7. How does the neutron population change with time?

Everything we have done in transport and diffusion theory so far has been for steady-state problems in which the neutron population is assumed to not change with time. Obviously this is not the case is transient scenarios such as reactor start-up, shutdown, temperature transients, control rod movement, etc. Thus our final problem in this course is

How does the neutron population change with time?

To answer this question we will need to address the propensity of a reactor configuration to accelerate our retard the neutron-fission chain reaction. We will investigate characteristic time scales and approximate dynamics.

7.1. Background

Reference notes, Chapter 9 of Bell and Glasstone.

7.2. In-Class Problems

1. From diffusion theory, derive expressions describing the time-dependent change of the neutron flux under the following two scenarios:
   1. Ignoring delayed neutrons.
   2. Ignoring the time-derivative of the flux in the diffusion equation.
2. Derive the (space-independent) point kinetics equations from transport theory by assuming time separability (or factorization) in the angular neutron flux.