Monte Carlo Fundamentals
Monte Carlo criticality lab
Every tutorial on this site ends at a deck you cannot run without installing a transport code. This page runs one. It is a real one-group Monte Carlo k-eigenvalue solver — the same fission-source power iteration behind MCNP, OpenMC, Serpent, and SCONE — compiled to run in your browser. Set the cross sections and geometry, press Run, and read k-eff with its Monte Carlo uncertainty.
One energy group and isotropic scattering. Pick a sphere, a cube, or a fuel sphere wrapped in a scattering reflector. A mirror face sends the neutron back in; a vacuum face lets it escape. Shrink the body and k-eff falls. Mirror every face, or grow the body, and k-eff climbs toward k∞ = νΣf/Σa. A thicker reflector returns more neutrons to the fuel, so k-eff rises. Run U-235 continuous energy is an infinite medium of elastic, capture, and fission from the ENDF/B-VIII.0 tables. It is not a Godiva result: those tables have no inelastic secondary neutrons. Run deck tracks the pasted MCNP geometry. Run 2-group reactor uses a flux-weighted collapse of an OpenMC pin cell (ENDF/B-VIII.0, reflective, k = 1.159). It is a pin-cell spectrum, not a full core. Run slab flux draws the flux across a 20 cm half-slab. Find critical radius searches a bare sphere until k is 1. Run lead shield is 1 MeV photons through 2 cm of lead, compared with e to the minus μx from the NIST attenuation coefficient. Step xenon integrates I-135 and Xe-135 at a constant fission rate. This is a teaching solver, not a licensed calculation.
Material (macroscopic, cm⁻¹)
k∞ = νΣf/Σa = 1.6000
Geometry and statistics
Mirror reflects the neutron like a specular wall, so a mirrored sphere has no leakage and k-eff must come out at k∞.
60 cycles, first 15 discarded while the fission source settles. Seed fixed at 1.
Or paste an MCNP sphere
Run deck reads this geometry with the same cell-finding engine the visualizer uses. The cross sections are the material card above, one energy group. Material 0 is void: a neutron that leaves the sphere is gone. 3,000 neutrons, 20 cycles.
How this ties together: the point kinetics lab shows what happens after you are near critical and perturb reactivity; this page shows how geometry and cross sections set k-eff in the first place. The code comparison covers how the four production codes express the same physics.