A measure of the probability that two nuclei will undergo a fusion reaction when they collide, expressed as an effective target area and central to predicting the reaction rate in any fusion plasma.
The cross-section σ quantifies the likelihood of a specific reaction when a projectile particle encounters a target. It has units of area (typically barns, where 1 barn = 10−28 m2) and depends strongly on the relative kinetic energy of the colliding pair.[1]
In a thermal plasma, the quantity that determines the fusion reaction rate per unit volume is the thermal reactivity ⟨σv⟩, the cross-section averaged over the Maxwellian velocity distribution.[2]
R = n1 n2 ⟨σv⟩ / (1 + δ12)
D–T has the largest ⟨σv⟩ at accessible temperatures, peaking near 64 keV at approximately 8.5 × 10−22 m3/s, enhanced by a nuclear resonance in 5He. D–D is roughly two orders of magnitude smaller at 10–20 keV. p–11B has a peak ⟨σv⟩ roughly 15–20 times smaller than D–T, requiring temperatures above 100 keV where bremsstrahlung losses become severe.[2]
The most precise and widely used parameterization was published by Bosch and Hale in 1992, based on R-matrix nuclear theory fits. Their analytic fits remain the standard reference in plasma physics and reactor design codes worldwide. Experimental uncertainties are 2–5% near the peak but larger at very low energies.[2]