Some people believe the triangular shape of the pyramids has special powers. Plasma physicists also have strong opinions about shapes, too, but it is not superstition: it’s all about how to get the maximum performance out of a fusion experiment. The power that interests physicists is not mystical, it is fusion power. Changing the shape of the plasma can lead to higher stability at its edge. This leads to higher density, and therefore more power.

The champion of plasma shaping is the TCV tokamak (Tokamak à Configuration Variable) at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. With its 16 poloidal shaping coils it can achieve an astounding array of plasma geometries, not just triangular and round, but square, pear-shaped, double-lobed like the number eight or the picturesquely-named “snowflake”.

The original rationale for departing from the conventional circular cross-section was a practical engineering consideration. The design team of the first large tokamak, JET, realised it is much easier to support D-shaped coils as they sit closer into the central column – conventional circular coils would need substantial support structures to prevent them drooping. However it was soon found that performance was enhanced by this shape: the plasma sits tighter around the central column, which is where the inside sections of the toroidal electromagnets sit closer together. This means the magnetic field is stronger, which makes for the better performance.

At JET the six poloidal shaping coils around the outside of the torus can be used to emphasise the triangularity – the coils at the apices of the triangle ( top and bottom of the torus, and two on the horizontal plane) are run in the same direction as the central solenoid, effectively pulling the apices of the triangle further out, while the two coils at 45 degrees above and below the midplane are run in the opposite direction, flattening the rounded sides of the triangle. The result is far from a true triangle, it is more D-shaped, but a considerable enhancement on the circular cross-section.

What these experiments with plasma geometry have shown is that the creation of a shape with better confinement has a downside. The high-confinement modes inevitably lose energy through turbulent events known as an edge-localised modes (ELMs) – and the geometries with higher confinement lead to less frequent, but more powerful ELMS.

Nonetheless the design team for ITER has opted for a triangular plasma, to maximise the power output of the device, and is trialling a number of other methods to reduce ELMs, such as specifically installed localised coils, or injecting pellets of frozen fuel to trigger higher frequency, but less damaging ELMs.

The plasma shape plays another major role in a tokamak, by determining where the plasma touches the walls. It is here that TCV’s snowflake geometry is significant: It gains its name not from its cross section, which is more-or-less triangular, but from the six-fold pattern of the magnetic field lines where it touches the divertor. This extended shape spreads the heat load from the plasma, helping to overcome the material challenges for future fusion devices

If these plasma shapes are successful in ITER then perhaps the respect the ancient Egyptians had for the triangular shape of the pyramids will re-surface in the future, as society begins to rely on a generation of high triangularity fusion power plants!

The Ecole Polytechnique Fédérale de Lausanne (EPFL) is the Swiss signatory to EFDA.