43-2 The Nuclear Reactor#
Prompts
A nuclear reactor maintains a critical chain reaction (section 43-1). What is the role of the moderator? Why must neutrons be slowed to thermal energies?
Control rods (boron, cadmium) absorb neutrons. How do inserting and withdrawing them change the reactor power? What happens if all control rods are fully inserted?
The fission energy appears as heat. What is the role of the coolant? How is heat converted to electricity?
What is a breeder reactor? How does it “produce more fuel than it consumes”? What is the role of \(^{238}\text{U}\)?
Compare a light-water reactor (water as moderator and coolant) with a heavy-water or graphite-moderated design. Why might one choose different moderators?
Lecture Notes#
Overview#
A nuclear reactor uses controlled fission to produce heat, which is converted to electricity. The chain reaction must be kept critical (section 43-1) — steady power, not growing or dying.
Key components: moderator (slows neutrons), control rods (regulate reactivity), coolant (removes heat).
Breeder reactors convert fertile \(^{238}\text{U}\) into fissile \(^{239}\text{Pu}\), producing more fuel than they consume.
The Moderator#
Fission neutrons are born fast (MeV). For \(^{235}\text{U}\), the fission cross section is much larger at thermal energies (~0.025 eV). A moderator slows neutrons by elastic collisions with light nuclei.
Good moderators: low mass (so neutrons lose energy per collision), low neutron absorption. Common choices:
Moderator |
Notes |
|---|---|
Light water (H\(_2\)O) |
Absorbs some neutrons; requires enriched uranium |
Heavy water (D\(_2\)O) |
Absorbs less; can use natural uranium |
Graphite |
Solid; used in some designs |
Why light nuclei?
In an elastic collision, a neutron transfers the most energy to a target of similar mass. A proton (mass ≈ neutron) is ideal; heavier nuclei absorb less energy per collision. Heavy water uses deuterium, which absorbs fewer neutrons than hydrogen.
Control Rods#
Control rods contain neutron absorbers (e.g., boron, cadmium). Inserting them removes neutrons from the chain reaction → power decreases. Withdrawing them allows more neutrons to cause fission → power increases.
Startup: Rods are withdrawn gradually until the reactor goes critical.
Steady operation: Rod position is adjusted to maintain criticality as fuel is consumed.
Shutdown: Rods are fully inserted (scram) to make the core subcritical.
Coolant and Power Conversion#
Fission fragments and neutrons deposit their kinetic energy in the core as heat. A coolant (often water, sometimes liquid metal or gas) flows through the core, carries heat to a heat exchanger, and produces steam. The steam drives a turbine connected to a generator → electricity.
The coolant also helps moderate (if it is water) and must not absorb too many neutrons.
Breeder Reactors#
Natural uranium is ~99.3% \(^{238}\text{U}\) (fertile) and ~0.7% \(^{235}\text{U}\) (fissile). A breeder reactor is designed so that more fissile material is produced than consumed:
Neutrons from fission both sustain the chain reaction and convert \(^{238}\text{U}\) to \(^{239}\text{Pu}\). The conversion ratio (or breeding ratio) can exceed 1 — more \(^{239}\text{Pu}\) is created than \(^{235}\text{U}\) (or \(^{239}\text{Pu}\)) is consumed. This extends the usable fuel supply.
Fast vs thermal breeders
Some breeders use fast neutrons (no moderator) because \(^{238}\text{U}\) has a higher fission cross section at high energies. The core design differs from thermal reactors.
Summary#
Moderator: Slows neutrons to thermal energies where \(^{235}\text{U}\) fission cross section is large; water, heavy water, or graphite.
Control rods: Absorb neutrons; insert to reduce power, withdraw to increase; scram for shutdown.
Coolant: Removes heat from core; steam drives turbine → electricity.
Breeder: Converts \(^{238}\text{U}\) to \(^{239}\text{Pu}\); can produce more fissile fuel than consumed.