Automated Variance Reduction Technique for 3-D Monte Carlo Coupled Electron-photon-positron Simulation Using Deterministic Importance Functions


Book Description

ABSTRACT: Three-dimensional Monte Carlo coupled electron-photon-positron transport calculations are often performed to determine characteristics such as energy or charge deposition in a wide range of systems exposed to radiation field such as electronic circuitry in a space-environment, tissues exposed to radiotherapy linear accelerator beams, or radiation detectors. Modeling these systems constitute a challenging problem for the available computational methods and resources because they can involve; i) very large attenuation, ii) large number of secondary particles due to the electron-photon-positron cascade, and iii) large and highly forward-peaked scattering. This work presents a new automated variance reduction technique, referred to as ADEIS (Angular adjoint-Driven Electron-photon-positron Importance Sampling), that takes advantage of the capability of deterministic methods to rapidly provide approximate information about the complete phase-space in order to automatically evaluate variance reduction parameters. More specifically, this work focuses on the use of discrete ordinates importance functions to evaluate angular transport and collision biasing parameters, and use them through a modified implementation of the weight-window technique. The application of this new method to complex Monte Carlo simulations has resulted in speedups as high as five orders of magnitude.




Automatic Variance Reduction for Monte Carlo Simulations Via the Local Importance Function Transform


Book Description

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditional Monte Carlo simulation of r̀̀eal ̀̀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 b̀̀lack 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.







Advanced Quadrature Selection for Monte Carlo Variance Reduction


Book Description

Neutral particle radiation transport simulations are critical for radiation shielding and deep penetration applications. Arriving at a solution for a given response of interest can be computationally difficult because of the magnitude of particle attenuation often seen in these shielding problems. Hybrid methods, which aim to synergize the individual favorable aspects of deterministic and stochastic solution methods for solving the steady-state neutron transport equation, are commonly used in radiation shielding applications to achieve statistically meaningful results in a reduced amount of computational time and effort. The current state of the art in hybrid calculations is the Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) methods, which generate Monte Carlo variance reduction parameters based on deterministically-calculated scalar flux solutions. For certain types of radiation shielding problems, however, results produced using these methods suffer from unphysical oscillations in scalar flux solutions that are a product of angular discretization. These aberrations are termed “ray effects”. The Lagrange Discrete Ordinates (LDO) equations retain the formal structure of the traditional discrete ordinates formulation of the neutron transport equation and mitigate ray effects at high angular resolution. In this work, the LDO equations have been implemented in the Exnihilo parallel neutral particle radiation transport framework, with the deterministic scalar flux solutions passed to the Automated Variance Reduction Generator (ADVANTG) software and the resultant Monte Carlo variance reduction parameters’ efficacy assessed based on results from MCNP5. Studies were conducted in both the CADIS and FW-CADIS contexts, with the LDO equations’ variance reduction parameters seeing their best performance in the FW-CADIS method, especially for photon transport.




Variance Reduction for Multi-physics Analysis of Moving Systems


Book Description

The quantification of the shutdown dose rate (SDR) caused by photons emitted by activated structural materials is an important and necessary step of the design process of fusion energy systems (FES). FES are purposefully designed with modular components that can be moved out of a facility after shutdown for maintenance. It is particularly important to accurately quantify the SDR during maintenance procedures that may cause facility personnel to be in closer proximity to activated equipment. This type of analysis requires neutron and photon transport calculations coupled by activation analysis to determine the SDR. Due to its ability to obtain highly accurate results, the Monte Carlo (MC) method is often used for both transport operations, but the computational expense of obtaining results with low error in systems with heavy shielding can be prohibitive. However, variance reduction (VR) methods can be used to optimize the computational efficiency by artificially increasing the simulation of events that will contribute to the quantity of interest. One hybrid VR technique used to optimize the initial transport step of a multi-step process is known as the Multi-Step Consistent Adjoint Driven Im- portance Sampling (MS-CADIS) method. The basis of MS-CADIS is that the importance function used in each step of the problem must represent the impor- tance of the particles to the final objective function. As the spatial configuration of the materials changes, the probability that they will contribute to the objec- tive function also changes. In the specific case of SDR analysis, the importance function for the neutron transport step must capture the probability of materials to become activated and subsequently emit photons that will make a significant contribution to the SDR. The Groupwise Transmutation (GT)-CADIS method is an implementation of MS-CADIS that optimizes the neutron transport step of SDR calculations. GT-CADIS generates an adjoint neutron source based on certain assumptions and approximations about the transmutation network. This source is used for adjoint transport and the resulting flux is used to generate the biasing parameters to optimize the forward neutron transport. For systems that undergo movement, a new hybrid deterministic/MC VR technique, the Time-integrated (T)GT-CADIS method, that adapts GT-CADIS for dynamic systems by calculating a time-integrated adjoint neutron source was developed. This work demonstrates the tools and workflows necessary to efficiently calculate quantities of interest resulting from coupled, multi-physics processes in dynamic systems.




Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications


Book Description

This book focuses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications. Special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields.




Automated Monte Carlo Biasing for Photon-generated Electrons Near Surfaces


Book Description

This report describes efforts to automate the biasing of coupled electron-photon Monte Carlo particle transport calculations. The approach was based on weight-windows biasing. Weight-window settings were determined using adjoint-flux Monte Carlo calculations. A variety of algorithms were investigated for adaptivity of the Monte Carlo tallies. Tree data structures were used to investigate spatial partitioning. Functional-expansion tallies were used to investigate higher-order spatial representations.







Monte Carlo Transport of Electrons and Photons


Book Description

For ten days at the end of September, 1987, a group of about 75 scientists from 21 different countries gathered in a restored monastery on a 750 meter high piece of rock jutting out of the Mediterranean Sea to discuss the simulation of the transport of electrons and photons using Monte Carlo techniques. When we first had the idea for this meeting, Ralph Nelson, who had organized a previous course at the "Ettore Majorana" Centre for Scientific Culture, suggested that Erice would be the ideal place for such a meeting. Nahum, Nelson and Rogers became Co-Directors of the Course, with the help of Alessandro Rindi, the Director of the School of Radiation Damage and Protection, and Professor Antonino Zichichi, Director of the "Ettore Majorana" Centre. The course was an outstanding success, both scientifically and socially, and those at the meeting will carry the marks of having attended, both intellectually and on a personal level where many friendships were made. The scientific content of the course was at a very high caliber, both because of the hard work done by all the lecturers in preparing their lectures (e. g. , complete copies of each lecture were available at the beginning of the course) and because of the high quality of the "students", many of whom were accomplished experts in the field. The outstanding facilities of the Centre contributed greatly to the success. This volume contains the formal record of the course lectures.




Monte Carlo Methods for Particle Transport


Book Description

Fully updated with the latest developments in the eigenvalue Monte Carlo calculations and automatic variance reduction techniques and containing an entirely new chapter on fission matrix and alternative hybrid techniques. This second edition explores the uses of the Monte Carlo method for real-world applications, explaining its concepts and limitations. Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, it is an ideal textbook and practical guide for nuclear engineers and scientists looking into the applications of the Monte Carlo method, in addition to students in physics and engineering, and those engaged in the advancement of the Monte Carlo methods. Describes general and particle-transport-specific automated variance reduction techniques Presents Monte Carlo particle transport eigenvalue issues and methodologies to address these issues Presents detailed derivation of existing and advanced formulations and algorithms with real-world examples from the author’s research activities