External-Field-Assisted Muon Reactivation in Muon-Catalyzed Fusion: A Rate-Network Criterion for Reducing Alpha Sticking

Abstract

Alpha sticking is a major loss channel in deuterium--tritium muon-catalyzed fusion. We study whether an additional external-field-assisted stripping channel can reduce the residual sticking loss after conventional collisional reactivation. The external contribution is written as $R_X=f_XP_X\eta_X$, where $f_X$ is the space--time overlap between the external field and the residual stuck $(\alpha\mu)^+$ population, $P_X$ is the microscopic stripping probability, and $\eta_X$ is the probability that the stripped $\mu^-$ is returned to the $d\mu/t\mu\to dt\mu$ fusion cycle before escape or decay. This gives $\omega_S^{\rm eff}=\omega_S^0(1-R_{\rm col})(1-R_X)$ and leads directly to a probability-level no-go condition, $\eta_X^{\rm crit}>1$, for any target improvement requiring more recycling than is probabilistically available. We construct an energy-resolved post-stripping rate network including slowing down, atomic capture, free escape, muon decay, atomic-stage loss, ordinary molecular formation, and an effective resonant $dt\mu$ channel. Benchmark scans show that the useful regime is a transport window: the stripped muon must be confined and recycled efficiently. With the reference inputs used here, the best-performing scenario increases the cycle yield from $N_{\rm fus,\mu}=112.6$ in the collision-only case to $N_{\rm fus,\mu}=156.5$. Resonant molecular formation suppresses atomic-stage loss and broadens the high-recycling region, but it cannot compensate for prompt escape or poor field--population overlap. The rate network therefore identifies the transport and overlap conditions required for external-field-assisted reactivation to reduce residual alpha sticking.