What it does
The point kinetics equations describe how the neutron population, and so the power, of a reactor changes when its reactivity changes, treating the whole core as one point. They include the delayed neutrons: about 0.65 % of the neutrons from U-235 fission come out seconds to minutes later, from the decay of fission products (the precursors). Those few neutrons are what make a reactor controllable.
dn/dt = (ρ − β)/Λ · n + Σ λᵢCᵢ dCᵢ/dt = βᵢ/Λ · n − λᵢCᵢ
This simulator:
- solves the six-group equations with a 3-stage Radau IIA implicit method (order 5, made for stiff equations like these, where the prompt neutrons change thousands of times faster than the precursors), with automatic step control;
- takes a step or a ramp of reactivity in dollars, cents, pcm or Δk/k, with an optional scram;
- shows the prompt jump β/(β − ρ), the stable period and doubling time from the inhour equation (all seven roots), and the power at chosen times;
- plots power (log or linear) and reactivity, and downloads the time series as CSV.
It is educational: there is no temperature feedback, spatial effect or decay heat, so it shows the bare kinetics only.
How to use it
- Pick the units and a step size, or a ramp rate and a value to hold at. Positive reactivity raises the power; negative lowers it.
- Tick Scram to drop the rods (a large negative step) at a chosen time.
- Leave the delayed-neutron groups at the rounded U-235 values, or type your own (β fraction and decay constant per group). Λ is the prompt neutron generation time.
Worked example
With the rounded U-235 data (β = 0.0065) and Λ = 10⁻⁴ s, a step of +0.1 $ gives a prompt jump of × 1.111, then a stable period of 98.72 s (doubling every 68.43 s). After 60 s the power is 2.342 times the start. A step of +0.5 $ jumps × 2 and settles to a 5.8 s period: 83,554 times the start after 60 s. A step of −1 $ drops the power to half at once and then to 0.06451 after 60 s, with a period of −83.9 s: a reactor can never shut down faster than its longest-lived precursor allows (about 80 s here). At +1 $ or more the reactor is prompt critical and the power rises on the prompt-neutron time scale alone.
FAQ
Why the jump and then a slow rise? The prompt neutrons settle in milliseconds (the jump); after that the growth is paced by the delayed neutrons.
Is anything uploaded? No. Everything runs in your browser and works offline.
Where the numbers come from
- Point kinetics equations, prompt-jump approximation and inhour equation as given in standard reactor physics textbooks (general physics).
- Delayed-neutron data: rounded six-group values for thermal fission of U-235 (β = 0.0065) as printed in common textbooks, rounded and editable; physical constants, not a copied data table.
- Checked against SciPy solve_ivp (Radau, rtol 1e-11) for seven transients including a ramp, a scram and a prompt-critical step (agreement better than 1 part in a million), and the inhour roots against NumPy polynomial roots.
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Last updated 2026-11-09.