How a Nuclear Reactor Works: Moderator, Control Rods, Fuel

Controlling a Chain Reaction

A single uranium-235 nucleus splitting releases about 200 MeV of energy, roughly fifty million times more than burning one carbon atom. A power station harnesses billions of these fissions every second, and the key engineering problem is control: the same chain reaction that runs a reactor steadily could, if uncontrolled, run away. This tutorial explains how a nuclear reactor works: the fission chain reaction, critical mass, enriched fuel, the roles of the moderator, control rods, coolant and shielding, the main reactor types, energy calculations, nuclear waste and safety. It builds on the tutorial on nuclear energy, mass defect and binding energy.

Fission and the Chain Reaction

When a uranium-235 nucleus absorbs a slow neutron, it becomes uranium-236, which is very unstable and splits into two medium-sized nuclei (fission fragments), releasing energy and two or three fast neutrons. A typical reaction is

²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + 3 ¹n + energy.

The released neutrons can cause further fissions, each releasing more neutrons. This is a chain reaction. The important quantity is the average number of neutrons from each fission that go on to cause another fission, called the multiplication factor k:

k < 1 (subcritical): the reaction dies out;
k = 1 (critical): each fission causes exactly one more, so the reaction runs at a steady rate. This is how a reactor operates;
k > 1 (supercritical): the number of fissions grows rapidly. A bomb is designed to be strongly supercritical; a reactor is only allowed to be slightly supercritical briefly when increasing power.

Neutrons can be lost by escaping from the surface of the fuel or by being absorbed without causing fission. The critical mass is the smallest mass of fissile material that can sustain a chain reaction; below it, too many neutrons escape.

The Fuel

Natural uranium is about 99.3% uranium-238 and only 0.7% uranium-235. Uranium-238 does not fission with slow neutrons and tends to absorb neutrons. Most reactors therefore use enriched uranium, increased to about 3 to 5% uranium-235, in the form of uranium oxide pellets stacked inside metal tubes called fuel rods. (Weapons need about 90% enrichment, so reactor fuel cannot explode like a bomb.)

Parts of a Nuclear Reactor

The moderator. Neutrons released by fission are fast, with energies of about 2 MeV. But uranium-235 is far more likely to absorb slow (thermal) neutrons, with energies of about 0.025 eV. The moderator slows the neutrons down through repeated elastic collisions with its nuclei. The best moderators have light nuclei, because a neutron loses most energy when it collides with something of similar mass (in a head-on elastic collision with an equal mass, it can stop completely). Common moderators are ordinary water, heavy water (D₂O) and graphite. They must also absorb few neutrons.

The control rods. Rods of a material that absorbs neutrons strongly, such as boron or cadmium, are moved in or out of the core. Lowering them absorbs more neutrons and reduces k; raising them allows k to increase. They keep the reaction exactly critical and can shut it down completely in an emergency (a "scram"), dropping in automatically if power fails.

The coolant. A fluid (water, heavy water, carbon dioxide gas or liquid sodium) is pumped through the core to carry away the heat. In most reactors the hot coolant passes through a heat exchanger to boil water into steam, which drives turbines and generators, just as in a coal or gas power station.

The shielding. The core is surrounded by a thick steel pressure vessel and a concrete shield several metres thick, which absorbs neutrons and gamma rays and protects workers. A containment building surrounds the whole reactor to stop radioactive material escaping in an accident.

Common Types of Nuclear Reactor

Pressurised water reactor (PWR): the most common type worldwide. Water acts as both moderator and coolant, kept under high pressure (about 150 times atmospheric) so it doesn't boil, and transfers heat to a separate steam circuit.
Boiling water reactor (BWR): the water boils in the core itself and the steam drives the turbine directly.
CANDU (heavy water) reactors: heavy water absorbs so few neutrons that these reactors can run on natural, unenriched uranium.
Research reactors: small reactors that produce neutrons for experiments, training and medical isotopes. Nigeria's research reactor NIRR-1 at Ahmadu Bello University, Zaria, is used for neutron activation analysis and training, and was converted from highly enriched to low-enriched uranium fuel in 2018.

Energy from Fission: Calculations

Each fission of uranium-235 releases about 200 MeV = 200 × 1.6 × 10⁻¹³ J = 3.2 × 10⁻¹¹ J.

Example 1. How much energy is released by the complete fission of 1 kg of uranium-235?

Number of nuclei = (1000/235) × 6.02 × 10²³ ≈ 2.56 × 10²⁴. Energy = 2.56 × 10²⁴ × 3.2 × 10⁻¹¹ ≈ 8.2 × 10¹³ J.

Burning 1 kg of coal releases about 3 × 10⁷ J, so 1 kg of uranium-235 is equivalent to roughly 2.7 million kg (2,700 tonnes) of coal.

Example 2. A reactor produces 3,000 MW of thermal power. How many fissions occur per second, and what mass of uranium-235 is used per day?

Fissions per second = 3.0 × 10⁹ / 3.2 × 10⁻¹¹ ≈ 9.4 × 10¹⁹. Energy per day = 3.0 × 10⁹ × 86,400 ≈ 2.6 × 10¹⁴ J, so mass used ≈ 2.6 × 10¹⁴ / 8.2 × 10¹³ ≈ 3.2 kg per day. With a typical efficiency of about 33%, this reactor would supply about 1,000 MW of electricity.

Nuclear Waste

Used fuel contains fission fragments, many of which are highly radioactive, and heavy elements such as plutonium formed when uranium-238 absorbs neutrons. Some waste remains dangerous for thousands of years. Spent fuel is first stored under water in cooling ponds (the water absorbs heat and radiation), then in sealed steel and concrete casks. The long-term plan in several countries is burial deep underground in stable rock formations. Low-level waste, such as contaminated gloves and tools, is compacted and stored in engineered facilities.

Safety and Accidents

Every nuclear reactor is designed with many layers of protection: automatic control rods, emergency cooling systems, the pressure vessel and the containment building. Even after shutdown, the decaying fission products produce a lot of heat (several per cent of full power at first), so cooling must continue. Loss of cooling was the cause of the accidents at Three Mile Island (1979) and Fukushima (2011), where an earthquake and tsunami disabled the cooling pumps. The Chernobyl accident (1986) was caused by an unsafe test on a reactor design that became unstable at low power. Modern designs include "passive" safety features that cool the core without pumps or operators.

Advantages and Disadvantages of Nuclear Power

Advantages: no carbon dioxide while generating; huge energy from a small mass of fuel; reliable, round-the-clock power.
Disadvantages: long-lived radioactive waste; high construction costs and long building times; risk of serious accidents; concerns about the spread of nuclear materials.

Summary

Slow neutrons split uranium-235, releasing about 200 MeV and 2 or 3 fast neutrons per fission.
A nuclear reactor is kept exactly critical (k = 1); below the critical mass a chain reaction cannot be sustained.
The moderator slows neutrons, control rods absorb them, the coolant removes heat and the shielding absorbs radiation.
1 kg of uranium-235 releases about 8 × 10¹³ J, equal to thousands of tonnes of coal.
Waste storage, decay heat and safety systems are central to reactor design.