[en] An asymptotic analysis is used to derive a set of diffusion approximations to the nonclassical transport equation with isotropic scattering. These approximations are shown to reduce to the simplified P_N equations under the assumption of classical transport, and therefore are labeled nonclassical SP_N equations. In addition, the nonclassical SP_N equations can be manipulated into a classical form with modified parameters, which can be implemented in existing SP_N codes. Numerical results are presented for an one-dimensional random periodic system, validating the theoretical predictions. (authors)

[en] Today's 'grand challenge' neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the Sn code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo's RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.

[en] Fusion systems are, in general, geometrically complex requiring detailed three-dimensional (3-D) nuclear analysis. This analysis is required to address tritium self-sufficiency, nuclear heating, radiation damage, shielding, and radiation streaming issues. To facilitate such calculations, we developed an innovative computational tool that is based on the continuous energy Monte Carlo code MCNP and permits the direct use of CAD-based solid models in the ray-tracing. This allows performing the neutronics calculations in a model that preserves the geometrical details without any simplification, eliminates possible human error in modeling the geometry for MCNP, and allows faster design iterations. In addition to improving the work flow for simulating complex 3- D geometries, it allows a richer representation of the geometry compared to the standard 2nd order polynomial representation. This newly developed tool has been successfully tested for a detailed 40 degree sector benchmark of the International Thermonuclear Experimental Reactor (ITER). The calculations included determining the poloidal variation of the neutron wall loading, flux and nuclear heating in the divertor components, nuclear heating in toroidal field coils, and radiation streaming in the mid-plane port. The tool has been applied to perform 3-D nuclear analysis for several fusion designs including the ARIES Compact Stellarator (ARIES-CS), the High Average Power Laser (HAPL) inertial fusion power plant, and ITER first wall/shield (FWS) modules. The ARIES-CS stellarator has a first wall shape and a plasma profile that varies toroidally within each field period compared to the uniform toroidal shape in tokamaks. Such variation cannot be modeled analytically in the standard MCNP code. The impact of the complex helical geometry and the non-uniform blanket and divertor on the overall tritium breeding ratio and total nuclear heating was determined. In addition, we calculated the neutron wall loading variation in both the poloidal and toroidal directions. The final optics system of the HAPL power plant includes several metallic and dielectric mirrors that are sensitive to radiation. Although some of these mirrors are not in the direct line-of-sight of the neutron source, radiation scattering and streaming through the laser beam ports requires an assessment of the nuclear environment at the final optics to predict their lifetime. Detailed CAD models of the ITER FWS modules were analyzed to produce high resolution maps of nuclear heating, radiation damage and helium production. These clearly show the impact of the design heterogeneity details with the many coolant channels embedded in the module. In addition, hot spots produced in the vacuum vessel behind the module as a result of streaming through these coolant channels were evaluated. These examples will be presented to demonstrate the applicability of the tool to nuclear analysis of complex fusion systems

[en] Graphics Processing Units (GPUs) have increased in computational power, offering a higher aggregate memory bandwidth and many more floating-point operations per second (FLOPS) than traditional central processing units (CPUs). As such, many new supercomputing platforms are being built to incorporate GPUs to increase computational capacity, and software must be adapted to or developed for these emerging architectures. WARP ('Weaving All the Random Particles') is a new code that efficiently performs three-dimensional (3D) continuous energy Monte Carlo neutron transport code on a GPU. Like traditional Monte Carlo neutron transport codes, WARP uses ray tracing and distance-to-collision calculations to follow the random walks of neutrons in a system. Specifically, WARP uses the OptiX ray tracing framework, a highly-optimized library developed by NVIDIA, to handle the system geometry. This work discusses the addition of delta-tracking to WARP as an alternative to the distance-to-collision calculation to explore the effects of the method when used in a Monte Carlo neutron transport code executed on a GPU. The delta-tracking method allows neutron random walks to continue over different material regions without stopping the particle at each boundary surface, and the geometry routine is reduced to determining the material at each collision point. It was found that the delta-tracking version of WARP incurs significantly longer runtimes than the original version. The figures-of-merit of the calculations performed by the different physics routine range from one order of magnitude greater than that of the original version of the code for the simplest tested geometry configuration to one order of magnitude worse than that of the original version of the code for more complex configurations. (authors)

[en] Serpent 2, a continuous-energy Monte Carlo Reactor physics burnup code developed at the VTT Technical Research Centre of Finland, uses a common rejection sampling technique, known as Woodcock delta-tracking. This method improves the efficiency of Monte Carlo in the complicated geometric layout of nuclear reactors and is widely used despite drawbacks that make it inefficient in specific cases, such as in the presence of strong absorbers. At present, Serpent actively uses delta-tracking, falling back to a surface tracking option in situations where delta-tracking is inefficient to partially offset these weaknesses. Morgan and Kotlyar introduced a Weighted Delta Tracking (WDT) routine to address these issues, replacing the rejection sampling of absorption events with an implicit event. In this research, we examine the theoretical basis for rejection sampling and implicit events, and how they relate to WDT. We then discuss implementation of a routine that extends the WDT routine to include scattering events. The routine is implemented and tested within Serpent. We examine various test cases including a Boiling Water Reactor (BWR) pin cell, and homogenous fuel media based on the content of the fuel of the Transient Test Reactor (TREAT) at Idaho National Lab (INL)

[en] The recent development of the compact stellarator concept delivered ARIES-CS - a compact stellarator with 7.75 m average major radius, approaching that of tokamaks. In stellarators, the most influential engineering parameter that determines the machine size and cost is the minimum distance between the plasma boundary and mid-coil (Δ_min). Accommodating the breeding blanket and necessary shield within this distance to protect the superconducting magnet represents a challenging task. Selecting the nuclear and engineering parameters to produce an economic optimum, modeling the complex geometry for 3-D nuclear analysis to confirm the key engineering parameters, and minimizing the radwaste stream received considerable attention during the ARIES-CS design process. This paper provides a perspective on the successful integration of the nuclear activity, economics, and safety constraints into the final ARIES-CS configuration. (author)

[en] This paper presents a Monte Carlo-computational fluid dynamics coupling of OpenMC and Nek5000 within the Moose framework. This coupling specifically aims to address and overcome challenges encountered in earlier coupling works such as file-based communication and overly restrictive one-to-one mesh mappings between the codes. In addition, coupling within the Moose framework offers the possibility of relatively easy coupling to any other Moose application. The advantages of the coupling framework are illustrated with a simple pin cell example; to demonstrate the ease of coupling to other Moose applications, a lightweight surrogate for Bison, called Buffalo, is used to solve for the nuclear fuel physics. (author)

[en] In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MG Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.

[en] Over the past 5-6 decades, stellarator power plants have been studied in the US, Europe, and Japan as an alternate to the mainline magnetic fusion tokamaks, offering steady-state operation and eliminating the risk of plasma disruptions. The earlier 1980s studies suggested large-scale stellarator power plants with an average major radius exceeding 20 m. The most recent development of the compact stellarator concept delivered ARIES-CS - a compact stellarator with 7.75 m average major radius, approaching that of tokamaks. For stellarators, the most important engineering parameter that determines the machine size and cost is the minimum distance between the plasma boundary and mid-coil. Accommodating the breeding blanket and necessary shield within this distance to protect the ARIES-CS superconducting magnet represents a challenging task. Selecting the ARIES-CS nuclear and engineering parameters to produce an economic optimum, modeling the complex geometry for 3D nuclear analysis to confirm the key parameters, and minimizing the radwaste stream received considerable attention during the design process. These engineering design elements combined with advanced physics helped enable the compact stellarator to be a viable concept. This paper provides a brief historical overview of the progress in designing stellarator power plants and a perspective on the successful integration of the nuclear activity into the final ARIES-CS configuration

[en] Within the ARIES-CS project, design activities have focused on developing the first compact device that enhances the attractiveness of the stellarator as a power plant. The objectives of this paper are to review the nuclear elements that received considerable attention during the design process and provide a perspective on their successful integration into the final design. Among these elements are the radial build definition, the well-optimized in-vessel components that satisfy the ARIES top-level requirements, the carefully selected nuclear and engineering parameters to produce an economic optimum, the modeling for the first time ever-of the highly complex stellarator geometry for the three-dimensional nuclear assessment, and the overarching safety and environmental constraints to deliver an attractive, reliable, and truly compact stellarator power plant.