Reactor Operations · Calibrated to the inhour equation

The Point Kinetics Simulator

Six-group delayed-neutron point kinetics. Dial in a reactivity step, ramp, or schedule and watch the prompt jump, the delayed-neutron-controlled rise, and — cross $1.00 — the collapse into prompt criticality.

NeutronRise
reactor physics tools

Scenario

Reactivity schedule

Reactivity (pcm)Duration (s)Mode

Reactivity feedback

⚠ positive α is unstable — the reactor will not self-limit

Feedback is a single lumped-temperature node — no spatial distribution, no real thermal-hydraulics, no coolant flow dynamics. α/K_heat/k_cool/T_coolant/T0 are illustrative defaults, not plant-specific values.

Hover the chart to read time, power, reactivity and instantaneous period.
Reactivity (schedule end)pcm
 %Δk/k
 $ (ρ/β)
Stable period Ts
SURDPM
Status

The model

dn/dt = ((ρ − β)/Λ)·n + Σ λi·Ci
dCi/dt = (βi/Λ)·n − λi·Ci  for i = 1..6

Six delayed-neutron precursor groups feed the neutron population alongside the prompt term. Below prompt critical (ρ < β) the precursors set the pace and the reactor settles into a stable period after a fast initial prompt jump. At ρ = β exactly — $1.00 — the prompt term takes over and the period collapses toward Λ; above it, power diverges on the prompt-neutron timescale alone.

Groupβiλi (s⁻¹)half-life
β total

Six-group U-235 thermal delayed-neutron data from Keepin (1965), Physics of Nuclear Kinetics, reproduced in DOE-HDBK-1019/1. Λ = 1×10⁻⁴ s is the NRC HRTD §2.1 order-of-magnitude figure, editable above (advanced). Stable-period and SUR readouts are solved from the inhour equation ρ(T) = Λ/T + Σ βi/(1+λiT), independently re-derived and checked against this table by verify-kinetics.js.

Validation

Recomputed live from the constants above via the inhour equation — nothing here is hard-coded. This is the pre-verified stable-period/reactivity table; the regression harness cross-checks the same numbers against the tool's own RK4 solver, not just this algebra.

Stable period TReference reactivityThis modelError

Source: NRC HRTD §2.1 reactivity/period relationship, reproduced from the inhour equation with the Keepin data and Λ = 1×10⁻⁴ s.

Model scope

Known limitations — read before citing
  • Point (zero-D) kinetics only. No spatial power distribution, no rod-worth shape, no flux tilt — one neutron population for the whole core.
  • Delayed-neutron data is U-235 thermal. A Pu-239-heavy end-of-life core has a meaningfully smaller β (roughly a third of U-235's) and behaves differently near prompt critical; that is not modelled here.
  • Reactivity feedback is a single lumped-temperature node. α/K_heat/k_cool/T_coolant/T0 are illustrative, not plant thermal-hydraulic constants — see the note above the feedback controls.
  • Fixed small-step RK4 (≤10⁻⁴ s), not an adaptive or implicit integrator. Correct against the benchmark, but a very long, very low-reactivity run is computationally heavy rather than fast.
  • Independent of the xenon and decay-heat tools. This model does not feed reactivity into, or take power history from, the other two — they are separate calculators that happen to share a core.