Nuclear scientists and engineers often need to know where neutrons are in an apparatus, in what direction they are going, and how quickly they are moving.
It is commonly used to determine the behavior of nuclear reactor cores and experimental or industrial neutron beams.
Neutron transport has roots in the Boltzmann equation, which was used in the 1800s to study the kinetic theory of gases.
As neutron distributions came under detailed scrutiny, elegant approximations and analytic solutions were found in simple geometries.
Today, with massively parallel computers, neutron transport is still under very active development in academia and research institutions throughout the world.
It is formulated as follows:[1] Where: The transport equation can be applied to a given part of phase space (time t, energy E, location
The third term on the right hand side is in-scattering, these are neutrons that enter this area of phase space as a result of scattering interactions in another.
For instance, a spent nuclear fuel cask requires shielding calculations to determine how much concrete and steel is needed to safely protect the truck driver who is shipping it.
If the system is not in equilibrium the asymptotic neutron distribution, or the fundamental mode, will grow or decay exponentially over time.
The resulting value of this eigenvalue reflects the time dependence of the neutron density in a multiplying medium.
In stochastic methods such as Monte Carlo discrete particle histories are tracked and averaged in a random walk directed by measured interaction probabilities.