A New Approach to the Lawson Criterion

For more than 70 years, fusion researchers have relied on the Lawson criterion to determine whether plasma can maintain enough temperature and density for long enough to sustain fusion without additional external heating. However, the equation does not explain which sequence of steps is most efficient for reaching those conditions.

PPPL physicists Luis Delgado-Aparicio, Masayuki Ono, and Jonathan Menard have developed a more comprehensive version of the criterion. By incorporating four additional factors that influence fusion performance, they mapped a possible route to ignition that could require significantly less energy than alternative approaches.

Their findings were published in Physical Review Letters.

The research focuses on plasma, often called the fourth state of matter. Plasma forms when a gas becomes so energetic that its particles become electrically charged. In a fusion reactor, this extremely hot material contains atomic nuclei that researchers hope to combine and use to release energy through nuclear fusion.

The ultimate goal is to create a combustion plasma, in which the fusion reaction generates enough heat to sustain itself without continuous external heating. Reaching this state efficiently remains one of the most important challenges in fusion energy research.

Heating Plasma Before Compression Could Save Energy

Delgado-Aparicio compares the discovery to finding a more efficient route through a mountain range.

Imagine that the energy required to ignite nuclear fusion creates a landscape filled with towering mountains. The destination is on the other side, but several routes can lead there.

Many proposed fusion strategies attempt to go directly over the mountain. These approaches first increase the plasma’s density and then provide the enormous amount of heat needed to reach ignition.

New calculations suggest that a different sequence could be considerably more efficient. Instead of increasing density first, researchers could heat the plasma before increasing its density. This alternative route may avoid the highest energy requirements while still achieving the conditions needed for fusion.

“A lot of companies want to climb the mountain headfirst and expend a tremendous amount of energy to get there. Go around the peak instead. You’ll get to the same place in a much smarter way, and you’ll use much less energy.”

— Luis Delgado-Aparicio

The “Cody Saddle” Could Offer a Lower-Energy Route

The researchers identified a particularly important region within this mathematical landscape called the Cody saddle.

In geography, a saddle is a low passage between higher elevations. In fusion physics, the Cody saddle represents a relatively accessible point along the boundary separating plasmas that still require external heating from those capable of sustaining their own fusion reactions.

To evaluate different pathways, the scientists used a measurement called Q. This value compares the power produced by the fusion reaction with the external heating power supplied to the plasma.

For example, a Q value of 5 means that the fusion reaction produces five times more power than the external heating system provides.

In an ideal plasma containing only pure fusion fuel, the Cody saddle occurs at approximately Q = 5. Real fusion systems, however, are more complex. Contaminants and very strong magnetic fields can shift the location of this pathway and increase the Q factor required to reach it.

Understanding how these conditions vary is essential for determining whether a proposed fusion reactor can realistically achieve ignition.

Four Factors That Can Change Fusion Ignition Requirements

One of the study’s key advances is that it evaluates several important physical processes together rather than examining them individually, as many previous studies have done.

The researchers incorporated four additional factors that can influence whether plasma reaches and sustains ignition:

1. Helium ash buildup: Fusion reactions produce helium as a byproduct. As this spent fuel accumulates, it can dilute the remaining fusion fuel and reduce performance.
2. Plasma contamination: Light and heavy impurities can enter the plasma from the materials lining the reactor and interfere with fusion conditions.
3. Synchrotron radiation: Electrons moving through a magnetic field emit radiation and carry energy away from the plasma.
4. Heat losses: Energy continually escapes from the plasma, and these losses can increase as temperature rises.

Including these effects provides a more realistic picture of the conditions future fusion reactors must achieve.

“I would say the design works well if you omit these effects. If you include them, the image will change and it will be quite important.”

— Masayuki Ono

The goal is to establish a more reliable and widely applicable model that scientists can use to evaluate fusion reactor designs before construction begins.

Treating the Lawson criterion as a single, unchanging threshold overlooks physical processes that can significantly alter ignition requirements. Incorporating these effects early in the design process could help prevent costly problems later.

“Fusion experiments cost a lot of money, and we don’t want to make mistakes that we could have discovered in advance.”

— Masayuki Ono

Small Amounts of Tungsten Could Make Fusion More Difficult

One particularly striking finding concerns tungsten, an extremely heat-resistant metal chosen for the inner walls of more than a dozen next-generation fusion machines.

Tungsten is attractive because fusion reactors must withstand plasma temperatures higher than those at the center of the Sun. However, the metal can cause serious problems if it enters the plasma, even in minute amounts.

The researchers calculated that tungsten contamination at a concentration of 1:10,000 could roughly double the pressure required to ignite fusion.

This represents a major increase caused by an exceptionally small amount of material.

The calculation was initially developed in two dimensions. When the researchers extended their analysis to three dimensions, they found that the pressure required for ignition could exceed the limit at which the plasma remains stable.

The result suggests that seemingly minor contamination can have a major impact on the feasibility of a particular fusion reactor design.

Energy Losses Could Also Help Stabilize Fusion

Some processes that make ignition more difficult may also help fusion reactors operate more safely and consistently.

Scientists have studied the possibility of thermal “runaway” instability for many years. This occurs when heat from the fusion reaction increases the reaction rate, generating even more heat and potentially creating a self-reinforcing cycle.

Researchers have found that energy loss within the plasma can naturally counteract this effect.

Although these losses make ignition more difficult, they can also provide a balancing influence that allows a burning plasma to maintain stable operating conditions without continuous adjustment.

This balance could be useful in future reactor designs. Unlike fission power plants, fusion systems can hold fuel for only a few seconds at a time. If control is lost, the plasma cools and the fusion reaction stops.

Liquid Lithium and Advanced Fuels Could Improve Fusion Performance

The study also identifies technologies that could help overcome some of the obstacles revealed by the calculations.

One possibility is coating the inside of a fusion reactor with liquid lithium, a technology PPPL researchers have studied for many years.

These coatings could prevent tungsten from entering the plasma while reducing heat loss, making it easier to maintain the extreme conditions needed for fusion.

Another promising approach uses spin-polarized fuels. This involves preparing atomic nuclei so that their spins align before fusion occurs, which can increase the fusion reaction rate.

Combining these strategies could improve the performance of future fusion reactors and make the path to ignition more achievable.

What Happens Next?

Despite the promising findings, the proposed heat-first approach has not yet been experimentally demonstrated.

The study is theoretical and based on mathematical calculations rather than direct measurements. Existing fusion experiments have not reached the temperatures associated with the Cody saddle, so scientists cannot yet test the predicted route under those conditions.

The PPPL team plans to investigate the approach further through digital experiments and computer-based simulations. These studies will examine whether heating plasma before increasing its density provides the expected benefits.

If future research confirms the calculations, the findings could provide an important foundation for designing more efficient fusion systems and help researchers make better decisions before building future fusion reactors.

“Although further research is needed, we are excited about these results, and they suggest a clear path forward for future research in this area.”

— Jonathan Menard

This research was supported by the DOE Office of Science, Office of Fusion Energy Sciences under contract DE-AC02-09CH11466. Additional support was provided through the 2015 Fusion Energy Science Early Career Award, the 2018 Diagnostic Innovation and Development Award, and the 2021 and 2025 Long Pulse Tokamak Research Programs.