SEARCH · Engineering Papers

Results for “Bateman Equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

9 records

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Verification of the REBUS Software

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. REBUS is central to this system. The driver for this effort requires the Triangular-Z and hexagonal-Z core geometry options of REBUS to be verified. Previous work identified the REBUS features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying REBUS’s ability to correctly intepret the user input model, verifying that the features identified yield the intended results, and verifying the correctness of the REBUS output tables. The REBUS software verification relies heavily upon the accuracy of the embedded DIF3D software, the verification of which was completed and documented elsewhere. Given that DIF3D produces an accurate solution, the primary focus of the verification in the REBUS software is to ensure that it properly uses the DIF3D solution and that the depletion system (Bateman equations) are correctly implemented. This manuscript reiterates the verification tasks and displays results with respect to the features needed for current design activities. Analytic solutions of the Batemen equations are displayed and the results calculated with REBUS are displayed demonstrating the accuracy. Since coupled Bateman and neutron diffusion/transport solutions are extremely difficult to obtain, much of the focus is placed on how REBUS uses a given DIF3D solution assuming the accuracy of the DIF3D solution. The verification effort identified no issues that are debilitating or otherwise impactful to the design usage of REBUS, and thus REBUS version 11.0, release 3012 is considered verified. It is important to note that several outputs of REBUS are identified to be inaccurate, such as burnup in MWD/MT. Most of the relevant ones for VTR are generally accurate with 10-20% errors which is not impactful as all regular REBUS users are aware of this issue and know how to hand calculate the results. The REBUS manual further makes it clear that these values are consistent with the methodology being used by REBUS and thus the “errors” are more of an inconsistent definition with respect to what a user would expect given a definition in literature. Other issues that were identified included unclear documentation and software bugs all of which were inconsequential to the final results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Gamma-ray Exportable Adjustable Spectrum Evolution

An initial number of fissions on a fissile/fissionable material, defined by ENDF library availability, is used to produce an initial inventory of fission products (FPs). The FPs are decayed using full, analytical solutions to the Bateman equations to calculate the FP inventory at a user-specified time. The radiation detector, a high-purity germanium (HPGe) detector, has been modeled using every gamma-ray in the ENDF/TENDL libraries individually, and the modeled response can be multiplied by the activity of each fission product to determine a full, energy dependent detector response, including dead time. The detector response can be output as a PeakEasy (.spe) file, or as a text file. Since each radioisotope's inventory is known, the proportion to the total may be shown for each isotope, as well as many radionuclides in a user-specified energy window. Full execution and display of results takes 1-3 seconds, depending on the complexity of the input parameters.

Holschuh, ThomasV [Idaho National Laboratory (INL)↗

DOE OSTI2025

Total Radioisotope Yield Calculator

Holschuh, ThomasV [Idaho National Laboratory (INL)↗

DOE OSTI2025

Calculator For Radioisotope Yields, Targets, And Products

An initial number of atoms in a material (by element or by isotope), defined by ENDF library availability, is used to produce an initial reaction products (RPs). The RPs are decayed using full, analytical solutions to the Bateman equations to calculate the RP inventory at a user-specified time. Since each radioisotope's inventory is known, the proportion to the total may be shown for each isotope. The total dose rate and activity is the main objective for experimenters. Built-in information about many reactors and irradiation positions is available. Full execution and display of results takes 5-10 seconds, depending on the complexity of the input parameters.

Holschuh, ThomasV [Idaho National Laboratory (INL)↗

DOE OSTI2025

Characterization of Neutron Emission Rates of Commercial 252 Cf Sources

Accurate knowledge of 252 Cf neutron emission rates is critical for modeling and fast-neutron experiments, yet commercial sources are often supplied without traceable calibration or uncertainty estimates. This report describes a method to characterize 252 Cf sources using a pulse-shape-discrimination (PSD) scintillator. The scintillator was efficiency-calibrated against a time-tagged 252 Cf fission chamber manufactured at ORNL over 40 years ago. Isotopic evolution of the calibration source was modeled using Bateman equations to account for changes in the effective average neutrons per fission at the time of measurement. The calibrated scintillator was then used to measure absolute emission rates of several commercial 252 Cf sources, revealing deviations of up to 12% from nominal manufacturer values. This methodology provides a practical approach for establishing uncertainty-quantified 252 Cf neutron emission rates, improving fidelity in simulations and supporting the accurate interpretation of measurements.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2026

Integration of Online Cross-Section Generation Capability with Depletion and Transient Solvers in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE)-based reactor multiphysics analysis application jointly developed by Argonne and Idaho National Laboratories under the DOENE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In FY25, an online crosssection generation capability based on the Self-Shielding Application Programming Interface (SSAPI) was demonstrated for TRISO-fueled reactor problems under steady-state conditions. This fiscal year, that capability was extended to support depletion and transient multiphysics calculations, enabling high-fidelity analyses that generate self-shielded cross sections on the fly from the actual evolving composition and temperature states rather than from pre-tabulated libraries. For depletion, a two-way coupling was established in which SSAPI computes compact-averaged self-shielded cross sections that the depletion solver then uses to advance the Bateman equations, with the updated compositions returned to SSAPI at each step; the depletion module was refactored to support both library-based and SSAPI-based cross sections, and additional logic was added to track daughter isotopes and to exclude minor isotopes for efficiency. For transient analysis, the SSAPI multigroup library was extended with the kinetics data required for time-dependent calculations, the Improved Quasi-Static (IQS) scheme was coupled with SSAPI, and several supporting capabilities were implemented, including a self-shielding treatment that lets control rods and drums move within a self-shielded model, which had previously been impossible and had ruled out rod- and drum-movement transients with on-the-fly cross sections altogether, a new mixing scheme for delayed-neutron precursor decay constants, a checkpoint-based restart workflow, and performance improvements such as pointwise cross-section interpolation and the bypassing of unnecessary Dancoff factor calculations. The implemented capabilities were verified against Serpent Monte Carlo solutions. For depletion, a prismatic pin-cell problem based on a Next Generation Nuclear Plant (NGNP) Very High Temperature Reactor benchmark showed excellent agreement, with eigenvalue differences within 200 pcm over the entire burnup range (up to 140 MWD/kgU) and fission-product and actinide inventories agreeing to within 0.8% and 2.5%, respectively; a heat-pipe microreactor assembly problem with a much higher fuel loading confirmed the same behavior and quantified the bias introduced when the multigroup equivalence effect is neglected. For transient analysis, a pin-cell problem with a step reactivity insertion and temperature feedback reproduced the analytically expected asymptotic power and showed close agreement between the direct and IQS solutions, and a two-dimensional microreactor core problem with control-drum rotation exercised the new moving-drum self-shielding treatment and demonstrated successful coupling of the online crosssection generation with both the direct and IQS transient methods. The capability was further exercised on a full-core pebble-bed problem, in which Griffin was coupled with the System Analysis Module (SAM) to simulate load-following operation of the gPBR with the Doppler feedback resolved at the TRISO fuel kernel temperature. These developments in Griffin provide a convenient, high-fidelity approach to cross-section generation for advanced thermal reactors with geometrically complex and highly heterogeneous configurations, including TRISO-fueled prismatic and pebble-bed systems, and support steady-state, depletion, and transient multiphysics calculations. They also enable self-shielded cross sections to be evaluated directly at the actual coupled state of the system, thereby establishing a foundation for high-fidelity, fully coupled multiphysics analysis of advanced reactors

Park, H.↗

DOE OSTI2026

Accelerated 133 Xe Quantification in Samples Containing Significant 133 mXe

The quantification of 133 Xe in the presence of its mother radionuclide 133 mXe requires the full quantification of both to perform the ingrowth correction for 133 Xe. Due to the nature of both of these radionuclides, the 133 mXe requires significantly more time to quantify by High Purity Germanium (HPGe) detectors due to lower production yields, lower gamma emission probabilities, and lower detection efficiencies. This work shows that 133 Xe and 133 mXe quantification can be accelerated by measuring the 133m:133 activity ratio for a large batch of material and applying this activity ratio to assays of lower activity subsamples of the same batch of material. Included in this report are derivations of the required decay correction equations, and experiments using actual samples to validate the performance of these equations. A detector calibration method is also shown that leverages this method as an alternative to existing calibration methods for 133 mXe quantification.

133mXe↗

NASA NTRS1994

Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

Dodonov, V. V.↗

NASA NTRS1923

The decay of a simple eddy

The principal result obtained in this report is a generalization of Taylor's formula for a simple eddy. The discussion of the properties of the eddy indicates that there is a slight analogy between the theory of eddies in a viscous fluid and the quantum theory of radiation. Another exact solution of the equations of motion of viscous fluid yields a result which reminds one of the well-known condition for instability in the case of a horizontally stratified atmosphere.

Bateman, H↗