How Does a Tokamak Work? Fusion in a Magnetic Bottle

The Sun makes its energy by fusing light nuclei together. Doing the same on Earth means heating fuel to temperatures far above anything a solid container could survive, and then holding it in place. A tokamak is the most developed answer: a doughnut-shaped machine that holds a superhot gas with magnetic fields, so it never touches the walls. Our Tokamak hoodie, with the slogan “Nested, Never Touching”, draws those magnetic layers. This post extends our explainer What Holds the Nucleus Together? and our earlier How Does the Sun Actually Work?

What reaction does a fusion reactor use?

Most tokamaks plan to fuse deuterium and tritium, two heavy forms of hydrogen. OpenStax University Physics gives the reaction as

²H + ³H → ⁴He + n + 17.6 MeV

where ²H is deuterium (one proton, one neutron), ³H is tritium (one proton, two neutrons), ⁴He is a helium-4 nucleus, n is a free neutron and 17.6 MeV (mega-electronvolts) is the energy released per reaction (OpenStax University Physics, §10.6^[1]). Sharing that energy so that momentum is conserved gives the neutron about 14.1 MeV and the helium nucleus about 3.5 MeV (our calculation, from the 4:1 mass ratio). The strong nuclear force that makes this happen is the domain of our character Corekeeper, on the Corekeeper tee.

The obstacle is electric repulsion. Both nuclei are positively charged, so they push each other away. They only get close enough for the strong force to act if they hit each other very fast, which means very hot fuel.

How hot does a tokamak have to be?

Hotter than the Sun. NASA puts the temperature of the Sun’s core at about 15 million °C (NASA^[2]). ITER, the international tokamak being built in France, says that to achieve fusion its plasma must reach 150,000,000 °C, with auxiliary heating bringing it into the range of 150 to 300 million °C (ITER^[3]). The Sun gets away with a lower temperature because its enormous gravity holds a huge, dense ball of plasma together for billions of years. A tokamak has to make up for its far smaller, thinner plasma with higher temperatures.

At those temperatures the fuel is a plasma: electrons are stripped from their nuclei, leaving a gas of charged particles. That fourth state of matter is the subject of our Plasma Drift tee.

How does a tokamak hold the plasma?

Charged particles in a magnetic field spiral around the field lines instead of flying straight across them. So if you make field lines that close on themselves, the plasma follows them round and round. The word itself tells you the design. ITER explains that “tokamak” comes from a Russian phrase meaning “toroidal chamber with magnetic coils” (ITER^[3]).

The US Department of Energy describes the field in three parts (US DOE^[4]):

• One set of coils makes an intense toroidal field, running the long way around the doughnut.
• A central solenoid drives a current in the plasma, which makes a poloidal field running the short way around.
• Together they produce a twisted magnetic field that confines the particles. A third set of coils shapes and positions the plasma.

The twist matters. A purely toroidal field is stronger on the inside of the doughnut than the outside, which makes particles drift and escape. Twisting the field lines carries each particle alternately past the inside and outside, so the drifts largely cancel. The twisted field lines trace out a set of nested surfaces, like the layers of an onion bent into a ring, which is exactly what our hoodie shows.

Who invented the tokamak?

ITER’s glossary says the tokamak was invented in the 1950s by the Soviet physicists Igor Tamm and Andrei Sakharov (ITER glossary^[5]). The DOE adds that the first tokamak, T-1, began operation in Russia in 1958 (US DOE^[4]).

What is the Lawson criterion?

Being hot is not enough. The plasma must also be dense enough, and hold its heat long enough, for fusion to out-produce the losses. In 1957 John Lawson set out this balance for a power-producing reactor (Lawson, 1957^[6]). Today it is usually written as a “triple product” of density, temperature and confinement time. A review by Samuel Wurzel and Scott Hsu of the US Department of Energy gives the minimum for deuterium–tritium ignition as

n T τ_E ≥ 2.9 × 10²¹ keV·m⁻³·s

where n is the fuel ion density in particles per cubic metre, T is the temperature in kiloelectronvolts (1 keV ≈ 11.6 million kelvin), and τ_E is the energy confinement time in seconds, the time the plasma takes to lose its heat if heating stops (Wurzel & Hsu, 2022^[7]). Their table puts this minimum at a temperature of 14 keV, about 160 million kelvin (our conversion), and gives 4.6 × 10²⁰ for the lower goal of fuel gain Q = 1. They also note that below about 4.3 keV, radiation losses beat fusion heating and ignition is impossible.

Our worked example: at 14 keV with a fuel density of 1 × 10²⁰ particles per m³, ignition needs τ_E ≥ 2.9 × 10²¹ / (14 × 10²⁰) ≈ 2 seconds.

Where does fusion stand today?

The DOE notes that in the 1990s, TFTR in the US and JET in the UK set fusion records (US DOE^[4]). JET, operating since 1983, finished its final deuterium–tritium experiments with a record 69 megajoules of fusion energy, produced over 5 seconds from just 0.2 milligrams of fuel (UKAEA^[8]).

The first experiment to release more fusion energy than the energy delivered to its fuel did not use a tokamak. At the National Ignition Facility, which compresses fuel with lasers, an experiment on 5 December 2022 produced 3.15 MJ of fusion energy from 2.05 MJ of laser energy delivered to the target (LLNL^[9]). An earlier NIF shot produced 1.37 MJ from 1.92 MJ of laser energy; its peer-reviewed paper reports that it reached ignition by nine different formulations of Lawson-like criteria (Abu-Shawareb et al., 2022^[10]). Both figures compare fusion output with the laser energy delivered to the target, not with the electricity drawn by the whole facility, so a working fusion power plant is still an open goal. ITER is designed to take tokamaks the next step.

Quick FAQ

What does tokamak mean?

It comes from a Russian phrase meaning “toroidal chamber with magnetic coils”.

Why does the plasma not melt the walls?

The magnetic field keeps the hot charged particles spiralling along closed field lines, away from the walls.

Is a tokamak hotter than the Sun?

Yes. ITER’s plasma must reach 150 million °C, about ten times the Sun’s core temperature of 15 million °C.

Has fusion produced net energy?

NIF produced more fusion energy than the laser energy delivered to the target in 2022, but that gain is measured against laser energy on target, not the facility’s total electricity use. A fusion power plant remains an open goal.

References

1. S. J. Ling, J. Sanny & W. Moebs, University Physics Volume 3 (OpenStax, Rice University), §10.6 “Nuclear Fusion”. https://openstax.org/books/university-physics-volume-3/pages/10-6-nuclear-fusion
2. NASA Science, “Sun: Facts”. https://science.nasa.gov/sun/facts/
3. ITER Organization, “What is a tokamak?”. https://www.iter.org/machine/what-tokamak
4. U.S. Department of Energy Office of Science, “DOE Explains…Tokamaks”. https://www.energy.gov/science/doe-explainstokamaks
5. ITER Organization, “Fusion glossary” (entry: tokamak). https://www.iter.org/fusion-glossary
6. J. D. Lawson (1957), “Some Criteria for a Power Producing Thermonuclear Reactor,” Proc. Phys. Soc. B 70, 6–10 (DOI 10.1088/0370-1301/70/1/303; metadata verified via Crossref). https://doi.org/10.1088/0370-1301/70/1/303
7. S. E. Wurzel & S. C. Hsu (2022), “Progress toward fusion energy breakeven and gain as measured against the Lawson criterion,” Phys. Plasmas 29, 062103 (arXiv:2105.10954). https://arxiv.org/pdf/2105.10954
8. UK Atomic Energy Authority (2024), “Fusion research facility’s final tritium experiments yield new energy record”. https://www.ukaea.org/news/fusion-research-facility-jets-final-tritium-experiments-yield-new-energy-record/
9. Lawrence Livermore National Laboratory (13 December 2022), “Lawrence Livermore National Laboratory achieves fusion ignition”. https://www.llnl.gov/article/49301/lawrence-livermore-national-laboratory-achieves-fusion-ignition
10. H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration) (2022), “Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment,” Phys. Rev. Lett. 129, 075001. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.075001

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.