Scott W. Mosher

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations

Abstract This paper presents a hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities (e.g., flux, dose, or reaction rate at a specific location). The basis of this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space-and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC (Monaco with Automated Variance Reduction using Importance Calculations) sequence of SCALE and the ADVANTG (Automated Deterministic Variance Reduction Generator)/MCNP framework. Application of the method to representative real-world problems, including calculation of dose rate and energy-dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance-reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.

ADVANTG An Automated Variance Reduction Parameter Generator

The primary objective of ADVANTG is to reduce both the user effort and the computational time required to obtain accurate and precise tally estimates across a broad range of challenging transport applications. ADVANTG has been applied to simulations of real-world radiation shielding, detection, and neutron activation problems. Examples of shielding applications include material damage and dose rate analyses of the Oak Ridge National Laboratory (ORNL) Spallation Neutron Source and High Flux Isotope Reactor (Risner and Blakeman 2013) and the ITER Tokamak (Ibrahim et al. 2011). ADVANTG has been applied to a suite of radiation detection, safeguards, and special nuclear material movement detection test problems (Shaver et al. 2011). ADVANTG has also been used in the prediction of activation rates within light water reactor facilities (Pantelias and Mosher 2013). In these projects, ADVANTG was demonstrated to significantly increase the tally figure of merit (FOM) relative to an analog MCNP simulation. The ADVANTG-generated parameters were also shown to be more effective than manually generated geometry splitting parameters.

ITER Neutronics Modeling Using Hybrid Monte Carlo/Deterministic and CAD-Based Monte Carlo Methods

Abstract The immense size and complex geometry of the ITER experimental fusion reactor require the development of special techniques that can accurately and efficiently perform neutronics simulations with minimal human effort. This paper shows the effect of the hybrid Monte Carlo (MC)/deterministic techniques—Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS)—in enhancing the efficiency of the neutronics modeling of ITER and demonstrates the applicability of coupling these methods with computer-aided-design-based MC. Three quantities were calculated in this analysis: the total nuclear heating in the inboard leg of the toroidal field coils (TFCs), the prompt dose outside the biological shield, and the total neutron and gamma fluxes over a mesh tally covering the entire reactor. The use of FW-CADIS in estimating the nuclear heating in the inboard TFCs resulted in a factor of ˜275 increase in the MC figure of merit (FOM) compared with analog MC and a factor of ˜9 compared with the traditional methods of variance reduction. By providing a factor of ˜21 000 increase in the MC FOM, the radiation dose calculation showed how the CADIS method can be effectively used in the simulation of problems that are practically impossible using analog MC. The total flux calculation demonstrated the ability of FW-CADIS to simultaneously enhance the MC statistical precision throughout the entire ITER geometry. Collectively, these calculations demonstrate the ability of the hybrid techniques to accurately model very challenging shielding problems in reasonable execution times.

Uncertainty Underprediction in Monte Carlo Eigenvalue Calculations

Abstract It is well-known that statistical estimates obtained from Monte Carlo criticality simulations can be adversely affected by cycle-to-cycle correlations in the fission source, which can lead to estimates of statistical uncertainties that are lower than the true uncertainty by a factor of 5 or more. However, several other more fundamental issues such as adequate source sampling over the fissionable regions and source convergence can have a significant impact on the uncertainties for the calculated eigenvalue and localized tally means, and these issues may be mistaken for effects resulting from cycle-to-cycle correlations. In worst-case scenarios, the uncertainty may be underpredicted by a factor of 40 or more. Since Monte Carlo methods are widely used in criticality safety applications and are increasingly being used for benchmarking reactor analyses, an in-depth understanding of the effects of these issues must be developed in order to support the practical use of Monte Carlo software packages. A rigorous statistical analysis of eigenvalue and localized tally results in Monte Carlo criticality calculations is presented using the SCALE/KENO-VI (continuous-energy version) and MCNP codes. The purpose of this analysis is to investigate the underprediction of uncertainty and its sensitivity to problem characteristics and calculational parameters using two of the most widely used Monte Carlo criticality codes. For the problems considered here, which are fuel rod and fuel assembly problems with reflecting boundary conditions on all four horizontal sides, we show that adequate source convergence along with proper specification of Monte Carlo parameters can reduce the magnitude of uncertainty underprediction to reasonable levels, below a factor of 2 in most cases.

Global Evaluation of Prompt Dose Rates in ITER Using Hybrid Monte Carlo/Deterministic Techniques

Abstract The hybrid Monte Carlo (MC)/deterministic techniques - Consistent Adjoint Driven Importance Sampling (CADIS) and Forward Weighted CADIS (FW-CADIS) - enable the full 3-D modeling of very large and complicated geometries. The ability of performing global MC calculations for nuclear parameters throughout the entire ITER reactor was demonstrated. The 2 m biological shield (bioshield) reduces the total prompt operational dose by six orders of magnitude. The divertor cryo-pump port results in a peaking factor of 120 in the prompt operational dose rate behind the bioshield of ITER. The equatorial port, plugged by 2 m of shielding, increases the prompt dose rate behind the bioshield by a factor of 47. The peak values of the prompt dose rates at the back surface of the bioshield were 240 μSv/hr and 94 μSv/hr corresponding to the regions behind the divertor cryo-pump port and the equatorial port, respectively.

A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation

We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.

Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.

Integration of the Full Tokamak Reference Model with the Complex Model for ITER Neutronic Analysis

Abstract The ITER International Organization has developed a number of reference Monte Carlo N-Particle (MCNP) models including the tokamak machine C-model, the Tokamak Complex model, and the neutral beam injection (NBI) systems model. The Tokamak Complex model primarily describes building structures beyond the bioshield. Representation of the tokamak and its systems are not included in this model. The Oak Ridge National Laboratory Radiation Transport Group has conducted two ITER neutronic analysis model integrations: (1) integration of the tokamak C-model with the Tokamak Complex model for shutdown dose rate characterization in Port Cell 16 at level B1, and (2) integration of the NBI model with the Tokamak Complex model for estimating the spatial distribution of biological dose rate at levels L1, L2, and L3 of the Tokamak Complex. The integrated models were further extended to include models of system components that are essential to the neutronic analyses. This paper presents the approach and computer tools used to integrate existing reference models, describes the additional design details implemented in the integrated models, and provides representative neutronic calculations based on the extended models.

Algorithmic Improvements to MCNP5 for High-Resolution Fusion Neutronics Analyses

Abstract Neutronics analyses of the ITER experimental fusion reactor rely on increasingly complex geometry models and estimates of energy-dependent neutron flux and radiation dose-rate distributions generated at ever higher resolutions. There are significant practical challenges with applying the Monte Carlo N-Particle (MCNP) continuous-energy transport code to high-resolution analyses. For models consisting of more than 100 000 surfaces and cells, geometry initialization can take several hours, thus slowing down model integration and transport analysis efforts. In multithreaded simulations, the amount of memory consumed by superimposed mesh tally data increases in proportion to the number of threads. This behavior limits either the tally resolution or the number of processor cores that can be utilized in the simulation. This paper describes algorithmic improvements that were implemented in a modified version of MCNP5 to overcome these limitations. These improvements are referred to as the Oak Ridge National Laboratory Transformative Neutronics (ORNL-TN) upgrade. A comparison of the performance and memory usage of both MCNP5 and ORNL-TN on several relevant fusion neutronics models is presented. In these tests and in actual high-resolution neutronics analyses, ORNL-TN reduces geometry processing times from hours to a few seconds and increases in-memory mesh tally capacity from the order of 108 to 1010 space-energy bins.

Validation of the MS-CADIS Method for Full-Scale Shutdown Dose Rate Analysis

Abstract Fusion energy systems present increasingly significant computational challenges as they grow in size and complexity. Once constructed, ITER will be a full-size nuclear facility with highly complicated structures and support systems, with an array of scientific equipment in close proximity to the neutron-emitting deuterium-tritium plasma. Characterization of shutdown dose rate (SDDR) distributions caused by the neutron activation of these structures is important to the final design and full-power operation of the device. This work summarizes the theoretical basis and parallel implementation of the Multi-Step Consistent Adjoint-Driven Importance Sampling (MS-CADIS) method designed specifically for highly efficient execution of multistep activation problems. Fusion SDDR benchmark problems have been solved with these new tools, and the results have been compared to experimental and other computational results to establish their validation basis.