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_velocity

Reaction Rate Density

reaction_rate = neutron_density * neutron_velocity * cross_section

Variables

VariableDescriptionDefault
neutron_densityNeutron Density (n)(n/cm³)100000000
neutron_velocityNeutron Velocity (v)(cm/s)220000
cross_sectionMacroscopic 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.

neutron_density = 100000000neutron_velocity = 220000cross_section = 0.1
  1. 01phi = 10⁸ × 2.2 × 10⁵ = 2.2 × 10¹³ n/(cm²·s)
  2. 02R = 2.2 × 10¹³ × 0.1 = 2.2 × 10¹² reactions/(cm³·s)

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