# Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

## Abstract

Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this work, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- Contributing Org.:
- Univ. of Rochester, NY (United States). Lab. for Laser Energetic

- OSTI Identifier:
- 1467265

- Alternate Identifier(s):
- OSTI ID: 1406655; OSTI ID: 1474387

- Report Number(s):
- LA-UR-17-24474; LLNL-JRNL-756484

Journal ID: ISSN 0021-8979

- Grant/Contract Number:
- AC52-06NA25396; AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 17; Journal ID: ISSN 0021-8979

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; neutron imaging; National Ignition Facility; NIF; Omega; Inertial confinement fusion; ICF; plasma confinement; thermal effects; integral transforms; abstract harmonic analysis; gamma rays; neutron sources; x-rays; isotopes; radioactive decay; Engineering - Instrumentation related to nuclear science and technology, Nuclear science and engineering, Physics - Plasma physics

### Citation Formats

```
Volegov, Petr Lvovich, Danly, Christopher R., Fittinghoff, David, Geppert-Kleinrath, Verena, Grim, Gary, Merrill, Frank Edward, and Wilde, Carl Huerstel. Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition. United States: N. p., 2017.
Web. doi:10.1063/1.4986652.
```

```
Volegov, Petr Lvovich, Danly, Christopher R., Fittinghoff, David, Geppert-Kleinrath, Verena, Grim, Gary, Merrill, Frank Edward, & Wilde, Carl Huerstel. Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition. United States. doi:10.1063/1.4986652.
```

```
Volegov, Petr Lvovich, Danly, Christopher R., Fittinghoff, David, Geppert-Kleinrath, Verena, Grim, Gary, Merrill, Frank Edward, and Wilde, Carl Huerstel. Thu .
"Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition". United States. doi:10.1063/1.4986652. https://www.osti.gov/servlets/purl/1467265.
```

```
@article{osti_1467265,
```

title = {Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition},

author = {Volegov, Petr Lvovich and Danly, Christopher R. and Fittinghoff, David and Geppert-Kleinrath, Verena and Grim, Gary and Merrill, Frank Edward and Wilde, Carl Huerstel},

abstractNote = {Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this work, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.},

doi = {10.1063/1.4986652},

journal = {Journal of Applied Physics},

number = 17,

volume = 122,

place = {United States},

year = {2017},

month = {11}

}

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