Illustration of cloud-like ionized plasma in the ITER tokamak fusion reactor. credit: ITER

Physicists at EPFL, in a major European collaboration, have revised one of the fundamental laws that has been established[{” attribute=””>plasma and fusion research for over three decades, even governing the design of megaprojects like ITER. The update demonstrates that we can actually safely utilize more hydrogen fuel in fusion reactors, and therefore obtain more energy than previously thought.

Fusion is one of the most promising future energy sources . It involves two atomic nuclei merging into one, thereby releasing enormous amounts of energy. In fact, we experience fusion every day: the Sun’s warmth comes from hydrogen nuclei fusing into heavier helium atoms.

There is currently an international fusion research megaproject called ITER that seeks to replicate the fusion processes of the Sun to create energy on the Earth. Its goal is to generate high-temperature plasma that provides the right environment for fusion to occur, producing energy.

Plasmas — an ionized state of matter similar to a gas – are made up of positively charged nuclei and negatively charged electrons, and are almost a million times less dense than the air we breathe. Plasmas are created by subjecting “the fusion fuel” – hydrogen atoms – to extremely high temperatures (10 times that of the core of the Sun), forcing electrons to separate from their atomic nuclei. In a fusion reactor, the process takes place inside a donut-shaped (“toroidal”) structure called a “tokamak.”

The tokamak thermonuclear fusion reactor at Swiss Plasma Center. Credit: Alain Herzog (EPFL)

“In order to create plasma for fusion, you have to consider three things: high temperature, high density of hydrogen fuel, and good confinement,” says Paolo Ricci at the Swiss Plasma Center, one of the world’s leading research institutes in fusion located at École polytechnique fédérale de Lausanne (EPFL).

Working within a large European collaboration, Ricci’s team has now released a study updating a foundational principle of plasma generation – and showing that the upcoming ITER tokamak can actually operate with twice the amount of hydrogen and therefore generate more fusion energy than previously thought.

“One of the limitations in making plasma inside a tokamak is the amount of hydrogen fuel you can inject into it,” says Ricci. “Since the early days of fusion, we’ve known that if you try to increase the fuel density, at some point there would be what we call a ‘disruption’ – basically you totally lose the confinement, and plasma goes wherever. So in the eighties, people were trying to come up with some kind of law that could predict the maximum density of hydrogen that you can put inside a tokamak.”

The answer came in 1988, when fusion scientist Martin Greenwald published a famous law relating fuel density to the small tokamak radius (the radius of the inner circle of a donut) and the current flowing in the plasma inside the tokamak. Since then, the “Greenwald limit” has become a central tenet of fusion research. In fact, ITER’s strategy for building the tokamak is based on this.

Ritchie explains: “Greenwald derives the law empirically, and this is entirely from empirical data—not a tested theory, or what we call ‘first principles.'” However, the limit worked well in the research. And in some cases, like DEMO (the successor to ITER), this equation is a big limit to its operation because it says you can’t increase the density of the fuel above a certain level.”

Working with the tokamak teams, the Swiss Plasma Center designed an experiment where highly advanced technology could be used to precisely control the amount of fuel injected into the tokamak. The massive trials were conducted at the world’s largest tokamak, the Joint European Tokamak (JET) in the UK, as well as the ASDEX upgrade in Germany (Max Planck Institute) and EPFL’s TCV tokamak. This major experimental effort was made possible by the EUROfusion Consortium, the European organization coordinating fusion research in Europe and in which EPFL is now involved through the Max Planck Institute for Plasma Physics in Germany.

At the same time, Maurizio Giacomene, a doctoral student in Ricci’s group, began analyzing the physical processes that limit tokamak density, in order to derive a law of elementary principles that could relate fuel density to tokamak volume. Part of that involves using an advanced simulation of plasma using a computer model.

“The simulations take advantage of some of the largest computers in the world, such as those made possible by CSCS, the Swiss National Center for Supercomputing, and EUROfusion,” says Ritchie. “And what we found, from our simulations, is that as you add more fuel to the plasma, parts of it travel from the tokamak’s outer cold layer, the boundary, to its core, because the plasma becomes more turbulent. Then, unlike the copper electric wires, Which becomes more resistant when heated, plasma becomes more resistant when it cools. So the more fuel you put in it at the same temperature, parts of it cool down — and the harder it is for current to flow in the plasma, which can lead to turbulence.”

This was a challenge to simulate. “Turbulence in a fluid is actually the most important open issue in classical physics,” Ritchie says. “But turbulence in plasma is more complex because you also have electromagnetic fields.”

In the end, Ritchie and his colleagues were able to decipher the code and put “pen on paper” to derive a new equation for the maximum fuel limit at the tokamak, which aligns well with the experiments. Published in the magazine Physical Review Letters On May 6, 2022, it does justice to the Greenwald border, by getting close to it, but it modernizes it in important ways.

The new equation assumes that the Greenwald limit can be raised approximately twice in terms of fuel at ITER; This means that tokamaks like ITER can actually use twice as much fuel to produce plasma without worrying about turbulence. “This is important because it shows that the intensity you can achieve in a tokamak increases with the power you need to run it,” Ritchie says. “In fact, DEMO will operate at much higher power than current tokamaks and ITER, which means you can add more fuel density without reducing the output, unlike Greenwald’s Law. And this is very good news.”

Reference: “First principles tokamak density limit meter based on turbulent edge transport and its reflections on ITER” By M. Giacomin, A. Pau, P. Ricci, O. Sauter, T. Eich, ASDEX Upgrade Team, JET Shareholders, and TCV Team , May 6, 2022, Physical Review Letters.
DOI: 10.1103/ PhysRevLett.128.185003

List of contributors

• Swiss Plasma Center EPFL
• Max Planck Institute for Plasma Physics
• EPFL TCV Team
• ASDEX Upgrade Team
• Contributors to JET

Funding: EUROfusion (Euratom Research and Training Programme), Swiss National Science Foundation (SNSF)