Forward-Weighted Consistent Adjoint Driven Importance Sampling Research Articles

Shutdown dose rate calculation for fission reactors: An application of the MS-CADIS method to OPAL

There have been considerable advances of shutdown dose rate (SDDR) calculation methods for fusion related problems, however applications of these methods in the fission reactor field have hitherto been sparse. The present study attempts to bridge this gap by investigating the applicability of SDDR calculation methods for fission reactor problems. Specifically, we aim to assess and validate whether recent advances in SDDR methods can be successfully applied in fission research reactors. To this end, we estimate the shutdown dose rate distribution at the Open Pool Australian Light water reactor (OPAL) using the rigorous two step (R2S) computational method, and we compare the calculated results with the experimental data. This method utilizes a 3D reactor model implemented in the Monte Carlo N-Particle (MCNP) transport code, the AutomeD VAriaNce reduction Generator (ADVANTG) code for geometry discretization and variance reduction calculations, and the Oak Ridge Isotope GENeration (ORIGEN) inventory code for activation calculations. To ensure robustness, we employ two variance reduction techniques, Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) and Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS). To the best of our knowledge, this is the first MS-CADIS method implementation for fission reactor problems. The SDDR is estimated at ten locations within the experimental hall, all situated more than 4 m away from the reactor core.The paper shows that, the experimental observations are within the lower and upper bounds of the simulation results for 4 out of 10 locations, while the remaining observations are within a factor of 7, with one significant outlier. The calculated average dose rate is within 5% of the nominal values of the experimental observations for 3 locations. The computational results are within statistical uncertainty by using two different variance reduction techniques, with significant computational advantage of MS-CADIS over FW-CADIS for SDDR calculations. The results indicate that the combination of SDDR distribution maps, estimated dose rate energy dependance, and activation information are powerful tools in identifying the radioisotopes and reactor components dominating the SDDR. These results can contribute to better radiation safety practices in contaminated areas, by enabling the minimal dose path planning or by improving radiation shielding.

Analysis of the HI-TRAC VW Transfer Cask Dose Rates for Spent Fuel Assemblies Loaded in Nuclear Power Plant Krsko Storage Campaign One

Abstract In this paper, shielding analysis was performed to determine neutron and gamma dose rates around the transfer cask HI-TRAC VW (Holtec International Transfer Cask Variable Weight) loaded with spent fuel assemblies (SFA) from nuclear power plant (NPP) Krsko spent fuel dry storage (SFDS) campaign one. The HI-TRAC VW is a multilayered cylindrical vessel designed to accept a multipurpose canister (MPC) during loading, unloading, and transfer to dry storage building. The MPC can contain up to 37 spent fuel assemblies. The analysis was divided into two steps. The first step was the source term generation using origen-s module of the scale code package. The source was calculated based on the operating history of spent fuel assemblies currently located in the NPP Krsko spent fuel pool. The obtained particle intensities and source spectra of the SFA were used in the second step to calculate the dose rates around the transfer cask. A comprehensive hybrid shielding analysis included the calculation of dose rates resulting from fuel neutrons and gammas, neutron-induced gammas (n-γ reaction), and hardware activation gammas under normal conditions and during accident scenario. To obtain the dose rates within the acceptable uncertainties, forward weighted consistent adjoint driven importance sampling (FW-CADIS) variance reduction scheme, as implemented in advantg code, was adopted for accelerating final mcnp6.2 calculations. The dose rates around HI-TRAC VW cask were calculated using mcnp6.2 code for all 16 cask loadings belonging to campaign one in order to illustrate the impact of fuel assembly selection schemes proposed by company responsible for project realization - Holtec International (HI).

Application of global variance reduction method to calculate a high-resolution fast neutron flux distribution for TMSR-SF1

The solid fuel thorium molten salt reactor (TMSR-SF1) is a 10-MWth fluoride-cooled pebble bed reactor. As a new reactor concept, one of the major limiting factors to reactor lifetime is radiation-induced material damage. The fast neutron flux (E > 0.1 MeV) can be used to assess possible radiation damage. Hence, a method for calculating high-resolution fast neutron flux distribution of the full-scale TMSR-SF1 reactor is required. In this study, a two-step subsection approach based on MCNP5 involving a global variance reduction method, referred to as forward-weighted consistent adjoint-driven importance sampling, was implemented to provide fast neutron flux distribution throughout the TMSR-SF1 facility. In addition, instead of using the general source specification cards, the user-provided SOURCE subroutine in MCNP5 source code was employed to implement a source biasing technique specialized for TMSR-SF1. In contrast to the one-step analog approach, the two-step subsection approach eliminates zero-scored mesh tally cells and obtains tally results with extremely uniform and low relative uncertainties. Furthermore, the maximum fast neutron fluxes of the main components in TMSR-SF1 are provided, which can be used for radiation damage assessment of the structural materials.

Comparing the performance of two hybrid deterministic/Monte Carlo transport codes in shielding calculations of a spent fuel storage cask

Abstract This study systematically compared two hybrid deterministic/Monte Carlo transport codes, ADVANTG/MCNP and MAVRIC, in solving a difficult shielding problem for a real-world spent fuel storage cask. Both hybrid codes were developed based on the consistent adjoint driven importance sampling (CADIS) methodology but with different implementations. The dose rate distributions on the cask surface were of primary interest and their predicted results were compared with each other and with a straightforward MCNP calculation as a baseline case. Forward-Weighted CADIS was applied for optimization toward uniform statistical uncertainties for all tallies on the cask surface. Both ADVANTG/MCNP and MAVRIC achieved substantial improvements in overall computational efficiencies, especially for gamma-ray transport. Compared with the continuous-energy ADVANTG/MCNP calculations, the coarse-group MAVRIC calculations underestimated the neutron dose rates on the cask's side surface by an approximate factor of two and slightly overestimated the dose rates on the cask's top and side surfaces for fuel gamma and hardware gamma sources because of the impact of multigroup approximation. The fine-group MAVRIC calculations improved to a certain extent and the addition of continuous-energy treatment to the Monte Carlo code in the latest MAVRIC sequence greatly reduced these discrepancies. For the two continuous-energy calculations of ADVANTG/MCNP and MAVRIC, a remaining difference of approximately 30% between the neutron dose rates on the cask's side surface resulted from inconsistent use of thermal scattering treatment of hydrogen in concrete.

Review of Hybrid Methods for Deep-Penetration Neutron Transport

Methods for deep-penetration radiation transport remain important for radiation shielding, nonproliferation, nuclear threat reduction, and medical applications. As these applications become more ubiquitous, the need for accurate and reliable transport methods appropriate for these systems persists. For such systems, hybrid methods often obtain reliable answers in the shortest time by leveraging the speed and uniform uncertainty distribution of a deterministic solution to bias Monte Carlo transport and reduce the variance in the solution. This work reviews the state of the art among such hybrid methods. First, we summarize variance reduction (VR) for Monte Carlo radiation transport and existing efforts to automate these techniques. Relations among VR, importance, and the adjoint solution of the neutron transport equation are then discussed. Based on this exposition, the work transitions from theory to a critical review of existing VR implementations in modern nuclear engineering software. At present, the Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS) hybrid methods are the gold standard by which to reduce the variance in problems that have deeply penetrating radiation. The CADIS and FW-CADIS methods use an adjoint scalar flux to generate VR parameters for Monte Carlo radiation transport. Additionally, efforts to incorporate angular information into VR methods for Monte Carlo are summarized. Finally, we assess various implementations of these methods and the degree to which they improve VR for their target applications.

Nth-order multi-response CADIS method to optimize regional variances in a hybrid Monte Carlo simulation

To increase the calculation efficiency of the Monte Carlo (MC) calculation, variance reduction (VR) techniques have been introduced. For an optimal MC calculation, it is necessary to properly determine the optimized parameters for VR techniques. To automatically determine those parameters, hybrid MC methods have been developed. For a single response, the Consistent Adjoint Driven Importance Sampling (CADIS) method, which uses a zero variance solution, was developed. For the inclusion of multiple responses, several methods have been proposed. Among them, the Forward-Weighted CADIS (FW-CADIS) method shows the best performance. In the previous study, the Multi-Response CADIS (MR-CADIS) method was proposed and it showed a better efficiency. However, it is noted that many adjoint calculations are needed to adopt the MR-CADIS method and the overall efficiency can be decreased. In this study, a new hybrid MC method, referred to as an Nth-order multi-response CADIS method (N-CADIS) is proposed for a more uniformly low variance. For verification of the proposed method, it is applied to simple problems and compared with the FW-CADIS method and the MR-CADIS method. These results show that the N-CADIS method can produce a better efficiency only for the MC calculation. Also, to avoid many deterministic calculations, the adjoint transport process was modified and applied in ADVANTG code. This process produces a VR parameter similar to that used in the N-CADIS method. This approach is also verified and compared with the FW-CADIS method. The results from the N-CADIS method have a more uniform and lower relative error than those from the FW-CADIS method. Therefore, it is expected that the N-CADIS method will contribute to efficient calculations for multiple responses in hybrid MC simulations.

Dose Rate Evaluation for the ES-3100 Package with HEU Content Using MCNP, ADVANTG, Monaco, and MAVRIC

This paper presents a comparative study of dose rate calculations for the ES-3100 package with highly enriched uranium (HEU) content for different source configurations using the following computer codes: MCNP, Automated Variance Reduction Generator (ADVANTG)/MCNP, Monaco, and Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC). The Model ES-3100 package was developed at the Y-12 National Security Complex for domestic and international transportation of Type B fissile radioactive material. In this study, six different source configurations (i.e., solid cylinder, cylindrical hemishell, cylindrical shell, rectangular plate, cylindrical rod, and cylindrical segment form) having 36 kg of HEU metal inside the package containment vessel (based on configurations in the ES-3100/HEU safety analysis report for packaging) are evaluated. Dose rates at 1 mm and 1 m from the package surfaces are calculated for these different source configurations. The MCNP and Monaco cases are run without any biasing options to accelerate the convergence. The Consistent Adjoint Driven Importance Sampling and the Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) methods developed at the Oak Ridge National Laboratory are implemented in the ADVANTG/MCNP and MAVRIC codes to accelerate the convergence. ADVANTG generates variance reduction parameters using the Denovo code, and MCNP is used with the variance reduction parameters to accelerate the convergence. MAVRIC uses the Denovo code to construct an importance map and a biased source distribution that are supplied to Monaco to accelerate the Monte Carlo simulation. The FW-CADIS option in ADVANTG and MAVRIC is used to accelerate the convergence in this study. The accelerated convergence cases (ADVANTG/MCNP and MAVRIC) are about 100 times faster with 100 times less particle simulation than those cases run without biasing options (analog MCNP and analog Monaco). The MCNP, ADVANTG/MCNP, Monaco, and MAVRIC calculated dose rates at 1 mm and 1 m from the package surfaces for the different source configurations are compared and are found to be in general agreement.

A proposal on multi-response CADIS method to optimize reduction of regional variances in hybrid Monte Carlo simulation

For fixed source problems, it is known that the analog Monte Carlo simulation method can show low efficiencies. To increase the calculation efficiency, variance reduction techniques (VRT) have been introduced and utilized. To apply these techniques, parameters to control particle transport behaviors should be properly determined. The hybrid Monte Carlo methods were developed to automatically determine the VRT parameters using information estimated from a deterministic simulation. In the case of a single response, the Consistent Adjoint Driven Importance Sampling (CADIS) method is well derived to decide VRT parameters. Recently, for plural response problems, a variety of methods have been proposed. It is noted that Forward-Weighted CADIS (FW-CADIS) method gives the best performance to optimize the parameters for plural response problems. However, it can create inefficiencies due to an assumption that uniform particle density is used to uniformly obtain low variance in each response. In the Multi-Response CADIS (MR-CADIS) method proposed in this study, a new weight function is derived to effectively reduce plural relative errors. With the proposed method, VRT parameters are decided by that the sum of squared relative errors for plural responses has a minimum value. To verify the MR-CADIS method, simple shielding and duct problems are estimated and compared to those estimated with the FW-CADIS method. These results show that the MR-CADIS method can produce better efficiency and uniformity than the FW-CADIS method for plural response problems.

The Analysis of the External Neutron Monitor Responses in a Simplified JET-Like Tokamak Using ADVANTG

The application of the Automated Variance Reduction Generator (ADVANTG) code to accelerate MCNP neutron transport calculations in fusion-relevant geometries is presented. The ADVANTG code generates variance-reduction parameters using the Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) methods based on deterministic transport calculations performed by the discrete ordinates code Denovo. The aim of ADVANTG is to reduce the MCNP computational time by automating the process of variance-reduction parameter generation. ADVANTG was tested on a simplified model of a JET-like tokamak that in spite of its simplicity retains all the major characteristics of such a tokamak. The performance of the nuclear data libraries provided with ADVANTG and of various other ADVANTG/Denovo settings on variance-reduction efficiency was tested. Several cases using deuterium-deuterium or deuterium-tritium (D-T) volumetric (plasma) sources and 252Cf or D-T point neutron sources were analyzed to find guidelines for successful use of the code for fusion applications. Additionally, the use of ADVANTG as a tool to identify major neutron pathways from the neutron source to the detector is demonstrated.

Analysis of dpa Rates in the HFIR Reactor Vessel using a Hybrid Monte Carlo/Deterministic Method*

The Oak Ridge High Flux Isotope Reactor (HFIR), which began full-power operation in 1966, provides one of the highest steady-state neutron flux levels of any research reactor in the world. An ongoing vessel integrity analysis program to assess radiation-induced embrittlement of the HFIR reactor vessel requires the calculation of neutron and gamma displacements per atom (dpa), particularly at locations near the beam tube nozzles, where radiation streaming effects are most pronounced. In this study we apply the Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) technique in the ADVANTG code to develop variance reduction parameters for use in the MCNP radiation transport code. We initially evaluated dpa rates for dosimetry capsule locations, regions in the vicinity of the HB-2 beamline, and the vessel beltline region. We then extended the study to provide dpa rate maps using three-dimensional cylindrical mesh tallies that extend from approximately 12 in. below to approximately 12 in. above the height of the core. The mesh tally structures contain over 15,000 mesh cells, providing a detailed spatial map of neutron and photon dpa rates at all locations of interest. Relative errors in the mesh tally cells are typically less than 1%.

Automatic Mesh Adaptivity for Hybrid Monte Carlo/Deterministic Neutronics Modeling of Difficult Shielding Problems

The well-established Consistent Adjoint Driven Importance Sampling (CADIS) and the Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) hybrid Monte Carlo/deterministic techniques have dramatically increased the efficiency of neutronics simulations, yielding accurate solutions for increasingly complex problems through full-scale, high-fidelity simulations. However, for full-scale simulations of very large and geometrically complex nuclear energy systems, even the CADIS and FW-CADIS techniques can reach the CPU and memory limits of all but the very powerful supercomputers. In this work, three mesh adaptivity algorithms were developed to reduce the computational resource requirements of CADIS and FW-CADIS without sacrificing their efficiency improvements. First, a macromaterial approach was developed to enhance the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm was developed to generate meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window (WW) coarsening (WWC) algorithm was developed to decouple the WW mesh and energy bins from the mesh and energy group structure of the deterministic calculations. By removing the memory constraint of the WW map from the resolution of the mesh and the energy group structure of the deterministic calculations, the WWC algorithm allows higher-fidelity deterministic calculations that, consequently, increase the efficiency and reliability of the CADIS and the FW-CADIS simulations. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms increased both the number of mesh tally elements in which nonzero results were obtained (+23.3%) and the overall efficiency of the calculation (a factor of >3.4). The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a 94-CPU computer cluster, eliminating the need for a world-class supercomputer.

Improved Monte Carlo Variance Reduction for Space and Energy Self-Shielding

Continued demand for accurate and computationally efficient transport methods to solve optically thick, fixed-source transport problems has inspired research on variance-reduction (VR) techniques for Monte Carlo (MC). Methods that use deterministic results to create VR maps for MC constitute a dominant branch of this research, with Forward Weighted–Consistent Adjoint Driven Importance Sampling (FW-CADIS) being a particularly successful example. However, locations in which energy and spatial self-shielding are combined, such as thin plates embedded in concrete, challenge FW-CADIS. In these cases the deterministic flux cannot appropriately capture transport behavior, and the associated VR parameters result in high variance in and following the plate.This work presents a new method that improves performance in transport calculations that contain regions of combined space and energy self-shielding without significant impact on the solution quality in other parts of the problem. This method is based on FW-CADIS and applies a Resonance Factor correction to the adjoint source. The impact of the Resonance Factor method is investigated in this work through an example problem. It is clear that this new method dramatically improves performance in terms of lowering the maximum 95% confidence interval relative error and reducing the compute time. Based on this work, we recommend that the Resonance Factor method be used when the accuracy of the solution in the presence of combined space and energy self-shielding is important.

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

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.

Hybrid biasing approaches for global variance reduction

A new variant of Monte Carlo—deterministic (DT) hybrid variance reduction approach based on Gaussian process theory is presented for accelerating convergence of Monte Carlo simulation and compared with Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) approach implemented in the SCALE package from Oak Ridge National Laboratory. The new approach, denoted the Gaussian process approach, treats the responses of interest as normally distributed random processes. The Gaussian process approach improves the selection of the weight windows of simulated particles by identifying a subspace that captures the dominant sources of statistical response variations. Like the FW-CADIS approach, the Gaussian process approach utilizes particle importance maps obtained from deterministic adjoint models to derive weight window biasing. In contrast to the FW-CADIS approach, the Gaussian process approach identifies the response correlations (via a covariance matrix) and employs them to reduce the computational overhead required for global variance reduction (GVR) purpose. The effective rank of the covariance matrix identifies the minimum number of uncorrelated pseudo responses, which are employed to bias simulated particles. Numerical experiments, serving as a proof of principle, are presented to compare the Gaussian process and FW-CADIS approaches in terms of the global reduction in standard deviation of the estimated responses.

Review of Hybrid (Deterministic/Monte Carlo) Radiation Transport Methods, Codes, and Applications at Oak Ridge National Laboratory

** This paper provides a review of the hybrid (Monte Carlo/deterministic) radiation transport methods and codes used at the Oak Ridge National Laboratory and examples of their application for increasing the efficiency of real-world, fixed-source Monte Carlo analyses. The two principal hybrid methods are (1) Consistent Adjoint Driven Importance Sampling (CADIS) for optimization of a localized detector (tally) region (e.g., flux, dose, or reaction rate at a particular location) and (2) Forward Weighted CADIS (FW-CADIS) for optimizing distributions (e.g., mesh tallies over all or part of the problem space) or multiple localized detector regions (e.g., simultaneous optimization of two or more localized tally regions). The two methods have been implemented and automated in both the MAVRIC sequence of SCALE 6 and ADVANTG, a code that works with the MCNP code. As implemented, the methods utilize the results of approximate, fast-running 3-D discrete ordinates transport calculations (with the Denovo code) to generate consistent space- and energy-dependent source and transport (weight windows) biasing parameters. These methods and codes have been applied to many relevant and challenging problems, including calculations of PWR ex-core thermal detector response, dose rates throughout an entire PWR facility, site boundary dose from arrays of commercial spent fuel storage casks, radiation fields for criticality accident alarm system placement, and detector response for special nuclear material detection scenarios and nuclear well-logging tools. Substantial computational speed-ups, generally O(10 2-4 ), have been realized for all applications to date. This paper provides a brief review of the methods, their implementation, results of their application, and current development activities, as well as a considerable list of references for readers seeking more information about the methods and/or their applications.

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

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.

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

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.

Automated Variance Reduction Applied to Nuclear Well-Logging Problems

Simulating nuclear well-logging devices with Monte Carlo methods is computationally challenging and requires significant variance reduction to compute detector responses with low statistical uncertainties in reasonable lengths of time. The consistent adjoint-driven importance sampling (CADIS) method, which provides consistent source and transport biasing parameters based on a deterministic adjoint (importance) function, has been demonstrated to be very effective for well-logging simulations and other deep-penetration problems. A recent extension to the CADIS method, FW-CADIS (forward-weighted CADIS), is designed to optimize the calculation of several tallies at once by using an adjoint function based on an adjoint source weighted by the inverse of the forward flux. These advanced variance reduction methods have been incorporated and automated into the MAVRIC sequence of SCALE, making them very easy to use. The CADIS and FW-CADIS methods are demonstrated and compared on simple benchmark models of both neutron- and photon-based well-logging devices. Both advanced variance reduction methods offer a substantial reduction in computing time, compared to analog simulation, for these applications.

Simultaneous Optimization of Tallies in Difficult Shielding Problems

Monte Carlo is quite useful for calculating specific quantities in complex transport problems. Many variance reduction strategies have been developed that accelerate Monte Carlo calculations for specific tallies. However, when trying to calculate multiple tallies or a mesh tally, users have had to accept different levels of relative uncertainty among the tallies or run separate calculations optimized for each individual tally. To address this limitation, an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which is used for difficult source/detector problems, has been developed to optimize several tallies or the cells of a mesh tally simultaneously. The basis for 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. This method utilizes the results of a forward discrete ordinates solution, which may be based on a quick coarse-mesh calculation, to develop a forward-weighted source for the adjoint calculation. The importance map and the biased source computed from the adjoint flux are then used in the forward Monte Carlo calculation to obtain approximately uniform relative uncertainties for the desired tallies. This extension is called forward-weighted CADIS, or FW-CADIS.