Physicists at PPPL in the US use calculations to show that a plasma heated first and then made denser reaches ignition with much less energy.
The model extends the more than 70-year-old Lawson criterion with helium ash, impurities from the walls, synchrotron radiation, and heat losses.
One tungsten atom per 10,000 particles can double the pressure required, and liquid lithium on the walls can keep the metal out.
For more than 70 years, fusion researchers have used one and the same equation to judge whether a plasma can get hot enough and dense enough, for long enough, to sustain itself. That point is called ignition. At that point, the plasma no longer needs heat from outside. The equation is called the Lawson criterion and was developed in the 1950s. It shows where the finish line is, but not how best to get there.
Now three physicists at PPPL, the Princeton Plasma Physics Laboratory in the US, have drawn a map of the route. Luis Delgado-Aparicio, Masayuki Ono, and Jonathan Menard have published the work in the journal Physical Review Letters. It could affect how tokamaks and stellarators are designed and built. A tokamak is a doughnut-shaped machine that holds the plasma in place with magnetic fields.
Around the mountain instead of over it
Delgado-Aparicio compares the energy required to a landscape. Ignition lies behind a high mountain peak. Many fusion projects climb straight up. They first make the plasma denser and then add heat.
The new map shows that it is possible to go around the mountain instead. You heat the plasma first and raise the density once it is already hot. According to Delgado-Aparicio, many companies try to go straight over the peak and spend enormous amounts of energy doing so. Going around the mountain, you reach the same place with much less energy.
Five times more power out than in
Mathematically, the easier route passes through what is called the Cordey saddle. It is the lowest point on a ridge that separates plasma that needs outside heating from plasma that burns on its own.
The researchers use a measure called Q. It is the ratio of the power that fusion produces to the heating power supplied. In an ideal plasma of pure fuel, the saddle sits where fusion produces about five times more power than the heating supplied. Impurities and very strong magnetic fields move the saddle and raise the Q value required.
The work is based on calculations, not measurements. No experiment today reaches the temperatures where the saddle sits. The researchers therefore plan digital experiments to test the route.
Four effects in one model
The researchers have extended the Lawson criterion with four effects. Until now, they have been studied one at a time. Now they are in the same model. The first is helium ash, that is, spent fuel that builds up and dilutes the plasma. The second is light and heavy impurities from the reactor's inner walls. The third is synchrotron radiation, energy that negatively charged particles lose as they travel. The fourth is heat that leaks out of the plasma and that increases with temperature.
According to Ono, a design looks like it will work when these effects are left out. When they are included, the picture changes. The goal is a common and more realistic model for assessing designs before they are built. Experiments are expensive, and mistakes should be caught in advance.
Small amounts of tungsten matter
More than a dozen next-generation fusion machines plan to have inner walls made of tungsten, because the metal can withstand extreme heat. The plasma must get hotter than the core of the sun.
Tungsten is already used in today's experimental reactors. In the French reactor WEST, which has tungsten in the part that removes heat and particles, researchers kept a plasma stable for just over 22 minutes. We have written about that world record before.
The calculations show that one tungsten atom per 10,000 particles in the plasma can roughly double the pressure required for ignition. That applies to a two-dimensional analysis. In three dimensions, the required pressure can rise past the limit at which the plasma is stable.
The researchers point to two ways to make the route easier. Walls covered with liquid lithium, which PPPL has researched for several years, can stop tungsten from entering the plasma. The lithium also helps the plasma hold on to its heat. Spin-polarized fuel, where the fuel's atomic nuclei are aligned in the same direction before they fuse, increases the rate of fusion reactions.
The losses keep the plasma stable
Designers have long worried about thermal runaway. That is when heat from fusion drives more fusion, which in turn produces even more heat. The researchers found that the same losses that make ignition harder also counteract that cycle. Together, they can keep a burning plasma stable on their own.
A fusion plant holds only a few seconds' worth of fuel at a time. If control is lost, the plasma cools and the fusion stops.
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