Monte Carlo Transport
Monte Carlo transport simulates radiation by following random particle histories and averaging their contributions to estimate transport quantities.
Sampling the transport equation
Monte Carlo methods solve the linear Boltzmann transport equation for neutrons, photons, or other particles by simulating individual particle histories. Each particle is born from a source, travels a distance sampled from the exponential attenuation law, undergoes a randomly selected interaction (scatter, absorption, fission), and either continues or terminates. Averaging over many histories gives estimates of fluxes, reaction rates, and energy deposition with quantifiable statistical uncertainty.
The method's defining strength is geometric and physical fidelity: it represents continuous energy, complex three-dimensional geometry, and detailed cross-section data without the discretization approximations that mesh-based deterministic methods require.
Estimators and variance
Quantities of interest are computed with estimators such as track-length or collision estimators that tally contributions along particle paths. The statistical error falls only as one over the square root of the number of histories, so halving the error requires quadrupling the work. This slow convergence motivates variance reduction.
Variance reduction
Techniques such as importance sampling, weight windows, splitting and Russian roulette, and next-event estimators steer computational effort toward the regions and events that matter for the answer, improving the figure of merit (inverse of variance times time) by orders of magnitude for deep-penetration or small-detector problems.
- Free-flight distances sampled from exponential attenuation
- Track-length and collision estimators for tallies
- Error scales as 1/sqrt(number of histories)
- Variance reduction: importance sampling, weight windows, splitting
In fusion neutronics, Monte Carlo transport is the reference tool for computing tritium breeding, neutron and gamma heating, activation, and shielding in complex blanket and vessel geometries, where accurate three-dimensional treatment is essential.