Global Variance Reduction Research Articles

Research on a Monte Carlo global variance reduction method based on an automatic importance sampling method

Research on a Monte Carlo global variance reduction method based on an automatic importance sampling method

Construction of GVR weight windows maps from very low density transport simulations

Fusion-related facilities present relevant neutron radiation fields even after penetrating through a considerable thickness of shielding material. Neutronic analyses performed via Monte Carlo codes, then, need Global Variance Reduction (GVR) techniques so that low statistical uncertainty is reached efficiently throughout the geometry.Mesh-based Weight Windows is a flexible methodology used extensively for variance reduction purposes, both for Local and Global Variance Reduction. Purely stochastic GVR methodologies based on Weight Windows usually construct weight maps so that they are proportional to the forward particle flux, which is unknown a priori. Therefore, an iterative cycle is established. In each iteration, a weight map is obtained from the forward flux that allows the next iteration to reach further into the geometry, until all of it is populated.However, this iterative cycle may take a considerable amount of computer time, as many iterations are needed to fully populate the geometry. An alternative to achieve relevant penetration in a single iteration is to perform calculations at very low densities. However, a reconstruction method is needed to estimate the flux at the real density. This work studies a scheme to reconstruct the fluxes from low density calculations and compares it to already existing techniques.

Development of multilevel mesh adaptivity for global variance reduction in Monte Carlo code cosRMC

The mesh-based weight window method is a widely used global variance reduction technique for Monte Carlo particle transport calculation. In order to meet the fine voxel division required for high-quality weight window distribution, the uniform structured mesh division will lead to large memory footprint pressure. This work focused on the research of the multilevel adaptive mesh algorithm, using a recursive algorithm to adjust the voxel resolution adaptively according to the material of geometry. Then the adaptive mesh algorithm was applied to the weight window generator based on the response matrix method by establishing the neighbor relationship of adaptive mesh. And an optimization method for memory allocation of the response matrix solver was proposed, effectively reducing the memory footprint of the response matrix solver in parallel computing. In the calculation of the CFETR model, the calculation efficiency under the weight window based on adaptive mesh was increased by 53.3 % compared with the weight window based on uniform mesh, and the proportion of voxels with a statistical error less than 10 % reached 93.33 %, which verified the effectiveness of the multilevel adaptive mesh algorithm.

An extension of NASCA for SDDR analysis of mobile activated components with global variance reduction

During the plasma operation period of fusion reactor facilities, neutrons generated by DT reaction can penetrate deeply into structures and induce strong activation. Highly activated components have to be transferred from the on-load position to the hot cell for the purpose of maintenance. This movement produces a high-dose field, originating from the mobile radiation source, which could affect the functionality of important devices or pose risks to the workers. Therefore, it is imperative to compute the shutdown dose rate (SDDR) maps while transporting activated components in the facility and develop an optimized solution for this calculation process. In this study, we established a new extension of the NASCA method combined with the OTF GVR method to compute SDDR maps. NASCA-OTF is a method developed based on the shutdown dose simulation code NASCA to ensure automatic modification of the geometry structure on the fly. In the meantime, it uses OTF method for speeding up the Calculation. Thus, this modified method produces convergent SDDR maps corresponding to different positions of activated components within a single Monte Carlo (MC) simulation. The NASCA-OTF was verified by comparison with R2S method through benchmark analysis. The method was also used for SDDR analysis of the mobile blanket sector for the China Fusion Engineering Test Reactor (CFETR), and the results indicated that the NASCA-OTF is feasible for computing the SDDR resulting from the movement of activated components.

Monte Carlo global variance reduction method combining source bias and weight window

The global tally problem has a wide range of applications in major research fields such as Monte Carlo simulations of pin-by-pin reactor models and time-dependent particle transport problems in multi-physics coupling calculations. Due to the uneven power distribution of the simulated system, the statistical errors of all tallies are unevenly distributed, resulting in some low global efficiency. For this kind of problem with global characteristics, it is necessary to develop global variance reduction techniques to obtain the accurate distribution of target tallies in the entire space. A large number of global variance reduction algorithms have been studied based on the consideration of flattening global tally error distribution, so as to improve global efficiency. This work focuses on the combination of two efficient global variance reduction algorithms, namely, the uniform tally density algorithm and the weight window algorithm, which belong to source bias and transport process bias, respectively. In tally, a method is proposed to adjust the weight window parameters by using the bias factor of the uniform tally density algorithm. Then, the weight window method will be used to reduce the weight fluctuation caused by the uniform tally density method. In this way, an organic combination of these two algorithms can be realized. A series of comparative tests are carried out based on the Hoogenboom-Martin pressurized water reactor benchmark, and it is verified that the hybrid global variance reduction algorithm proposed in this work is better than the single weight window algorithm or the uniform tally density algorithm. In terms of reducing the maximum error, the global efficiency of the hybrid algorithm is 2.6 times and 3 times that of the weight window algorithm and the uniform tally density algorithm, respectively. In addition, through the comparative analysis of computational asymmetry degree and computational efficiency, it is verified that the uniform tally density algorithm has better performance than the classical uniform fission site algorithm, and the performance advantages of the uniform tally density algorithm are quantitatively evaluated based on some new indicators. The results show that the hybrid global variance reduction algorithm proposed in this work can solve the global tally problem efficiently, thereby further promoting research in related fields.

Optimal Monte Carlo particle splitting for neutron transport equation

Global tallying problem is hard to be solved efficiently when using Monte carlo method to simulate neutron transport equation, especially for sys- tem with big scale and/or strong imbalanced characteristics. Among numerous global variance reduction methods, particle splitting is an easy-to-implement method, but the efficiency is hard to be satisfying for practical problems. The essential challenge lies in the fact there are too many parameters to be opti- mized. In this paper, a systematic approach for setting all splitting parameters is proposed based on maximization of some global efficiency indicator. Results of two models show this approach can increase the global efficiency indicator up to two orders of magnitude while keeping the results unbiased.

MAGIC-GPS global variance reduction method for large-scale shielding calculation

We propose a Method of Automatic Generation Importance by Calculation with Growth Population Scheme (MAGIC-GPS) for efficient and accurate shielding calculation. The new method adopts a Growth Population Scheme (GPS) in the reciprocal iteration process of flux and importance for the Monte Carlo fixed-source calculation. Mathematical derivation is performed to prove that the GPS scheme is conducive to a rapid flux distribution convergence and can improve the Figure of Merit (FOM) of the Monte Carlo deep-penetration simulation. The effectivity of the MAGIC-GPS method is tested by a single concrete rod model, the H.B. Robinson-2 reactor benchmark (HBR2) and the China Fusion Engineering Test Reactor (CFETR). The results show that the MAGIC-GPS method can accelerate the Monte Carlo deep-penetration simulation, and the faster the population of particles increases, the better the acceleration. The MAGIC-GPS method is helpful for large-scale shielding calculation.

Density-extrapolation Global Variance Reduction (DeGVR) method for large-scale radiation field calculation

The lack of a universal and effective Global Variance Reduction (GVR) method for the deep-penetration Monte Carlo calculation makes it difficult or impossible to calculate the radiation field of large nuclear facilities. We propose a Density-extrapolation Global Variance Reduction (DeGVR) method for the large-scale radiation field calculation. After reducing the density of all materials to avoid the deep penetration problem, two global flux distributions of the two different material densities are obtained with two fixed-source calculations, and then the global flux distribution of the original material density is obtained by extrapolating the two global flux distributions. The global flux distribution of the original material density is then used for global variance reduction. In a large-scale model with a flux attenuation of 1080, the DeGVR method only takes 40.3 minutes to build the radiation field, improves the Average Figure-of-Merit (AV.FOM) up to 85652 times and the counting rate per time (CRPT) up to 88107 times compared with the standard Monte Carlo method. In addition to the high efficiency, the DeGVR method has high universality and robustness because it constructs the global information in a clever way that does not rely on the complex mathematical derivation and geometric modeling. The DeGVR method shows excellent application potential in large-scale radiation analysis.

Development of Monte Carlo hybrid parallel algorithm and application in high resolution spatial-energy flux distribution calculation

Monte Carlo transport calculations for fusion reactors are very challenging due to factors such as large radiation decay gradients, complex geometric structures, and strong neutron anisotropy. For such deep penetration shielding calculation problems, in order to obtain accurate global flux distribution, variance reduction methods and parallel computing are necessary means. When using the global weight window variance reduction technique, the huge deviation of the particle arrival weight and the weight window can lead to an extreme number of splits, which is the long history problem. If a process encounters the long history problem in parallel computing and takes a lot of time to complete, other processes will stop computing because the histories allocated in the computing cycle have been completed, seriously degrading computing efficiency. In addition, the calculation of the shutdown dose rate, a key issue in fusion neutronics calculations, requires a high “space-energy” resolution, which brings huge challenges to computational memory, especially in parallel computing. In order to overcome the degradation of parallel efficiency caused by the long history problem and the memory limitation in large-scale shutdown dose rate calculation, a hybrid parallel algorithm based on shared memory was researched. Finally, the hybrid parallel architecture was built in the Monte Carlo code cosRMC to realize dynamic load balancing between threads. Through the memory sharing among all threads of a single node, the pressure of memory consumption can be effectively relieved. In order to verify the effectiveness of the hybrid parallel algorithm developed in this paper, it was applied to the calculation of CFETR. The results showed that the hybrid parallel algorithm can effectively alleviate the impact of the long history problem on the parallel efficiency. In terms of saving memory, the hybrid parallel algorithm also showed a significant effect, which provides a guarantee for large-scale shutdown dose rate calculation.

Pointing probability Driven semi-analytic Monte Carlo Method (PDMC) – Part I: Global variance reduction for large-scale radiation transport analysis

We propose a Pointing Probability Driven Semi-Analytic Monte Carlo Method (PDMC) to replace the traditional Monte Carlo method for reactor physics analysis and radiation transport analysis. This paper describes the calculation principle and acceleration effect of the PDMC method in radiation transport analysis, highlighting its advantages in dealing with the deep-penetration problem. The PDMC method no longer requires particles to be transported to the detector. During the particle transport process, the global response of each particle state is calculated with a pointing probability to construct global information quickly. The statistical unbiasedness of the global response of a single particle state is demonstrated through rigorous mathematical derivation. The PDMC method does not rely on a deterministic program or iterative calculation, ensuring its universality and efficiency of global variance reduction (GVR). The PDMC method is tested in the China Fusion Engineering Test Reactor (CFETR) and the HBR2 benchmark. The results show that the PDMC method can significantly improve the efficiency of Monte Carlo deep-penetration simulation and is helpful for the GVR for large-scale radiation analysis.

Development and application of variance reduction technique based on response matrix method in the cosRMC code

In the Monte Carlo particle transport calculations, it is difficult to generate reasonable weight window distributions for the deep penetration problem. This work focused on the generation of importance function by the response matrix method. A built-in importance solver was implemented in the Monte Carlo code cosRMC. In addition, this work improved the iterative process of the weight window of the response matrix method for global variance reduction and realized the accelerated convergence of the global weight window generation. The application of the response matrix method to the local and global variance reduction problems verified the good effect of local variance reduction. The effectiveness of the method has also been further verified in the application of CFETR, where the computational efficiency was 21 times that of the initial analogue simulation, and the time of weight window convergence of the improved response matrix method was reduced by about 24.9%.

Global variance reduction method for Monte Carlo simulation of thermal radiation transport

The implicit Monte Carlo (IMC) method is an important numerical approximation method of simulating the thermal radiative transfer problems under high temperature condition. However, one problem plaguing the IMC method is that the calculation error distributions of the radiation specific intensities are highly asymmetric in space and time. By theoretical analysis and numerical simulations, we find that the error is affected by the records of track in the tallying mesh. Accordingly, a global variance reduction method for implicit Monte Carlo simulation is developed and the corresponding formulas are derived. This method includes three key techniques: 1) the automated dynamic distribution method for the Monte Carlo simulation source particles; 2) the dynamic weight-window technique and the none-bias weight revise algorithm that is suited to the particle distribution method; 3) the analytical estimation variance reduction method of the radiation specific intensity. In view of the above, a three-dimensional simulation code, named IMC3D, is developed to simulate the thermal radiative transfer phenomena. The typical thermal radiative transport problem, known as Marshak wave, is simulated. The simulation results indicate that the global variance reduction method for implicit Monte Carlo makes the statistical errors much more symmetric in space and time and the maximum of error is controllable, thereby increasing the calculation speed approximately 10 times. The new IMC method and code are used for simulating the radiative transportation in hohlraum of ICF successfully.

Neutronics Modeling and Nuclear Analysis Based on the Full CAD Geometry of CFETR

Radiation field analyses of the fusion reactor are vital to machine design and personal/environmental irradiation protection. Owing to the complicated and toroidal symmetry of fusion reactors, these nuclear analyses have been performed based on a sector model with reflecting boundary conditions. However, not all sections of a fusion reactor are symmetrical in the toroidal direction, particularly the neutron flow channels introduced by auxiliary systems from which particles can leak directly from the plasma. Hence, the reflecting boundary conditions cannot accurately describe the particle transport. Consequently, radiation field analyses based on a full-sector model must be performed to verify the results obtained. In this regard, the neutronics model of CFETR has been built in 360 deg. Meanwhile, the development of the automatic geometry conversion platform cosVMPT has enabled an entire 360-deg model of the CFETR to be established. The model contains all primary components and the outer house building. Sixteen upper/lower ports and six equatorial ports are included, in which two of them are slanted for neutral beam injection, whereas the other ports are filled with a shielding block. The on-the-fly (OTF) global variance reduction method is utilized to accelerate neutron/photon coupling transport. The results show that cosVMPT and the OTF method are reliable, and that the obtained neutron/photon flux is asymmetric outside the main machine. The computational results of the 360-deg model are compared with those of the sector model such that the application scope of simplifying the modeling and calculation using the sector model can be further confirmed.

Improvements of the on-the-fly MC variance reduction technique with dynamic WW upper bounds

This paper presents the recent progress in the development of the on-the-fly global variance reduction (OTF-GVR) method for Monte Carlo (MC) shielding calculations. OTF-GVR method provides on-the-fly weight window mesh (WWM) generation along with the particle transport simulation. In the previous study, the solution for the so-called ‘long-history’ problem, in which particles are unnecessarily over-split, is empirical and not fully effective. In this work, an innovative method using dynamic WWM upper bounds was proposed, which diminishes the over-splitting particles by relaxing the weight-windows upper bounds. This method has been proven effective through applications for several fusion reactors and neutron source facilities, with excellent performances over analogue simulations and variance reduction runs using common GVR methods.

A cell-based population control of Monte Carlo particles for the global variance reduction for transport equations

We present a population control method with sampling and regulation steps for Monte Carlo particles involved in the numerical simulation of a transport equation. We recall in the first section the difficulties related to the variance reduction methods in the general framework of transport equations; we continue with a brief presentation of the mathematical tools invoked when solving the radiative transport equations and we focus on the importance of the emission and control of existing Monte Carlo particles.The next part discusses several novel methods based on the cell-based population control method proposed in [27]. To this end, we analyze theoretically two types of splitting: one is conservative in energy (at the particle level) and the other is not. Thanks to these results, a new algorithm is introduced that uses cell-based population control and a spatial distribution. A numerical comparison of the different types of splitting is proposed in a simplified framework, then the various algorithms presented are compared against two benchmarks: the propagation of a Marshak wave and the propagation of two waves having different intensity and speed scales. To carry out these last tests, we use the multi-physics code FCI2 [13].

Implementation and benchmarking of the local weight window generation function for OpenMC

OpenMC is a community-driven open-source Monte Carlo neutron and photon transport simulation code. The Weight Window Mesh (WWM) function and an automatic Global Variance Reduction (GVR) method was recently developed and implemented in a developmental branch of OpenMC. This WWM function and GVR method broaden OpenMC's usage in general purposes deep penetration shielding calculations. However, the Local Variance Reduction (LVR) method, which suits the source-detector problem, is still missing in OpenMC. In this work, the Weight Window Generator (WWG) function has been developed and benchmarked for the same branch. This WWG function allows OpenMC to generate the WWM for the source-detector problem on its own. Single-material cases with varying shielding and sources were used to benchmark the WWG function and investigate how to set up the particle histories utilized in WWG-run and WWM-run. Results show that there is a maximum improvement of WWM generated by WWG. Based on the above results, instructions on determining the particle histories utilized in WWG-run and WWM-run for optimal computation efficiency are given and tested with a few multi-material cases. These benchmarks demonstrate the ability of the OpenMC WWG function and the above instructions for the source-detector problem. This developmental branch will be released and merged into the main distribution in the future.

Progress on neutronic analysis for CFETR

The neutron-induced irradiation field is a key problem in a fusion reactor related to nuclear responses, shielding design, nuclear safety and thermo-hydraulic analysis. To support the system design of the China Fusion Engineering Test Reactor (CFETR), a comprehensive analysis of the irradiation field has been conducted in support of many newly developed advanced tools. This paper first summarizes recent progress on the related effort to develop neutronics code including the geometry conversion tool cosVMPT, Monte Carlo variance reduction technology and ‘on-the-fly’ global variance reduction. Such developed tools have been fully validated and applied to the CFETR nuclear analysis. The neutron irradiation has been evaluated on the CFETR water-cooled ceramic breeder blanket, divertor, vacuum vessel (VV), superconductive coils and four kinds of heating systems: electron cyclotron resonance heating, ion cyclotron resonance heating, low hybrid wave and neutral beam injection. The nuclear responses of tritium breeding ratio, heating, irradiation damage and the hydrogen/helium production rate of material have been analyzed. In the case of neutron damage and overheating, deposition on the superconductive coils and VV, the interface and the shielding design among heating systems, and the blanket and other systems, has been initialized. The results show the shielding design can meet the requirement of coil and VV after several iterated neutronics calculations.

Application of local Monte Carlo method in neutronics calculation of EAST radial neutron camera

The Local Monte Carlo (LMC) method is used to solve the problems of deep penetration and long time in the neutronics calculation of the radial neutron camera (RNC) diagnostic system on the experimental advanced superconducting tokamak (EAST), and the radiation distribution of the RNC and the neutron flux at the detector positions of each channel are obtained. Compared with the results calculated by the global variance reduction method, it is shown that the LMC calculation is reliable within the reasonable error range. The calculation process of LMC is analyzed in detail, and the transport process of radiation particles is simulated in two steps. In the first step, an integrated neutronics model considering the complex window environment and a neutron source model based on EAST plasma shape are used to support the calculation. The particle information on the equivalent surface is analyzed to evaluate the rationality of settings of equivalent surface source and boundary. Based on the characteristic that only a local geometric model is needed in the second step, it is shown that the LMC is an advantageous calculation method for the nuclear shielding design of tokamak diagnostic systems.

SP3-coupled global variance reduction method based on RMC code

SP3-coupled global variance reduction method based on RMC code

Development of shutdown dose rate calculation code based on cosRMC and application to benchmark analysis

Accurate estimation of shutdown dose rate (SDR) has important reference significance for the design, operation and maintenance of fusion devices. In order to obtain the decay gamma source distribution with higher spatial resolution, a shutdown dose rate calculation code was developed based on the Rigorous two-step (R2S) method. The Monte Carlo code cosRMC and the radioactivity inventory code ALARA were coupled to calculate SDR in complex geometry based on mesh-tally. The ray tracking method was used to obtain the voxel-averaged nuclide density, and a decay photon sampling module was developed to accurately describe the distribution of the activation source. In order to improve the computational efficiency in deep penetration problems, the global variance reduction technique based on iterative weight window was adopted. The developed code was firstly verified with rectangular parallelepiped model consists of steel and water, in which the effect of bremsstrahlung photon was also discussed. Then the code was applied to the calculation and analysis of the ITER port plug benchmark, by comparing with other SDR calculation codes. The influence of different activation libraries on the decay gamma spectra and the effect of mesh resolution on the calculation accuracy were investigated. The results showed that the SDR function in cosRMC code is able to calculate SDR accurately with high spatial resolution for deep penetration problems.