一种受劳森启发的氘 - 氚μ子催化核聚变循环闭合判据
A Lawson-inspired Cycle-Closure Criterion for Deuterium--Tritium Muon-Catalyzed Fusion
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中文总结 AI 辅助
研究氘 - 氚μ子催化核聚变的循环闭合问题，提出受劳森启发的判据，定义有效循环强度等参数，得出所需循环强度和条件附着边界，能区分不同限制 regimes，为评估改进方向提供诊断方法。
中文摘要 AI 辅助
氘 - 氚μ子催化核聚变受到循环闭合问题的限制：一个负μ子必须在衰变或有效的α粒子附着将其从再利用中移除之前完成足够的催化循环。我们为这个单μ子循环制定了一个受劳森启发的判据。有效循环强度定义为$\mathcal{L}_\mu=\Lambda_c\tau_\mu$，其中$\Lambda_c$是有效循环完成率，$\tau_\mu$是μ子寿命。它与残余有效附着概率$\omega_S^{\rm eff}$一起，给出每个有用μ子的平均聚变产额$N_{\rm fus,\mu}=\mathcal{L}_\mu/(1+\omega_S^{\rm eff}\mathcal{L}_\mu)$。引入有用的D - T循环能量$E_{\rm use}$、系统因子$\eta_{\rm sys}$和有效μ子成本$E_\mu^{\rm cost}$，单μ子增益为$G_\mu=(\eta_{\rm sys}E_{\rm use}/E_\mu^{\rm cost})N_{\rm fus,\mu}$。这导致所需的循环强度$\mathcal{L}_\mu^{\rm req}=G_\mu N_L/(1-\omega_S^{\rm eff}G_\mu N_L)$，其中$N_L=E_\mu^{\rm cost}/(\eta_{\rm sys}E_{\rm use})$，以及条件附着边界$\omega_S^{\rm eff}<1/(G_\mu N_L)$。该判据在$(\omega_S^{\rm eff},\mathcal{L}_\mu)$平面中区分了速率限制、附着限制和成本限制 regimes。当代表性的历史D - T $\mu{\rm CF}$锚点投影到这个平面上时，它们位于高产量区域，但在传统的多GeVμ子成本核算下仍受有效附着边界的限制。该框架提供了一个紧凑的诊断方法，用于评估未来的改进是否主要通过提高有效循环完成率、减少残余附着或降低输送μ子的有用成本来实现。
英文摘要
Deuterium--tritium muon-catalyzed fusion is limited by a cycle-closure problem: a negative muon must complete enough catalytic cycles before decay or effective alpha sticking removes it from reuse. We formulate a Lawson-inspired criterion for this single-muon cycle. The effective cycle strength is defined as $\mathcal{L}_μ=Λ_cτ_μ$, where $Λ_c$ is the effective cycle-completion rate and $τ_μ$ is the muon lifetime. Together with the residual effective sticking probability $ω_S^{\rm eff}$, it gives the mean fusion yield per useful muon, $N_{\rm fus,μ}=\mathcal{L}_μ/(1+ω_S^{\rm eff}\mathcal{L}_μ)$. Introducing the useful D--T cycle energy $E_{\rm use}$, the system factor $η_{\rm sys}$, and the effective muon cost $E_μ^{\rm cost}$, the one-muon gain is $G_μ=(η_{\rm sys}E_{\rm use}/E_μ^{\rm cost})N_{\rm fus,μ}$. This leads to the required cycle strength $\mathcal{L}_μ^{\rm req}=G_μN_L/(1-ω_S^{\rm eff}G_μN_L)$, with $N_L=E_μ^{\rm cost}/(η_{\rm sys}E_{\rm use})$, and to the conditional sticking boundary $ω_S^{\rm eff}<1/(G_μN_L)$. The criterion separates rate-limited, sticking-limited, and cost-limited regimes in the $(ω_S^{\rm eff},\mathcal{L}_μ)$ plane. When representative historical D--T $μ{\rm CF}$ anchors are projected onto this plane, they lie in a high-yield region but remain constrained by the effective-sticking boundary under conventional multi-GeV muon-cost accounting. The framework provides a compact diagnostic for assessing whether future improvements act mainly by increasing the effective cycle-completion rate, reducing residual sticking, or lowering the useful cost of delivered muons.
