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The Australian National University recently renovated their fusion reactor. This magnetic marvel harnesses immense pressures and temperatures to replicate the reactions that power our Sun. And there’s a lot of maths that helps to keep the reactions going!

A fusion donut

Fusion reactors use hydrogen as fuel. Under intense heat and pressure, the electrons leave the atoms, and the gas becomes a plasma. To hold the plasma in place, scientists build a magnetic bottle made out of a set of electromagnetic coils. These are arranged into a donut shape, known as a torus.

The plasma particles (electrons and ions) follow the magnetic lines of force in a path looping around and around inside the donut. If a particle keeps circling around the torus, it will eventually drift out of the chamber because the magnetic field is higher on the inside than the outside. To stop particles escaping, the magnetic field lines are made to twist like stripes on a candy cane as they track around the torus.

Counting out instability

But it’s not so simple to get the right number of twists. If the magnetic field twists around exactly once per lap of the donut, particles end up exactly where they started and instabilities can form. A fractional number of twists, say two-and-a-half, is better – a particle will go around the loop multiple times before it comes to the same place. Even then, instabilities can arise when any whole number of laps around the torus brings the particle back to its starting point. For example, two laps of two-and-a-half twists equals five twists. That puts the particle back where it started.

The ideal solution would have a number of twists per lap that cannot be written as a rational fraction or ratio. This irrational twist would make sure a particle can never follow the same path twice. Tiny imperfections in a fusion reactor make such a twist practically impossible, but clever calculations can maximise the mixing. And that clever maths ensures the plasma stays stable.

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