Software Supercharges Stellarator Design

Key Takeaways

[music] >> Welcome back from the lunch break. Now we going to learn how we can build a fusion reactor. >> [panting] >> And get become familiar with the tools. Thank you Jonathan for joining us. >> Thanks a lot for having me. So what this is all about is >> [clears throat] >> stellarator design. So building fusion reactors like this one over here. And I had the honor couple of weeks ago on the 16th of April to welcome a certain person in our lab that I built up and run at Proxima Fusion. And I'm going to let them tell you what this is all about. So here we go. >> So talking about fusion energy. Let's start with fusion, which is the nuclear reactors. They take a big atom like uranium and you break it in pieces to create energy. Fusion is different. You take a small one and you fuse it. So there comes a problem. Normally these atoms they don't want to fuse. They have a repelling electric reaction. First thing is what you want to do, you take a small atom like hydrogen. Actually it's deuterium but it's hydrogen. Which is a gas which has a proton and electron. First you want to strip off the electron. How do you do that? You heat it up to 150 million degrees in the sun. That's where it happens in the sun. Here on earth we need 150 million degrees. So 10 times hotter than the sun. Then the electron goes away. And then you have a kind of a gas which is called plasma. It's electrons and protons moving around. Now you have a gas which conducts. And if it conducts you can use magnets to accelerate it. Why do you want to do that? Because in order to come across this repelling reaction, you need to bump them into each other. So, accelerate them, create a core chaotic uh bumper chamber, and let these atoms, these protons, bump against each other and eventually fuse and create energy. And now I show you how this bumper chaotic bumper area would look like. A bumper area for plasma contained in big magnets. All right. Here we go. And >> [clears throat] >> after this, you already know everything, and uh we just do a little bit of a further deep dive in this talk, obviously. The The big thing that we want to do is we want to build a fusion reactor, because fusion is the ultimate source of clean energy. It's a process that powers the stars by forcing light nuclei, so the cores of atoms together. The mass difference from the resulting product is converted according to E equals mc squared, a formula that some of you might know, into energy. The thing is though that the sun, which we know as the closest star, is uh remarkably inefficient at doing that, and it needs its gravitational forces to keep the particles together so that eventually, after billions of years, they fuse. And what we want to do here on Earth is that we use this process to generate a um clean, safe, and effectively limitless energy source by using a slightly different process than the sun though. And uh I would boldly claim that when we enter the fusion era, we will end energy scarcity on Earth, which in particular in the age of AI is a big topic. Little bit about me. I'm co-founder and head of labs at Proxima Fusion. I have a PhD in plasma physics at the uh from the Max Planck Institute for Plasma Physics in Greifswald in the very northeast corner of Germany, where I did modeling, numerical modeling, physics, um, analysis for the so-called Wendelstein 7-X stellarator experiment. And my open source interests >> [clears throat] >> span between mostly numerics, physics, a little bit of reverse engineering. So, here you see my private GitHub repo. Feel free to check that out. Um, and a couple of contributions to the open source community is like a tutorial for the FFTW fast Fourier transform library. Uh, some infrared camera image reading, um, reverse engineering which I did together with my brother, Benny. Then, uh, we have some 15-digit accurate magnetic field computations which was published in '23 and is also an open source library now. Uh, I did recently a reverse engineering of the original Macintosh 68K ROM for a little bit of, uh, historic computing project. And the, [clears throat] something that I will talk, uh, or cover in this talk, is that I cleaned up and rewrote the variational moments equilibrium code, which is a numerical tool that is used to model these kind of stellarators that we looked at. >> [snorts] >> And, uh, VMEC++ is open source and also 200 pages of latest documentation, which you can find on archive that I wrote in the context. Now, also in DocLing in the original repo, so that we can use it for, uh, AI-assisted improvements on the code base itself. And, uh, I also like a little bit of hands-on engineering, so I did some high-voltage experiments in my younger times. For example, here built a 25 kilovolt high-voltage transformer that can make some arcs. And, uh, also some machine tools reconditioning. So, this is an old milling machine which I acquired during COVID and then overhauled. And, uh, this gentleman here in the center is Thomas Klinger, who's the head of the Wendelstein 7-X project during its construction time and we spent an awful time, uh, a lot of time uh, where he explained to me what went wrong, what we would do better in the, um, upcoming fusion experiments now after Wendelstein 7-X and essentially everything that I know about fusion, I know from him, and this is uh, [clears throat] why I'm very grateful about uh this. I'm going to talk about three things in this talk. One is Proxima Fusion in general. What is even the roadmap? What do we want to do? What's our approach? The second thing is that I'm going to give a little bit of background on this VMEC++ tool. What was difficult in building it? How is it uh structured? What are use cases? How can you get access to it and contribute to it? And the third one is a little bit something about the constellation challenge, which is a AI machine learning challenge that we posed together with Hugging Face last year. This is one of the most openly available large-scale applications of this VMEC tool then in the context of fusion. >> [clears throat] >> Proxima Fusion aims to build a stellarator, and it does it not a tokamak like ITER, this big machine in southern France, because design, and not control, holds the key to fusion. What do we mean by that? If you look at the tokamak, it looks like a very much simpler design, and it creates the magnetic field that you need uh in this machine to contain the plasma with the current that runs through this plasma. And this is simple to design because it's axisymmetric, but it's very hard to operate. Stellarators, on the other hand, if you look at this, this looks like a completely different beast, obviously, in terms of the engineering complexity. And this is because this twisted magnetic field, which looks a little bit like a Möbius strip, is generated by numerically optimized coils like these silvery um arm rings that you can see here around. And they are harder to design, but in the end, the machine becomes simpler to operate. So, this is what we chose for Proxima because we want to get eventually to a steady state uh continuously 24/7 running power plant. And for that, we consider this to be the better approach. How do we get there to a commercial fusion power plant with this approach? We start from the well-known Wendelstein line of stellarators that have been built in the last 60 years in the context of the Max Planck Institute for Plasma Physics in Garching and eventually later in Greifswald for Wendelstein 7-X. And we want to get to Stellaris, our first proposed fusion power plant concept. And as an intermediate step, we introduce a machine which we call Alpha, which is supposed to deliver the first smallest step basically on the path towards the fusion power plant, which is that in the from this plasma ring, which is where the actual fusion reactions happen, you want to get more energy in terms of neutrons out than you have to put in in terms of microwave heating power. This is like say, if you cannot even do that, then there's no hope to ever build a power plant which actually delivers power to the grid or eventually also makes you money. How do we get there exactly? So, we have Wendelstein 7-X, this machine in Greifswald, and we want to get to the fusion power plant. And something that we can directly carry over from W7-X is steady state operation. Because W7-X is a fully superconducting machine. That means all these magnet coils, in this case here orange and red, are cooled down to minus 269° C, roughly 4 Kelvin. It's the temperature of liquid helium. And at these temperatures, if you build the coils out of certain materials, in this case it's called niobium titanium, this becomes superconducting, so you don't have losses, electrical losses, when you generate these big magnetic fields, which is a game changer for creating these strong magnetic fields that we need to contain this hot fusion plasma. And Wendelstein 7-X has shown already how to do this and also how to eventually operate this machine for 30 minutes steady state, at which point also thermal equilibration effects come into play. And so, you really need to properly design this machine for that. And W7-X is the first machine where this was rigorously carried through. And in between we we Alpha. This builds on top of Wendelstein 7-X which is roughly the same size. So, this is 16 m end-to-end. Wendelstein 7-X weighs roughly 700 tons and Alpha is probably going to be uh weighing 2,000 tons, although also only 16 m. That's roughly, I think, from here to the end of the room. So, it's it's a big machine, but it's not unsinkably large. And uh it expands over Wendelstein 7-X in the sense that we go to a different kind of superconductor, high-temperature superconductors, which becomes superconducting already at temperatures of 80 or 90 Kelvin. But then we cool them down a little bit further to 10 20 Kelvin, where the um magnetic field that you can produce becomes still a lot higher. And so, with this choice, we can go roughly a factor of four in fusion uh in in magnetic field strength. And because the fusion power depends on the magnetic field strength with the fourth power, now people can think four to the power of four is 256. So, basically, Alpha would have an equivalent fusion power more than 200 times of that of Wendelstein 7-X. And Wendelstein 7-X has like 1%, so we get with this times 200 roughly to a factor of above one. So, the key deliverable of Alpha is that we get to this Q greater than one, which is like the first step towards a fusion power plant, which we want to demonstrate. And also, we operate with deuterium and tritium, these two hydrogen isotopes that actually make up the fusion fuel that you need in the power plant. Tritium itself is radioactive with a half-time a half-life of 12 years, roughly. And this introduces a lot of operational complexity, which we said like we cannot delay further. We need to put this into Alpha already, learn how to use it, learn how to design a machine to do this kind of stuff. And then, when we have Alpha up and running, the step to Stellarator is still a significant one, but it's um totally it's a lot easier than going directly from Wendelstein 7-X to Stellarator, which some other companies suggest to do but we think that's just presumptuous. And uh if we have alpha we'd go towards the law of us by introducing the so-called blanket, which is where we re-breed the tritium in the machine. Because tritium is not so much available on Earth. We need to recreate it from lithium within the process of that machine. And also we need to introduce remote maintenance. So there's a lot of robotics, PLC, and so on. So I think I'm in the right community for that here. To actually get these whole of remotely controlled operations figured out. If we now look at where we stand in terms of physics performance, it's all about big [clears throat] machines and uh using them with new machine generations to increase certain key properties, key deliverables, key numbers that allow us to judge how close are we to a fusion power plant. And one of them is the so-called triple product, which is the density times the ion temperature times the energy confinement time. >> [cough] >> And all of these three numbers multiplied together give you a uh num a single number that you can use to like ballpark judge how close you are to a fusion power plant. And all these little dots here in the background that you see, those are from tokamaks. And we have here with Wendelstein 7-X the blue triangles. And you see that Wendelstein 7-X really delivers towards the horizontal axis, which is the duration of this high performance phase. And uh we can see here that some of the Pareto optimal points here from the tokamak world have been acquired in JET, the Joint European Torus in UK, which features a plasma volume of 80 cubic meters and was operating in the so-called high confinement mode where they kind of have a two x improvement over the low confinement mode, which W7-X was operating in for the same performance, and with roughly 1/3 of the plasma volume. So it's not only that the tokamaks and the stellarators are more or less on par with performance is like with these optimized stellarators because you have these contorted coils which are numerically optimized. With the modern optimization tools or like this this optimization approach which was already used for Wendelstein 7-X, we're in the point in the position now where we can design these machines to perform better than the tokamaks which traditionally stole the show for the stellarators. And then with Alpha, our machine, we say like the horizontal axis is what the Wendelstein 7-X has to deliver on and we are focusing with Alpha on the vertical axis, so we're aiming only for 10 seconds of plasma operation maximal at only deuterium and with DT actually only at a couple of seconds which is the time scale on which we need to prove that this works for this to be the relevant next step. And then with Stellaris, we go then again in the horizontal axis, but this means that we can demonstrate basically the technology already in Alpha and this little bit of vertical increase here simply comes from Stellaris being a bigger machine. It's not a different technology anymore which means that a lot of the engineering learnings that we will acquire during building Alpha will immediately carry over to Stellaris. Here's our roadmap, how we see this. And then we start with Wendelstein 7-X which is the basis for all of this which uh we say like in 2022 roughly it became clear that it was really performing very well, much nicer than we would have anticipated and it broke several records in terms of this physics performance. Then in 2023, we spun out Proxima Fusion from IPP and um directly built on Wendelstein 7-X, so that's done. In 2024 and then published in 2025, we did work on a power plant concept how based on this technology one could conceive a fusion power plant concept that as its most uh relevant feature was self-consistent. Because in the academic context, lots of people typically do like this deep dives in a certain topic, certain aspect of such a machine. But it doesn't necessarily mean that you can make a full power plant out of that because obviously that entails more components than just I don't know. How can you make a great coil set that achieves a beautiful magnetic field, but it's like so contorted that you cannot manufacture it? And with this Stellaris concept, we tackled really the whole breadth of it. And this was published in 2025. We're currently working on building the so-called stellarator model coil or SMC, which is a 3 and 1/2 m magnet. So, that's roughly the size of this screen plus a little bit. Weighs, I don't know, 10 tons, I think. And it's going to be the demonstrator for this new high-temperature superconductor magnet technology applied to stellarators. And you see it's a little bit stellaratory. Other people in China and the US have already built coils of that scale which are planar, which is the thing that you need for tokamaks. So, in principle, we know that's working. Then in the early 2030s, we hope we'll be able to take Alpha into operation. And then I think like optimistically speaking, within the 2030s, it is possible. It would be a hell of a ride, but I think it's possible to get the first Stellaris, first-of-a-kind power plant thing into operation. In May 2026, we stand with 150 engineers, physicists, and operators in Proxima Fusion. We have offices in Munich, in Zurich, actually in Villingen at the Paul Scherrer Institute, and in Oxford. So, this is where this JET tokamak was operated until 2023. We have raised 230 million dollars roughly of private and public financing, plus we have a 450 million commitment from the Bavarian government and RWE towards financing Alpha as a facility in Bavaria. There's a couple of logos from our investors and render of Stellaris, which was this peer-reviewed publication in 2025 came out. This made quite a big wave when this came out. So, the Dennis White, the head of the fusion um plasma fusion science center in MIT said this was the biggest development in fusion technology since the breakthrough in tokamaks a decade ago. And it's an open access paper. You can just download it. It's roughly 70 pages or so. So, it's good bedtime lecture reading. And a couple of quick facts here. It's a quasi-isodynamic stellarator based on the so-called squid configuration family that was developed at the Max Planck Institute for Plasma Physics. So, it's a collaborative effort that we did together with the research institute and us. And the KIT, the Karlsruhe Institute for Technology. It features these non-planar high-temperature superconducting magnets. Uses microwave heating with 50 MW at 240 GHz. And the pellet fueling has an island divertor, which is a certain way to reduce or get rid of the ash from the plasma. Very well developed in Wendelstein 7-X. And then we use sector splitting for remote maintenance. So, if you think this machine is like a torus, like a and you view it from the top, it looks like a pizza that we just had. And then actually, just like the pizza slices, uh you cut it in four pieces and these four pieces you can then move apart from each other. And thereby, you gain access kind of to this whole cross-section here, which is very beneficial for doing maintenance of the components inside of this machine. Which eventually will feature a little bit of wear from being bombarded with neutrons during the lifetime of this machine. And then a couple of quick facts here. In the end, it's maybe the the last number is the most important one. We're aiming for a gigawatt-scale power plant here. This is not some kind of small thing that you put on a truck, which I would myself say is a little bit unrealistic at the moment with our current fusion understanding. But this is really something which you could put in places of existing power plants, either being them traditional uh don't know, or gas-burning power plants or fission power plants. Those nicely are already taken out of operation, so it's a little little bit easier to motivate the utility companies to make these sites free. And with RWE, we are actually in the discussions already how to prepare the Gundremmingen nuclear fission power plant site near Bavaria in near Munich for the first fusion power plant. They are super eager to get engaged with this because this allows them to reuse the site with all its infrastructure instead of having to return it to total greenfield. This is a render of Alpha. A funny side note, maybe this rendering has been made completely with open source tools. So, the CAD files here for this thing are built with CutQuery, which is a tool that allows you to programmatically construct step files or like CAD geometries in memory, and then [snorts] use them in CAD files. And I think the render itself is done in Blender. So, we're very heavily leaning into the open source software community, and as I will show later, also a little bit contribute to it. And uh you see here again these like contorted coils. Then you have a lot of support structure in between them. In the middle, you have the plasma. That is the where the business goes on. A couple of human access ports where you can crawl into the machine, do some installations or repairs. And you see it's like barely big enough. It's a It's a big machine, but I think it's uh roughly the size which is at the right compromise between being small enough that small uh enough that we can actually consider building this in this like couple of years that are there until early '30s. And like large enough and relevant enough that it actually pushes this whole field step forward. We are act very actively de-risking the assembly process of this machine. In Wendelstein 7-X, the first coils, so this the magnetic field coils, they arrived on site in 2004. But it took until 2015, so roughly 10 years later, for the machine to actually do its first plasma. In this whole 10 years was the job of Lutz Wegner, consultant to Proxima and ex-head of assembly of Wendelstein 7-X, >> [snorts] >> to figure out how to assemble this machine, how to really put it together. And the key challenge with that was that as the components kept coming in, because there was no like fully sought through CAD model plus assembly process that was validated with experiments and so on, excuse me, they needed to figure out a lot of this how to put this thing together, how to align it, how to achieve the accuracies, the tolerances, the like even just threading the coils over the plasma vessel with like 6 tons of coil on the crane and 5 mm clearance to put it over there. Many more or less semi-manually. This is a formidable challenge and I have the biggest respect for the team who pulled this off. at all. Um but of course in Alpha we cannot afford this long time scale. And so we are aiming for 3 years and this is one of the key projects that I personally am involved in. And what we do is that we build MARS. MARS is the maintenance and assembly research sector, which is essentially one of these pizza slices of the machine of Alpha made in real hardware, not with the full fidelity, so we're not building actual superconducting coils, but we just cast them out of iron. So this is a nice job at the foundry. We have some nice videos of that casting process on YouTube if you're interested. Quite impressive. I still remember this feeling when I was there in the casting hall and then they put the metal in and the Styrofoam that they replaced with the molten metal was burning off and that thunder from these flames still vibrated like you're in the when this place is actually used as a discotheque. So, it's a yeah, properly impressive process here. And the nice benefit of that is that we now have these components which we can precisely align and try out like how is it really to align these heavy big components. So, this one is roughly 5 m from side to side. The top coil weighs 8.5 tons, the bottom one 10.3. And uh like you can lean against it and nothing happens. Even when they are like a little bit wiggly on the floor, it's like you you cannot but there's no chance. This is just super heavy stuff. And it's necessitates that you really figure out your assembly processes because when you're dealing with the actual coils which will cost, I don't know, 5 to 10 million each uh in assembling I 5 this needs to work picture perfect. And so, we're we're very actively leaning with the partner company here DWE in Deggendorf who has done similar stuff for Wendelstein 7-X already into de-risking this and really developing these processes. We embrace the principle of open science and close engineering deliberately because fusion has this notion of like it's always 20 years away which very happy to discuss it. I think it's a little bit of an ill-posed question. But like uh I think the approach for Proxima that has worked really well for us is that we ride this wave of credibility that has come out of this Max Planck Institute which has done 60 years of publicly funded research with peer-reviewed papers and this like a thousand scientists who've who've worked there and uh really established a solid ground of understanding on which we can now build our machines and our planning, of course. And so, with the scientific aspect of that which is nothing which you can patent anyway or where it's more valuable to have this trusted and verified and like um critically reviewed even by our competitors, I would argue. Uh there we are happy to open source that to publish this kind of stuff. But the engineering bits of how to actually build such a machine, this is where the real value generation happens for us as a private company, and this is why this part is closed and will remain closed. And one open source project is this VMAX++ ideal MHD equilibrium solver. Sounds very complicated. In the end, what it gives you is the form, so the geometric shape and the magnetic field of the plasma. And this is the basis for all further uh following performance predictions and analysis. And along there with that, I said this 200 pages of latest documentation handwritten. This was all in the age of pre-AI ages. Then also this constellation data set that I will say something a little bit later about, which consists of roughly 150,000 quasi-isodynamic stellarator designs that you can download yourself. I don't know, it's 500 GB or so, including performance metrics, which we post in as a challenge to for people to apply their AI tools to and machine learning approaches and like um try to find better ways of designing these machines. And most recently also ray tracks, which is one of these microwave ray tracing tools that we use to model the heating of the plasma. And David Straub, one of our team members, is now a professor at the technical school in Munich, and he's even on his private blog posting about ray tracks still because he's like um supporting this further. And then I would also like to point out that we sponsor and present at a couple of conferences, for example, this open source software for fusion energy conference, where one of our team members is in the steering committee. And we have a couple of contributions to open MC, cut query, pants, dog MC, Simsopt by five proximal fusion team members, and also sponsorship of these projects. So, we we try to really embrace the open source world in which we um from which we profit so much with all these tools. That's it for the first part of the talk. We have two more parts to go, so bear with me. Second one is now about VMEC++ itself, cuz this is a project that I started as part of my PhD. And in the announcement for this talk, I promised to give a little bit of a background story to that. So, first of all, what problem does VMEC even solve? Or what why is it a tool that's worth investing any effort in? It happens to occur that this is the central modeling tool in two essential, but slightly different, uh, uh, workflows when you want to work with stellarators. And one of them is the stellarator design workflow, and the other one is called equilibrium reconstruction. So, the left part is basically how you want to build such a machine, how you want to design a stellarator. And the right one is if you have the if you have a stellarator, what the hell is going on inside of it? Because this this plasma, it's like a you can think of a bicycle tube tire tube. Normally in a bicycle, you have the mantle. But if you know, maybe you've played around with it yourself as well as I did. You take the rubber tube itself, and you pump it up by itself. And then the shape that it takes is like a circular cross-section, but as you pump it out, it comes it it gets a little bit bigger in the in the radius itself, right? This is the hoop force is what pushes it out. And it's a little bit similar with the plasma in the magnetic field cage. So, in the case of the bicycle tire, you have the inward [snorts] pressure from the air that you pump into it. And you have the outward pressure, which is from the ambient, I don't know, 1,025 millibar or so that we have here in the and the force balance between these two pressure force from the inside, the rubber force, and the outward pressure force, this is what gives you the shape of the uh, of this tire. And in the plasma, it's basically the pressure from inside this plasma, where you heat it up, so you have hot particles that are confined, so they want to move out. And from the outside, you have the magnetic field pressure, which pushes this stuff together. And so, this pressure balance is what gives you the shape of the plasma, and this changes. So, you need to somehow compute it. And in accelerator design, is what you do is that you parameterize this pressure profile, so how the pressure changes within the plasma, and the coil current, so how much current do you run through the coils, as well as with as which shape do they have. And then you feed this into the simulation tool, and you get out either metrics of physics performance that you then can iterate over for so-called scenario modeling, so how will this machine work over a a time span of an experiment, and you can also calculate from the coil shapes and the plasma output some engineering metrics like how much heat load is going to be on a certain place of the internal of the wall and so on. And then you can iterate here over the engineering design. And in equilibrium reconstruction, you have the same modeling setup, except that now you have fixed coil shapes, because when you have the machine, you want to analyze it, the coils are not going to move, and then you calculate predictions for what the measurement instrument the diagnostics will measure, and you have some actual diagnostic measurements in your uh experiment, and then you look whether they match, and if they don't match, you iterate over the inputs to the simulation code. And you see that this is a rather similar workflow, so you have always this simulation code in the center, some parameterized input, and some metrics that you optimize for. And essentially what we do is that we then uh formalize this as a uh N-to-M function, and that we feed them to a multi-objective optimizer, scipy.optimize.whatever. It's really as simple as that. But that means that the simulator tool you need to call an awful number of times, because you need to really iterate over the simulation. And [snorts] >> [clears throat] >> so, this is why we decided, or I during my PhD, when I was working on this right on the equilibrium reconstruction of W7X decided to invest a little bit of time into that. And like so, speaking a little bit more formally, VMEC gives you like these surfaces here, these shapes that you see here in the center, and the magnetic field of that it solves a certain partial differential equation for that. Not going to go into the detailed analysis. It's just important to know that this is such a complicated geometry that you cannot simply solve this analytically, so you really need numerical tools to do this. And VMEC is the most well-established tool for this. Also, because since it was written in 1983 until I rewrote it in 2019-2020, it was the single tool and the single implementation in Fortran, which was the world reference for stellarator research. So, something needed to change. And this is how this computation looks like. So, you start from a certain initial guess, and then as the force residual moving these shapes into force balance reduces here, you see that they move eventually into this nicely contorted shape. How did How did this come about? So, again, the status quo for like 40 years or so in stellarator research was that VMEC was the central tool. There was only this one legacy implementation. There was virtually no documentation of the core numerical approach. A couple of research papers, but they didn't really Also, like thinking about Duckling one of these like totally unreadable noisy PDF scans. >> [snorts] >> So, I'm very curious to try that out. And but the problem was that even there were these papers, they didn't really agree with what was actually implemented in the code. Which is also not super helpful, obviously. And then the memory management was broken. So, when you ran this code a million times, I don't know, 10, 20 times out of so, it would randomly segfault because it took like this one weird approach one weird code path, which then led to a problem. Because like in the context of running this code within an optimization tool chain, you're essentially fuzzing it with its input and nobody had fuzz V Mac in this whole It was all usually the workflow was like somebody sent someone an email with the input profiles and then the V Mac expert at the institute was running the code himself and then it was emailing back the results and then they were discussing with the emails and Na ja. We have progressed since then. And the like most abstract level reasoning I think in the end was that with Wendelstein 7-X we saw that this machine was really working well. But we said like it seems a little bit bonkers to have this billion-dollar class of machines that we want to build here. Wendelstein 7-X cost 1.4 billion euros and took us like 10 years to build. So it's a massive investment that you make. And this engineering design for this machine was based on this black box Fortran code from the '80s that nobody understood. >> [laughter] >> And so we thought about okay, it works well, but we want to build the next billion-dollar class machine. So are we really going to do that based on this black box that nobody understands? No. So the journey. I was I started 2018 with my PhD thesis and then for the first year or so I listened to what my supervisors told me. >> [snorts]>> And then I thought [clears throat] hey, I really need V Mac and I don't want to do it with this legacy Fortran implementation. So I suggested openly to do something about that and analyze it, rewrite it, I don't know, clean it up. I had to survive a lot of pushback there obviously because they were worried that this would take a little bit longer and guess what? It took in the end 4 years. But uh yeah, in the end they said the only thing you need to do is listen to our feedback and then in the end it's your project. You're the project manager of your PhD project. If you mess it up, you just don't have a PhD. It's okay. I was fine with that. So So put the PhD topic aside and like fully focus on this rewrite of VMEC. I defined a couple of reference cases, dumped reference data from the Fortran implementation. If people are interested about the details, I have a couple of backup slides. I'll be I'll show you actually on the on the laptop how this worked. And then um used that for a one-to-one, like literally like line by line, by hand, again pre-AI times, uh copying what was done in the Fortran implementation into Java with the Eclipse IDE because I liked it and this was where I was at home. And then uh well, it's questionable life choices, but here we go. And then once that was working and I had full set of integration tests that achieved the same numerical results as the Fortran implementation for the relevant set of input files, I said sat back a little bit, wrote a lot of this documentation, and in the process always implemented then a clean version of how I understood the numerics to work in Python. And then my PhD contract ended because clearly I was not working on my PhD topic again. But the thing is this project had matured far enough and also we saw we really with the Wendelstein 7-X results that uh something was happening in the case of fusion. And also third part, in 2018, a certain American spinout from a certain American university raised $1.8 billion based on building their version of this demonstrator coil for building their version of their tokamak power plant. So we said, "Okay, something is happening in fusion. We need to somehow get now to do something based on Wendelstein 7-X because if we don't do it, somebody's else is going to do that and what would that be?" And so we co-founded uh together with a couple of friends co-founded Proxima Fusion. And then we did the from-scratch proper high-performance implementation of this VMEC code in C++. And this is also the one that's now open sourced. >> [snorts] >> I have to give a huge shout-out to Enrico, Veronica, and Philip, who were three early team members who helped a lot in particular Enrico with the performance optimization and rigorous integration tests. What uh Veronica mostly worked on the verification and validation against the Fortran implementation to the point that we decided to open source release it in uh end of 2014. I think it actually became online in 2025. And it's in daily use at Proxima Fusion since 2024. It's our core simulator for these plasma shapes. And uh yeah, this numerics of VMEC++ which is this document that was released uh along the side. It's now also available also on archive and we have a growing example collection very nicely also now with more and more contributions from the community where just somebody opens an issue and how here's how you visualize the magnetic field. I'm like nice. VMEC++ is a modern Python-friendly VMEC implementation. We still do a lot of our we we do a lot of our analysis and modeling in Python. It's easy to install. You can install VMEC++. It's uh all uh supported mostly on Linux and macOS. It has some direct integration on C++ via Basil and CMake. It's downloaded mostly in the United States, second mostly in China. And uh MIT license so you can do whatever you like with it. The API is a single method, single static function call. And uh here's a couple of examples. So in particular, this middle one is the self-contained VMEC run something that this Fortran code would do. And it uh I you can read the details later. It's well documented and tested. We have a bunch of CIs set up. And the documentation is validated against the Fortran reference. So we have here some demo plots where the blue and the red are overlaying here picture perfect with 10 to the minus 12 relative error. So we say like this is close enough that it's just like how the compiler optimizes certain ordering of operations differently and then okay, you get a little bit of numerical noise, but like for all practical purposes, it's the same code. And this is also something that I decided with V make. I don't want to dive into writing a new code actually having to understand the theoretical physics that go on there. I'm just a experimental physicist who has this code. We know it works. I'm going to port it to a modern code base and then we can think about the physics variations of that, which is something that we're getting into these days. And let's see also how this enabled us to accelerate this execution of the code a little little bit. So because I mentioned this original implementation was more or less the same since the 1980s. Back in the day it was written for the Cray 1, which is a vector supercomputer and that means all the operations were operations on a single 1D scalar array, which is like not exactly ideal for modern CPU architectures. And so by reformulating the ordering of the operations a little bit, we were able to help the compilers auto vectorize a lot of these operations and that gave us a nice speed up. The gray always the old one, this um turquoise here the the new one. And something else that was the key motivation for me to embark on this project is that since an iterative code which needs like 5,000 iterations and then you do a little bit of finite difference step, you only need to do the last 100 iterations a little bit different and all the like previous iterations are the same more or less and that means that when you can save the internal state of that code and like hot restart it from that converged state when you do the perturbation, you can save 90% of the time. And obviously this involves a little bit of memory management and you need need to get quite detailed into the inner of this code. And this was then also easy with V make plus plus. I gave up after 2 months of trying to do that in the Fortran code base because I simply couldn't figure it out. And uh here you see basically then run time reductions from the normal every run from scratch implementation of an actual optimization problem down to like a tenth of that if you use this hot restart feature. Okay, then I come to the last topic, this constellation challenge. Constellation is basically what you see here on the right. It's like every little thing here is a stellarator design. It's 160,000 in total of this plasma boundary, so like the shape of the outermost surface of this plasma. The actual equilibrium calculation and the metrics they're available on this hugging face data set here. There's three optimization benchmarks with the tools and the baseline results. And we have a public leaderboard on the challenge with hugging face where people are submitting their results and competing for fame, I think mostly. And we also have a paper on archive that goes a little bit into more of the details of this challenge. Why do we need this even? With stellarator design you always have to trade off between certain objectives. This is also what I mentioned earlier with the stellarator design where we really leaned into this consistency and like being okay at everything instead of super good at something and very bad at something else. Maybe the easiest to comprehend is like this bottom two where you have the dark red which is the economic target, so like this is very cheap and this is very expensive. And then the orange bit here is the physics target, so this has very nice physics and this has not so great physics. And you obviously can see that this is a much simpler design. But it just doesn't work so well. And this one is where the physicists were really happy with, but it's like horrible to build when you look at these coils. And so in this space you need to choose where you want to put your uh your your X and this is what we try to trigger with this constellation challenge. And then um how does this work in practice? We have here this plasma boundary which contains most of the information that we need for this calculation. It's a bunch of Fourier coefficients. Here you see like the the values of those. Then we put this into VMEC + + which computes the full magnetic field inside the plasma also with these inner flux surfaces which is like how the plasma is internally organized in this model. And then we compute a bunch of metrics which are just scalars or 1D profile 1D arrays or so of certain numbers and some of them you want to be high, some of them you want to be low. Then you feed this into an optimizer and then the optimizer suggests a new candidate. Sorry. And then you just iterate this loop until you're below a certain convergence target. The optimization benchmarks that we have published are three of the uh increasing complexity. So first one is the simple geometric one where you just want to have certain metrics below a given threshold. Second one is a simple to build quasi-isodynamic stellarator where we have this Elgrad B metric which is a metric that is related to how wiggly these coils need to be. And the third one is the MHD-stable quasi-isodynamic multi-objective problem which is uh the minimal minimum viable subset of metrics that are actually relevant for the stuff that we do during our daily optimization work. If you're curious for more, I think the first thing is ask Roland Busch because again he's been at our lab and he knows Actually, he did his PhD on high-temperature superconductor. So it's really nicely closes the loop. And uh otherwise check out our code. Here we have our GitHub project and then there's uh my email address and also the one of Santiago for the constellation um constellation challenge. And uh if you actually consider uh contributing to this project, we also have a link here to our page of open positions. Thank you. >> [applause] >> I have a question. Or my question have been answered, so we know which tool we can use to design one. But I guess nobody here has the money to build one. >> [laughter] >> Siemens certainly has the money to build such a machine. >> You're right. >> That would actually be my part of my question. So, can you shed a bit of light on if you have ideas already how to operate these things control-wise? Now, we are control engineers, so we are interested, okay, what problems you do solve at this level, what controllers you need, what speed you need, and things like this. Are there ideas for that? I mean, they must be from the operation of W7-X, I guess. >> The thing is that's a little bit of an unfortunate message for you, I think. Accelerators are just so stable that you don't need so much control. >> [laughter] >> But, there's always a but. Um you do need, of course, certain control systems for accelerator, and that is I don't have a picture of for that now. Um but, if you look at these time trace plots where you like go over the time, and then you have multiple quantities, you always see that, for example, the plasma density typically it has a set point, and then it wiggles a little bit around that. And this is because the PID controller for that density feedback is not really tuned properly uh as it is when you just have spent 10 years building the machine, and then you want to operate it. But, like um yeah, there's a couple of control mechanisms on the higher level of physics around this machine that you keep it at a certain operating point. The response times for that are on the order of like fastest is maybe a millisecond down to 100 milliseconds, so easy to do, I think. We could go to S5, maybe. Who knows? [clears throat] And then uh other than that, I mean, there's really no fast the this the next interesting bit is then when you have done such an experiment, how quickly can you download the data from the data acquisition units, do some preliminary physics analysis, and use that to inform the machine operators what they want to change for the next experiment. Because in at least in Venice and 7X, it's always run for I don't know, 10 to 30 seconds. And then you have 5 to 10 minutes of a break where people try to understand what the hell just happened. And plan [clears throat] to make a couple of knobs and ah, maybe we need to up the density a little bit. And then da da da da da. And uh yeah, this would benefit a lot from automation also and we're not there yet with what is possible, even at Venice and 7X, not yet. Um but there's a lot of potential. Other questions? >> Yeah, thank you. I actually have two questions. So, my first one, you mentioned while assembling all of that, you run into shortages of material sometimes. Like, do you see in the future if I mean, when it will work and scale to multiple sites that in the world we will have a shortage of something you need? >> Maybe I misspoke. Like, the problem is not that we have we don't have the material coming in. The problem is we have a so many components coming in at the same time and we need to be able to assemble them together quickly enough that they don't pile up in the logistics hall and then you don't find the one screw that is just at the bottom of the pile. So, even if we go to multiple accelerators, I think there there's a couple of things which are not at the production scale yet as we would need it. For example, this high-strength stainless steel that we need for the magnet coils. But this is nothing that could not be ramped up in the proper industry sector when the demand is there because actually like there's billions or tens of billions of euros, dollars, whatever flowing into this industry and the demand being there. At the moment, the demand is not there yet and therefore the capability is not there yet. >> Uh thank you. And the second one is a little bit more personal. Did you ever think when assembling to put four robotic arms on your back? >> [laughter] >> It's a nice idea. I haven't figured out the design of this neural link yet. >> [laughter] >> So, that's why we still have to revert to good old cranes and hooks and all this kind of stuff. But, nice idea. >> Perfect. Thank you very much Jonathan for those insights. >> [applause]