This is a spatially resolved companion to the 3D iodine-pit simulator: instead of one lumped Iodine/Xenon pair for the whole core, the reactor is split into 24 slices along its height. Every simulated tick solves the real steady-state one-group neutron diffusion equation for the axial flux shape φ(z) — a finite-difference eigenvalue problem, solved by power iteration (the same "outer iteration" method production reactor-physics codes use):
−D·φ″(z) + Σₐ(z)·φ(z) = (1/k)·νΣf·φ(z), φ(0)=φ(L)=0
Σₐ(z) = Σₐ₀ + γ·Xe(z) (local xenon adds local absorption)
P(z) = P_avg · φ(z) / mean(φ)
Each slice then runs its own local Iodine-135/Xenon-135 balance, using the same rate constants as the 3D simulator (I-135 half-life 6.57 h, Xe-135 half-life 9.10 h):
dI/dt(z) = λ_I · (P(z) − I(z))
dXe/dt(z) = λ_I · I(z) − λ_X · Xe(z) − σ · Xe(z) · P(z)
Because xenon buildup depresses flux locally, a brief asymmetric perturbation (inserting a rod into just the top or bottom half) leaves behind a slowly evolving top/bottom power tilt — the axial offset, AO = (P_top − P_bottom)/(P_top + P_bottom) — that migrates from one end of the core to the other and back, decaying or sustaining itself over roughly 15–30 simulated hours depending on how strongly neighbouring slices are neutronically coupled together.
- Neutronic coupling — the effective diffusion strength between slices. Physically this stands in for core size: small, tightly-coupled cores (naval reactors) strongly resist any axial tilt; large, loosely-coupled commercial cores let a tilt persist and oscillate, which is exactly why large PWRs run automatic axial-offset control systems.
- Insert top/bottom rod — briefly raises absorption in one half of the core, seeding an asymmetric xenon transient. Try it at both coupling extremes.
- The left strip shows the instantaneous axial power profile; the main panel is a waterfall of that same profile over time (space is vertical, time runs left→right); the bottom plot tracks the axial offset itself.
Real-world relevance: axial xenon oscillations are a real limiting phenomenon in large power reactors, first analysed after early PWRs exhibited slow top-to-bottom power swings; every large commercial PWR core today runs continuous axial-offset-control logic to damp exactly this mode.