Fusion Energy Lab

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Fusion Energy Lab

How hot, dense and well-insulated must a deuterium-tritium plasma be to give out more energy than it takes in? Move temperature, density and confinement time, watch the fusion power, the gain Q and the ignition line react, then build a tokamak or fire an inertial-confinement capsule.

In the news: fusion has become a headline topic. A national laboratory reported fusion ignition in 2022 and has since repeated it, tokamaks and stellarators keep setting records for plasma duration and confinement, and a 2026 report suggested that the order in which plasma-heating methods are applied might heat the plasma more efficiently (reported, not modelled here; the heating-absorption slider only shows what better coupling would mean). Educational model, simplified 0-D physics.

Presets

Plasma

Live readouts

Graphs

Experiments

Pick an experiment: the simulation measures a result and compares it with the analytic estimate.

The science

D-T fusion. D + T -> He-4 (3.5 MeV) + n (14.1 MeV), Q-value 17.6 MeV. The alpha particle stays in the plasma and heats it; the neutron escapes and carries 4/5 of the energy, so the alpha heating is P_alpha = P_fus/5.

Reactivity (Bosch-Hale, 1992, Nucl. Fusion 32, 611). For a Maxwellian plasma <sigma v> = C1 θ sqrt(ξ / (m_r c^2 T^3)) exp(-3 ξ) with θ = T / (1 - T(C2 + T(C4 + T C6)) / (1 + T(C3 + T(C5 + T C7)))) and ξ = (B_G^2 / 4θ)^(1/3), B_G = 34.3827 sqrt(keV), m_r c^2 = 1 124 656 keV, C1 = 1.17302e-9, C2 = 1.51361e-2, C3 = 7.51886e-2, C4 = 4.60643e-3, C5 = 1.35e-2, C6 = -1.0675e-4, C7 = 1.366e-5 (T in keV, result in cm^3/s; valid 0.2 to 100 keV). It is an empirical fit to the cross-section, accurate to a few per cent.

Power balance (50:50 D:T, n_i = n_e = n, no impurities).

P_fus = (n^2/4) <sigma v> E_f V E_f = 17.6 MeV P_alpha = P_fus / 5 P_loss = 3 n T V / τ_E (stored energy W = 3 n T V) P_brem = 5.35e-37 n^2 sqrt(T) V (W; n in m^-3, T in keV) P_heat = P_loss + P_brem - P_alpha Q = P_fus / P_heat ignition when P_alpha >= P_loss + P_brem

Lawson triple product. Solving the ignition condition for nτ_E gives nτ_E = 3T / (<sigma v> E_alpha / 4 - C_br sqrt(T)); multiplying by T gives n T τ_E, which has a minimum near T = 14 keV of about 3x10^21 keV s m^-3. The classic estimate uses <sigma v> ~ 1.1x10^-24 T^2 m^3/s (8-25 keV): nTτ >= 12 T^2 / (E_alpha <sigma v>) = 3.1x10^21. The Experiments card finds the minimum from this simulation's own balance and compares the two.

Tokamak confinement time. The empirical IPB98(y,2) H-mode scaling (ITER Physics Basis, Nucl. Fusion 39, 1999): τ_E = 0.0562 H I^0.93 B^0.15 P^-0.69 n19^0.41 M^0.19 R^1.97 ε^0.58 κ^0.78 (s; I in MA, B in T, P loss power in MW, n19 in 10^19 m^-3, M = 2.5 amu, R in m, ε = a/R). The exponents are a regression fit to many experiments, not a derivation; H is an adjustable quality factor. Here P = W/τ is solved self-consistently, the volume is V = 2 pi^2 R a^2 κ, and the temperature evolves as d(3nTV)/dt = P_alpha + P_heat - P_loss - P_brem. The Greenwald limit n_G = I / (pi a^2) (10^20 m^-3, MA, m) and a cylindrical safety factor q95 are shown as warnings. The model is 0-D with flat profiles and no fuel dilution, helium ash, impurities, or separate ion and electron temperatures; real ITER-class plasmas have peaked profiles and different ion and electron temperatures. The ITER-like preset is only an illustrative fit (it lands near its design Q = 10 with 50 MW).

Inertial confinement. A laser-heated hohlraum (a gold cavity) converts laser light to X-rays that ablate the outer shell of a capsule and compress its DT fuel. Alpha particles are stopped when the hot-spot areal density exceeds about ρR ~ 0.3 g/cm^2; here the deposited fraction is 1 - exp(-ρR_hs / 0.3). The hot spot is a sphere of radius R_hs and density ρ = ρR / R_hs, held together by its own inertia for τ = 4 R_hs / c_s with c_s = 3.6x10^5 sqrt(T) m/s (T in keV); the factor 4 is a calibration to typical stagnation times (~100 ps), not a derived number. The self-heating ratio x = f_alpha P_alpha / (P_loss + P_brem) crosses 1 at ignition; then a burn wave consumes a fraction φ = ρR / (ρR + 6 g/cm^2) of the fuel (the 6 g/cm^2 scale is the standard order-of-magnitude burn-up constant) and the target gain is G = Y / E_laser, with fully burnt DT releasing 338 MJ per mg. Below ignition the yield is only the compression-heated fusion output boosted by 1/(1-x). Conduction and radiation losses, hydrodynamic instabilities, and laser-to-capsule coupling (a few per cent) are not modelled. The NIF-like preset is tuned so that the model gives a gain near the publicly reported 3.15 MJ from 2.05 MJ of laser energy (Dec 2022, ignition shot, reported by the national laboratory; later shots reported higher), it is not a prediction of any real shot.

Frontier map. Points for historical devices are approximate, order-of-magnitude values read from public summaries (T-3 1968, PLT 1978, TFTR and JET D-T campaigns 1990s, JT-60U 1996, W7-X, an inertial-fusion ignition shot, and the ITER design value). They are for orientation only; different devices quote ion or electron or volume-averaged or peak values.

Key references (plain text). J. D. Lawson, Proc. Phys. Soc. B 70, 6 (1957). H.-S. Bosch and G. M. Hale, Nucl. Fusion 32, 611 (1992). ITER Physics Basis, Nucl. Fusion 39, 2175 (1999). A. B. Zylstra et al., Nature 601, 542 (2022), and H. Abu-Shawareb et al., Phys. Rev. Lett. 129, 075001 (2022), for the first inertial-fusion shot with target gain above 1. J. Wesson, Tokamaks (Oxford) for the triple-product estimate.

Educational only: the model is a teaching simplification, not a design tool. No real laboratory branding is shown; machines are generic.