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核工程·反应堆/辐射
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核工程·反应堆/辐射
12
engines
放射性衰变链(Bateman 方程)
Radioactive decay chain (Bateman equations)
母→子→孙 · Bateman方程 · 瞬变/长期平衡
Parent → daughter → granddaughter: grow-in, peak and decay, and transient equilibrium
长期平衡(secular equilibrium)
Secular equilibrium
母T½≫子 · ~7个子半衰期后A_子=A_母 · 活度累积
When the parent half-life ≫ the daughter's: the daughter activity rises to equal the parent's (A_d → A_p)
比结合能曲线(B/A – 质量数 A)
Binding energy per nucleon (B/A vs mass number A)
B/A vs A · 铁-56峰~8.8MeV · 聚变/裂变趋峰释能
Rising to the iron-56 peak (≈8.8 MeV/nucleon) then falling: both fusion of light nuclei and fission of heavy nuclei move toward the peak and release energy
核裂变能量释放(U-235)
Nuclear fission energy release (U-235)
Δmc²=931.5MeV/u · U-235≈200MeV · 碎片/中子/γ分配
Fission Q from the mass defect Δm·c², how ~200 MeV is shared, and the energy per gram of uranium
D-T 核聚变反应
Deuterium–tritium fusion
D-T→⁴He+n+17.6MeV · 库仑势垒 · Lawson nTτ
²H + ³H → ⁴He + n + 17.6 MeV; the Coulomb barrier and the Lawson triple-product ignition criterion
中子截面与束流衰减
Neutron cross-section and beam attenuation
微观σ(靶恩) · 宏观Σ=Nσ · 平均自由程1/Σ
Microscopic σ (barns), macroscopic Σ = N·σ, mean free path λ = 1/Σ and exponential attenuation I = I₀e^(−Σx)
反应堆临界(四因子 / 六因子公式)
Reactor criticality (four/six-factor formula)
k∞=ηfpε · k_eff · 次临界/临界/超临界 · 逐代N·kᵍ
From k∞ = η·f·p·ε and k_eff = k∞·P_NL, judge sub-/critical/super-critical and watch the per-generation neutron count
中子慢化(慢化到热能)
Neutron moderation (slowing down to thermal)
对数能降ξ · 热化碰撞n=ln(E0/Eth)/ξ · 轻核良慢化
Average logarithmic energy decrement ξ and collisions to thermalise n = ln(E₀/E_th)/ξ: why light nuclei (H, D, C) are good moderators
中子通量与反应堆功率
Neutron flux & reactor power
通量φ · R=Σφ · 热功率P=Rf·Ef(200MeV)
Reaction rate R = Σ·φ, fission power P = Σ_f·φ·E_f·V: relate flux, cross-section and power
控制棒反应性与积分棒价值
Control-rod reactivity & integral rod worth
ρ=(k−1)/k · 美元ρ/β · 棒价值S形积分曲线
Reactivity ρ=(k−1)/k, in dollars ρ/β; inserting a rod adds negative reactivity, integral worth traces an S-curve
光子屏蔽与指数衰减
Photon shielding & exponential attenuation
I=I0e^(−μx) · HVL=ln2/μ · TVL=ln10/μ · (½)^n
Narrow-beam I=I₀·e^(−μx); HVL=ln2/μ, TVL=ln10/μ, TVL/HVL=ln10/ln2≈3.32
辐射剂量:吸收 / 当量 / 有效剂量
Radiation dose: absorbed / equivalent / effective
吸收Gy · 当量Sv=Gy·wR(α20/γ1) · 有效ΣwT·HT
D (Gy = J/kg) → H = D·wR (Sv) → E = Σ wT·HT; weighting factors scale biological effect