What Is the Nuclear Reactor Period & Inhour Reactivity Calculator?
Reactor period is the time required for nuclear fission reactor power to increase by a factor of e (approximately 2.718).
How Does the Nuclear Reactor Period & Inhour Reactivity Calculator Work?
Delayed neutrons emit seconds after fission, slowing down the neutron population growth rate to manageable human timescales.
Nuclear Reactor Period & Inhour Reactivity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
T \approx \frac{\beta - \rho}{\lambda \rho}, \quad T_{\text{double}} = T \ln(2), \quad \$ = \frac{\rho}{\beta}
One-group Inhour equation for asymptotic reactor period below prompt critical.
How to Use the Nuclear Reactor Period & Inhour Reactivity Calculator
- Input prompt neutron lifetime, delayed neutron fraction beta, precursor decay constant, and inserted reactivity.
Step-by-Step Example Calculation
U-235 Reactor Startup Transient
Input Values:
promptNeutronLifetimeSeconds:0.0001
delayedNeutronFractionBeta:0.0065
precursorDecayConstantLambdaS:0.08
reactivityRho:0.001
Worked Steps: Predicts reactor period T = 68.8 seconds with power doubling time of 47.7 seconds ($0.154 reactivity).
Understanding Your Result
Shows reactor period in seconds, doubling time in seconds, and reactivity normalized in dollars ($).
Factors That Affect the Result
- If reactivity exceeds beta ($1.00), the reactor becomes prompt critical with sub-millisecond runaway periods.
When Should You Use This Calculator?
- Nuclear power plant control room operations, startup transients, and safety analysis reports.
Assumptions & Limitations
- Valid for sub-prompt-critical operations (rho < beta) using one effective delayed neutron group.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Derived by Eugene Wigner and Alvin Weinberg.