Principal Research Physicist Stephen Jardin recalls walking down the hall in the Theory Wing of the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL) in the 1970s and seeing legendary physicists Katherine Weimer, John Greene and John Johnson working together at a blackboard. One of the physicists would write calculations while the other two would watch for errors. 

“I would just walk down the hall looking at the names of the offices, and they were all legendary theorists who had made big contributions from the beginning,” Jardin recalls. 

PPPL’s Theory Department has counted famous plasma physicists in its ranks from the founding of the Laboratory, starting with famed physicist Lyman Spitzer, who began the Laboratory as a secret government project, “Project Matterhorn,” in 1951. Spitzer initially hired a staff of just four theorists, who became pioneers of theoretical plasma physics. They worked out complex equations with pencil and paper to develop foundational principles of plasma physics that are still taught today as the world edges closer to developing fusion energy as a safe, clean and virtually limitless energy source.

“The Lab was founded by a theoretician, and throughout its history, theorists have played a crucial role by contributing to the physics in our fusion energy program,” said Steve Cowley, current Lab director, who was a theorist at PPPL early in his career. “It has had and will continue to have an integral part in the evolution of plasma physics from a descriptive science to a predictive science. That’s a huge paradigm shift.”
 

A 70-year history 

Now, the Theory Department boasts more than 20 scientists, and the Computational Sciences Department, which recently grew out of the Theory Department, has a comparable size, with some researchers having joint appointments. The tools of PPPL’s theorists have evolved over its 70-year history from pencil and paper to computers and then to supercomputers and artificial intelligence (AI) as the theorists have moved from foundational plasma physics to employing complex computer codes, AI tools and supercomputers to answer complex plasma physics questions.

PPPL’s theoretical researchers have moved out of the aging Theory Wing, home to countless stars in plasma physics in the building’s 50-year history and will welcome a new era when they move into the Princeton Plasma Innovation Center, which breaks ground in May. 

Felix Parra-Diaz, the head of the department, said these are exciting times for theoreticians. President Biden’s “Bold Decadal Vision for Commercial Fusion Energy” has laid out a path for the commercial development of fusion energy, and numerous private companies are working to put fusion energy on the grid. “We’re at a time when fusion theory is going to be crucial because we’re trying to accelerate fusion development,” he said. “When fusion companies build something, they need to know it’s going to work. Our theoretical models will help fusion power plants’ builders decide what they should or shouldn’t do.”

Laying a foundation 

The top secret Project Matterhorn began constructing the Model A stellarator in 1951, the first fusion device of its kind, to test out Spitzer’s invention of the figure-eight stellarator. Experiments began in 1953. A year later, Russell Kulsrud was offered a job, and he accepted, even though he didn’t know what the project was about. After getting a security clearance, Kulsrud recalled Spitzer taking him to the Project Matterhorn campus and telling him about his stellarator and fusion energy research. “I was extremely excited because I knew it would be such an exciting future for humanity if we could get controlled fusion,” he recalled later. 

Kulsrud became part of a team of theorists, along with physicists Edward Frieman, Martin Kruskal and Ira Bernstein, who used complex calculations to develop a foundational “energy principle” that uses magnetohydrodynamics to calculate the requirements for plasma equilibrium and the use of energy conservation to predict plasma stability. 

As a secret project, “we couldn’t go to public meetings. We couldn’t publish. All we could do was calculate,” Kulsrud recalled. Instead, they would present to each other and be subject to a rigorous and sometimes heated examination of their work. 

Kulsrud, Frieman, Kruskal and Bernstein wrote several papers on the energy principle. In 1958, Project Matterhorn was declassified, and PPPL scientists attended the second United Nations’ International Conference on the Peaceful Uses of Atomic Energy, better known as the Atoms for Peace Conference, with scientists from Russia and elsewhere to share their fusion energy research. The energy principle was presented at the conference, where PPPL also displayed a working model stellarator.

Another of the Project Matterhorn theorists was John Dawson, who realized the value of simulations to test theories and large construction plans in the late 1950s. Dawson did seminal work on plasma waves and became head of theory in the 1960s. Later, he worked on plasma-based particle accelerators at the University of California.  

The 1950s also saw the beginning of the Princeton Program in Plasma Physics, with the first students graduating in 1959. 

The Tokamak Fusion Test Reactor 

In the 1960s, Project Matterhorn was renamed the Princeton Plasma Physics Laboratory. The Model C stellarator began operating in 1962, replacing the figure-8 stellarators of the 1950s. By the late 1960s, Russia announced a breakthrough in performance in a donut-shaped fusion device called a “tokamak” that they had invented in the 1950s. PPPL constructed a series of tokamaks during the 1970s, including the Symmetric Tokamak (ST), the Adiabatic Toroidal Compressor (ATC), the Princeton Large Torus (PLT) and the Poloidal Divertor Experiment (PDX), culminating with the Tokamak Fusion Test Reactor (TFTR), which operated from 1982 to 1997. It was the first in the world to use a 50/50 mixture of deuterium and tritium, yielding an unprecedented 10.7 million watts of fusion power and making headlines worldwide. 

One of the major accomplishments in the Theory Department in the 1980s and 90s was the development of nonlinear gyrokinetic equations by Ed Frieman, Liu Chen and others, along with the first computer simulations of these equations by Wei-li Lee and others. These sophisticated equations allowed computer simulations to be up to a billion times faster while still accurately treating small-scale turbulence that affects a fusion reactor.  

The TFTR used an operating regime called “supershots,” and a key question was why supershots were so super. Building on the work of Frieman, Chen and others, Greg Hammett, Bill Dorland, Mike Kotschenreuther (University of Texas) and others developed gyrofluid codes (and eventually full gyrokinetic codes) that could explain the improved performance in TFTR. “It came from a positive feedback that reduced the turbulence,” Hammett said. “That also helped us understand why other tokamaks could find improved operating regimes by increasing the edge temperature.” 

There were close ties between the Theory Department and the famous physicist Marshall Rosenbluth when he was at the Institute for Advanced Study from 1967 to 1982. Rosenbluth worked with many young scientists on plasma theory, including Jim Van Dam, who later became head of Fusion Energy Sciences at the DOE. Roscoe White also worked with Rosenbluth before coming to PPPL in 1974.

White remembers the excitement of those days. “If you understand how the instabilities work, you can design the device so you can avoid them, and that’s what’s been going on for almost 50 years,” he said. “So now, we’re pretty close, but it’s still not obvious we can do it. It’s hard. It’s a lot harder than sending someone to the moon.” 

White retired in 2021 after a 47-year career in which he made numerous contributions to magnetohydrodynamic research. He developed the ORBIT code, now used in many fusion research laboratories to improve confinement. White wrote a textbook on plasma theory and another on mathematics, and he served as chair of the Theory Department from 1986 to 1993. “If we manage to get fusion to an energy source that does not produce CO₂, it means the end of global warming plus an inexhaustible source of energy,” he said.
 

Entering the age of computers

When Jardin came to the Theory Department as a graduate student in 1973, computers were just starting to appear. PPPL researchers had access to a computer at Princeton University and could sign out a calculator, but most still used pencil and paper and slide rules. “Computers changed almost everything because now we can actually solve those equations on the computer,” Jardin said. “We can predict what’s going to happen inside the tokamak, how the plasma is going to behave, if instabilities will develop and how the transport works.” 

In the 1980s, research by Allen Boozer, a Columbia University professor who conducted research at PPPL, laid the foundation for many theoretical concepts regarding stellarators, the twisty-coiled fusion devices originated by Spitzer. Boozer developed the idea of quasisymmetry, a hidden symmetry within stellarators that leads to good plasma confinement. Researchers at PPPL have recently built MUSE, a stellarator that uses permanent magnets and builds on Boozer’s theory.
 

Developing computer modeling 

By the 1990s, computers were being used to solve complex problems that paper and pencil could not, and many theoretical physicists at PPPL were working on computers. Many were focusing on complex computer codes that would be used to analyze and predict plasma behavior. “Pencils and paper were good for fundamental theories, but to predict what you really want to see happen in realistic problems, you need codes,” said Choongseock (CS) Chang, who came to PPPL as a visiting scientist in the 1980s and became a Theory Department member in 2011. He noted that PPPL’s theory staff, including Wei-li Lee, helped develop gyrokinetic codes. “The gyrokinetic particle code approach was invented here,” Chang said. “This is the mecca of gyrokinetic particle code development.”
 

Exascale computing 

Chang was one of the pioneers working on giant supercomputers from the first such computer at the National Magnetic Fusion Energy Computer Center. He worked for over two decades on giant supercomputers and later exascale computers, which are so powerful they are the equivalent of a billion laptops, according to Chang. Some of that work was dedicated to solving some of the challenges faced by the international ITER experiment, which is being built in southern France. 

In 1997, PPPL began constructing the National Spherical Torus Experiment (NSTX), which was designed to test whether a compact spherical tokamak could provide a model for future fusion power plants. That was the year Elena Belova, a physicist from Russia, came to the Laboratory as a postdoc after receiving her doctoral degree at Dartmouth College. She began working on simulation codes for field reversed configuration studies and modified the code to be used on NSTX and the National Spherical Torus Experiment-Upgrade (NSTX-U), which is currently being rebuilt. “A lot of it involves very large simulation codes,” Belova said. 

Belova has also researched experimental results at the DIII-D National Fusion Facility and, more recently, has worked with private fusion energy companies trying to develop commercial fusion energy through the DOE’s Innovation Network for Fusion Energy (INFUSE).
 

Looking to the future 

The Theory Department will be employing new tools like artificial intelligence for some of the calculations needed to optimize and control the plasma to produce fusion energy, Parra-Diaz said. For example, physicist Fatima Ebrahimi is working on a project that uses artificial intelligence known as machine learning to find the most effective ways to confine a plasma on a commercial-scale tokamak without instabilities at the plasma’s edge. Running a highly detailed simulation on supercomputers should allow the researchers to hypothesize about scenarios beyond those covered by the data. Ultimately, this could provide valuable insights into the best ways to keep plasma stable in a commercial-scale fusion vessel.

In addition to devising new ways to model fusion energy, theorists at PPPL are also branching out into new areas like microelectronics and continuing to explore astrophysics and basic science research. As Parra-Diaz put it, “It’s going to be a very interesting next decade for theory.” 

Greg Hammett and Rachel Kremen contributed to this story.