Analysis of inconsistent source sampling in monte carlo weight-window variance reduction methods

A new global variance reduction technique based on pseudo flux method

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.

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.

To characterize an ionization chamber BEV‐CC01 as a standard of absorbed dose to water Dw at SSDL‐Mexico, the approach developed by the BIPM for 60Co gamma radiation, [1] has been chosen. This requires the estimation of a factor kp, which stems from the perturbation introduced by the presence of the ionization chamber in the water phantom, and due to finite size of the cavity. This factor is the product of four terms: ψw,c, (μenρ)w,c, (1 + μ′.ȳ)w,c and kcav. Two independent determinations are accomplished using a combination of the Monte Carlo code MCNP4C in ITS mode [2,3] and analytic methods: one kp∥=1.1626 ± uc=: 0.90% for the chamber axis parallel to the beam axis; and another kp =1.1079± uc=0.89% for the chamber axis perpendicular to the beam axis. The variance reduction techniques: splitting‐Russian roulette, source biasing and forced photon collisions are employed in the simulations to improve the calculation efficiency. The energy fluence for the 60Co housing‐source Picker C/9 is obtained by realistic Monte Carlo (MC) simulation, it is verified by comparison of MC calculated and measured beam output air kerma factors, and percent depth dose curves in water, PDD. This spectrum is considered as input energy for a point source (74% is from primary photons and the rest 26% is from scattered radiation) in the determination of the kp factors. Details of the calculations are given together with the theoretical basis of the ionometric standard employed.To characterize an ionization chamber BEV‐CC01 as a standard of absorbed dose to water Dw at SSDL‐Mexico, the approach developed by the BIPM for 60Co gamma radiation, [1] has been chosen. This requires the estimation of a factor kp, which stems from the perturbation introduced by the presence of the ionization chamber in the water phantom, and due to finite size of the cavity. This factor is the product of four terms: ψw,c, (μenρ)w,c, (1 + μ′.ȳ)w,c and kcav. Two independent determinations are accomplished using a combination of the Monte Carlo code MCNP4C in ITS mode [2,3] and analytic methods: one kp∥=1.1626 ± uc=: 0.90% for the chamber axis parallel to the beam axis; and another kp =1.1079± uc=0.89% for the chamber axis perpendicular to the beam axis. The variance reduction techniques: splitting‐Russian roulette, source biasing and forced photon collisions are employed in the simulations to improve the calculation efficiency. The energy fluence for the 60Co housing‐source Picker C/9 is obtained by reali...

Hybrid biasing approaches for global variance reduction

Global variance reduction method based on multi-group Monte Carlo adjoint calculation

<sec>Monte Carlo method is an ideal way to simulate criticality, shielding and nuclear detection. JMCT is a multipurpose 3D Mont Carlo (MC) neutron-photon-electron and coupled neutron /photon /electron transport code which is developed by IAPCM. The program is developed based on the combinatorial geometry parallel infrastructure JCOGIN and has the most functions of general Monte Carlo particle transport code, including the various variance reduction techniques. In addition, some new algorithms, such as Doppler broadening on-the-fly (OTF), uniform tally density (UTD), consistent adjoint driven importance sampling (CADIS), fast criticality search of boron concentration (FCSBC), the domain decomposition (DD), the two-level parallel computation of MPI and OpenMP, etc. have been developed, where the number of geometry zones, materials, tallies, depletion zones, memories and period of random number are big enough to simulate various extremely complicated problems. Also the JMCT is hybrid the discrete ordinate SN program JSNT to generate source biasing factors and weight window parameters for deep-penetration shielding problems. The input is based on the CAD modeling, and the result is a visualized output. The JMCT can provide technology support for radiation shielding design, reactor physics and criticality safe analysis. Especially, the JMCT is coupled depletion and thermal-hydraulic code for simulating the reactor feedback effect, including depletion, thermal feedback. In recent years, new function of γ-ray spectrum analysis has been developed. </sec><sec>In this paper, the working principles of timing measure are introduced. The advanced calibration count is developed for distinguishing between inelastic γ-ray and capture γ-ray based on time bin tally. On the other hand, when neutron collides with nuclide, the secondary photon is labeled into the primary line photon and primary continuous photon, where energy of primary line photon does not change with the incident neutron energy, such as carbon spectral-line at 4.43 MeV and oxygen spectral-line at 6.13 MeV. The element components of detected object can be determined by the primary line photon. On the other hand, expect value estimator (EVE) is used to produce the secondary photons. The advantage of EVE does not leak any event even with a small probability which is important for detecting the hide exploder. However the shortage of the EVE results in producing a great number of photons with small weight. If all of these small weight photons are simulated one by one, a great amount of computation time and memory will be consumed. For avoiding this case, a new algorithm is design by coupling EVE and DE (direct estimator). The all of secondary photons from EVE only make the direct tally take a little computing time, then end the photon history and return to the DE production photon model (one photon production at most). Final, the total tally is a summation of EVE direct tally and DE scattering tally. The use of new algorithm to realize the analysis of γ-ray spectrum will increase only a little computing time. The numerical tests are done by using own Monte Carlo code JMCT. The correctness and validity of the algorithm are shown preliminarily.</sec>

Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.

Grundlagen der Monte-Carlo-Methode für die Dosisberechnung in der Strahlentherapie

Microbeam radiation therapy (MRT) is a synchrotron radiotherapy technique that explores the limits of the dose-volume effect. Preclinical studies have shown that MRT irradiations (arrays of 25-75-μm-wide microbeams spaced by 200-400 μm) are able to eradicate highly aggressive animal tumor models while healthy tissue is preserved. These promising results have provided the basis for the forthcoming clinical trials at the ID17 Biomedical Beamline of the European Synchrotron Radiation Facility (ESRF). The first step includes irradiation of pets (cats and dogs) as a milestone before treatment of human patients. Within this context, accurate dose calculations are required. The distinct features of both beam generation and irradiation geometry in MRT with respect to conventional techniques require the development of a specific MRT treatment planning system (TPS). In particular, a Monte Carlo (MC)-based calculation engine for the MRT TPS has been developed in this work. Experimental verification in heterogeneous phantoms and optimization of the computation time have also been performed. The penelope/penEasy MC code was used to compute dose distributions from a realistic beam source model. Experimental verification was carried out by means of radiochromic films placed within heterogeneous slab-phantoms. Once validation was completed, dose computations in a virtual model of a patient, reconstructed from computed tomography (CT) images, were performed. To this end, decoupling of the CT image voxel grid (a few cubic millimeter volume) to the dose bin grid, which has micrometer dimensions in the transversal direction of the microbeams, was performed. Optimization of the simulation parameters, the use of variance-reduction (VR) techniques, and other methods, such as the parallelization of the simulations, were applied in order to speed up the dose computation. Good agreement between MC simulations and experimental results was achieved, even at the interfaces between two different media. Optimization of the simulation parameters and the use of VR techniques saved a significant amount of computation time. Finally, parallelization of the simulations improved even further the calculation time, which reached 1 day for a typical irradiation case envisaged in the forthcoming clinical trials in MRT. An example of MRT treatment in a dog's head is presented, showing the performance of the calculation engine. The development of the first MC-based calculation engine for the future TPS devoted to MRT has been accomplished. This will constitute an essential tool for the future clinical trials on pets at the ESRF. The MC engine is able to calculate dose distributions in micrometer-sized bins in complex voxelized CT structures in a reasonable amount of time. Minimization of the computation time by using several approaches has led to timings that are adequate for pet radiotherapy at synchrotron facilities. The next step will consist in its integration into a user-friendly graphical front-end.

Monte Carlo (MC) simulations are often used in calculations of radiation transport to enable accurate prediction of radiation-dose, even though the computation is relatively time-consuming. In a typical MC simulation, significant computation time is allocated to following non-important events. To address this issue, variance reduction techniques (VRTs) have been suggested for reducing the statistical variance for the same computation time. Among the available MC simulation codes, electron gamma shower (National Research Council of Canada) (EGSnrc) is a general-purpose coupled electron-photon transport code that also features an even-handed, rich set of VRTs. The most well-known VRTs are the photon splitting, Russian roulette (RR), and photon cross-section enhancement (XCSE) techniques. The objective of this work was to determine the optimal combination of VRTs that increases the simulation speed and the efficiency of simulation, without compromising its accuracy. Selection of VRTs was performed using EGSnrc MC User codes, such as cavity and egs_chamber, for simulating various ion chamber geometries using 6 MV photon beams and 1.25 MeV 60Co photon beams. The results show that the combination of XCSE and RR yields the highest efficiency for ion-chamber dose calculations inside a 30 cm × 30 cm × 30 cm water phantom. Hence, properly selecting a different VRT without altering the underlying physics increases the efficiency of MC simulations for ion-chamber dose calculation.

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.

Godiva IV is a system comprised of highly enriched uranium alloyed with molybdenum in the form of fuel plate rings. The reactor, along with its predecessors, was designed with the unique ability to satisfy interests in the super-prompt-critical reactor operation space. Originally, the reactor was part of the Los Alamos Critical Experiments Facility (LACEF) at Technical Area-18 (TA-18). The radiation field around Godiva at this facility was well characterized and understood. As a fast neutron system, the neutron spectrum in and around Godiva was close to a Watt Fission spectrum. The Kiva where Godiva IV was located at LACEF was made of thin, sheet metal walls which did not contribute significantly to the neutron spectrum. Following the transition of LACEF to the National Critical Experiments and Research Center (NCERC) in Nevada, Godiva-IV was moved from TA-18 to the Device Assembly Facility (DAF) at the Nevada National Security Site (NNSS). Part of this move brought renewed interest in radiation field characterization. The new facility introduced significant changes to the environment surrounding Godiva, and preliminary foil irradiation results suggested that the room contribution to the neutron spectrum was significant. Unlike at TA-18, a large thermal neutron signature was added to the fast spectrum from Godiva due to significant room return. A primary goal due to the additional complexity that the room return adds to the Godiva IV radiation emission spectrum was the development of an efficient Monte Carlo N-Particle (MCNP) calculation capable of characterizing the neutron spectrum anywhere in the room around Godiva. A campaign of activation foil irradiations and analysis were completed to support the validation of the MCNP model. The modeling of these foils in MCNP can be easily done with a standard volumetric neutron flux tally. However, given the multitude of locations and reaction rates to be modeled, further steps must be taken to increase the efficiency of these calculations in MCNP. During this study, a benchmark model currently under development for Godiva IV was used. A qualitative assessment of the thermal neutron contributors was performed using spatial neutron distribution plots. Additional detail was added to the model based on the qualitative results showing the thermal spectrum’s large sensitivity to hydrogenous material. Neutron energy spectra was evaluated at discrete locations in the room around Godiva to quantify the relative contribution of various components. It was discovered that the concrete walls are the largest contributor to the thermal signature, with minor contributions from plastic components surrounding Godiva. Following these results, two different variance reduction techniques were implemented to improve the problem efficiency in these calculations. In the first approach, an F5 point detector tally was implemented in the standard Godiva IV criticality problem. The second approach involved a weight-window generator implementation with an F5 point detector tally in a fixed source problem. The weight window implementation reduced the runtime from 42739.55 minutes to 1803.34 minutes (computer time), compared to the F5 KCODE implementation.

Nowadays, there is a problem of a lack of computer power to conduct high-precision reactor analysis. There are several factors that increase the excessive computational load and make it difficult to calculate nuclear reactor full-scale models using Monte Carlo method. Among them is the large neutron-flux attenuation, which is observed in deep penetration problems. Various reduction techniques are used to increase the efficiency of Monte Carlo calculations in such tasks. It allows to reduce the statistical uncertainty of the functional evaluation without increasing the number of neutron histories. This work is devoted to study and testing of variance reduction techniques in the deep penetration problem. To demonstrate the possibility of using non-analogue Monte Carlo modeling a test problem was formulated. To quantify the efficacy of applying the variance reduction methods, FOM characteristic is considered, which is a function of the relative error in a flux estimate and the computational time of the simulation. The article considers non-analogue techniques implemented in the MCU (Monte Carlo Univarsal) and OpenMC codes. As part of the study, a module of the OpenMC code was developed that allows to automatically generate weight windows. It is shown that variance reduction techniques increase the calculation efficiency by several times, particularly, the weight windows method in OpenMC make it possible to achieve a 7-fold increase in the efficiency of neutron flux estimation with the same number of simulated histories. The formulated recommendations can be used in the calculation of innovative nuclear reactors full-scale models.

Monte Carlo Integration and Variance Reduction