Formula & Calculator
Neutron Flux
Measures the total path length traveled by neutrons per unit volume per unit time, combining neutron density and speed.
Interpretation
φ = n·v. Neutron flux is the product of neutron density (n) and average speed (v). Represents the intensity of neutrons crossing a unit area per unit time. Key parameter in reactor physics.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| φ | Neutron flux | n/(cm2*s) |
| n | Neutron density | n/cm3 |
| v | Neutron speed | cm/s |
What it means
Neutron flux (φ) is a fundamental quantity in nuclear reactor physics and neutronics. It is defined as the product of the neutron density n (number of neutrons per unit volume) and their average velocity v. Physically, it represents the total path length travelled by all neutrons in a unit volume per unit time, or the number of neutrons crossing a unit area per second. The flux is used to calculate reaction rates: reaction rate per unit volume = Σ φ, where Σ is the macroscopic cross‑section. In a reactor, the flux distribution determines the power distribution and fuel burnup. Neutron flux is measured using neutron detectors and is a key parameter in reactor control and safety. Understanding flux is essential for reactor design, core management, and radiation shielding calculations.
Worked example
Neutron Flux – Two Examples
Real‑World| Parameter | Value |
|---|---|
| n | 1×10⁸ n/cm³ |
| v | 2.2×10⁵ cm/s |
| Parameter | Value |
|---|---|
| n | 5×10⁷ n/cm³ |
| v | 2.2×10⁵ cm/s |
Common mistakes
- Neutron flux φ: The number of neutrons crossing a unit area per unit time – units: n/(cm²·s) or n/(m²·s).
- Neutron density n: The number of neutrons per unit volume – units: n/cm³ or n/m³.
- Neutron speed v: The average speed of the neutrons – in cm/s or m/s.
- Flux vs. fluence: Flux is a rate (per time); fluence is the time integral.
- Energy dependence: Flux is often energy‑dependent – use the appropriate group flux for multi‑group calculations.
Applications
Neutron flux, φ = n·v, is the product of neutron number density and their average speed. It is a measure of the intensity of neutron radiation and is a key parameter in nuclear reactor design and shielding. Reactor physicists use neutron flux to determine the reaction rates, the burnup of fuel, and the activation of structural materials. In research reactors, the flux determines the availability of neutrons for scattering experiments and isotope production. In radiation protection, knowledge of neutron flux is essential for designing shielding and for assessing dose rates to personnel. By accurately determining neutron flux, engineers can optimise reactor operation, ensure safety, and enable advanced neutron‑based research.
- Nuclear reactor core design and neutronics analysis
- Calculation of nuclear reaction rates and fuel consumption
- Design of neutron sources and research reactors
- Radiation shielding design against neutron radiation
- Neutron activation analysis and materials characterisation
Frequently Asked Questions
Neutron flux (φ) is a measure of the neutron intensity in a reactor. It is defined as the product of neutron density (n) and neutron speed (v): φ = n · v. Its units are cm⁻²·s⁻¹ (neutrons per square centimetre per second). It represents the total path length travelled by neutrons per unit volume per unit time.
Neutron flux (φ) is a scalar quantity representing the intensity of neutrons at a point, regardless of direction. Neutron current (J) is a vector representing the net flow of neutrons in a particular direction. The flux is used in reaction rate calculations, while the current is used in diffusion and transport equations.
The reaction rate (e.g., fission or absorption) per unit volume is R = Σ · φ, where Σ is the macroscopic cross section (cm⁻¹). Thus, the flux determines how many nuclear reactions occur per second in the core.
In a commercial nuclear reactor, the average thermal neutron flux is about 10¹³ – 10¹⁴ neutrons·cm⁻²·s⁻¹. In research reactors, fluxes can be higher, up to 10¹⁵. Fast neutron fluxes in the core are also significant.
Neutrons have a range of energies, from thermal (≈0.025 eV) to fast (up to MeV). The flux is often expressed as a function of energy: φ(E). The total flux is the integral over all energies. The energy distribution affects reaction rates and the design of the reactor.
Confusing neutron flux (a scalar rate) with neutron current (a directional vector). They are related by Fick's law, but cannot be used interchangeably. Also, forgetting that flux varies spatially in the reactor; it is not constant.
Using neutron detectors (e.g., fission chambers, activation foils). The detectors are placed at various positions in the core to map the flux distribution. Activation foils (e.g., gold, cobalt) are irradiated and then their activity is measured to infer the flux.
Reactor power is proportional to the fission rate, which is Σ_f · φ. Thus, the power is roughly proportional to the average flux. Control rods adjust the flux by absorbing neutrons, thus controlling power.
Flux is in cm⁻²·s⁻¹. Macroscopic cross section Σ is in cm⁻¹. The product Σ·φ gives reactions per cm³ per second.
The flux is highest in the centre of the core and decreases towards the edges and near control rods. This is described by neutron diffusion theory, which takes into account the distribution of fuel, moderator, and absorbers.