Neutron Physics Lecture Notes

Introduction

• Last lecture on neutron physics
• Focus on time-dependent perturbation of reactors
• Use of reactor period analog panel meter in power manipulations

Criticality and Perturbations

Single Group Criticality

• Analyze criticality in light water reactors or thermal reactors
• Effects of inserting control rods:
  • Nu (ν): Neutrons per fission; changes over time with plutonium buildup, not by rod insertion
  • Sigma Fission (Σ_f): Changes with volume fraction of materials; small decrease with control rod insertion
  • Sigma Absorption (Σ_a): Large increase with control rod insertion
  • Diffusion Constant (D): Decreases with increased absorption cross-section
  • Geometric Buckling: Slight increase due to diffusion constant change
• Overall effect: K effective (K_eff) decreases with control rod insertion

Feedback Mechanisms

Boiling Coolant

• Sigma Fission: Slight increase
• Sigma Absorption: Decrease due to loss of absorbing water
• Diffusion Coefficient: Increase, neutrons travel further
• Effect: K effective decreases

Fuel Temperature Increase

• Resonance broadening decreases fission cross-sections
• Diffusion increases as coolant density decreases
• Effect: K effective decreases

Fast Reactors

• Sodium fast reactors rely on fast fission of U-238
• Voiding coolant can lead to positive void coefficient
• High boiling points for fast reactor coolants to prevent boiling

Reactor Transients

Infinite Medium Approximation

• K Infinity (K_∞): No leakage in infinite medium
• Flux change proportional to production-destruction imbalance_

Reactor Period

• Formula for flux as function of time
• Typical thermal reactor period ~0.1 seconds
• Delayed neutrons (~0.064 fraction) critical for stability

Delayed Neutrons and Reactor Control

• Delayed neutrons slow the reaction, increasing reactor period to ~100 seconds
• Prompt criticality can make reactors unsafe if control rods are removed too quickly

Intuition and Implications

• Flux Graph:
  • Prompt rise followed by delayed feedback results in non-linear power increase
• Control systems prevent prompt supercriticality
• Homework involves simulating scenarios

Conclusion

• Questions encouraged
• Next class will focus on problem-solving strategies
• Janus software tutorial to assist with problem sets

These notes cover key concepts in reactor physics related to perturbations, criticality, feedback mechanisms, and the role of delayed neutrons in reactor safety and operation. For further detailed study, review problem sets and simulations using software tools like Janus.