Mathematical noodling leads to new insights into an old fusion problem


Date:
June 30, 2020
Source:
DOE/Princeton Plasma Physics Laboratory
Summary:
Scientists have gained new insight into a common type of plasma
hiccup that interferes with fusion reactions. These findings could
help bring fusion energy closer to reality.



FULL STORY ==========================================================================
A challenge to creating fusion energy on Earth is trapping the charged
gas known as plasma that fuels fusion reactions within a strong magnetic
field and keeping the plasma as hot and dense as possible for as long
as possible. Now, scientists at the U.S. Department of Energy's (DOE)
Princeton Plasma Physics Laboratory (PPPL) have gained new insight into
a common type of hiccup known as the sawtooth instability that cools the
hot plasma in the center and interferes with the fusion reactions. These findings could help bring fusion energy closer to reality.


========================================================================== "Conventional models explain most instances of the sawtooth crashes,
but there is a tenacious subset of observations that we have never been
able to explain," said PPPL physicist Christopher Smiet, lead author of a
paper reporting the results in Nuclear Fusion. "Explaining those unusual occurrences would fill a gap in understanding the sawtooth phenomenon
that has existed for almost 40 years." Fusion combines light elements
in the form of plasma -- the hot, charged state of matter composed
of free electrons and atomic nuclei -- and in the process generates
massive amounts of energy in the sun and stars. Scientists are seeking
to replicate fusion in devices on Earth for a virtually inexhaustible
supply of safe and clean power to generate electricity.

Researchers have known for decades that the temperature at the core
of fusion plasma often rises slowly and can then suddenly drop -- an
unwanted occurrence since the cooler temperature reduces efficiency. The prevailing theory is that the crash occurs when a quantity called the
safety factor, which measures the stability of the plasma, drops to a measurement of close to 1. The safety factor relates to how much twist is
in the magnetic field in the doughnut- shaped tokamak fusion facilities.

However, some observations suggest that the temperature crash occurs
when the safety factor drops to around 0.7. This is quite surprising
and cannot be explained by the most widely accepted theories.

The new insight, coming not from plasma physics but from abstract
mathematics, shows that when the safety factor takes specific values,
one of which is close to 0.7, the magnetic field in the plasma core can
change into a different configuration called alternating-hyperbolic. "In
this topology, the plasma is lost in the core," Smiet says. "The plasma
is expelled from the center in opposite directions. This leads to a new
way for the magnetic cage to partially crack, for the temperature in the
core to suddenly fall, and for the process to repeat as the magnetic field
and temperature slowly recover." The new insights suggest an exciting
new research direction toward keeping more heat within the plasma and
producing fusion reactions more efficiently. "If we can't explain these
outlier observations, then we don't fully understand what's going on in
these machines," Smiet said. "Countering the sawtooth instability can lead
to producing hotter, more twisty plasmas and bring us closer to fusion."
This model arose from purely abstract mathematical research. Smiet
found a mathematical way to describe the magnetic field in the center
of a tokamak. All possible configurations can then be associated with
an algebraic structure called a Lie group. "The mathematics is really
quite beautiful," Smiet says.

"This mathematical group gives you a birds-eye view of all possible
magnetic configurations and when one configuration can change into
another." The new model shows that one of the times the magnetic
configuration in a tokamak can change is when the safety factor falls
to precisely two-thirds, or 0.666. "This is eerily close to the value of
0.7 that has been seen in experiments, particularly so when experimental uncertainty is taken into account," Smiet said. "One of the most beautiful parts of these results," he said, "is that they came from just noodling
around with pure mathematics." Smiet hopes to verify the new model by
running experiments on a tokamak. "The mathematics has shown us what to
look for," he said, "so now we should be able to see it."

========================================================================== Story Source: Materials provided by
DOE/Princeton_Plasma_Physics_Laboratory. Original written by Raphael
Rosen. Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Christopher Berg Smiet, Gerrit J Kramer, Stuart R
Hudson. Bifurcations of
the magnetic axis and the alternating-hyperbolic sawtooth. Nuclear
Fusion, 2020; DOI: 10.1088/1741-4326/ab9a0d ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/06/200630193209.htm

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