scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: III. Effects of Imprecisely Known Microscopic Fission Cross Sections and Average Number of Neutrons per Fission

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4100 ◽  
Author(s):  
Cacuci ◽  
Fang ◽  
Favorite ◽  
Badea ◽  
Rocco
Keyword(s):  
Cross Sections ◽  
Nuclear Data ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Response Distribution ◽  
Adjoint Sensitivity ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Analysis Methodology ◽  
Scattering Cross Sections

The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the first-order and second-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental system with respect to the following nuclear data: Group-averaged isotopic microscopic fission cross sections, mixed fission/total, fission/scattering cross sections, average number of neutrons per fission (), mixed /total cross sections, /scattering cross sections, and /fission cross sections. The numerical results obtained indicate that the 1st-order relative sensitivities for these nuclear data are smaller than the 1st-order sensitivities of the PERP leakage response with respect to the total cross sections but are larger than those with respect to the scattering cross sections. The vast majority of the 2nd-order unmixed sensitivities are smaller than the corresponding 1st-order ones, but several 2nd-order mixed relative sensitivities are larger than the 1st-order ones. In particular, several 2nd-order sensitivities for 239Pu are significantly larger than the corresponding 1st-order ones. It is also shown that the effects of the 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s parameters underlying the average number of neutrons per fission, , on the moments (expected value, variance, and skewness) of the PERP benchmark’s leakage response distribution are negligible by comparison to the corresponding effects (on the response distribution) stemming from uncertainties in the total cross sections, but are larger than the corresponding effects (on the response distribution) stemming from uncertainties in the fission and scattering cross sections.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1431 ◽  
Author(s):  
Ruixian Fang ◽  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Source Parameters ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Response Distribution ◽  
Adjoint Sensitivity ◽  
Scattering Cross ◽  
Analysis Methodology ◽  
Scattering Cross Sections

By applying the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the polyethylene-reflected plutonium (PERP) benchmark, this work presents results for the first- and second-order sensitivities of this benchmark’s leakage response with respect to the spontaneous fission source parameters. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity of the leakage response to the source parameters for the two fissionable isotopes in the benchmark are all positive, signifying that an increase in the source parameters will cause an increase in the total neutron leakage from the PERP sphere. The 1st- and 2nd-order relative sensitivities with respect to the source parameters for 239Pu are very small (10−4 or less). In contradistinction, the 1st-order and several 2nd-order relative sensitivities of the leakage response with respect to the source parameters of 240Pu are large. Large values (e.g., greater than 1.0) are also displayed by several mixed 2nd-order relative sensitivities of the leakage response with respect to parameters involving the source and: (i) the total cross sections; (ii) the average neutrons per fission; and (iii) the isotopic number densities. On the other hand, the values of the mixed 2nd-order relative sensitivities with respect to parameters involving the source and: (iv) the scattering cross sections; and (v) and the fission cross sections are smaller than 1.0. It is also shown that the effects of the 1st- and 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s source parameters on the moments (expected value, variance and skewness) of the PERP benchmark’s leakage response distribution are negligibly smaller than the corresponding effects (on the response distribution) stemming from uncertainties in the total, fission and scattering cross sections.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: II. Effects of Imprecisely Known Microscopic Scattering Cross Sections

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4114 ◽  
Author(s):  
Fang ◽  
Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Second Order ◽  
The Other ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
First Order ◽  
Scattering Cross ◽  
Analysis Methodology ◽  
Scattering Cross Sections

This work continues the presentation commenced in Part I of the second-order sensitivity analysis of nuclear data of a polyethylene-reflected plutonium (PERP) benchmark using the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM). This work reports the results of the computations of the first- and second-order sensitivities of this benchmark’s computed leakage response with respect to the benchmark’s 21600 parameters underlying the computed group-averaged isotopic scattering cross sections. The numerical results obtained for the 21600 first-order relative sensitivities indicate that the majority of these were small, the largest having relative values of O (10−2). Furthermore, the vast majority of the (21600)2 second-order sensitivities with respect to the scattering cross sections were much smaller than the corresponding first-order ones. Consequently, this work shows that the effects of variances in the scattering cross sections on the expected value, variance, and skewness of the response distribution were negligible in comparison to the corresponding effects stemming from uncertainties in the total cross sections, which were presented in Part I. On the other hand, it was found that 52 of the mixed second-order sensitivities of the leakage response with respect to the scattering and total microscopic cross sections had values that were significantly larger than the unmixed second-order sensitivities of the leakage response with respect to the group-averaged scattering microscopic cross sections. The first- and second-order mixed sensitivities of the PERP benchmark’s leakage response with respect to the scattering cross sections and the other benchmark parameters (fission cross sections, average number of neutrons per fission, fission spectrum, isotopic atomic number densities, and source parameters) have also been computed and will be reported in subsequent works.

scholarly journals ON THE IMPORTANCE OF SECOND-ORDER RESPONSE SENSITIVITIES TO NUCLEAR DATA IN REACTOR PHYSICS UNCERTAINTY ANALYSIS

2021 ◽  
Vol 247 ◽  
pp. 15021
Author(s):  
Dan G. Cacuci
Keyword(s):  
Cross Sections ◽  
Neutron Transport ◽  
Nuclear Data ◽  
Expected Value ◽  
Second Order ◽  
Model Parameters ◽  
Response Distribution ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Total Cross Sections

This invited keynote presentation compares the relative importance of 1st-order versus 2nd-order sensitivities of the leakage response of an OECD/NEA benchmark (polyethylene-reflected plutonium sphere) to the nuclear data characterizing this benchmark. The imprecisely known parameters underlying the neutron transport computational model for this benchmark include 180 group-averaged total microscopic cross sections, 21600 group-averaged scattering microscopic cross sections, 60 parameters describing the fission process, 30 parameters describing the fission spectrum, 10 parameters describing the system’s sources, and 6 isotopic number densities. Thus, this benchmark comprises 21886 1st-order sensitivities of the leakage response with respect to the model parameters, and 478,996,996 2nd-order sensitivities, of which 239,509,441 are distinct. The exact deterministic computation of all of these 1st- and 2nd-order sensitivities was made possible by the application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci. Thousands (out of the 32 400 elements) of the 2nd-order sensitivities of the leakage response with respect to the total cross sections turned out to be significantly larger than the largest corresponding 1st-order sensitivities, contrary to some previously held beliefs in the reactor physics community. Hence, it will be shown that neglecting the 2nd-order sensitivities to total cross sections would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The 2nd-order sensitivities also cause the response distribution to be skewed towards positive values relative to the expected value, which, in turn, is significantly larger than the computed value of the leakage response. The result presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are not available at this time.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involving Isotopic Number Densities

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2580 ◽  
Author(s):  
Ruixian Fang ◽  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Number Density ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Energy Group ◽  
Analysis Methodology

This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the mixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities and the other benchmark imprecisely known parameters, including: (i) the 6 × 180 mixed 2nd-order sensitivities involving the total microscopic cross sections; (ii) the 6 × 21,600 mixed 2nd-order sensitivities involving the scattering microscopic cross sections; (iii) the 6 × 60 mixed 2nd-order sensitivities involving the fission microscopic cross sections; and (iv) the 6 × 60 mixed 2nd-order sensitivities involving the average number of neutrons produced per fission. It is shown that many of these mixed 2nd-order sensitivities involving the isotopic number densities have very large values. Most of the large sensitivities involve the isotopic number density of 239Pu, and the microscopic total, scattering or fission cross sections for the 12th or 30th energy groups of 239Pu or 1H, respectively. The 2nd-order mixed sensitivity of the PERP leakage response with respect to the isotopic number density of 239Pu and the microscopic total cross section for the 30th energy group of 1H is the largest of the above mentioned sensitivities, attaining the value −94.91.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities on Response Uncertainties

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1674 ◽  
Author(s):  
Dan G. Cacuci ◽  
Ruixian Fang ◽  
Jeffrey A. Favorite
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Relative Sensitivity ◽  
Second Order ◽  
Model Parameters ◽  
Adjoint Sensitivity Analysis ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
First Order ◽  
Analysis Methodology

This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the 1st-order and unmixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity to the isotopic number densities for the two fissionable isotopes have large values, which are comparable to, or larger than, the corresponding sensitivities for the total cross sections. Furthermore, several 2nd-order unmixed sensitivities for the isotopic number densities are significantly larger than the corresponding 1st-order ones. This work also presents results for the first-order sensitivities of the PERP benchmark’s leakage response with respect to the fission spectrum parameters of the two fissionable isotopes, which have very small values. Finally, this work presents the overall summary and conclusions stemming from the research findings for the total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to all model parameters of the PERP benchmark, as presented in the sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”.

scholarly journals Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics

2021 ◽  
Vol 2 (2) ◽  
pp. 114-123
Author(s):  
Dan G. Cacuci
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Practical Method ◽  
Expected Value ◽  
Second Order ◽  
Response Distribution ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Total Cross Sections ◽  
The Mean

This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters.

Photoelectric cross sections derived from the total absorption cross sections in the energy range 5–130 keV

1979 ◽  
Vol 57 (1) ◽  
pp. 92-98 ◽  
Author(s):  
K. S. Puttaswamy ◽  
Ramakrishna Gowda ◽  
B. Sanjeevaiah
Keyword(s):  
Energy Range ◽  
Cross Sections ◽  
Proportional Counter ◽  
Atomic Data ◽  
Total Absorption ◽  
Absorption Cross ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Data Tables ◽  
Scattering Cross Sections

Total absorption cross sections in the elements C, Al, S, Cu, Zr, Ag, Sn, Ta, Au, and Pb for photons of energies 5.0, 5.9, 6.4, 8.1, 10.6, 14.4, 24.7, 32.9, 36.9, 66.6, and 129 keV are measured using a krypton-filled proportional counter in the energy range 5 to 25 keV and a thin NaI(Tl) detector in the energy range 30 to 130 keV. The measured total absorption cross sections are compared with those of Miller and Greening and McCrary, Plassman, Paekett, Conner, and Zimmermann. The scattering cross sections obtained by interpolation using the Atomic Data Tables are subtracted from the total cross sections to obtain the photoelectric cross sections and these are further compared with the recent theoretical values of Scofield.

scholarly journals Semi-classical bounds on scattering cross sections in two dimensional magnetic fields

1997 ◽  
Vol 147 ◽  
pp. 25-61
Author(s):  
Hideo Tamura
Keyword(s):  
Magnetic Fields ◽  
Energy Range ◽  
Cross Sections ◽  
Classical Limit ◽  
Uniform Boundedness ◽  
Classical Dynamics ◽  
Two Dimensional ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Scattering Cross Sections

AbstractWe prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.

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