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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

eSHIVA in IOTA: Experiment on Stochasticity in High Intensity Variable Accelerators

Nonlinear integrable optics, the basis of IOTA, is a very special form of Hamiltonian system, called completely integrable. The consequences are many, most importantly the absence of fixed points that are in one-to-one correspondence with (overlapping) resonances. This, in turn, does not limit the dynamic aperture and allows large amplitude dependent tune shifts without adverse effects. In fact, it helps significantly in alleviating issues with collective instabilities. We developed and tested different numerical methods to give a more complete picture of the dynamics of integrable and near-integrable nonlinear Hamiltonian systems consisting of motion of charged particles in electromagnetic fields. Comparison of the results allowed us to discern real phenomena from numerical artifacts and come up with conclusions that will facilitate pushing the intensity frontier in beam dynamics even further for the benefit of the accelerator community as a whole and society as the consequence of the science and technological advancements it will make possible. We concluded that, while novel structure preserving integrators would be ideal, symplectic methods under mild restrictions offer adequate invariant preservation. We especially highlighted the very good performance of the Stormer-Verlet method at low accuracy and a modified Lobatto method at high accuracy for the Integrable Optics Test Accelerator (IOTA). However, we showed that symplectic integrators are limited by numerically induced resonances, which make interpretation of some simulation results challenging. These limitations and workarounds have been addressed.The nonlinear integrable optics test accelerator IOTA at Fermilab -- a very special experimental accelerator designed to investigate nonlinear optics under severe space-charge conditions – has recently completed its construction and initial commissioning of the ring has begun. We report first, under 2 (a) below: the progress on the nonlinear tune-shift measurements for various values of the nonlinear strength potential and their comparison with theoretical expectations, thus benchmarking the nonlinear characteristics of the ring; then, under 2 (b) below: the progress on simulation and design of a gas-jet monitor to measure beam profile and in particular its diffusive halo, expected to develop during stochastic diffusion of large amplitude particles under nonlinear forces of the magnetic lattice and Coulomb space-charge. Since the development of a proton beam source in IOTA is delayed and to be completed only in the future pending financial support, the gas-jet monitor is planned for testing with real proton beams elsewhere at Fermilab (e.g. in the Main Injector or PIP-II source possibly). Once proton beams are available in IOTA, the understanding of the nonlinear properties of IOTA combined with the developed gas-jet monitor, will enable a thorough experimental analysis of nonlinear stochastic diffusion in IOTA nonlinear ring, and boosted by proper theoretical understanding of the same.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

A simple json format for storing and exchanging code calculation and experimental results

Calculation codes and code systems give their results in a plethora of different formats and/or files. For instance, MCNP gives a user the MCNP specific output file, the mctal file, the ptrac file, etc. while PARTISN has a PARTISN specific output file and a number of binary files with various kinds of information about the calculation. However, the results we are interested in are always the same. These can be single values such as the effective multiplication factor k eff or the effective delayed neutron fraction β eff . It can be histogram data (such as particle spectra, reaction rates, sensitivity profiles, etc.) or even pointwise data (for example the nuclide composition as a function of time, etc.). It is also worthwhile to note that this would also apply to experimental data that we may wish to compare with as well. Calculation and experimental results can basically be split into two components: attributes (or metadata) and the actual result itself. Attributes represent information about the result that are not necessarily required for its’ interpretation but that are still good to have. Often, these attributes are what we will want to filter results on. This means that these attributes are often the answer to specific questions we may have about the result. The following is a non exhaustive list of such basic questions: what type of result is it: e.g. the effective multiplication factor k eff , the effective delayed neutron fraction β eff , etc.; which case does it relate to: e.g. a specific ICSBEP case such as PU-MET-FAST-001-001; which code and version produced this result: e.g. MCNP 6.2, etc.; which nuclear data library was used to obtain the result: e.g. ENDF/B-VIII.0 or JEFF 3.3; which nuclide and reaction does it apply to (for reaction rates and sensitivity profiles); which volume in the geometry was it calculated in? The second component of the calculation or experimental result is the actual numerical data of the result. It is this data that we want to compare, exchange, plot, interpret, etc. It consists of values with optional uncertainties and units. It also includes the underlying structure (if any structure is required to interpret the result). Depending on the type of result, it may be a single value (e.g. the effective multiplication factor), an array of values (e.g. a reaction rate or particle spectrum) or even a multidimensional array. In order to exchange results between different organisations, for instance for benchmarking, people often resort to spreadsheets or custom text files that need to be filled out. While this approach works well if little information is to be exchanged, it can become cumbersome when dealing with large amounts of data (like for instance particle spectra for thousands of cases). In addition, such an approach does not always capture the metadata we may be interested in to allow for automated processing of these files. The purpose of this report is to propose a standardised json structure to store any type of result and present an associated python interface to interact with these results directly. For such a structure to be useful, it must fulfill a specific set of functional requirements that we try to meet with this proposal. The format must allow for the calculation result to stand by itself. This means that we should not have to look in multiple places to be able to understand it. For example, if the result relates to a particle spectrum, the group structure in which the result is given should be stored with it. The format should be code agnostic. This means that we do not need to know where it came from to understand it. The format should be result type agnostic. This means that the format must be generic enough so that we can even use it for results we have not thought of yet. The format should be relatively easy to interact with through different scripting or programming languages (i.e. the machine interface) while still providing a clean structure that can be used directly by any human.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1991

Computational attributes of the integral form of the equation of transfer

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Frankel, J. I.↗
NASA NTRS2001

Particle Engulfment and Pushing (PEP): Past Micro-Gravity Experiments and Future Experimental Plan on the International Space Station (ISS)

The interaction of an insoluble particle with a growing solid-liquid interface (SLI) has been a subject of investigation for the four decades. For a metallurgist or a material scientist understanding the fundamental physics of such an interaction is relevant for applications that include distribution of reinforcement particles in metal matrix composites, inclusion management in castings, and distribution of Y2Ba1Cu1O5 (211) precipitates (flux pinning sites) in Y1Ba2Cu3O7 (123) superconducting crystals. The same physics is also applicable to other areas including geological applications (frost heaving in soils) and preservation of biological cells. Experimentally this interaction can be quantified in terms of a critical growth velocity, Vcr, of the SLI below which particles are pushed ahead of the advancing interface, and above which the particles are engulfed. Past experimental evidence suggests that this Vcr is an inverse function of the particle radius, R. In order to isolate the fundamental physics that governs such a relationship it is necessary to minimize natural convection at the SLI that is inherent in ground based experiments. Hence for the purpose of producing benchmark data (Vcr vs. R) PEP is a natural candidate for micro-gravity experimentation. Accordingly, experiments with pure Al containing a dispersion of ZrO2 particles and an organic analogue, succinonitrile (SCN) containing polystyrene particles have been performed on the LMS and USMP-4 mission respectively. In this paper we will summarize the experimental data that was obtained during these two micro-gravity missions and show that the results differ compared to terrestrial experiments. We will also discuss the basic elements of our analytical and numerical model and present a comparison of the predictions of these models against micro-gravity experimental data. Finally. we will discuss our future experimental plan that includes the ISS glovebox and MSRRl.

Sen, Subhayu↗
DOE OSTI2024

Microstructure effects on high velocity microparticle impacts of copper

Constitutive models can fail to predict high-rate deformation behavior due to their inability to account for microstructural effects. In part, this is because of a dearth of experimental benchmarking data in the high strain-rate, low pressure regime, since many high-rate experiments also probe a region of strong shockwaves, at which point microstructure effects no longer play a primary role. This work uses laser-induced particle impact testing to quantitatively study high velocity impacts of small, rigid alumina microspheres on flat copper substrates with varying amounts of initial cold work in the weak shock regime, but at very high strain rates up to ~10 7 s –1 . Through paired experiments and numerical simulations, this work shows that the initial microstructure condition can have significant influence on dynamical mechanical properties in this range. Specifically, prior work hardening of the copper substrate leads to increased rebounding of the microparticles (i.e., less plastic dissipation in the impact) as well as smaller craters. Each of these experimental measurables can be converted into a strength measure, i.e., the dynamic yield strength or dynamic hardness, respectively, neither of which is well predicted consistently by existing constitutive laws. The general trend of hardening can be captured by such models by incorporating an existing “pre-strain,” suggesting that future calibration of the materials parameters may yield a good fit over a broader range of conditions. Our results emphasize the importance of reporting the microstructural condition in dynamic studies, as well as the necessity of accounting for these factors when formulating and optimizing constitutive models.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of insulator end cap thickness on time-dependent Hartmann flow in a rotating mirror

We present a framework for analysing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device CMFX (centrifugal magnetic fusion experiment), which will employ more sophisticated physics and realistic magnetic field geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Previous work [E. Ackad and M. Horbatsch, Phys. Rev. A 78, 062711 (2008)] on supercritical Dirac resonance parameters from extrapolated analytic continuation, obtained with a Fourier grid method, is generalized by numerically solving the coupled Dirac radial equations to a high precision. The equations, which contain the multipole decomposition of the two-center potential, are augmented by a complex absorbing potential and truncated at various orders in the partial wave expansion to demonstrate convergence of the resonance parameters in the limit of vanishing absorber. The convergence of the partial-wave spinor and of the multipole potential expansions is demonstrated in the supercritical regime. The comparison of critical distances with literature values shows that the work provides benchmark results for future two-center calculations without multipole expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Efficient simulation of moiré materials using the density matrix renormalization group

Here we present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques - even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley, and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moiré materials in future work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer. Conclusions: The simulation results showed that the deterministic method can be effectively used to estimate the absorbed dose in a CTDI phantom. The accuracy of the discrete ordinates method was close to that of a Monte Carlo simulation, and the primary benefit of the discrete ordinates method lies in its rapid computation speed. It is expected that further optimization of this method in routine clinical CT dose estimation will improve its accuracy and speed.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2001

A Hybrid Numerical Method for Turbulent Mixing Layers

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

Georgiadis, Nicholas J.↗
DOE OSTI2015

Quantification of calculation accuracy for code systems in burn-up credit applications by recalculations of experimental data - 14480

For application in criticality safety, numerical code systems require profound validation against experimental data. In terms of burn-up credit, this refers to the inventory determination as well as the subsequent criticality calculation. Within this framework, a dedicated, conservative estimation of uncertainties, bias and bias uncertainties for the resulting calculated multiplication factor k{sub eff} is indispensable. However, measures to reduce excess conservatism may become desirable, depending on the application case. For this reason GRS implemented a methodology to validate a calculation code system for criticality safety analyses for systems with irradiated nuclear fuel. The work at hand demonstrates this methodology by means of the GRS home-built inventory determination system KENOREST and ORNL's well-known SCALE 6 CSASS criticality safety calculation sequence. A number of 40 radiochemical analysis samples taken from SFCOMPO and elsewhere have been calculated to derive isotopic correction factors in different ways, depending on the required level of conservatism and the calculational efforts to be carried out. This includes bounding methods as well as different Monte Carlo sampling approaches. Furthermore, from the ICSBEP a number of 515 critical benchmark experiment configurations comprising water moderated low enriched UO{sub 2} fuel rods and water moderated mixed oxide (MOX) fuel rods have been selected and evaluated. Important absorber and structure materials are also covered. Various trending and sensitivity and uncertainty analysis methods have been applied, again to derive conservative estimates on the various contributions to k{sub eff} uncertainties. The overall methodology is applicable to low enriched, water moderated PWR uranium dioxide fuels in a burn-up range of about 10 to 60 GWd/tHM, and validates the reactivity contributions of the major uranium and plutonium isotopes. The methodology itself has no limitation which requires the exclusion of further isotopes as e.g. fission products. However, its application is constrained by the experimental database being publicly available. After the potential provision of an extended database in the future, the range of applicability can easily be extended to more nuclides. In addition, it is not limited to the code systems being used here but can also be applied using different numerical tools. For a generic PWR spent fuel pool rack and different enrichment and burn-up combinations, the impact of the current level of validation on k{sub eff} is demonstrated and quantified. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

An interface capturing scheme for modeling atomization in compressible flows

The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten–Lax–van Leer–Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps

In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Deploy production sliding mesh capability with linear solver benchmarking.

Wind applications require the ability to simulate rotating blades. To support this use-case, a novel design-order sliding mesh algorithm has been developed and deployed. The hybrid method combines the control volume finite element methodology (CVFEM) with concepts found within a discontinuous Galerkin (DG) finite element method (FEM) to manage a sliding mesh. The method has been demonstrated to be design-order for the tested polynomial basis (P=1 and P=2) and has been deployed to provide production simulation capability for a Vestas V27 (225 kW) wind turbine. Other stationary and canonical rotating ow simulations are also presented. As the majority of wind-energy applications are driving extensive usage of hybrid meshes, a foundational study that outlines near-wall numerical behavior for a variety of element topologies is presented. Results indicate that the proposed nonlinear stabilization operator (NSO) is an effective stabilization methodology to control Gibbs phenomena at large cell Peclet numbers. The study also provides practical mesh resolution guidelines for future analysis efforts. Application-driven performance and algorithmic improvements have been carried out to increase robustness of the scheme on hybrid production wind energy meshes. Specifically, the Kokkos-based Nalu Kernel construct outlined in the FY17/Q4 ExaWind milestone has been transitioned to the hybrid mesh regime. This code base is exercised within a full V27 production run. Simulation timings for parallel search and custom ghosting are presented. As the low-Mach application space requires implicit matrix solves, the cost of matrix reinitialization has been evaluated on a variety of production meshes. Results indicate that at low element counts, i.e., fewer than 100 million elements, matrix graph initialization and preconditioner setup times are small. However, as mesh sizes increase, e.g., 500 million elements, simulation time associated with \setup-up" costs can increase to nearly 50% of overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

CoSyR: A novel beam dynamics code for the modeling of synchrotron radiation effects

The self-consistent nonlinear dynamics of a relativistic charged particle beam interacting with its complete self-fields is a fundamental problem underpinning many of the accelerator design issues in high brightness beam applications, as well as the development of advanced accelerators. Particularly, synchrotron radiation induced effects in a magnetic dispersive beamline element can lead to collective beam instabilities and emittance growth. A novel beam dynamics code is developed based on a Lagrangian method for the calculation of the particles’ radiation near-fields using wavefront/wavelet meshes via the Green’s function of the Maxwell equations. These fields are then interpolated onto a moving mesh for dynamic update of the beam. This method allows radiation co-propagation and self-consistent interaction with the beam in 2D/3D simulations at greatly reduced numerical errors. Multiple levels of parallelisms are inherent in this method and implemented in our code CoSyR to enable at-scale simulations of nonlinear beam dynamics on modern computing platforms using MPI, multi-threading, and GPUs. Here, the current 2D implementation of CoSyR has been used to evaluate the transverse and longitudinal coherent radiation effects on the beam and to investigate beam optics designs proposed for mitigation of beam brightness degradation in a magnetic bunch compressor. In this paper, the design of CoSyR, as well as the benchmark with other coherent synchrotron radiation models, are described and discussed. Extension of the core algorithms to 3D is possible and planned.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A Verification of Flux Sensitivity Estimates Using the MCNP Tally Perturbation Tool

Nuclear data is commonly used in applications such as nuclear nonproliferation, safeguards, and criticality safety. More specifically, nuclear data is used in predictive simulation codes like the Monte-Carlo N-Particle (MCNP ® ) transport code, Serpent, and similar radiation transport codes. The improvement of nuclear data enables more precise and accurate simulations, which result in higher fidelity designs and reduced operational/procedural costs. Therefore, the improvement of nuclear data is of paramount importance across the nuclear community. Nuclear data is improved and validated through integral benchmark experiments. The design of benchmark experiments is an extensive process; therefore, these experiments are often optimized on multiple characteristics, including sensitivity to the nuclear data, during the design process. Sensitivity is a measure of how much a quantity changes due to changes in independent variables such as experimental configuration. An experimental design that has a larger sensitivity to the nuclear data of interest will have a larger impact on the accuracy and precision of the validated data. Past integral benchmark experiments have primarily used the effective multiplication factor ($k_{eff}$) as the predominant measured quantity; however, experiments designed with other quantities in mind would be able to optimize on validating different areas of the nuclear data. A primary goal of the EUCLID project is to design, constrain, and reduce compensating errors in experiments focused on quantities other than $k_{eff}$ to better validate nuclear data across the board. Currently, there is a capability in MCNP to easily calculate the sensitivity of $k_{eff}$ to specific nuclear data of numerous reactions types and isotopes (KSEN card); however, the sensitivity of other quantities must be estimated in more strenuous manners. For example, the perturbation feature (PERT card) of MCNP can be used to estimate first-order sensitivities of some response in fixed source simulations. A recent announcement revealed that the first- and second-order perturbation features in previous releases of MCNP contained a bug. It was identified that particles were being scored into the wrong energy bin. The bug is in the most recent public release (MCNP6.2); however, a patch has been added to the most up to date version (MCNP6.2.2) that has not been released publicly. A direct comparison of the PERT card results for an F4 (neutron flux averaged over a cell) tally before and after the patch are shown in figure 1. All simulations used in the sensitivity estimates in this report were performed with MCNP6.2.2. This work verifies the patched MCNP perturbation tool by comparing first order sensitivities made using the PERT card to estimates made using manual perturbation of the compact ENDF (ACE) files.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗