Definitions

• We had seen previously in the course that the intensity of neutrons in a beam was defined as the number of neutrons crossing a plane per unit area and unit time and this was shown to be

• Since the beam travels in the same direction unless it is absorbed, the problem is a scalar as there is no change of direction is involved.
• However, when we deal with neutrons in a reactor, they are born at different places and travel in different directions.
• Further their directions are modified due to the process of scattering.
• To predict the neutron population density variation in a reactor we need a more complex treatment.
• It will be practically impossible to track every neutron and study its motion as there are very large number of neutrons present in the system.
• To handle this problem in a simple manner, the concept of diffusion is introduced.
• Before we formally look at the concept of diffusion, we shall define a few terms.
• The term Neutron Flux, φ, is defined as the product of neutron density and the speed of the neutron and it is a scalar quantity.

• Another term Neutron Current, J, is defined as number of neutrons crossing a unit area per unit time in a specific direction.
• J is a vector quantity and shall have components such as J_x, J_y, etc.
• Consider the case of several beams intersecting at a point as shown in the figure below.
• At the point of intersection

• When several beams cross, it is easy to visualise that, the former is a scalar sum, while the latter is a vector addition.
• If all the neutrons travel in the same direction as in a single beam, both φ and J are identical in a non scattering system.