Maths ‘noodling’ could lead to more twisty plasmas in nuclear fusion

1 Jul 2020

Image: © Gorodenkoff/

Researchers have taken another step closer to stable nuclear fusion after learning more about a ‘hiccup’ known as the sawtooth instability.

Researchers playing around with abstract mathematics have helped gain new insight into one of the major hurdles to overcome before achieving stable nuclear fusion. Once achieved, nuclear fusion could provide an electricity source – equivalent to a miniature sun harnessed in a reactor – that is near limitless, clean and very cheap.

Writing in Nuclear Fusion, scientists from the US Department of Energy’s Princeton Plasma Physics Laboratory (PPPL) said they have learned more about a common type of hiccup known as the sawtooth instability. This phenomenon cools the hot plasma in the centre of a reactor and interferes with the fusion reactions.

PPPL physicist Christopher Smiet, lead author of the latest study, said that conventional models have explained most instances of the sawtooth crashes, but a subset of observations over the span of almost four decades have never been explained. Within the reactor, sawtooth crashes are seen when the temperature at the core of fusion plasma rises slowly and then suddenly drops.

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 a magnetic field in the doughnut-shaped tokamak fusion reactor.

‘Noodling around with pure mathematics’

Some observations suggest, however, that the crashes occur when the safety factor drops to around 0.7, which cannot be explained by existing theories. Now, using mathematics, the researchers have shown that when the safety value comes close to 0.7, the magnetic field in the plasma core can change into a different configuration called alternating-hyperbolic.

When this happens, plasma is expelled from the centre of the reactor in opposite directions that can repeat as the magnetic field and temperature slowly recover.

“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.”

The newly developed 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 added. “One of the most beautiful parts of these results is that they came from just noodling around with pure mathematics.”

Colm Gorey was a senior journalist with Silicon Republic