Efforts to produce a working nuclear fusion reactor have led one scientist to create a formula to make them more cost-effective to build.

While some researchers theorise that nuclear fusion is just around the corner, we have yet to see a reactor that can successfully recreate the power of the sun for any useful length of time. However, a physicist at the US Department of Energy’s Princeton Plasma Physics Laboratory (PPPL) has developed a mathematical technique that simplifies the design of complex magnetic coils within the twisty machines that house fusion reactions.

Using this new technique, these machines, referred to as stellarators, could be made significantly cheaper, which would potentially bring nuclear fusion within closer reach.

Caoxiang Zhu, lead author of the research published to Nuclear Fusion, said the breakthrough can let physicists know in advance when coil shapes and placements could harm the plasma’s magnetic confinement. Aside from reducing costs, he added, it would also shorten a reactor’s construction time.

Complex alternative

Twisted, cruller-shaped stellarators are an alternative to the doughnut-shaped tokamaks that are more commonly used by scientists seeking to replicate fusion on Earth for a virtually inexhaustible supply of power to generate electricity.

What gives stellarators an advantage is that their production of highly stable plasmas is less liable to the damaging disruptions that tokamaks can incur. However, their complex design has made them trickier to work, until now.

For example, the coils of a stellarator must be constructed and arranged around a vacuum chamber with great precision. Otherwise, the resulting bumps and wiggles in the magnetic field could allow the plasma to escape and ruin the reactor.

In the past, scientists have used computer simulations to best determine coil placements. However, according to Zhu, this approach requires “massive computation resources and man-hours”.

The technique proposed by Zhu relies on something called a Hessian matrix, a mathematical tool that allows researchers to figure out which perturbations you have to control or avoid, and which you can ignore.

The new technique could help scientists design better stellarators, Zhu added. It could make possible ways to identify an optimal coil arrangement that no one had considered before.