Researchers 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 during experimental
efforts to harness on Earth the fusion power that drives the sun and stars.
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.

Fusion produces enormous energy by combining light elements in the form of
plasma—the hot, charged gas composed of free electrons and atomic nuclei, or
ions, that makes up 99 percent of the visible universe. Scientists around
the world are seeking to reproduce the fusion process to provide a safe,
clean and abundant power to generate electricity.

### Solving the equation

A key hurdle for researchers developing fusion on doughnut-shaped devices
called tokamaks, which confine the plasma in magnetic fields, has been
solving the equation that describes the motion of free-wheeling electrons as
they collide and bounce around. Standard methods for simulating this motion,
technically called pitch-angle scattering, have proven unsuccessful due to
the complexity of the equation.

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," said 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 a solution. 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,"
Fu said. "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."

A major benefit of this knowledge is improved guidance for fusion
researchers who pump electric current into tokamak plasmas to create the
magnetic field that confines the superhot gas. Another benefit is better
understanding of the pitch-angle scattering on energetic runaway electrons
that pose danger to the fusion devices.

### Rigorous proof

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," said Hong Qin, a principal research physicist, advisor to Fu
and a coauthor of the paper. "Previously, there was no working algorithm for
this equation, 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 launched Computational Sciences Department
(CSD) at PPPL and expands an earlier paper coauthored by Fu, Qin and
graduate student Laura Xin Zhang, a coauthor of this paper. 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 CSD, founded this year as part of the Lab's expansion into a
multi-purpose research center, supports the critical fusion energy sciences
mission of PPPL and serves as the home for computationally intensive
discoveries. "This technical advance displays the role of the CSD," Qin
said. "One of its goals is to develop algorithms that lead to improved
fusion simulations."

The problem with getting to fusion nuclear energy is not enough mass on earth to create it. They will need 3.8337 trillion tons of the element hydrogen just to start the energy production of fusion in a small red star. Also once you start a fusion reaction there is no control over it like a fission reactor's control panel.

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