Upper Limit of Fusion Reactivity in Laser-Driven $p+{}^{11}\mathrm{B}$ Reaction

Abstract

We explore the averaged fusion reactivity of the $p+{}^{11}\mathrm{B}$ 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 $T_e$ and the dimensionless acceleration time ${\omega }_{pi}{t}_{\mathrm{acc}}$, where ${\omega }_{pi}$ 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 $⟨\sigma v⟩=8.12\times 10^{-16}\mathrm{c}{\mathrm{m}}^3/s$ at $k_B{T}_e=10.0\mathrm{MeV}$ and ${\omega }_{pi}{t}_{\mathrm{acc}}=0.503$. These findings suggest that an upper limit exists for the fusion reactivity achievable in laser-driven $p+{}^{11}\mathrm{B}$ fusion experiments, even under optimized conditions.