This simulation models the time-dependent behaviour of a thermal nuclear reactor using the point-kinetics equations. Rather than tracking neutrons in space, it treats the whole core as a single point, evolving the normalised neutron population N and six groups of delayed-neutron precursors. The governing equations are dN/dt = (ρ−β)/Λ·N + ΣλᵢCᵢ and dCᵢ/dt = βᵢ/Λ·N − λᵢCᵢ, with β = 0.0065 and prompt generation time Λ = 10⁻⁵ s.
The single control-rod slider sets reactivity ρ (rod out gives roughly +3000 pcm, fully in about −5000 pcm), while the Doppler feedback toggle adds a temperature-dependent negative term that stabilises the core. Presets reproduce cold startup, steady power, a step rise, an emergency SCRAM and an unstable positive-void accident. Such models underpin real reactor control, operator training and the safety analysis of pressurised-water reactors.
Frequently Asked Questions
What does this nuclear reactor simulation actually show?
It shows how the neutron population and power of a reactor core change over time as you move the control rods. A flux map, a power-versus-time chart and a status panel display reactivity, core temperature and the six delayed-neutron precursor groups, so you can watch the core go subcritical, critical or supercritical.
What are the point-kinetics equations?
They are a pair of coupled differential equations: dN/dt = (ρ−β)/Λ times N plus the sum of λᵢCᵢ, and dCᵢ/dt = βᵢ/Λ times N minus λᵢCᵢ. N is the normalised neutron flux and Cᵢ are precursor concentrations. They describe the whole core as a single point, capturing how power rises or falls without modelling spatial detail.
What does the control rod slider do?
The slider sets rod insertion from 0 to 100 per cent. Withdrawing rods (towards 0) adds positive reactivity, raising power, while inserting them (towards 100) adds negative reactivity and shuts the reaction down. In this model fully withdrawn gives about +3000 pcm and fully inserted about −5000 pcm.
What is reactivity and why is it measured in pcm?
Reactivity ρ measures how far the reactor is from criticality, defined as the fractional departure of the multiplication factor from one. It is small, so it is quoted in pcm (per cent mille), where 1 pcm equals 10⁻⁵ in Δk/k. Positive ρ means power rises, negative means it falls, and zero means a steady critical state.
Why are delayed neutrons so important?
About 0.65 per cent of fission neutrons (β = 0.0065) are emitted seconds to minutes after fission by decaying precursors. These delayed neutrons slow the reactor's response enormously, giving operators time to act. Without them the prompt generation time of just 10⁻⁵ s would make the core uncontrollable, which is why the simulation tracks six precursor groups.
What is the Doppler feedback toggle?
Doppler feedback represents how a hotter fuel broadens the U-238 absorption resonances, capturing more neutrons and adding negative reactivity. In the model this is α times the temperature rise above 293 °C, with α = −2.5×10⁻⁵ per °C. Switching it on stabilises power; switching it off makes the core prone to runaway, as in the positive-void preset.
What does prompt critical mean?
The reactor becomes prompt critical when reactivity reaches the delayed-neutron fraction β (about 650 pcm), so it sustains itself on prompt neutrons alone. Power then rises on the very short prompt timescale rather than the slow delayed one. The status panel flags this as a dangerous condition because the reactor is no longer easily controllable.
How is doubling time calculated here?
When reactivity is positive the panel estimates the time for power to double using T = ln(2)·Λ/(ρ−β), the prompt approximation. A short doubling time means power is climbing rapidly. The figure is shown only above about 10 pcm, since near or below criticality the power is steady or falling and a doubling time is not meaningful.
What is a SCRAM?
A SCRAM is an emergency shutdown that drops all control rods fully into the core, slamming reactivity strongly negative and halting the chain reaction. Pressing the SCRAM button or preset sets rod insertion to 100 per cent and displays a warning banner. Delayed neutrons mean the power does not vanish instantly but decays as the precursors die away.
How physically accurate is this model?
It uses realistic U-235 kinetics constants, the standard six-group delayed-neutron data and a genuine Doppler coefficient, so the qualitative behaviour is faithful. However, it is a lumped point model with simplified rod-worth, heating and cooling terms, so the numbers are illustrative rather than reactor-grade. It is built for learning the concepts, not for licensing calculations.
Where are point-kinetics models used in the real world?
Point kinetics underpins reactor control-system design, full-scope operator training simulators and transient safety analyses for pressurised-water and other reactors. Because it is fast to compute yet captures the essential delayed-neutron physics, it is the workhorse model for studying startups, load changes, rod ejections and shutdown behaviour before more detailed spatial codes are applied.