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.

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.


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.