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  • Startup: Rods are withdrawn gradually until the reactor goes critical.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.

\[ \text{Fission heat} \to \text{Steam} \to \text{Turbine} \to \text{Electricity} \]

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:

(464)#\[ ^{238}\text{U} + n \to ^{239}\text{U} \to ^{239}\text{Np} \to ^{239}\text{Pu} \]

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.