another. The fourth term on the right is a generic source. The equation is usually solved to find , since that will allow for the calculation of reaction rates, which are of primary interest in shielding and dosimetry studies. Types of neutron transport calculations Several basic types of neutron transport problems exist, depending on the type of problem being solved. Fixed source A fixed source calculation involves imposing a known neutron source on a medium and determining the resulting neutron distribution throughout the problem. This type of problem is particularly useful for shielding calculations, where a designer would like to minimize the neutron dose outside of a shield while using the least amount of shielding material. 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. Criticality Fission is the process through which a nucleus splits into (typically two) smaller atoms. If fission is occurring, it is often of interest to know the asymptotic behavior of the system. A reactor is called “critical” if the chain reaction is self-sustaining and time-independent. If the system is not in equilibrium the asymptotic neutron distribution, or the fundamental mode, will grow or decay exponentially over time. Criticality calculations are used to analyze steady-state multiplying media (multiplying media can undergo fission), such as a critical nuclear reactor. The loss terms (absorption, out-scattering, and leakage) and the source terms (in-scatter and fission) are proportional to the neutron flux, contrasting with fixed-source problems where the source is independent of the flux. In these calculations, the presumption of time invariance requires that neutron production exactly equals neutron loss. Since this criticality can only be achieved by very fine manipulations of the geometry (typically via control rods in a reactor), it is unlikely that the modeled geometry will be truly critical. To allow some flexibility in the way models are set up, these problems are formulated as eigenvalue problems, where one parameter is artificially modified until criticality is reached. The most common formulations are the time-absorption and the multiplication eigenvalues, also known as the alpha and k eigenvalues. The alpha and k are the tunable quantities. K-eigenvalue problems are the most common in nuclear reactor analysis. The number of neutrons produced per fission is multiplicatively modified by the dominant eigenvalue. The resulting value of this eigenvalue reflects the time