Conversion ratio

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Conversion ratio

Postby Yrobel » Thu Jul 26, 2018 10:11 am

Hi,
I want to determine the conversion ratio (CR) (or breeding ratio: BR) at the EOC. In the output file I get the following (BOC):
Code: Select all
% Analog reaction rate estimators:

CONVERSION_RATIO          (idx, [1:   2]) = [  1.03233E+00 0.00046 ];
U235_FISS                 (idx, [1:   4]) = [  1.98940E+16 0.00146  4.55527E-02 0.00143 ];
U238_FISS                 (idx, [1:   4]) = [  6.70919E+16 0.00078  1.53624E-01 0.00071 ];
PU239_FISS                (idx, [1:   4]) = [  2.58631E+17 0.00039  5.92206E-01 0.00025 ];
PU240_FISS                (idx, [1:   4]) = [  2.62546E+16 0.00126  6.01166E-02 0.00120 ];
PU241_FISS                (idx, [1:   4]) = [  5.00569E+16 0.00086  1.14619E-01 0.00080 ];
U235_CAPT                 (idx, [1:   4]) = [  5.97379E+15 0.00267  7.83864E-03 0.00266 ];
U238_CAPT                 (idx, [1:   4]) = [  4.01032E+17 0.00029  5.26224E-01 0.00022 ];
PU239_CAPT                (idx, [1:   4]) = [  8.19300E+16 0.00066  1.07507E-01 0.00065 ];
PU240_CAPT                (idx, [1:   4]) = [  3.50556E+16 0.00114  4.59990E-02 0.00112 ];
PU241_CAPT                (idx, [1:   4]) = [  9.80615E+15 0.00193  1.28674E-02 0.00193 ];


But I have doubts with the values of the output, for example, for the PU239 I have two values, these are fission rate (PU239_FISS) and capture rate (PU239_CAPT). But the second column, is it some fraction?.
So how does Serpent calculate the reported BR? I suppose for example considering U235, U238, Pu239, Pu240 and Pu241:
BR = (U238_CAPT + PU240_CAPT) / (U235_ABS + PU239_ABS + PU241_ABS)
where:
ABS = CAPT + FISS
Is this correct?.

Now, at the EOC I get the following:

Code: Select all
% Analog reaction rate estimators:

CONVERSION_RATIO          (idx, [1:   2]) = [  1.00421E+00 0.00044 ];
U233_FISS                 (idx, [1:   4]) = [  4.28608E+10 1.00000  9.77316E-08 1.00000 ];
U235_FISS                 (idx, [1:   4]) = [  1.20607E+16 0.00172  2.76339E-02 0.00167 ];
U238_FISS                 (idx, [1:   4]) = [  6.51332E+16 0.00086  1.49236E-01 0.00077 ];
PU239_FISS                (idx, [1:   4]) = [  2.80428E+17 0.00038  6.42532E-01 0.00024 ];
PU240_FISS                (idx, [1:   4]) = [  2.87445E+16 0.00117  6.58615E-02 0.00116 ];
PU241_FISS                (idx, [1:   4]) = [  3.56016E+16 0.00113  8.15722E-02 0.00109 ];
U235_CAPT                 (idx, [1:   4]) = [  3.56865E+15 0.00356  4.43998E-03 0.00357 ];
U238_CAPT                 (idx, [1:   4]) = [  3.86981E+17 0.00031  4.81463E-01 0.00025 ];
PU239_CAPT                (idx, [1:   4]) = [  8.73435E+16 0.00072  1.08669E-01 0.00069 ];
PU240_CAPT                (idx, [1:   4]) = [  3.76165E+16 0.00102  4.68008E-02 0.00103 ];
PU241_CAPT                (idx, [1:   4]) = [  6.93195E+15 0.00235  8.62432E-03 0.00233 ];
XE135_CAPT                (idx, [1:   4]) = [  4.69017E+11 0.32314  5.84395E-07 0.32327 ];
SM149_CAPT                (idx, [1:   4]) = [  2.14517E+15 0.00462  2.66893E-03 0.00462 ];


For the U233 and XE135, why is the error 1.00 and 0.32 respectively? (although its production is very small).

Regards.
Yrobel
 
Posts: 38
Joined: Thu Feb 09, 2017 3:59 am

Re: Conversion ratio

Postby Ville Valtavirta » Fri Aug 03, 2018 1:51 pm

Hi,

the conversion ratio is calculated as (fissile production rate)/(fissile loss rate).

The fissile production rate includes

1. (n,gamma) reactions with Th232, U232, U234, U238, Pu238 and Pu242.
2. (n,2n) reactions with U234, U236, Pu240 and Pu242.

The fissile loss rate includes

1. fission reactions with U233, U235, Pu239 and Pu241.
2. capture reactions with U233, U235, Pu239 and Pu241.
3. (n,xn) reactions with U233, U235, Pu239 and Pu241.

The second data-value in the _FISS and _CAPT rate estimators describes the fraction of total fission rate or capture rate.

The large uncertainties for the U233 fission rate and Xe135 capture rate are most likely due to the small reaction rates. As these are analog reaction rate estimators they are scored only when a reaction is actually sampled with the target nucleus, which might happen rarely if the reaction type is not common, e.g. due to low atomic density.

-Ville
Ville Valtavirta
 
Posts: 258
Joined: Fri Sep 07, 2012 1:43 pm

Re: Conversion ratio

Postby Yrobel » Fri Aug 03, 2018 7:24 pm

Thanks for your clarification.

Regards
Yrobel
 
Posts: 38
Joined: Thu Feb 09, 2017 3:59 am


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