Neutron Diffusion

Neutrons collide many times with nuclei inside of the reactor and move around in a complicated zigzag way. Let r, Ω and E be the position, the angle, and the kinetic energy of neurons. After time dt, they appear at a different position (r′), toward a different angle (Ω′) and with a different kinetic energy (E′). In this alternation, the neutrons are transported from the “primary position and energy state” to the “secondary position and energy state”. This phenomenon is studied in transportation theory. The equation that governs the phenomena of transportation is called the Boltzmann equation or the transport equation. Solving the Boltzmann equation is much more difficult than deriving it. However, in certain conditions, this equation can be simplified and solved easily. This is called diffusion theory. In most part of this chapter, all neutrons are supposed to have the same energy. This is called single speed diffusion theory.