Xenon-135: A Powerful Neutron Absorber

Among the numerous fission products generated inside a nuclear reactor, xenon‑135 holds a special place. With an astonishingly high thermal neutron absorption cross-section of about two million barns, this isotope acts as a potent poison that can shut down the chain reaction. During steady operation, a balance exists between xenon production—primarily from the decay of iodine‑135—and destruction through neutron capture and its own radioactive decay. When a reactor rapidly decreases power or scrams entirely, the neutron flux plummets while iodine continues to decay into xenon. The resulting surge, known as xenon poisoning, absorbs neutrons so efficiently that the reactor may be unable to restart for many hours. Understanding the timeline of xenon buildup and decay is vital for operators planning maintenance or responding to grid demands.

Simplified Production and Decay Model

The calculator implements a classic two-nuclide model involving iodine‑135 and xenon‑135. Let $\mathrm{\lambda \_I}$ and $\mathrm{\lambda \_X}$ denote their decay constants, related to half-lives by $\lambda =\frac{\ln \left(2\right)}{\mathrm{T\_\{1/2\}}}$. Prior to shutdown the reactor is assumed to operate at equilibrium, meaning xenon concentration $\mathrm{X\_e}$ remains constant. At time zero the chain reaction stops, eliminating neutron absorption. The iodine concentration decays exponentially: $I(t)=\mathrm{I\_0}{e}^{-\mathrm{\lambda \_I}t}$. Xenon then evolves according to . Solving these equations with initial equilibrium conditions yields xenon concentration during the outage:

$X(t)=\mathrm{X\_e}{e}^{-\mathrm{\lambda \_X}t}+\frac{\mathrm{\lambda \_I}}{\mathrm{\lambda \_X}-\mathrm{\lambda \_I}}\mathrm{X\_e}(e^{-\mathrm{\lambda \_I}t}-e^{-\mathrm{\lambda \_X}t})$.

This expression reveals the familiar behavior observed in real reactors: xenon initially climbs because iodine decay outruns xenon decay, peaking several hours after shutdown. Eventually the absence of neutron capture allows xenon itself to decay, reducing poisoning. The calculator evaluates this formula at the specified shutdown duration to obtain the xenon concentration at restart, normalized relative to the original equilibrium.

Estimating Recovery Time

Once operators attempt to restart the reactor, xenon continues to decay toward equilibrium at a rate governed by $\mathrm{\lambda \_X}$. For simplicity, the model assumes power returns instantly to pre-shutdown levels, so neutron absorption immediately balances production again. The xenon concentration then decays exponentially: $X(t)=\mathrm{X\_0}{e}^{-\mathrm{\lambda \_X}t}+\mathrm{X\_e}(1-e^{-\mathrm{\lambda \_X}t})$, where X₀ is the xenon level at restart. The calculator determines the time required for X to fall within five percent of equilibrium by solving $X(t)=1.05\hspace{0.17em}\mathrm{X\_e}$. In practice, if xenon buildup pushes X₀ far above equilibrium, this recovery time can exceed a day, creating what operators term a “xenon pit.”

Risk Interpretation

The output includes a logistic risk score representing the likelihood that recovery exceeds 24 hours. The function $R=\frac{100}{1+e^{-0.2(\mathrm{t\_r}-24)}}$ converts the computed recovery time $\mathrm{t\_r}$ into a percentage. High values warn planners that a prolonged wait may disrupt grid operations or maintenance schedules, while low values indicate quick restart is feasible.

Limitations and Practical Considerations

Real reactors rarely behave as neatly as the idealized equations suggest. Power often ramps down gradually, and residual neutron flux during cooldown partly burns off xenon. Control rods or soluble boron may be used to compensate for poisoning, allowing restarts even when xenon exceeds equilibrium. The production of xenon is also tied to reactor power history: a reactor operating at low power before shutdown will experience less buildup than one running at full output. Furthermore, other poisons like samarium‑149 can influence reactivity over longer timescales. The calculator assumes a single, instantaneous shutdown and restart, neglecting these subtleties. Nevertheless, it captures the dominant trend and offers a transparent tool for students and operators to appreciate the temporal dynamics of xenon.

Historical Context

Xenon poisoning played a dramatic role in early nuclear history. During the startup of the first large-scale reactor at Hanford in 1944, operators were baffled when power levels mysteriously declined hours after reaching criticality. Only after hurried calculations did physicist John Wheeler predict the buildup of a strong neutron absorber—later identified as xenon‑135. Adjustments to control rod design allowed the reactor to achieve its mission of producing plutonium for the Manhattan Project. Decades later, xenon transients factored into the Chernobyl disaster, where a rapid power reduction followed by an attempted power increase contributed to unstable conditions. These incidents underscore why understanding xenon behavior remains central to nuclear safety.

Table: Shutdown vs Recovery

Shutdown (h)	Xe at Restart (×eq)	Recovery Time (h)
6	1.55	15
12	2.01	23
24	2.38	30

Broader Implications

Accurate forecasting of xenon transients aids not only reactor restart planning but also load-following strategies, where power output must track variable demand. As nuclear plants integrate with renewable-heavy grids, the ability to maneuver safely through xenon pits becomes increasingly valuable. Operators might schedule maintenance during expected high xenon periods or plan power reductions gradually to minimize buildup. Research into advanced fuels and reactor designs seeks to mitigate xenon effects altogether. Until such innovations mature, tools like this calculator offer a bridge between theoretical kinetics and day-to-day operational decisions, illuminating the invisible dynamics that govern the heart of a nuclear reactor.