NeSST: A Python Tool for Neutron Spectra and Synthetic Diagnostics in Inertial Confinement Fusion

Abstract: We present the Neutron Scattered Spectra Tool (NeSST), an open-source Python package for rapidly constructing primary and singly scattered neutron spectra from inertial confinement fusion (ICF) implosions. NeSST evaluates primary spectra for deuterium-tritium (DT), deuterium-deuterium (DD) and tritium-tritium (TT) reactions. Differential and total nuclear cross sections are read directly from Evaluated Nuclear Data File (ENDF) libraries. This enables elastic ($n$D, $n$T) and inelastic [D$(n,2n)$p, T$(n,2n)$D] scattering from DT fuel, as well as scattering from additional ablator materials such as $^{12}$C, to be treated within a common framework. Relativistic corrections to elastic scattering kinematics are included. Areal density asymmetries are incorporated through a Legendre mode expansion of the neutron-averaged projected areal density, allowing the spectral signatures of implosion non-uniformities to be computed and fitted. The effect of scattering ion velocities on the neutron backscatter edge shape is handled through pre-computed ion-velocity-dependent scattering kernels. A synthetic neutron time-of-flight (nToF) module converts energy spectra into detector signals with a full forward model that includes configurable instrument response functions (IRFs), energy-dependent scintillator sensitivity, and beamline attenuation. The code is publicly available at https://github.com/aidancrilly/NeSST

• The paper introduces NeSST, an efficient Python framework bridging Monte Carlo and analytic models for neutron spectral diagnostics in ICF.
• It employs advanced spectral modeling with modified Gaussian fits, R-matrix formalism, and matrix-based single scattering to yield accurate results.
• Its integrated synthetic neutron time-of-flight module and sensitivity studies facilitate precise extraction of plasma parameters and assessment of detector uncertainties.

NeSST: A Python Framework for Neutron Spectral Modeling and Synthetic Diagnostics in Inertial Confinement Fusion

Introduction

The Neutron Scattered Spectra Tool (NeSST) is introduced as an open-source Python package designed for efficient modeling of neutron spectral features from inertial confinement fusion (ICF) implosions. NeSST occupies a niche between computationally intensive Monte Carlo neutron transport codes and over-simplified analytic models, targeting rapid generation and fitting of synthetic diagnostics in the regime dominated by single neutron scattering. The code supports primary and singly scattered neutron spectra from key fusion reactions—deuterium-tritium (DT), deuterium-deuterium (DD), and tritium-tritium (TT)—and can incorporate contributions from various materials present in typical ICF targets and ablator configurations, leveraging ENDF nuclear data standards. Notably, NeSST provides an integrated synthetic neutron time-of-flight (nToF) diagnostic capability, including sophisticated modeling of detector response and the effects of non-uniform plasma conditions.

Primary Neutron Spectral Modeling

NeSST models the principal fusion reactions relevant to ICF—DT, DD, and TT—using both established analytic parameterizations and reference simulations. For DT and DD reactions, the tool adopts the Ballabio et al. spectral-moment fits that include essential relativistic corrections to the spectral centroid and width, with functional forms outperforming classical descriptions like Brysk’s approximation, particularly at higher temperatures. Accurate spectral profiles are obtained through parametrized Gaussians (and their Ballabio-modified forms), and for more stringent benchmarking, NeSST interfaces with the pyDRESS Monte Carlo code.

The TT three-body spectrum is treated with an R-matrix formalism (e.g., Brune et al.), with multiple tabulated center-of-mass frame distributions. These models are Doppler-broadened according to Appelbe et al.'s prescription, capturing essential temperature-induced effects. Yield ratios among the primary reactions are based on canonical reactivity fits (Bosch-Hale for DT, DD; ENDF-derived for TT). The package supports modeling with arbitrary mixtures of D and T, with the ability to include explicit corrections for fluid velocity distributions via Doppler shifts.

Single-Scatter Spectral Model

NeSST focuses on the efficient evaluation of singly scattered neutron spectra, which predominate under moderate areal density conditions $$(\langle \rho R \rangle \lesssim 200~\mathrm{mg}/\mathrm{cm}^2)$$. The approach is matrix-based: primary spectra are folded with pre-computed energy-angle-resolved scattering matrices derived from ENDF cross sections. Elastic (nD, nT) and inelastic [D(n,2n)p, T(n,2n)D] processes are included, and the method supports additional scattering media (e.g., $^{12}$C ablator) seamlessly.

A strength is the integration of areal density asymmetries via a Legendre mode expansion, enabling quantitative predictions of the spectral consequences of implosion non-uniformities. The tool can rapidly evaluate the effect of arbitrary areal density distributions on scattered spectra by numerically integrating over the associated angular distributions.

Ion Kinematics and Backscatter Edge Modeling

The kinematic backscatter edge from elastic nT/nD neutron scattering is a crucial diagnostic of shell conditions in ICF experiments. NeSST implements a full relativistic treatment of the edge, using pre-tabulated, velocity-dependent scattering kernels for efficient convolution with user-specified ion velocity distributions. Both mean flow (bulk velocity) and velocity spread (temperature) are encoded in the model, accurately capturing shifts and broadening in the spectral edge. This enables fitting of dense shell flow and temperature from experiments, distinguishing NeSST from spectral tools that lack this level of kinematic detail.

Extensions to Higher Areal Density: Double Scattering and Attenuation

While NeSST’s core design is for the single-scatter regime, the tool implements approximate double-scatter and transmission corrections relevant to higher areal densities. These are generated by recursive application of the single-scatter kernel and inclusion of Beer-Lambert-style exponential attenuation. The accuracy of the double-scatter approximation is validated against 1D neutron transport solutions (Minotaur), showing strong agreement for primary and single-scatter features, with the expected degradation in fidelity for higher-order scattering at elevated areal densities.

Generalization to Various Scattering Materials

Through an extensible interface to ENDF-formatted nuclear data, NeSST can evaluate the neutron scattering spectrum from arbitrary materials encountered in ICF experiments, including common ablator and structural constituents (H, D, T, $^{12}$C, $^9$Be, etc.). Elastic, inelastic, and (n,2n) processes are parsed from ENDF or CENDL datasets, and results have been benchmarked against modern theoretical (e.g., Deltuva) and experimental (Forrest) data for specific reactions.

Synthetic Neutron Time-of-Flight Diagnostics

A salient feature of NeSST is the forward modeling of synthetic nToF signals. This includes (i) realistic detector response via a matrix IRF formalism (top-hat, inverse-Gaussian neutron response, convolved with analytic or fitted X-ray IRFs); (ii) energy-dependent scintillator sensitivity (with multiple models, including Verbinski tabulation and Birks/Craun-Smith parameterizations, all reliant on ENDF cross sections for neutron-proton and neutron-carbon interactions); and (iii) explicit line-of-sight attenuation (using ENDF cross sections for beamline and surrounding media).

The nToF module correctly implements the required Jacobians for energy-time conversion, supports arbitrary detector placements and configurations, and can account for time-dependent source emission (finite burn duration, evolving plasma conditions). These features allow direct synthesis and fitting of experimental signals, facilitating robust diagnostic inferences.

Parameter Inference and Detector Model Sensitivity

NeSST enables demonstration and validation of plasma parameter extraction via synthetic forward-model fitting, incorporating realistic instrumental response, noise, and backgrounds. The software supports systematic sensitivity studies, quantifying the effect of detector model uncertainties (in IRF parameterization and sensitivity characterization) on inferred physical parameters such as ion temperature, areal density, and hotspot velocity. The authors show that inaccuracies in the detector model can induce substantial biases in fitted plasma parameters, highlighting the necessity for rigorous in situ detector calibration.

Software Architecture, Performance, and Extensibility

NeSST is implemented as a modular, dependency-light Python package, relying on standard scientific libraries (NumPy, SciPy, matplotlib) and dedicated ENDF readers. Matrix-based kernel computation with caching ensures that individually synthesized spectra or signals are produced with minimal computational overhead, supporting parameter scans, UQ, and regression-based inference loops. Full documentation and automated testing are provided; the tool is open-source with active pathways for extension to new nuclear data, materials, or diagnostic scenarios.

Limitations and Scope

NeSST intentionally restricts itself to the single-scatter regime, where analytical approaches are valid and computational efficiency is paramount. Multi-scatter effects and transport phenomena central at high areal densities or in spatially extended configurations require full transport codes (e.g., MCNP, OpenMC, IRIS3D). Detector model fidelity relies on detailed and campaign-specific calibrations; systematic and nuclear data uncertainties must be acknowledged in rigorous experimental interpretation.

Implications and Future Directions

NeSST fills a critical gap in the fusion diagnostic ecosystem by providing a rapid, extensible, and physically motivated tool for neutron spectral and diagnostic response modeling in the singly scattered regime. This enables advanced parameter inference, uncertainty quantification, and design studies for ICF experiments, where rapid iteration and interpretability are at a premium. The modular architecture facilitates integration with high-level Bayesian inference frameworks and cross-platform synthetic diagnostic generation for both ICF and magnetic confinement fusion (MCF) environments.

Future work will likely focus on (i) enhanced modeling of multi-scatter and spatial transport processes to elevate fidelity at higher areal densities; (ii) expansion to incorporate additional reaction channels and isotopic materials as relevant to evolving ICF target designs; (iii) improved integration with data acquisition and pulse shape analysis pipelines; and (iv) systematic nuclear data evaluation for reactions where uncertainties are limiting diagnostic precision.

Conclusion

NeSST represents a technically robust and computationally efficient platform for modeling neutron spectra and synthetic diagnostics in inertial confinement fusion research. By combining validated physics, flexible material support, a sophisticated synthetic diagnostic module, and an open extensible codebase, it facilitates modern approaches to experiment interpretation and synthetic data generation. Nevertheless, for regimes beyond the single-scatter approximation, or when detector uncertainties dominate, complementary advanced transport modeling and experimental characterization remain imperative.