I do research at W7-X, so I can confirm that to the best of my knowledge, the design was computed a long time ago. Building the actual device took a while.
I'm not the expert on this, but I was curious so I looked into it a bit. I don't believe it required significant resources or crazy algorithms, but a clever selection of physics criteria to optimize. It was a ~20-dimensional Neumann boundary value problem [1], and a code named NESCOIL was used to figure out the shape of the coils that would produce the required magnetic field [2], which it did using Fourier series.
By the way, the unusual shapes of the coils can be understood intuitively from this picture: https://imgur.com/a/Bq3ABfQ. A plasma needs to be confined with a magnetic field in order to be heated to extreme temperatures, and a toroidal field (produced by the currents in the red coils) is unstable due to particle orbit drifts. You need to add a twist to the field for it to be stable (using the green coils). But if you unroll the surface of the torus, you can approximate the currents in both green and red coils using the discrete blue coils, and they're easier to build.
Do you have any links to a high level description of how this would be hooked up to a powerplant? Would this be used to heat water as per a typical fission plant?
"The Helias (Helical Advanced Stellarator) reactor is based on the Wendelstein stellarator line and takes into account the design criteria of a power reactor."
Alas, it "just" seems to talk about extending the coil design for a reactor, not the rest. I am guessing most of that would be similar as for other fusion reactors, see for example MIT's Pathway to Fusion Energy:
Thanks for the links. Had a bit of a google for Helias. Looks like the Wendelstein team are exploring using something called a "Helium Cooled Pebble Bed Blanket", which was designed for ITER. To me it looks like a closed loop heat exchanger using helium. This would then be fed into a typical steam system.
Though I don't really understand the significance of the "pebbles" in this system.
The pebbles will most likely be made of Lithium because it is a solid/liquid at the operating temperatures of the cooling system and therefore has a high density. It is also an element with a very low atomic mass, which makes the crosssections for interactions with fast neutrons comparably high. So the Lithium will have collisions with the fast neutrons from the D-T-fusion that leave the plasma confinement with most of the energy from the reaction. These will heat up the pebbles due to the energy transfer and from time to time a Lithium-6 atom will catch a neutron. This will make the Lithium core fission into a Helium code amd Tritium core. Tritium is one of the two fuels required for fusion and has a very low natural abundance due to its rather short half life. So breeding it seems to be the best option to obtain it in sufficient quantities.
The W7-X isn't a fusion power plant, so such a description doesn't exist. It's the chemistry equivalent of a test tube, not an internal combustion engine.
Would you happen to know what kind of compute power was required? Was it run on a colleague's PC or workstation or did it require supercomputer time?