Abstract
Abstract
Every non-thermal proton–boron-11 scheme now pursued places its fast ions at the 675 keV resonance of the ¹¹B(p,3α) cross section. The rate coefficient, however, is the product σ(E) v(E), and because the relative velocity grows as the square root of energy, the true maximum of the rate coefficient lies at 3.7 MeV. While this theoretical displacement governs ignition, a driven device is governed by a different, practically accessible quantity: the fusion yield integrated over the slowing-down history of the fast ion, weighted by the energy invested. We evaluate this engineering gain per unit injected energy analytically. We find that the optimum injection energy for a beam-driven device is 0.85 MeV, which is a little above the resonance but far below the 3.7 MeV kinematic ceiling. Injecting protons at 0.85 MeV rather than at the widely targeted 675 keV resonance raises the beam-driven gain per unit energy invested by 25 per cent. This improvement requires no new physics, no new confinement scheme, and no change of magnetic configuration — only a higher injector voltage.