Upper limit of fusion reactivity in laser-driven p+¹¹B reaction

We explore the averaged fusion reactivity of the p+¹¹ B reaction in tabletop laser experiments using a plasma expansion model. We investigate the energy distribution of proton beams accelerated by lasers as a function of electron temperature Tₑ and the dimensionless acceleration time ωₚᵢ tacc, where ωₚᵢ is the ion plasma frequency. By combining these distributions with the fusion cross-section, we identify the optimal conditions that maximize the fusion reactivity, with σ v = 8.12 × 10⁻¹⁶\, cm³/s at kB Tₑ = 10.0\, MeV and ωₚᵢ tacc = 0.503. These findings suggest that an upper limit exists for the fusion reactivity achievable in laser-driven p+¹¹ B fusion experiments, even under optimized conditions.