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A boiling water reactor is a nuclear reactor in which water boils inside the reactor vessel and the resulting steam directly drives a turbine. Water serves as both coolant and neutron moderator. Moisture separators and dryers remove entrained liquid before steam reaches the turbine; a condenser and feedwater system return it to the vessel.^[ref]

The heat balance makes its purpose concrete: in a simplified steady model, $\dot{Q}\simeq \dot{m}(h_{\mathrm{steam}}-h_{\mathrm{feedwater}})$, where $\dot{m}$ is the water mass flow and $h$ is specific enthalpy. With an illustrative enthalpy increase of $2MJ/kg$, transporting $2\mathrm{GW}$ of heat requires approximately $1000kg/s$. This is a thermal balance, not the electrical output, because the turbine cycle rejects heat to the condenser.

A boiling water reactor differs from a pressurized water reactor, which keeps its primary coolant liquid and transfers heat to a separate steam-producing circuit. Shutting down the chain reaction does not remove decay heat, so heat removal remains necessary after shutdown.

Let $n(E)dE$ be the number of neutrons per unit volume in an energy interval. The scalar neutron flux per unit energy is $\varphi (E)=v(E)n(E)$, with $v(E)$ the speed. Its integral has units of inverse area per unit time. It counts path length traversed per volume per time, including all directions; it is not the signed current through an oriented surface.

For a small uniform specimen containing $N_T$ target atomic nuclei, a reaction-specific collision cross-section ${\sigma }_a(E)$ gives the expected production rateAssume the incident field is little changed within the specimen, target depletion is negligible and each counted reaction creates the product of interest. If that product has a production branching fraction below one, include it in ${\sigma }_a$ or as an additional factor. A single neutron activation measurement supplies one weighted integral of an energy distribution, not a unique reconstruction of that distribution.

For an original two-group example, stipulate response collision cross-sections ${\sigma }_s=10{\sigma }_f$. With the same total scalar neutron flux $\Phi$, changing from all fast neutrons to half slow and half fast changes $R/(N_T{\sigma }_f\Phi )$ from $1$ to $5.5$. No additional neutrons need be emitted by the source. The chosen factor ten is not a historical silver measurement.

For some capture reactions over a limited low-energy interval, ${\sigma }_a\propto 1/v$ is a useful approximation. At fixed neutron flux, it gives increasing reaction probability per path length as speed decreases. At fixed neutron number density, ${\sigma }_{a}v$ is constant in this approximation, so the rate per target is unchanged. A real neutron moderator changes the local density, energy distribution, escape and absorption together. Neither all collision cross-sections nor all neutron activation rates vary monotonically as $1/v$.

Neutron moderation reduces the kinetic energy of fast neutrons through repeated collisions in a neutron moderator. In a simple elastic collision model, hydrogen is especially effective because a proton and a neutron have nearly equal masses: the maximum elastic recoil energy fraction can approach one. The mean logarithmic energy decrement describes typical accumulated slowing, whereas the maximum transfer describes a single endpoint.

Slowing, absorption and escape compete. A material can remove neutrons by neutron capture before they become thermal neutrons, and some neutrons escape its boundaries. Describing a neutron moderator therefore requires more than collision kinematics. Near thermal equilibrium, target thermal motion can also give energy back to a neutron; the initially stationary target approximation must then be replaced.

Neutron physics studies the production, interaction, transport and detection of neutrons. A neutron has no net electric charge, so it does not experience the long-range Coulomb repulsion that impedes charged particles approaching a positively charged atomic nucleus. Its nuclear interactions nevertheless depend strongly on energy and target isotope.

Elastic scattering can slow neutrons in a neutron moderator, capture can change a nucleus, and suitable reactions can initiate nuclear fission. Neutron magnetic moments also couple to magnetic structure, enabling magnetic neutron diffraction. A measured attenuation therefore combines different reaction channels and must not be interpreted as one universal absorption probability.

A nuclear reactor sustains and controls a nuclear chain reaction to produce heat or a useful neutron field. Nuclear fission supplies fresh neutrons; absorption and neutron leakage remove them. A steady neutron population requires a balance between production and losses, the condition of nuclear criticality.

The functions of its components are different. Fuel supplies fissioning atomic nuclei; control rods change neutron absorption; coolant transports heat. In a thermal reactor, a neutron moderator reduces neutron energies before subsequent reactions. Slowing neutrons and cooling the fuel are separate physical functions even when the same material performs both.

Chicago Pile-1 demonstrated a controlled self-sustaining chain reaction in 1942 using a uranium–graphite assembly and neutron-absorbing controls. The decisive observation was the neutron population's response to changing absorption, rather than generation of useful electrical power.^[ref] A power reactor adds heat-transfer and conversion equipment; decay heat persists after the chain reaction is stopped.

The coolant removes heat from the fuel region and carries it to a heat exchanger or directly to a turbine system. It can also act as a neutron moderator in some reactor types, but cooling and moderation are distinct functions and need not be performed by the same material.

Each equation is stored thermal energy changing at the rate “input minus output”. Define the three heat capacities $C_j=M_j{c}_j$, and introduce the internal heat-transfer ratesIn the fuel balance, $C_F{\dot{\overline{T}}}_F$ is accumulation, $P$ is thermal power generation and $Q_{FM}$ is transfer to the neutron moderator. In the moderator balance, $Q_{FM}$ enters, $Q_{MC}$ leaves and $C_M{\dot{\overline{T}}}_M$ is accumulation. In the coolant balance, $Q_{MC}$ enters, $C_C{\dot{\overline{T}}}_C$ is accumulation and $2W_C{c}_C({\overline{T}}_C-T_i)$ is net energy carried away by flowing coolant.

The factor two follows the model's arithmetic-mean approximation ${\overline{T}}_C=(T_i+T_o)/2$, since the advective energy removal is $W_C{c}_C(T_o-T_i)$. The parameters $R_1$ and $R_2$ are effective thermal resistances, in $\mathrm{K}{\mathrm{W}}^{-1}$, for fuel-to-moderator and moderator-to-coolant transfer. They summarize the relevant geometry and heat-transfer mechanisms; they are not heat capacities.

A reactor coolant must remove heat reliably while remaining compatible with the core. Desirable properties include adequate heat capacity and heat transfer, manageable viscosity and pumping demand, stability over the operating range, limited corrosion of fuel and structures, acceptable neutron absorption and activation, and a tolerable leakage or chemical-reaction hazard. water is a standard example in light-water reactors: it transfers heat well and also moderates, but pressure, boiling behaviour, corrosion chemistry and loss of inventory must be managed. No single reactor coolant is best independently of reactor design.

A control-rod material must absorb neutrons effectively and retain mechanical and chemical integrity. It needs a suitable absorption cross section over the relevant spectrum, adequate absorber inventory over life, manageable capture heating and transmutation products, and compatibility with its sheath and reactor coolant. boron carbide is an example. Depletion, gas generation, radiation-induced swelling and cracking must be allowed for; a large initial cross section alone does not establish lifetime performance.

A neutron moderator must slow neutrons efficiently while absorbing relatively few. Light nuclei provide effective energy transfer per collision, but absorption, density, radiation stability, purity and temperature-dependent properties determine the usable moderation. heavy water is an example combining effective slowing with low parasitic absorption; graphite is another possible material in different designs. Heat removal and compatibility remain necessary even though moderation is its principal neutronic role.

nuclear fuel cladding must retain fuel and fission products while transferring heat and carrying load. Desirable properties include corrosion resistance, low neutron absorption, adequate thermal conductivity, strength and ductility, resistance to irradiation growth, void swelling and creep, and compatibility with fuel and reactor coolant. A zirconium alloy such as Zircaloy is a light-water-reactor example. Hydrogen uptake, corrosion and irradiation response constrain service; the low absorption benefit does not eliminate these materials problems.

A slow neutron has low kinetic energy relative to the fast neutrons commonly emitted in nuclear reactions. The term covers an energy range, rather than a single speed. A neutron moderator transfers kinetic energy to surrounding matter through collisions. Slowing a neutron can increase its chance of causing particular neutron capture reactions, even though each collision has reduced its kinetic energy. The Fermi slow-neutron activation experiment made this surprising distinction experimentally visible.