A small research reactor uses removable cadmium control rods inserted into a cylindrical core made of low-enriched uranium fuel. Cadmium is an excellent neutron absorber.
Assume that when all control rods are withdrawn, the reactor is slightly super-critical, while full insertion of the rods makes the reactor safely sub-critical.
(a) Describe the physical role played by the cadmium control rods in regulating the fission chain reaction inside the core.
(b) Explain why withdrawing the control rods too quickly can lead to a rapid rise in reactor power even though the total mass of fissile material in the core does not change.
(c) Suppose the reactor is operating at steady power with the control rods partially inserted. If an additional non-absorbing moderator is inadvertently added to the core, predict qualitatively how the required rod position must change to maintain criticality. Justify your answer using neutron economy arguments.
(d) During an emergency shutdown, the rods are fully inserted. Describe two independent physical mechanisms—one geometric and one nuclear—that immediately reduce the effective multiplication factor of the core.