations that can lead to better control of the plasma.”
A major benefit of this understanding is enhanced assistance for combination scientists who pump electric existing into tokamak plasmas to create the electromagnetic field that boundaries the superhot gas. Another benefit is much better understanding of the pitch-angle scattering on energetic runaway electrons that pose threat to the combination gadgets.
Strenuous evidence
The finding supplies a strenuous mathematical evidence of the first working algorithm for solving the intricate formula. “This offers experimentalists a better theoretical description of whats going on to help them develop their experiments,” stated Hong Qin, a primary research physicist, consultant to Fu and a coauthor of the paper. “Previously, there was no working algorithm for this formula, and physicists got around this difficulty by changing the equation.”
The reported study represents the research activity in algorithms and applied math of the recently released Computational Sciences Department (CSD) at PPPL and expands an earlier paper coauthored by Fu, Qin and graduate trainee Laura Xin Zhang, a coauthor of this paper. While that work produced an unique energy-conserving algorithm for tracking fast particles, the approach did not include electromagnetic fields and the mathematical precision was not carefully shown.
The CSD, established this year as part of the Labs growth into a multi-purpose proving ground, supports the crucial blend energy sciences objective of PPPL and works as the home for computationally extensive discoveries. “This technical advance shows the role of the CSD,” Qin said. “One of its goals is to develop algorithms that result in enhanced fusion simulations.”
Reference: “A clearly solvable energy-conserving algorithm for pitch-angle scattering in allured plasmas” by Yichen Fu, Xin Zhang and Hong Qin, 8 October 2021, Journal of Computational Physics.DOI: 10.1016/ j.jcp.2021.110767.
Assistance for this work comes from the DOE Office of Science.
PPPL, on Princeton Universitys Forrestal Campus in Plainsboro, N.J., is dedicated to producing new understanding about the physics of plasmas– ultra-hot, charged gases– and to developing practical services for the production of fusion energy.
“Solving the stochastic differential equation gives the probability of every path the scattered electrons can take,” stated Yichen Fu, a graduate student in the Princeton Program in Plasma Physics at PPPL and lead author of a paper in the Journal of Computational Physics that proposes an option. “However, the trajectories are probabilistic and we do not understand exactly where the electrons would go since there are lots of possible courses,” Fu stated. “But by resolving the trajectories we can know the likelihood of electrons selecting every path, and knowing that makes it possible for more accurate simulations that can lead to better control of the plasma.”
The CSD, founded this year as part of the Labs expansion into a multi-purpose research study center, supports the critical blend energy sciences mission of PPPL and serves as the house for computationally extensive discoveries. “One of its objectives is to develop algorithms that lead to improved combination simulations.”