Calculators / Reactor and fuel cycle
Reactor period calculator: the inhour equation
The stable period is set by the delayed neutrons. A one-group approximation misses it badly — 2.3× too long at +$0.50 — so the app solves the six-group inhour equation.
Free · no account · works offline · iOS, Android and web
The inhour equation (prompt lifetime neglected)
ρ / β = Σᵢ aᵢ / (1 + λᵢ·T) T = stable period doubling time = T · ln 2
Period against reactivity (β = 0.0065)
| REACTIVITY | pcm | PERIOD | DOUBLING TIME |
|---|---|---|---|
| +$0.05 | 32.5 | 227 s | 157 s |
| +$0.10 | 65 | 98.5 s | 68.3 s |
| +$0.20 | 130 | 36.8 s | 25.5 s |
| +$0.30 | 195 | 18.2 s | 12.6 s |
| +$0.50 | 325 | 5.72 s | 3.96 s |
| +$0.70 | 455 | 1.84 s | 1.28 s |
| −$0.10 | -65 | -172 s | — |
| −$1.00 | -650 | -83.9 s | — |
| −$5.00 | -3,250 | -81.2 s | — |
After a large negative step the power settles to a −80.6 s period, set by the longest-lived precursor group (T½ = 55.9 s), however much reactivity was inserted.
Delayed-neutron groups (Keepin, U-235 thermal)
| GROUP | ai | λi (s−1) | T½ (s) |
|---|---|---|---|
| 1 | 0.033 | 0.0124 | 55.9 |
| 2 | 0.219 | 0.0305 | 22.7 |
| 3 | 0.196 | 0.111 | 6.24 |
| 4 | 0.395 | 0.301 | 2.3 |
| 5 | 0.115 | 1.14 | 0.608 |
| 6 | 0.042 | 3.01 | 0.23 |
Assumptions
- Point kinetics, U-235 thermal delayed-neutron data; Pu-239 and fast cores have a smaller β and different groups.
- Prompt neutron lifetime neglected, which is accurate well below prompt critical ($1).
Sources
- Keepin, G. R., Physics of Nuclear Kinetics (1965).
- Lamarsh & Baratta Ch. 7; Duderstadt & Hamilton Ch. 6.
Numbers on this page computed by the physics code of Nuclear Toolkit 1.4.1, the same code as the app. How it is checked.
Related calculators
Scope. A reference and calculation tool for people who work
in the field. It is not certified for safety-critical or regulatory use and
does not replace analysis by a qualified health physicist or nuclear
engineer. See the Terms.