☀️Nuclear Fusion Simulator - Reactivity, Lawson Criterion, Tokamak, ICF

How to use Nuclear fusion & tokamaks

1. 1In Reactions, tick reactions and drag the temperature to compare ⟨σv⟩ and power density
2. 2In Coulomb barrier, pick a reaction and temperature to see the barrier height, Gamow peak and tunnelling probability
3. 3In Lawson criterion, set density, temperature and confinement time, or click on the chart, to see how far you are from ignition
4. 4Play the Tokamak and Inertial confinement animations, adjust the safety factor and field, and get β and target gain
5. 5In Energy & gain, compare fuel energy densities and use the ITER and NIF presets to compare Q_sci and Q_eng

FAQ

Why does fusion need about 100 million kelvin rather than billions?

Deuterium and tritium nuclei are both positive and must get within about 4 fm before the strong force takes over, so they face a Coulomb barrier of roughly 400 keV, which classically means billions of kelvin. Quantum tunnelling lets nuclei below the barrier through with probability about exp(−√(E_G/E)), while the number of fast particles falls off as exp(−E/kT). The product is the Gamow peak: at 10 keV (about 116 million K) most D-T fusion happens near 30 keV. That is why 100–200 million K is enough.

What do the Lawson criterion and the triple product mean?

For a plasma to keep burning, alpha-particle heating (1/5 of the D-T energy) must replace what is lost by conduction and radiation. As a power balance, 3nkT/τ_E + C_B n²√T = (n²/4)⟨σv⟩E_α, which rearranges into a requirement on n·T·τ_E. For D-T the minimum is at T ≈ 14 keV, nTτ_E ≈ 3×10²¹ keV·s·m⁻³. The tool also draws curves for Q = 1, 5 and 10, where Q is fusion power over external heating power; ignition is Q = ∞.

Why does a tokamak need both a toroidal and a poloidal field?

Charged particles spiral along field lines and barely move across them, but a purely toroidal field is stronger on the inside than the outside. That makes ions drift one way vertically and electrons the other, and the resulting electric field pushes the whole plasma outward. The poloidal field from the plasma current twists the field lines into helices so particles alternate between top and bottom and the drifts cancel. The safety factor q is how many toroidal turns a field line makes per poloidal turn; edge q above 2–3 is needed to avoid instabilities.

NIF has achieved ignition, so why is fusion power still far away?

In December 2022 NIF fired 2.05 MJ of laser light at a target and got 3.15 MJ of fusion energy, a target gain of about 1.5, which counts as scientific ignition. But the lasers drew about 300 MJ from the grid, a wall-plug efficiency below 1%, and with about 40% thermal-to-electric conversion the engineering gain is only around 0.01. A power plant needs efficient drivers, several shots per second and targets with Q_sci of tens or more.

How accurate are the numbers?

D-T, D-D and D-³He reactivities use the Bosch–Hale 1992 fit, accurate to about 0.3% between 0.2 and 100 keV. p-¹¹B comes from a simplified S-factor integral and is order-of-magnitude only. The Lawson curves are a zero-dimensional model without temperature and density profiles or impurities, so the 0-D Q estimate for ITER comes out high. Device points, tokamak β and implosion parameters are approximate public values: good for learning and comparison, not for design work.