Fusion generates energy by combining light elements in the form of plasma. Scientists worldwide seek to reproduce the fusion process to provide a safe, clean and abundant power to generate electricity.

The doughnut-shaped devices are called tokamaks to confine the plasma in magnetic fields. However, the problem in developing plasma in such devices includes solving the equation that describes the motion of free-wheeling electrons as they collide and bounce around.

Standard methods for simulating this motion, called pitch-point dispersing, have demonstrated ineffective because of the complexity of the equation. A successful set of computational rules, or algorithms, would solve the equation while conserving the energy of the speeding particles.

Scientists at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory have developed an effective computational method to simulate the crazy-quilt movement of free electrons. The method cracks a complex equation that can enable improved control of the random and fast-moving moving electrons in the fuel for fusion energy.

Yichen Fu, a graduate student in the Princeton Program in Plasma Physics at PPPL and lead author of a paper, said, *“A successful set of computational rules, or algorithm, would solve the equation while conserving the energy of the speeding particles. Solving the stochastic differential equation gives the probability of every path the scattered electrons can take.”*

*“Such equations yield a pattern that can be analyzed statistically but not determined precisely.”*

*“The accurate solution describes the trajectories of the electrons being scattered. However, the trajectories are probabilistic, and we don’t know exactly where the electrons would go because there are many possible paths. But by solving the trajectories, we can know the probability of electrons choosing every path, and knowing that enables more accurate simulations that can lead to better control of the plasma.”*

Hong Qin, a principal research physicist, advisor to Fu, and a co-author of the paper, said,Â *“The finding provides a rigorous mathematical proof of the first working algorithm for solving the complex equation. This gives experimentalists a better theoretical description of what’s going on to help them design their experiments. Previously, there was no working algorithm for this equation, and physicists got around this difficulty by changing the equation.”*

While that work created a novel energy-conserving algorithm for tracking fast particles, the method did not incorporate magnetic fields, and the mathematical accuracy was not rigorously proven.

The study is published in the Journal of Computational Physics.