Reactor Four-Factor Multiplication Calculator
Nuclear reactor physics: Compute k_inf via the four-factor formula (ε, p, η, f), fast/thermal non-leakage probabilities, geometric buckling, and k_eff.
Four-Factor Core Nuclear Physics
Criticality & Multiplication State
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Frequently Asked Questions
What is the physical meaning of each factor in the four-factor formula?
1. Fast Fission Factor (ε): Ratio of total fast neutrons generated (including fast fissions in U-238) to thermal fission neutrons. 2. Resonance Escape Probability (p): Fraction of fast neutrons that successfully slow down past the dense U-238 resonance capture peaks without being absorbed. 3. Thermal Utilization Factor (f): Fraction of thermal neutrons absorbed in the nuclear fuel versus total absorption in fuel, moderator, cladding, and structure. 4. Thermal Reproduction Factor (η): Number of fission neutrons produced per thermal neutron absorbed in fuel.
How does geometric buckling (B_g²) govern reactor criticality?
Geometric buckling (B_g²) measures the curvature of the neutron flux profile dictated by core geometry and boundary conditions. A smaller core has higher curvature and higher B_g², leading to greater neutron leakage. For a reactor to be critical, material buckling (B_m² = (k_inf - 1) / M²) must equal geometric buckling (B_g²).
Why can CANDU reactors operate on natural uranium while PWRs require enriched fuel?
Heavy water (D₂O) has an exceptionally low neutron absorption cross-section compared to light water (H₂O). This yields a very high thermal utilization factor (f) and high resonance escape probability (p), enabling CANDU lattices to achieve k_inf > 1.07 with unenriched natural uranium (0.71% U-235), whereas light water captures too many neutrons and requires 3% to 5% enriched fuel.