What Is the Fermi Four-Factor Reactor Criticality Calculator?
The four-factor formula models the complete neutron life cycle in an infinite thermal reactor lattice.
Multiplying by non-leakage factors yields the effective multiplication factor k_eff for a realistic, finite reactor core.
How Does the Fermi Four-Factor Reactor Criticality Calculator Work?
k_eff = 1.0 represents exact steady-state criticality.
k_eff > 1.0 indicates a supercritical state where neutron population and fission power grow exponentially.
k_eff < 1.0 indicates a subcritical state where chain reactions diminish without an external source.
Fermi Four-Factor Reactor Criticality Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Calculates the effective multiplication factor and reactivity in percent mille (pcm).
How to Use the Fermi Four-Factor Reactor Criticality Calculator
- Input the four lattice factors (eta, f, p, epsilon) based on fuel enrichment and moderator geometry.
- Set the geometric non-leakage probabilities for the finite core size.
- Review the calculated k_eff, core reactivity (pcm), and operating criticality state.
Step-by-Step Example Calculation
Fermi Four-Factor Standard Case
Input Values:
Understanding Your Result
Reactivity is reported in pcm (1 pcm = 10^-5 delta-k/k).
A balanced core typically operates within +/- 10 pcm during normal power generation.
Large positive reactivity values indicate prompt-critical hazard conditions.
Factors That Affect the Result
- Fuel enrichment: Increases eta by providing more fissile U-235 per absorption.
- Moderator-to-fuel ratio: Balances thermal utilization against resonance capture.
- Core size and buckling: Larger cores exhibit higher non-leakage probabilities.
When Should You Use This Calculator?
- Nuclear engineering lattice physics education and reactor design feasibility studies.
- Estimating fuel burnup compensation and control rod reactivity worth.
Assumptions & Limitations
- Assumes a homogeneous or quasi-homogeneous thermal neutron energy spectrum.
- Does not account for spatial xenon-135 or samarium-149 poison transients.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard two-group diffusion theory formulation for thermal fission reactors.