Neutron Flux Distribution Calculator
Calculates the total neutron population and effective reaction rate within a cylindrical reactor core using thermal and fast flux, core geometry, and a standard neutron yield constant. Used by nuclear engineers assessing core physics and power distribution.
About this calculator
Neutron flux is the measure of neutron intensity in a reactor core, expressed in neutrons per square centimetre per second (n/cm²·s). In a typical reactor, both thermal neutrons (slow, highly reactive) and fast neutrons (high energy, less reactive) are present simultaneously. This calculator combines them as an effective flux: effectiveFlux = thermalFlux + fastFlux × 0.1, where the 0.1 factor accounts for the lower fission probability of fast neutrons relative to thermal neutrons in most reactor designs. The core volume for a cylinder is V = π × r² × h, with r and h converted from centimetres to metres. The result is then multiplied by 2.42 × 10¹⁴, a constant representing the proportional neutron generation or reaction rate at reference conditions. Full formula: result = (thermalFlux + fastFlux × 0.1) × π × (coreRadius/100)² × (coreHeight/100) × 2.42×10¹⁴.
How to use
Example: thermalFlux = 3×10¹³ n/cm²·s, fastFlux = 1×10¹³ n/cm²·s, coreRadius = 150 cm, coreHeight = 350 cm. Step 1: effectiveFlux = 3×10¹³ + 1×10¹³ × 0.1 = 3×10¹³ + 1×10¹² = 3.1×10¹³. Step 2: r in metres = 150/100 = 1.5 m, h in metres = 350/100 = 3.5 m. Step 3: coreVolume = π × 1.5² × 3.5 = π × 2.25 × 3.5 ≈ 24.74 m². Step 4: result = 3.1×10¹³ × 24.74 × 2.42×10¹⁴ ≈ 1.86×10²⁹. Enter all values and the calculator returns this reaction-rate index instantly.
Frequently asked questions
What is the difference between thermal neutron flux and fast neutron flux in a reactor?
Thermal neutrons are slow neutrons that have been moderated (slowed down) to near room-temperature energy levels, typically below 0.025 eV. They have a much higher probability of causing fission in fissile materials like U-235, making them the primary drivers of the chain reaction in most commercial reactors. Fast neutrons are produced directly by fission events at energies of around 1–2 MeV and have not yet been moderated. While fast neutrons are less likely to cause fission in U-235, they are essential in fast-spectrum reactors and can breed new fissile material in fertile isotopes like U-238. This calculator weights fast flux at 10% of thermal flux to reflect typical thermal reactor conditions.
Why is the factor 2.42×10¹⁴ used in the neutron flux distribution formula?
The constant 2.42×10¹⁴ is a scaling factor that relates the combined effective neutron flux and core volume to an overall reaction rate or neutron population index at reference conditions. It incorporates unit conversions and reference cross-section values normalised to a standard flux level. In full reactor physics calculations, this term would be replaced by material-specific macroscopic cross-sections (Σ) and neutron multiplication factors, but this calculator uses a fixed reference constant for general-purpose estimation. Users needing precise neutronic analysis should use dedicated codes such as MCNP or SCALE with material-specific nuclear data libraries.
How does core geometry affect neutron flux distribution in a cylindrical reactor?
In a bare cylindrical reactor, the neutron flux follows a cosine distribution axially (along the height) and a Bessel function distribution radially (along the radius). This means flux peaks at the centre of the core and falls to near zero at the boundaries. Increasing the core radius or height increases the total core volume and therefore the total neutron population, but it also changes the flux shape and leakage fraction. A larger core reduces neutron leakage relative to production, making the reactor easier to sustain criticality. Reflectors placed around the core flatten the flux profile, improving fuel utilisation and power uniformity.