Neutron Flux Calculator Formula
Understand the math behind the neutron flux calculator. Each variable explained with a worked example.
Formulas Used
Neutron Flux (phi)
flux = neutron_density * neutron_velocityReaction Rate Density
reaction_rate = neutron_density * neutron_velocity * cross_sectionVariables
| Variable | Description | Default |
|---|---|---|
neutron_density | Neutron Density (n)(n/cm³) | 100000000 |
neutron_velocity | Neutron Velocity (v)(cm/s) | 220000 |
cross_section | Macroscopic Cross Section (Sigma)(1/cm) | 0.1 |
How It Works
Neutron Flux and Reaction Rate
Neutron flux is a fundamental quantity in nuclear reactor physics. It determines the rate of nuclear reactions.
Formulas
phi = n × v (neutron flux)
R = phi × Sigma = n × v × Sigma (volumetric reaction rate)
where n is neutron density, v is neutron speed, and Sigma is the macroscopic cross section. Thermal neutron velocity at room temperature is about 2200 m/s.
Worked Example
A thermal reactor with n = 10⁸ n/cm³, v = 2.2 × 10⁵ cm/s, Sigma = 0.1 cm⁻¹.
- 01phi = 10⁸ × 2.2 × 10⁵ = 2.2 × 10¹³ n/(cm²·s)
- 02R = 2.2 × 10¹³ × 0.1 = 2.2 × 10¹² reactions/(cm³·s)
Frequently Asked Questions
What are typical reactor neutron fluxes?
Research reactors: 10¹²-10¹⁴ n/(cm²·s). Power reactors: 10¹³-10¹⁴. High-flux research reactors: up to 10¹⁵. The sun produces about 6 × 10¹⁰ neutrinos/cm²·s at Earth (different from neutrons).
What is macroscopic vs microscopic cross section?
Microscopic cross section (sigma) is per atom, in barns (10⁻²⁴ cm²). Macroscopic cross section (Sigma) = N × sigma, where N is atom density. Sigma has units of 1/cm and represents the probability of interaction per unit path length.
What is thermal vs fast neutron flux?
Thermal neutrons (< 1 eV) have been slowed by a moderator and have high fission cross sections. Fast neutrons (> 0.1 MeV) are produced directly by fission. Most reactors use thermal neutrons for sustained chain reactions.
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Open Neutron Flux Calculator