# Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses

## Abstract

This work presents an application of Cacuci’s Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the simplified Boltzmann equation that models the transport of uncollided particles through a medium to compute efficiently and exactly all of the first- and second-order derivatives (sensitivities) of a detector’s response with respect to the system’s isotopic number densities, microscopic cross sections, source emission rates, and detector response function. The off-the-shelf PARTISN multigroup discrete ordinates code is employed to solve the equations underlying the 2nd-ASAM. The accuracy of the results produced using PARTISN is verified by using the results of three test configurations: (1) a homogeneous sphere, for which the response is the exactly known total uncollided leakage, (2) a multiregion two-dimensional (r-z) cylinder, and (3) a two-region sphere for which the response is a reaction rate. For the homogeneous sphere, results for the total leakage as well as for the respective first- and second-order sensitivities are in excellent agreement with the exact benchmark values. For the nonanalytic problems, the results obtained by applying the 2nd-ASAM to compute sensitivities are in excellent agreement with central-difference estimates. The efficiency of the 2nd-ASAM is underscored by the fact that, for the cylinder, only 12 adjoint PARTISN computations weremore »

- Authors:

- Univ. of South Carolina, Columbia, SC (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation (NA-20)

- OSTI Identifier:
- 1441310

- Report Number(s):
- LA-UR-17-28959

Journal ID: ISSN 0029-5639

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 190; Journal Issue: 2; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; second-order adjoint sensitivity analysis; particle and radiation transport; response variance and skewness

### Citation Formats

```
Cacuci, Dan G., and Favorite, Jeffrey A.
```*Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses*. United States: N. p., 2018.
Web. doi:10.1080/00295639.2018.1426899.

```
Cacuci, Dan G., & Favorite, Jeffrey A.
```*Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses*. United States. doi:10.1080/00295639.2018.1426899.

```
Cacuci, Dan G., and Favorite, Jeffrey A. Fri .
"Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses". United States.
doi:10.1080/00295639.2018.1426899. https://www.osti.gov/servlets/purl/1441310.
```

```
@article{osti_1441310,
```

title = {Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses},

author = {Cacuci, Dan G. and Favorite, Jeffrey A.},

abstractNote = {This work presents an application of Cacuci’s Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the simplified Boltzmann equation that models the transport of uncollided particles through a medium to compute efficiently and exactly all of the first- and second-order derivatives (sensitivities) of a detector’s response with respect to the system’s isotopic number densities, microscopic cross sections, source emission rates, and detector response function. The off-the-shelf PARTISN multigroup discrete ordinates code is employed to solve the equations underlying the 2nd-ASAM. The accuracy of the results produced using PARTISN is verified by using the results of three test configurations: (1) a homogeneous sphere, for which the response is the exactly known total uncollided leakage, (2) a multiregion two-dimensional (r-z) cylinder, and (3) a two-region sphere for which the response is a reaction rate. For the homogeneous sphere, results for the total leakage as well as for the respective first- and second-order sensitivities are in excellent agreement with the exact benchmark values. For the nonanalytic problems, the results obtained by applying the 2nd-ASAM to compute sensitivities are in excellent agreement with central-difference estimates. The efficiency of the 2nd-ASAM is underscored by the fact that, for the cylinder, only 12 adjoint PARTISN computations were required by the 2nd-ASAM to compute all of the benchmark’s 18 first-order sensitivities and 224 second-order sensitivities, in contrast to the 877 PARTISN calculations needed to compute the respective sensitivities using central finite differences, and this number does not include the additional calculations that were required to find appropriate values of the perturbations to use for the central differences.},

doi = {10.1080/00295639.2018.1426899},

journal = {Nuclear Science and Engineering},

number = 2,

volume = 190,

place = {United States},

year = {Fri Apr 06 00:00:00 EDT 2018},

month = {Fri Apr 06 00:00:00 EDT 2018}

}