In an operating reactor, the point of equilibrium for a given nuclide is when its rate of decay equals its rate of production. Since a stable isotope doesn’t decay, it does not achieve equilibrium until the reactor stops operating.
- For a radioactive nuclide (we submit) it takes ten half-lives to achieve equilibrium.
- This contention requires validation from a competent nuclear authority!
- There are seven long-lived fission products (LLFP) with half-lives from 200,000 to 15 million years. It is unlikely that you can run a reactor long enough for these to reach equilibrium.
The first chart shows nuclides with half-lives less than one second, in TimeBin 0_Zero. (The “0” serves to sort the TimeBins properly in certain charts.)
TimeBin: 0_Zero
There are >400 nuclides piled up on the horizontal axis! These have a half-life = 0, therefore a cumulative yield of zero.
- This chart also shows “TimeStep_Negative_1”, from an older output data set.
- In the exponential time scheme, this is POWER(2,-1) = 0.5 seconds, the moment of fission.
- The population of each nuclide at 0.5 sec is its initial yield, straight from the Sigma data.
- Note that between 0.5 and 1.0 sec (TimeStep 0) the only activity is decay.
- In the exponential time scheme, this is POWER(2,-1) = 0.5 seconds, the moment of fission.
TimeBin: 1_Sec
These nuclides have half-lives that are reported in seconds. (The raw data were not terribly consistent in their time units!) The longest-lived of these nuclides all come to equilibrium by 600 seconds, according to our rule. TimeStep 10, aka the Kilosec snapshot, is taken 1024 seconds after reactor startup. They hav e all flat-lined by then.
TimeBin: 2_Min
These nuclides have half-lives greater than 60 seconds, but less than an hour. The vertical axis shows that only one nuclide has an equilibrium population of more than 200 atoms.
TimeBin: 3_Hour
These half-lives are usually reported in hours. (A half-life reported as 35 hours belongs in the 4_Day bin.) The troublesome 135-Xe super-absorber is highlighted here. The twist is that 135-I drains directly into 135-Xe. This complicates the 135-Xe yields for a few days before and after refueling.
TimeBin: 4_Day
This chart has nuclides with half-lives less than a year. TimeStep 28 is eight years. The population of 144-Ce is barely increasing by then. 103-Ru flattened out long before that, at TimeStep 25. TimeStep 25 is labelled 1_yr, but it’s really 388 days, almost exactly ten times 103-Ru’s half-life.
TimeBin: 5_Year
This bin has nuclides with half-live from 1-1000 years. The three isotopes with half-lives in the decades range (TimeBin = Years) will not come to equilibrium in the 34 years of IFFY sim operation. Those with less than a 3.4 half-life will. Note that these data do not include neutron capture. The 151-Sm is mostly 152-Sm by the end of the simulation.
Conclusion
The equilibria are an interesting but not often important aspect of nuclear operations. They do provide a different approach to simulation validation and verification.
Note: The charts above mostly come from an early debugging run, based on 245-Cm fuel. We had to redo the TimeBin 3_Hour chart with 235-U data.