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CHAPTER 2 - GEOMETRY, DATA, PHYSICS, AND MATHEMATICS
CRITICALITY CALCULATIONS
The standard deviations are computed at the end of the problem. Because the σ2s decrease as
1/(It − Ic), ∆keff is independent of the number of active cycles. Recall that ∆keff is proportional to
1/N, the number of neutrons per keff cycle.
Eqn. (2.31) can be written146 as the following inequality:
∆k eff ( I t – I c )σ keff
-------------< ---------------------------σk eff
2k eff
.
(2.35)
This inequality is useful for determining an upper limit to the number of active cycles that should
be used for a calculation without having ∆keff dominate σ keff . If σ k eff ⁄ k eff is 0.0010, which is a
reasonable value for criticality calculations, and It − Ic is 1000, then ∆k eff ⁄ σ k eff < 0.5 and ∆keff
will not dominate the keff confidence interval. If σ k eff is reasonably well approximated by MCNP's
estimated standard deviation, this ratio will be much less than 0.5.
The total running time for the active cycles is proportional to N(It − Ic), and the standard deviation
in the estimated eigenvalue is proportional to 1 ⁄ N ( I t – I c ) . From the results of the convergence
run, the total number of histories needed to achieve the desired standard deviation can be estimated.
It is recommended that 200 to 1000 active cycles be used. This large number of cycles will provide
large batch sizes of keff cycles (for example, 40 batches of 10 cycles each for 400 active cycles) to
compare estimated standard deviations with those obtained for a batch size of one keff cycle. For
example, for 400 active cycles, 40 batches of 10 keff values are created and analyzed for a new
average keff and a new estimated standard deviation. The behavior of the average keff by a larger
number of cycles can also be observed to ensure a good normal spatial mode. Fewer than 30 active
cycles is not recommended because trends in the average keff may not have enough cycles to
develop.
3.
Analysis of Criticality Problem Results
The goal of the calculation is to produce a keff confidence interval that includes the true result the
desired fraction of the time. Check all WARNING messages. Understand their significance to the
calculation. Study the results of the checks that MCNP makes that were described starting on
page 2–178.
The criticality problem output contains a lot of useful information. Study it to make sure that: 1) the
problem terminated properly; 2) enough cycles were skipped to ensure that the normal spatial mode
for fission sources was achieved; 3) all cells with fissionable material were sampled; 4) the average
combined keff appears to be varying randomly about the average value for the active cycles; 5) the
average combined keff–by–cycles–skipped does not exhibit a trend during the latter stages of the
calculation; 6) the confidence intervals for the batched (with at least 30 batch values) combined keff
do not differ significantly from the final result; 7) the impact of having the largest of each of the
three keff estimators occurring on the next cycle is not too great on the final confidence interval; and
8) the combined keff figure of merit should be stable. The combined keff figure of merit should be
reasonably stable, but not as stable as a tally figure of merit because the number of histories for
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