# Empowering the Future of Fusion Energy

## Simons Collaboration on Hidden Symmetries and Fusion Energy

Since the 1940s, scientists have dreamed of creating fusion energy reactors, which could make energy cheaply and safely, producing less radiation and waste than conventional nuclear-fission reactors. So far, though, no design has managed to generate more energy than was put in, leading cynics to perennially quip that fusion is the energy source of the future — and always will be.

The Simons Collaboration on Hidden Symmetries and Fusion Energy, using a new design approach and fresh insights into the mathematics of symmetry, may yet prove the cynics wrong.

Fusing nuclei together in a controlled way requires creating a starlike environment: In stars, high temperatures result in enough kinetic energy to squash hydrogen nuclei together, forming helium and releasing energy.

Here on Earth, physicists have managed to come up with a few strategies to fuse hydrogen. One method requires heating hydrogen atoms in a container to 100 million degrees to give them enough energy to overcome the mutual repulsion of their nuclei. Under those conditions, hydrogen gas ionizes, which means electrons are stripped from their atoms and float around freely with the nuclei in a mix called plasma.

One promising early model was first tested out in 1958. In that design, a doughnut-shaped (or toroidal) tokamak holds plasma by pumping electrical currents through a series of metal coils, which create magnetic fields that contain the hydrogen and squeeze it together, causing fusion.

Tokamaks have a major drawback, however: The magnetic field created by the coils that wrap around the toroidal tokamak also induce a current in the plasma. Researchers usually pulse that current, which makes it difficult to maintain the plasma in the stable steady state necessary for fusion. Furthermore, the system can be disrupted by instability, dissipating the plasma after even a few milliseconds. Scientists have built dozens of experimental tokamaks, but none has yet resulted in a net gain of energy, although research continues.

Princeton astrophysicist Lyman Spitzer thought of another configuration: a stellarator. A stellarator is also torus-like, but because of a complicated helical structure in its coils, the plasma holds no current and hence can operate in steady state devoid of disruptive instabilities, in principle creating ideal conditions for fusion. The challenge is to build an optimum set of coils that will realize the dream of gains in energy via fusion.

The collaboration hopes that new mathematical and numerical techniques will solve that challenge. This collection of 33 mathematicians, computer scientists and plasma physicists from 16 universities across the globe is working on the next generation of stellarators, whose coils test the limits of design and manufacturing precision.

“We are developing novel optimization methods that will enable us to design the stellarator of the future with as much engineering simplicity as possible,” says Princeton University professor of astrophysical sciences Amitava Bhattacharjee, director of the collaboration. “When you put physics and the science of precise optimization together, you can come up with sophisticated designs which were impossible before; the ways to do that is the primary focus of the Simons project.”

**The theoretical side of hidden symmetries**

Symmetries in objects simplify analyses and allow people to use less energy — think of how circular wheels work better than oval-shaped or square-shaped ones. Unlike those in the doughnut-shaped tokamak, which has an obvious symmetry, the twisting coils of a stellarator don’t appear symmetric in terms of the usual *x*, *y* and *z* coordinates. But when their structures are viewed in relation to magnetic fields instead of those axes, in a coordinate system defined by one of the collaboration’s founding investigators, Columbia University professor of applied physics and applied mathematics Allen Boozer, stellarators do have an approximate ‘hidden’ symmetry, or quasisymmetry.

“The symmetry is hidden in the sense that if you look at one of these magnetic fields it looks like a Salvador Dali painting: It’s distorted and wobbly,” says co-investigator Matt Landreman, an associate research scientist at the Institute for Research in Electronics and Applied Physics at the University of Maryland. “But the equations tell us that even if you can’t see it by eye, the electrically charged particles in these magnetic fields experience a symmetry. It’s sort of like you trick electrons and protons into thinking they’re in a symmetric system. That’s an exciting and beautiful motivating concept for the project.”

The containing magnetic field of the stellarator can be described using quasi-symmetric equations. Previous numerical research using computers found around 20 possible configurations for the field that minimize the ‘approximateness’ of the quasi-symmetry. But Landreman says that the black-box solution “was emotionally unsatisfying because we don’t know why the computer takes me to this shape. How many possible shapes are out there?”

Instead, the collaborators used different numerical methods to approximate the quasi-symmetry equations. They found all possible configurations, ensuring that future stellarator designs won’t overlook a magnetic field alignment that could optimize energy output.

**Experiments to prove the theories**

Unlike a constantly tended tokamak, a stellarator is a steady-state system, which means that “you can turn it on in the morning and turn it off in the evening,” says co-investigator Thomas Sunn Pedersen, a professor of physics at the Max Planck Institute for Plasma Physics, where he runs experiments on one of the largest stellarators in the world, the Wendelstein 7-X (W7-X).

Although stellarators such as the W7-X were built and optimized to the best extent possible at the time, the collaboration hopes to use more advanced computing power to better optimize the next generation. Thus far, all the results from the theoretical side have been borne out by data from the W7-X.

“These experiments make me excited,” Pedersen says. “The optimization that was done two decades ago with computers we can laugh about today in terms of computational power works; we can do so much more now.”

**The hub of an international community**

The collaboration’s shared postdocs are also in on the fun. These eight people embody one of the unusual hallmarks of the project: encouraging travel between multiple institutions, ferrying knowledge and achieving collaboration between departments.

“What I really like about being a shared postdoc is not working by yourself in an office. You really can talk to people and do a lot of interesting problems,” says postdoc Silke Glas, who travels between Cornell University and New York University. “I enjoy the variety I have, and I think it’s a win for the collaboration as well.”

These postdocs help nail down jargon between different fields, a role also played by the biweekly video chats between the theoretical and experimental collaboration members.

“Another challenge of the interdisciplinary nature of this work is trying to come up with concepts that are interesting to the people in both theoretical and experimental communities,” says Landreman. “One thing we’ve done a lot of this first year is define precisely stated mathematical problems that numerical optimization people can study that are interesting enough from a physics point of view, but don’t have all the complexities of physical experiments.”

Nowadays, nonmembers of the collaboration sit in on the biweekly “Simons Hour” as well. The international research community showed up in droves at the first annual meeting of the collaboration, which took place in late March at the Simons Foundation in New York City. Seventy-five researchers came from around the world for research updates from the collaboration and poster presentations from non-collaboration researchers.

“The general sense of enthusiasm about the hidden symmetries project is very high; I’m very gratified by it,” says Bhattacharjee. “I think what Simons did was support an idea which was very timely in which there were not enough resources invested, and in the process created something that was very much needed by the stellarator community.”

The collaboration also co-hosted a plasma physics summer school at the Princeton Plasma Physics Laboratory for 33 graduate students and postdocs with backgrounds in optimizing magnetic fields, who will hopefully join the community and continue contributing at the frontier of one of the world’s foremost science problems.

“You have here a marriage of fundamental science, wonderful mathematics and physics, dedicated to an engineering cause of great importance,” Bhattacharjee says.