A tokamak (from the Russian "toroidal'naya kamera s magnitnymi katushkami") confines hot plasma in a doughnut-shaped (toroidal) vessel using a combination of toroidal and poloidal magnetic fields. The resulting helical field lines wind around the torus in nested flux surfaces, preventing particles from drifting outwards. This design, developed in the USSR in the 1950s–1960s, is the leading approach to achieving controlled thermonuclear fusion, with ITER (under construction in France) targeting a Q = 10 fusion energy gain.
This simulation visualises helical magnetic field lines formed by the superposition of toroidal and poloidal field components, key particle drift motions (gradient drift, curvature drift), and the concept of the safety factor q—the number of toroidal turns a field line makes for each poloidal turn. Irrational q values are required for MHD stability and to avoid resonant surfaces that can trigger instabilities.
What is a tokamak and how does magnetic confinement work?
A tokamak uses a powerful toroidal magnetic field (5–12 T in modern devices) produced by superconducting coils, plus a poloidal field from a toroidal plasma current induced by a central solenoid. The combined field lines spiral helically around the torus, keeping the plasma away from the vessel walls. ITER will have a plasma volume of 840 m³ and aims to produce 500 MW of fusion power from 50 MW of heating input.
What is the safety factor q and why must it be irrational?
The safety factor q = r Bt/(R Bp) measures how many times a field line winds toroidally for each poloidal circuit. Rational q values (e.g., q = 2, 3/2) mean field lines close on themselves after a finite number of circuits, allowing resonant MHD instabilities (tearing modes) to grow at those flux surfaces. Irrational q values cause field lines to ergodically cover the entire flux surface, preventing resonant mode growth and improving plasma stability.
What fusion reaction does a tokamak aim to sustain?
The primary reaction is D + T → ⁴He (3.5 MeV) + n (14.1 MeV), where D is deuterium and T is tritium (isotopes of hydrogen). The neutron carries 80% of the energy and will be absorbed in a lithium blanket to breed more tritium and generate heat. At 150 million kelvin (10 times hotter than the Sun's core), deuterium and tritium nuclei overcome the Coulomb barrier and fuse. Lawson's criterion requires nτE T > 3 × 10²¹ m⁻³·s·keV for ignition.
Even in a perfectly toroidal field, charged particles experience gradient drift (vG ∝ ∇B × B/B²) and curvature drift (vC ∝ Rc × B/B²), both perpendicular to the field and to the gradient/curvature direction. These drifts are in opposite directions for ions and electrons, creating a charge separation that would cause the plasma to drift outward if not countered by the poloidal field. The helical winding of field lines averages out these drifts, enabling confinement.
Beta (β) is the ratio of plasma pressure to magnetic pressure: β = 2μ₀nkBT/B². It measures how efficiently the magnetic field confines the plasma. High β means more fusion power per unit of magnetic field energy. Typical tokamaks operate at β ≈ 1–5%. Exceeding the Troyon limit (βmax ≈ 3.5 I/(aB) in practical units) triggers ballooning and kink instabilities that disrupt the plasma.
Edge-localised modes (ELMs) are periodic instabilities at the plasma edge that periodically expel bursts of energy and particles. In ITER-scale devices, large ELMs could deposit 10–20 MJ on the divertor in 0.1–1 ms, potentially damaging the plasma-facing components. Disruptions are sudden, complete losses of plasma confinement releasing stored energy (up to 400 MJ in ITER) in milliseconds. Mitigation strategies include shattered pellet injection and killer-gas injection.
Fusion reactions require plasma temperatures of 100–200 million K (10–20 keV). Heating methods include ohmic heating (the plasma acts as a resistor, but its resistance falls with T, limiting this to ∼20 MK), neutral beam injection (NBI: fast neutral atoms injected at 80–1000 keV), and radiofrequency heating at ion cyclotron (ICRH) or electron cyclotron (ECRH) frequencies. ITER will use 73 MW of combined NBI and RF heating.
Superconducting magnets carry current with zero electrical resistance below a critical temperature. ITER uses Nb3Sn conductors cooled to 4 K (−269°C), carrying 68,000 A to produce 11.8 T fields. Compared to conventional copper magnets, superconducting magnets consume no ohmic power in the coils themselves, making large steady-state magnetic fields economically feasible. The entire ITER magnet system stores 51 GJ of magnetic energy.
A tokamak requires a toroidal plasma current (typically induced by transformer action) to generate its poloidal field, creating disruption risk. A stellarator uses specially shaped helical coils to produce both toroidal and poloidal fields externally, with no net plasma current and therefore no disruptions. The Wendelstein 7-X stellarator in Germany is the world's largest; its complex coil geometry is optimised computationally to minimise particle drifts and turbulence.
ITER (International Thermonuclear Experimental Reactor) is a 23,000-tonne, 840 m³ tokamak being built in Cadarache, France by 35 nations. It is designed to produce 500 MW of fusion power from 50 MW of input—a Q = 10 gain—in plasma pulses of 300–500 seconds. First plasma is expected around 2025–2027; deuterium-tritium fusion experiments are planned for the mid-2030s. ITER is an experiment, not a power plant; the follow-on DEMO project aims to demonstrate commercial fusion electricity.