Reactor Point Kinetics & Reactivity Insertion

Reactivity Insertion

Reactivity ρ 0.00 $

Reactor Parameters

Fuel / precursor set

Prompt generation time Λ 1.0×10⁻⁴ s

Live Readouts

Power (n / n₀)

1.00

Reactivity

0.00 $

Reactor period τ

∞

Elapsed time

0.0 s

How it works

The one-group point-kinetics equations track neutron population n(t) and delayed-neutron precursor concentration C(t) as a linear system:

dn/dt = (ρ-β)/Λ · n + λC
dC/dt = β/Λ · n − λC

ρ is reactivity, β the delayed-neutron fraction, Λ the prompt neutron generation time, λ the effective precursor decay constant. This 2×2 linear system has an exact analytic solution: its eigenvalues ω₁, ω₂ solve the inhour-style quadratic

ω² − (a−λ)ω − λρ/Λ = 0,  a = (ρ-β)/Λ
n(t) = c₁e^(ω₁t) + c₂e^(ω₂t)

solved fresh from the current n, C every time you change ρ — so the simulation is never numerically integrated (no stiffness, no drift, exact even for a tiny Λ).

ρ < β (subprompt-critical) — both roots are finite; power rises or falls on the stable reactor period set by delayed neutrons (seconds to minutes), with a fast initial "prompt jump" then a slow drift.
ρ ≥ β (prompt critical) — the dominant root is driven by Λ alone; power diverges on a millisecond timescale, exactly the regime real reactors are designed to never enter.
SCRAM — inserts a large negative reactivity step (control rods fully in), driving power back down; an automatic trip does the same if power exceeds 100× nominal.

Real-world relevance: this is the same linear point-kinetics model used for reactor safety analysis and control-system design in every operating power reactor.

Fuel rods (glow ∝ power) Control rod bank

PWR n/n₀

1.00×

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