# (U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing

## Abstract

The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates is derived in Refs. 1 and 2. In Ref. 2, we solved problems for the uncollided leakage from a homogeneous sphere and a multiregion cylinder using the PARTISN multigroup discrete-ordinates code. In this memo, we derive solutions of the 2nd-LASS for the particular case when the response is a flux or partial current density computed at a single point on the boundary, and the inner products are computed using ray-tracing. Both the PARTISN approach and the ray-tracing approach are implemented in a computer code, SENSPG. The next section of this report presents the equations of the 1st- and 2nd-LASS for uncollided particles and the first- and second-order sensitivities that use the solutions of the 1st- and 2nd-LASS. Section III presents solutions of the 1st- and 2nd-LASS equations for the case of ray-tracing from a detector point. Section IV presents specific solutions of the 2nd-LASS and derives the ray-trace form of the inner products needed for second-order sensitivities. Numerical results for the total leakage from a homogeneous sphere are presented in Sec. Vmore »

- Authors:

- 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)

- OSTI Identifier:
- 1411336

- Report Number(s):
- LA-UR-17-30851

TRN: US1801158

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; SENSITIVITY ANALYSIS; RADIATION DETECTORS; PARTICLES; ISOTOPES

### Citation Formats

```
Favorite, Jeffrey A.
```*(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing*. United States: N. p., 2017.
Web. doi:10.2172/1411336.

```
Favorite, Jeffrey A.
```*(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing*. United States. doi:10.2172/1411336.

```
Favorite, Jeffrey A. Thu .
"(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing". United States.
doi:10.2172/1411336. https://www.osti.gov/servlets/purl/1411336.
```

```
@article{osti_1411336,
```

title = {(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing},

author = {Favorite, Jeffrey A.},

abstractNote = {The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates is derived in Refs. 1 and 2. In Ref. 2, we solved problems for the uncollided leakage from a homogeneous sphere and a multiregion cylinder using the PARTISN multigroup discrete-ordinates code. In this memo, we derive solutions of the 2nd-LASS for the particular case when the response is a flux or partial current density computed at a single point on the boundary, and the inner products are computed using ray-tracing. Both the PARTISN approach and the ray-tracing approach are implemented in a computer code, SENSPG. The next section of this report presents the equations of the 1st- and 2nd-LASS for uncollided particles and the first- and second-order sensitivities that use the solutions of the 1st- and 2nd-LASS. Section III presents solutions of the 1st- and 2nd-LASS equations for the case of ray-tracing from a detector point. Section IV presents specific solutions of the 2nd-LASS and derives the ray-trace form of the inner products needed for second-order sensitivities. Numerical results for the total leakage from a homogeneous sphere are presented in Sec. V and for the leakage from one side of a two-region slab in Sec. VI. Section VII is a summary and conclusions.},

doi = {10.2172/1411336},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Nov 30 00:00:00 EST 2017},

month = {Thu Nov 30 00:00:00 EST 2017}

}