Calculator Inputs
Use the loss-based method when cross sections, diffusion, and buckling are known. Use the generation-time method when reactor kinetics data is already available.
Example Data Table
| Case | Method | Key inputs | Prompt neutron lifetime | Engineering note |
|---|---|---|---|---|
| Thermal core sample | Loss-based | v = 2200 m/s, Σa = 4 1/m, D = 1.2 m, B² = 0.5 1/m² | 9.881423e-05 s | Moderate lifetime shaped by absorption and leakage. |
| Fast system sample | Loss-based | v = 2.0e7 m/s, Σa = 0.002 1/m, D = 0.02 m, B² = 5 1/m² | 4.901961e-07 s | Very short lifetime with rapid neutron loss dynamics. |
| Kinetics data sample | Generation-time | Λ = 80 µs, keff = 1.002 | 8.016000e-05 s | Useful when direct transport parameters are unavailable. |
Formula Used
Loss-based lifetime: l = 1 / [v × (Σa + D × B²)]
Generation-time relation: l = keff × Λ
Derived removal rate: R = 1 / l = v × (Σa + D × B²)
Here, l is prompt neutron lifetime, v is neutron speed, Σa is macroscopic absorption cross section, D is diffusion coefficient, B² is geometric buckling, keff is effective multiplication factor, and Λ is prompt neutron generation time.
How to Use This Calculator
- Enter a case label so exported results are easier to track.
- Select the loss-based method when transport and reactor geometry data are known.
- Select the generation-time method when kinetics reports already provide Λ and keff.
- Choose units carefully before calculating, especially for cross section and buckling.
- Review the displayed lifetime, removal rate, and derived generation time values.
- Download CSV for records or PDF for reporting and review packages.
Frequently Asked Questions
1. What does prompt neutron lifetime represent?
It is the average time a prompt neutron exists before removal by absorption or leakage. It is a core kinetics parameter that affects how rapidly reactor power can respond to reactivity changes.
2. Why does neutron speed matter so much?
Speed directly scales the removal rate in the loss-based equation. Higher neutron speed usually shortens lifetime because neutrons traverse the medium and encounter removal processes more quickly.
3. What is the role of geometric buckling?
Geometric buckling represents leakage tendency caused by core shape and size. Larger buckling values increase the leakage term, which raises total loss and reduces the prompt neutron lifetime.
4. When should I use the generation-time method?
Use it when reactor kinetics studies already provide prompt neutron generation time and effective multiplication factor. It is also useful when detailed transport parameters are unavailable or uncertain.
5. Is this calculator suitable for exact safety analysis?
It is best for engineering estimates, screening studies, and educational work. Formal design or licensing analysis should use validated neutronics methods, project assumptions, and plant-specific data.
6. Why can a very large lifetime indicate input issues?
An unusually large result may occur when speed, cross section, or buckling units are entered incorrectly. Check whether values were mixed between meters and centimeters or between seconds and microseconds.
7. Does this page account for delayed neutrons?
No. This tool focuses on prompt neutron lifetime and the prompt generation relation. Delayed neutron fractions and precursor groups belong to broader point-kinetics or transient analysis models.
8. What should I export, CSV or PDF?
Choose CSV when you want structured values for spreadsheets, reports, or further calculations. Choose PDF when you need a quick shareable summary with the key result and derived reactor metrics.