The process of verifying and validating the concepts that underlie the IFFY database and its models starts here.
- The overall project uses a simulation to evolve fission fragments and store the results in a database. The reasons behind the choice of simulation style are discussed here.
- The fission fragment simulation is done. The results are “in the can”. There will be no simulation users, just database explorers.
- Users will have a measure of control in the fuel evolution simulation. We are still developing some of those concepts. (more to come)
Fission Fragment Evolution Concepts
The IFFY simulation has four major concepts that distinguish it from other models:
- Exponential time – most simulations use a regularly ticking clock.
- Data cloning – the first second of reactor operation is repeated a billion times.
- One-pass processing – this is valid only if the nuclides are ordered “properly”.
- Half-life equivalency, perhaps the iffiest concept.
Exponential Time concept
A simulation designer faces a basic choice between accuracy and run time. One can always make a model more accurate by reducing the size of the time-step. This increases the run time. For comparison, IFFY’s 31 time-steps took ten hours to process on a Surface Pro 4.
Alternately, we could run 34 iterations at a fixed rate of one year per time-step. This would consume about the same time it took to run the exponential version of IFFY. Obviously, we lose a lot of detail on the short-lived isotopes with that approach.
- We could “sample” the reactor once a day with a 3650 hour (five month) run.
- More accurately, a time-step of one hour would require ten years of CPU time.
- Replicating IFFY on a second-by-second basis would take 36,000 years.
The exponential approach is a compromise between accuracy and run time. We use a small time-step when things are changing fast. Then, we increase the size (span) of the time-step as the rate of change decreases.
Data cloning
The IFFY fission event produces a pair of composite (aggregated) atoms, each with exactly the same proportion of elements and isotopes. There are nearly 1000 micro-pieces of every possible fission fragment within this composite. Obviously, this is unnatural, but the math works.
IFFY is a deterministic model, which means no randomness. Every fission event produces the same composite pair. The second event looks just like the first. Therefore, we can reuse that data. In fact, we use the same data for the very last second of reactor operation, 34 years after startup.
The first second of reactor operation is special. It is the only time-step with an explicit fission event. This occurs at the 0.5 second mark, which is the best “average” placement for a single event in a one second time span. In addition to the fission event, there is one more process; the fission fragments are decayed for 0.5 seconds. Then we take the first snapshot of the waste composition (Snap0).
In the next second the exact same thing happens. However, we cannot just double the inventory. This would ignore the fact that the first fission fragments are now 1.0 seconds older. Therefore, we apply a second round of decay to the first fission fragments. At the end of the simulation, the first fission fragments will have been decayed 31 times.
In effect, our assumption is that a string of fission events (with decay) is the same as any other string of the same length.
One-pass processing
Unstable nuclei decay in the same sequence every time, at least in a deterministic simulation. A digital computer, inherently a sequential processor, can handle this accurately.
We developed the “proper” order for processing all 1322 nuclides over time. This effort resulted in a set of rules for assigning Rung values to each nuclide. The reasons behind the rules are described in more detail, including special cases, here. The final rule set is given below:
- Proceed down the Decay Chains from Atomic Weight 172 to 65,
- For each chain count down the Rungs,
- Decay the Unstable Islands first,
- Process the Shadowed Chains next.
- Process the Main Chains last.
- For each chain count down the Rungs,
Half-life Equivalency
We use this concept to process neutron capture in much the same way (and with the same equation!) as we calculated radioactive decay.
The basic assumption is that a substance under neutron bombardment acts much like a naturally radioactive substance. That is, after a characteristic amount of time, half of it will be gone – or rather transformed.
- In the case of fuel atoms, fission transforms fuel into fission fragments (boom).
- Nuclei that capture neutrons get plumper by the mass of the neutron.
- This may make them unstable and they transmute to the next higher element on the periodic table.
- Some physicists call it a transmutation if the daughter is stable. In contrast, when the result of a capture is simply another isotope of the same element, we say the neutron “plumps” the nucleus.
The rate at which fission occurs is proportional to the fission cross-section of the fuel atom. Neutron capture depends on the capture cross-section of the nuclide under bombardment. We measure cross-section area in barns, as in “…couldn’t hit the broad side of…”
Our concept pivots on 235-U. In most of today’s reactors the 235-U comprises about 4% of new fuel. This “burns” down to 1% after about four years. That means the population of 235-U atoms has been cut in half twice in four years. Therefore, we claim 235-U to have a Half-Life Equivalent (HLE) of two years. Of course, this value depends of the neutron flux.
1266 barns = lose half your mass in a year
The rate at which 235-U burns depends on its known fission cross-section of 583 barns. Since the fission of half of the fuel takes two years, we set the pivot point at 2 x 583 or 1266 (per year). We pin any nuclide’s HLE to this. For example, an isotope that has a neutron capture cross section of 126.6 barns will take ten years for half of it to plump.
- We store the HLE values for relevant nuclides in the Absorbers table. We measure HLE in seconds for compatibility with the decay calculations.