NTN REACT cheat sheet

Multiplication factor: k = (neutrons produced in generation n+1)/(neutrons produced in generation n); k = 1 critical, k > 1 supercritical, k < 1 subcritical.

Six-factor formula: k = ε·p·f·η·P_FNL·P_TNL, where ε is fast fission factor, p resonance escape probability, f thermal utilization, η reproduction factor, and the two terms are fast and thermal non-leakage probabilities.

Reactivity: ρ = (k − 1)/k, expressed in dollars as ρ/$ where $ = β (delayed neutron fraction, about 0.0065 for U-235 thermal fission).

Prompt neutron lifetime ℓ and generation time Λ relate to the stable reactor period via the inhour equation; for small positive ρ, T ≈ Λ/ρ.

Delayed neutrons (about 0.65% of fissions in U-235) make reactors controllable; the reactor is prompt critical when ρ ≥ β.

Point kinetics: dn/dt = [(ρ − β)/Λ]n + Σλ_i C_i, with six delayed precursor groups; effective delayed fraction β_eff depends on core composition.

Four-factor formula for an infinite lattice: k∞ = ε·p·f·η; leakage is accounted for by adding the non-leakage probabilities P_FNL and P_TNL.

Xenon-135 poisoning: peak post-shutdown reactivity worth occurs roughly 8–10 hours after shutdown due to I-135 decay outpacing Xe burnout; equilibrium Xe worth is largest at high flux.

Samarium-149 is a stable poison approaching equilibrium slowly (half-life of its precursor Pm-149 is about 53 hours); it does not burn out appreciably.

Startup is performed on the source range (count rate) instruments; approach-to-critical uses the inverse count rate (1/M) plot, and 1/M extrapolates to zero at criticality.

Criticality safety rule: maintain at least two independent, diverse indications of criticality (e.g., startup channels and intermediate range) before withdrawing control rods further.

Control rod worth is measured by the rod drop method or the period (doubling time) method; integral worth curves are S-shaped, with differential worth peaking near mid-core.

Temperature coefficients: a negative moderator temperature coefficient provides inherent load-following and shutdown feedback; a positive coefficient requires administrative limits on power level.

Power defect is the reactivity change from zero to full power caused by Doppler, moderator temperature, and void feedback; it must be compensated by rod withdrawal.

Shutdown margin is the reactivity worth of all rods minus the highest-worth rod stuck fully withdrawn, with the reactor at power and equilibrium poisons; it must remain positive.

Boration/dilution controls long-term reactivity: boron concentration changes are made in small steps with mixing time allowed before evaluating reactivity response.

Surveillance testing of rod exercise, trip breakers, and instrument channels is required at defined intervals; failure to complete surveillance within the grace period requires a shutdown or power reduction.

Dose quantities: absorbed dose in gray (1 Gy = 1 J/kg); equivalent dose in sievert = absorbed dose × radiation weighting factor w_R (photons = 1, neutrons = 2–20 depending on energy, alpha = 20).

Occupational dose limits (ICRP/typical national): 20 mSv/y averaged over 5 years, 50 mSv in any single year; lens of eye 20 mSv/y; extremities and skin 500 mSv/y.

Public dose limit: 1 mSv/y from licensed practices; the ALARA principle requires doses to be as low as reasonably achievable, economic and social factors considered.

Inverse square law: dose rate falls as 1/r²; doubling distance from a point source reduces dose rate to one quarter.

Shielding: half-value layer (HVL) reduces intensity by half; attenuation I = I₀·e^(−μx), and HVL = ln2/μ.

Contamination control: survey with a thin-window detector for beta emitters; smear (wipe) tests detect removable contamination; fixed contamination requires decontamination or shielding.

Neutron dose is measured with rem-meters or TLDs with neutron-sensitive elements; gamma dose with ionization chambers or TLDs; use energy-compensated instruments for mixed fields.

Derived air concentration (DAC) and annual limit on intake (ALI) are used to control airborne radioactive material; DAC-based monitoring is required in areas where airborne activity may exceed specified fractions.

Defense in depth: multiple independent barriers (fuel matrix, cladding, primary boundary, containment) and redundant safety systems protect against release of fission products.

Emergency classification levels typically escalate: Notification of Unusual Event → Alert → Site Area Emergency → General Emergency, based on actual or potential radiological impact.

Emergency action levels (EALs) are pre-defined instrument readings or conditions that trigger each classification; they must be based on measurable parameters.

Emergency core cooling system (ECCS) acceptance criteria (10 CFR 50.46): peak cladding temperature ≤ 2200°F (1204°C), cladding oxidation ≤ 17% of initial thickness, and coolable geometry maintained.

Critical safety functions: reactivity control, reactor coolant inventory, heat removal, and containment integrity; emergency operating procedures are symptom-based, not event-based.

SCRAM (reactor trip) inserts all control rods by gravity or spring force; failure of a single rod to insert must not prevent safe shutdown (single-failure criterion).

Post-accident monitoring: containment hydrogen concentration is controlled to below 4% (flammability limit) by recombiners or venting; hydrogen is generated by zirconium-water reaction and radiolysis.

Emergency plan exercises and drills are required at defined frequencies (e.g., biennial full-scale exercises) with evaluated corrective actions for identified deficiencies.

Pressurized water reactor (PWR): primary coolant at ~15.5 MPa (2250 psig) with subcooled liquid; steam generator secondary side produces saturated steam at ~6–7 MPa.

Boiling water reactor (BWR): direct cycle; reactor coolant boils in the core at ~7 MPa (1000 psia); steam separators and dryers produce ~99.9% quality steam to the turbine.

Primary coolant pumps provide forced circulation; loss of forced flow (natural circulation) reduces heat removal capability and may require power reduction or trip.

Pressurizer maintains primary pressure via heaters (raise pressure) and spray (lower pressure); it also accommodates coolant volume changes during power maneuvers.

Steam generator tubes are a boundary between primary and secondary; tube degradation is monitored by eddy current testing, and tube plugging reduces heat transfer area.

Containment systems include the containment spray, fan coolers, and isolation valves; containment isolation valves must close on a containment isolation signal.

Residual heat removal (RHR) system removes decay heat after shutdown and cools the refueling pool; it requires adequate coolant inventory and flow path alignment.

Safety injection systems (high-pressure and low-pressure) inject borated water to restore inventory and reactivity control after a loss-of-coolant accident.

Source range (startup) detectors are proportional counters sensitive to individual neutrons; count rate is proportional to neutron population and used during shutdown and startup.

Intermediate range uses compensated ion chambers; log power is measured in decades per minute (DPM); high flux trip setpoints are typically around 10–40% of rated power.

Power range uses uncompensated ion chambers; the axial offset (AO) is (top power − bottom power)/(top + bottom power), used to monitor core power distribution.

Redundancy and diversity: safety-related instrumentation uses at least two or three independent channels with coincident logic (2-out-of-4 voting) to avoid spurious trips and failure to trip.

Setpoint uncertainty includes instrument accuracy, calibration error, and drift; trip setpoints must be established so the safety limit is not exceeded even with uncertainty.

Period meters measure reactor period T = (ln 2)/λ; a period of 18 seconds corresponds to a doubling time of 18 seconds and is a typical startup alarm threshold.

In-core detectors (fission chambers or self-powered neutron detectors) map local flux to verify power distribution and detect localized anomalies.

Control systems include manual, automatic, and computer-based controls; safety-related controls must be qualified to environmental and seismic standards (IEEE 323, IEEE 344).

Technical specifications (Tech Specs) define limiting conditions for operation (LCOs), surveillance requirements, and action statements with completion times.

Safety limits are the limits on important process variables (e.g., fuel cladding temperature, primary pressure) that must not be exceeded; safety system settings are setpoints that protect the safety limits.

10 CFR 50 Appendix B establishes the quality assurance criteria for nuclear facilities; 10 CFR 50.59 governs changes to the facility without prior license amendment.

Design basis accidents (DBAs) are the postulated accidents against which the facility is designed; beyond-design-basis events are addressed by probabilistic risk assessment (PRA).

Operating license conditions include the license expiration date, authorized power level, and required reports; license renewal is typically for 20 additional years.

Event reporting: 10 CFR 50.72 requires immediate notification of specified events, and 10 CFR 50.73 requires written licensee event reports (LERs) within 60 days.

ALARA program documentation includes dose goals, trending, and corrective actions; occupational dose records are maintained and reported to the NRC (or national regulator).

Emergency plan requirements (10 CFR 50.47 and Appendix E) include plume exposure pathway EPZ of about 10 miles and ingestion pathway EPZ of about 50 miles for planning purposes.