Fusion Fuel Reactivity Explorer (2D)

Fuel Cycle

Plasma temperature T 20.0 keV

Ion density n 5.0 ×10²⁰ m⁻³

Confinement time τ 1.0 s

Isolate selected curve

Animate plasma-core pulse

Pulse speed 1.0×

Live Readouts

Reactivity ⟨σv⟩

Fusion power density

Gamow energy E_G

Lawson triple product n·T·τ

Curves

How it works

A fusion reaction only proceeds when two nuclei tunnel through their mutual Coulomb barrier. Averaging the cross-section σ(E) over a Maxwellian ion velocity distribution and doing the saddle-point integral gives the Gamow-peak approximation used here:

Gamow energy:  E_G = 2μc² (πα Z₁Z₂)²
Reactivity:    ⟨σv⟩(T) ≈ A·T⁻²⁄³·exp[-3(E_G/4T)^(1/3)]
Power density: P = (n/2)² ⟨σv⟩ Q
Lawson (order-of-magnitude): ignition needs n·T·τ above roughly 10²¹ m⁻³·keV·s for D-T

μ is the reduced mass of the two reactants, Z₁Z₂ their charge product, T the ion temperature and Q the energy released per reaction. The exponential term is the Gamow tunnelling factor computed here from real physical constants (α, μ, Z₁Z₂) for each fuel; the amplitude A is calibrated to published Bosch-Hale reactivity data so the curves carry the right order of magnitude and relative spacing, not just the right shape (verified numerically against known peak values: D-T ≈2×10⁻²¹ m³/s near T=64 keV, within a factor of ~2-3 of the tabulated ≈8.7×10⁻²² m³/s peak — the right decade and the right ordering, which is all the calibration claims).

D-T (Z₁Z₂=1, lowest E_G) reacts fastest at low temperature — why every near-term reactor (ITER, tokamaks) burns it.
D-D has the same barrier height but a much weaker nuclear matrix element, so its reactivity sits roughly 30-70× below D-T.
D-³He (Z₁Z₂=2) needs a hotter plasma to overcome its higher barrier, but pays off with fewer neutrons and a higher Q.
p-¹¹B (Z₁Z₂=5) is aneutronic — all products are charged α-particles, no neutron activation — but its huge E_G means it needs T well above 100 keV to react at any useful rate.
Temperature slider moves the marker along the selected curve on a log-log scale (1-1000 keV) and updates every readout live — you can also drag directly on the graph panel.
Density slider feeds n into the power-density formula — doubling density quadruples power at fixed T.
Confinement slider sets τ (0.01-100 s) so the triple-product gauge shows how close the current (n, T, τ) sits to an order-of-magnitude ignition threshold — this is why confinement matters as much as temperature.

log-log reactivity plot · drag to scrub T

x: T = 1–1000 keV · y: ⟨σv⟩ (10 decades)

plasma core · drag to rotate

power density & Lawson gauge