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How to use
Run the full-power equilibrium, then try the presets: pull the rods 2 %, trip the pumps, follow a load change at 60 times speed, or shut down and watch xenon at 600 times speed. The SCRAM button drops all rods. Graphs show power, the reactivity budget, temperatures, xenon and the startup rate. Space pauses, R resets.
Drag to orbit, wheel to zoom. Fuel colour is a schematic radial/axial temperature map; the blue haze scales with neutron power. The 3D reactor is a generic educational illustration and not a model of any real plant. Models and baked PBR textures made in Blender.
The science
Scope. This is a textbook point-kinetics model of a generic pressurised-water reactor core with illustrative numbers. It teaches how a chain reaction is controlled; it is not a design, a safety analysis or a model of any real plant.
Point kinetics with six delayed-neutron groups. With relative neutron population n, precursor concentrations C_i, effective delayed fraction β = Σβ_i = 0.0065 and prompt neutron lifetime Λ:
dn/dt = [(ρ - β)/Λ] n + Σ λ_i C_i
dC_i/dt = (β_i/Λ) n - λ_i C_i
Reactivity ρ = (k-1)/k is measured in pcm (1e-5) or in dollars ($ = ρ/β). Delayed neutrons make the reactor controllable: a step of +0.2 β produces a prompt jump to n = β/(β-ρ) = 1.25 and then a slow rise with the stable period given by the inhour equation ρ = Λω + Σ β_i ω/(ω + λ_i), T = 1/ω (checked below). Delayed-neutron data are Keepin-type typical values for U-235.
Feedback. ρ = ρ_excess - rods - boron + α_f (T_f - T_f0) + α_c (T_c - T_c0) - xenon. Fuel temperature (Doppler broadening) and moderator temperature give negative coefficients, so a power rise heats the core and brakes itself. Heat is transferred through a two-node model C_f dT_f/dt = P - UA (T_f - T_c), C_c dT_c/dt = UA (T_f - T_c) - 2 W (T_c - T_in). Rod worth follows the integral S-curve w(z) = z - sin(2 π z)/(2 π) of insertion fraction z; boron is diluted or borated slowly (8 ppm per minute of plant time) at 9 pcm per ppm (typical order of magnitude).
Xenon-135. Iodine-135 (half-life 6.6 h) decays into Xe-135 (9.1 h), the strongest neutron absorber known. Normalised to full-power equilibrium: ι' = λ_I (n - ι), ξ' = a n + b ι - (λ_X + σφ_0 n) ξ. After a power reduction or shutdown xenon first rises (iodine keeps feeding it while burn-out stops) and peaks after about 10 hours, the "xenon pit" that can make a restart impossible without extra reactivity. The closed-form solution for n = 0 is compared with the integrator below.
Decay heat is a four-group exponential sum totalling 6.5 % of full power (order of magnitude only), which is why cooling must continue after a scram. The protection system scrams on 118 % neutron flux, fuel above 1250 K or outlet coolant above 625 K, dropping the rods in 2.5 s. At large time warps the stiff prompt term is replaced by the prompt-jump approximation n = Λ Σ λ_i C_i / (β - ρ), which is exact for slow transients; the reactivity is capped at 0.9 β so the model never enters the prompt-critical regime.
Limits. No spatial effects (xenon oscillations, flux tilts), single average fuel and coolant node, constant coefficients, no burnup, no pressure or steam dynamics, generic constants. Compare numbers with a textbook before quoting them.