Run a plasma pulse in a compact tokamak hall. Heat it, fuel it, keep it stable, and watch the ions spiral along the real twisted field while a 0-D power balance tells you the fusion gain Q.
Orange curve: ignition requirement (alpha heating alone balances conduction loss). White dashed line: your present temperature; read your own triple product in the table.
The science
Magnetic confinement. A charged particle in a field B gyrates at Ω = qB/m with Larmor radius ρ = m v⊥ /(qB) (6.8 mm for a 10 keV deuteron at 3 T) and streams along the field line. The toroidal field falls as Bt = B0R0/R; the plasma current adds a poloidal field Bp so the lines twist helically, q = r Bt /(R0Bp) turns toroidally per poloidal turn. The twist cancels the vertical grad-B/curvature drift that would otherwise carry ions and electrons apart. Particles with small v∥/v are reflected on the strong-field side (mirror trapping, criterion v∥/v < √(2ε/(1+ε))) and trace "banana" orbits; at the low aspect ratio of a spherical tokamak (ε = a/R0 = 0.6) that is most of them. Orbits here use the Boris integrator (rotation by t = qBΔt/2m), which conserves speed in a pure magnetic field exactly.
Power balance (0-D). dW/dt = Paux + PΩ + Pα − Prad − W/τE, with stored energy W = 3 n T V. D-T fusion power Pfus = (n²/4)⟨σv⟩ Efus V (Efus = 17.6 MeV, ⟨σv⟩ from the Bosch-Hale fit), of which 20% (3.5 MeV) heats the plasma as alpha particles. Bremsstrahlung Prad = 5.35×10³ Zeff n20² √T W/m³. Fusion gain Q = Pfus/(Paux+PΩ). The energy confinement time uses the empirical IPB98(y,2) scaling τE = H·0.0562 I0.93B0.15P−0.69n0.41M0.19R1.97ε0.58κ0.78.
Lawson criterion. Setting alpha heating equal to conduction loss gives n T τE ≥ 12 T² /(⟨σv⟩ Eα), about 3×1021 keV s m-3 near 15 keV.
Limits. Greenwald density nG = Ip/(πa²) (1020 m-3, MA, m); edge safety factor from the ITER-style shape-corrected formula q95 = (5a²B/(R Ip)) (1+κ²(1+2δ²−1.2δ³))/2 · (1.17−0.65ε)/(1−ε²)²; normalised beta βN = β[%]·aB/Ip, β = 2μ0⟨p⟩/B², with a Troyon-type limit near 3.5-4.
Simplifications, stated plainly. One temperature for ions and electrons, flat profiles, no impurity or helium-ash dynamics, no transport model beyond the empirical scaling (which was fitted to conventional-aspect-ratio machines and is extrapolated here; the plasma current needed for Q > 1 at R0 = 1 m is far above present experiments, so treat all parameters as model values). The field for the orbits is an ideal circular torus with the poloidal pitch taken from the model q; no Shafranov shift, triangularity or electric field. The Larmor radius is exaggerated for visibility (the factor is shown) and the electron-to-ion mass ratio is reduced for the same reason. The coils, hall and vessel are a generic design, not any real project; not affiliated with any fusion programme or company. Peaceful energy physics only; no prediction of commercial timelines. Models built with Blender, scene by Three.js.