Description
Proton–boron ($p$-$^{11}\mathrm{B}$) fusion is an aneutronic reaction that predominantly produces energetic $\alpha$ particles with negligible neutron yield. In laser-driven schemes, injected $\mathrm{MeV}$ protons and fusion-born $\alpha$ particles are suprathermal and slow down through Coulomb collisions with plasma electrons and ions. An $\alpha$-driven chain reaction has been proposed under the assumption that collisional energy losses are negligible [1]; however, its feasibility critically depends on realistic stopping physics. Suprathermal chain-reaction formalisms incorporating stopping effects were originally developed for $D$–$T$ plasmas [2], and feasibility has been evaluated using a multiplication-factor approach [3].
Here, we develop a kinetic framework to quantify proton and $\alpha$-particle stopping using a binary-collision model [4], benchmarked against Monte Carlo Coulomb-collision modeling in particle-in-cell simulations. We further extend the analysis to proton–boron plasmas with nitrogen admixture, which modifies electron density and effective stopping power and is relevant to practical target designs. Based on validated stopping rates, we construct a simplified parametric model to determine whether secondary fusion and $\alpha$-particle heating can overcome collisional thermalization. The resulting multiplication factor provides a quantitative criterion for self-amplifying behavior and delineates the density–temperature parameter space required for experimental realization of suprathermal chain reactions in proton–boron–nitrogen plasmas.
References
[1] V. S. Belyaev, V. P. Krainov, B. V. Zagreev, and A. P. Matafonov, Phys. Atom. Nuclei 78, 537 (2015).
[2] A. Peres and D. Shvarts, Nucl. Fusion 15, 687 (1975).
[3] F. Belloni, Plasma Phys. Control. Fusion 63, 055020 (2021).
[4] N. E. Frankel, K. C. Hines, and R. L. Dewar, Phys. Rev. A 20, 2120 (1979).
Keywords: laser plasma; proton-boron fusion; theoretical model; particle-in-cell simulation.