A Monte Carlo criticality simulation of a reactor core records the cycle-wise…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement

Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output

Problem

A Monte Carlo criticality simulation of a reactor core records the cycle-wise multiplication factor

k^{(i)}_{\rm eff}

for

N = 6400

active cycles, after discarding inactive (source-settling) cycles. The mean is

\overline{k_{\rm eff}} = 1.00250

and the per-cycle standard deviation is

\sigma_k = 0.0060

. Successive cycles are correlated because each cycle's fission source shape carries memory of the previous one. Blocking gives the standard error of the mean,

\hat\sigma_b

, at block size

b

(in cycles):

b

: 1, 2, 4, 8, 16, 32, 64, 128, 256

\hat\sigma_b

: 0.000075, 0.000101, 0.000132, 0.000165, 0.000192, 0.000210, 0.000219, 0.000225, 0.000205 A run with

50

discarded inactive cycles and one with

100

discarded inactive cycles give mean

k_{\rm eff}

values differing by

0.00010

; take this as the numerical (equilibration) uncertainty. The nuclear cross-section library carries an uncertainty that, propagated linearly, gives an input uncertainty

u_{\rm input} = 0.00050

\overline{k_{\rm eff}}

. ((a)) For each block size, find the number of blocks

n_b

and the relative scatter

1/\sqrt{2(n_b-1)}

\hat\sigma_b

. Using the chapter's plateau criterion, find the block sizes over which the curve is level, say which point must be set aside and why, and read off the plateau value. ((b)) Find

s

\tau_{\rm int}

(in cycles) and the effective number of independent cycles

N_{\rm eff}

. ((c)) Assemble the uncertainty budget for

\overline{k_{\rm eff}}

and quote the final result.

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