Radiation Transport Problems Research Articles

Discrete Ordinates Quadratures Based on Linear and Quadratic Discontinuous Finite Elements over Spherical Quadrilaterals

We present a new family of discrete ordinates (Sn) angular quadratures based on discontinuous finite elements (DFEMs) in angle. The angular domain is divided into spherical quadrilaterals (SQs) on the unit sphere surface. Linear discontinuous finite element (LDFE) and quadratic discontinuous finite element (QDFE) basis functions in the direction cosines are defined over each SQ, producing LDFE-SQ and QDFE-SQ angular quadratures, respectively. The new angular quadratures demonstrate more uniform direction and weight distributions than previous DFEM-based angular quadratures, local refinement capability, strictly positive weights, generation to large numbers of directions, and fourth-order accurate high-degree spherical harmonics (SH) integration. Results suggest that particle-conservation errors due to inexact high-degree SH integration rapidly diminish with quadrature refinement and tend to be orders of magnitude smaller than other discretization errors affecting the solution. Results also demonstrate that the performance of the new angular quadratures without local refinement is on par with or better than that of traditional angular quadratures for various radiation transport problems. The performance of the new angular quadratures can be further improved by using local refinement, especially within an adaptive Sn algorithm.

AREVA Developments for an Efficient and Reliable use of Monte Carlo codes for Radiation Transport Applications

In the context of the rising of Monte Carlo transport calculations for any kind of application, AREVA recently improved its suite of engineering tools in order to produce efficient Monte Carlo workflow. Monte Carlo codes, such as MCNP or TRIPOLI, are recognized as reference codes to deal with a large range of radiation transport problems. However the inherent drawbacks of theses codes - laboring input file creation and long computation time - contrast with the maturity of the treatment of the physical phenomena. The goals of the recent AREVA developments were to reach similar efficiency as other mature engineering sciences such as finite elements analyses (e.g. structural or fluid dynamics). Among the main objectives, the creation of a graphical user interface offering CAD tools for geometry creation and other graphical features dedicated to the radiation field (source definition, tally definition) has been reached. The computations times are drastically reduced compared to few years ago thanks to the use of massive parallel runs, and above all, the implementation of hybrid variance reduction technics. From now engineering teams are capable to deliver much more prompt support to any nuclear projects dealing with reactors or fuel cycle facilities from conceptual phase to decommissioning.

Application of Variational Variance Reduction for Source-Detector Problems in Nuclear Non-proliferation

ABSTRACTThe VVR (Variational Variance Reduction) method has been tested extensively on criticality problems and has proven to be effective, but its application for shielding problems has been limited. In this work, the VVR method is tested on source-detector type problems that are of interest in nonproliferation applications. A 3D multigroup Monte Carlo code that uses parts of the framework of Attila, a production deterministic code for radiation transport problems, was developed to prototype hybrid (Deterministic/Monte Carlo) variance reduction techniques. The VVR method is applied to the forward Monte Carlo simulations based on a deterministically calculated adjoint solution using Attila. The performance of the VVR method when applied with 3 different configurations of the forward simulation are tested: (1) Monte Carlo calculation with implicit absorption, (2) Monte Carlo calculation with the Consistent Adjoint Driven Importance Sampling (CADIS) based weight windows method and (3) Monte Carlo calculation with the Local Importance Functional Transform (LIFT) method. The simulations were performed on 2 benchmark test problems for nonproliferation applications, the “Mulch Box” photon test problem and the PANDA neutron test problem. The angular domain was discretized for efficient evaluation of the VVR functional using a discrete ordinates based approach and a spherical harmonics based approach. For the mulch test problem, the VVR method provided only marginal improvements in the figure of merit (FOM) when applied to the Monte Carlo calculation with only implicit absorption, but provided up to two times improvement in FOM when applied with the CADIS based weight windows method. For the PANDA neutron problem, VVR method did not provide improvements in FOM due to the highly scattering nature of the problem. It was also observed that the VVR method when combined with the LIFT method is detrimental to the overall performance.

Lattice Boltzmann method for solving non-equilibrium radiative transport problems

Recently developed lattice Boltzmann equation (LBE) framework (Bindra et al., 2012; McCulloch and Bindra, 2016) for radiation transport is extended to solve time-dependent non-equilibrium radiative and neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE solutions are compared against the existing semi-analytical P1 benchmark and show good agreement for different times. Furthermore, a two-dimensional D2Q8 lattice Boltzmann method is proposed for solving the neutron transport equation in a heterogenous media (e.g., checkerboard lattice with pure scattering and absorbing cells). The results obtained with LBE are in good agreement with the existing discrete ordinate method results for the benchmark problem.

Green Function Formulation and Finite Element Discretization for Solving the Heat Radiative Transfer in a Slab

ABSTRACTThe radiative transport problem involving the nonlinear coupling between temperature and radiative transfer poses several difficulties to be solved numerically. In this paper, we sought numerical solutions for the transient one-dimensional model by applying the Green Function Decomposition Method to the radiative transport equation and a finite element scheme to the energy balance equation. We apply this new numerical implementation to calculate the evolution of temperature in a slab of glass. The proposed scheme has been found computationally efficient and we have achieved better accuracy than the previous results from the literature.

A new proof of geometric convergence for the adaptive generalized weighted analog sampling (GWAS) method.

Generalized Weighted Analog Sampling is a variance-reducing method for solving radiative transport problems that makes use of a biased (though asymptotically unbiased) estimator. The introduction of bias provides a mechanism for combining the best features of unbiased estimators while avoiding their limitations. In this paper we present a new proof that adaptive GWAS estimation based on combining the variance-reducing power of importance sampling with the sampling simplicity of correlated sampling yields geometrically convergent estimates of radiative transport solutions. The new proof establishes a stronger and more general theory of geometric convergence for GWAS.

Analysis of the LIFT Variance-Reduction Method Applied to Monte Carlo Radiation Transport Simulations of a Realistic Nonproliferation Test Problem

The Local Importance Function Transform (LIFT) method is a sophisticated automated variance-reduction technique for Monte Carlo simulation of radiation transport problems. In previous publications, the LIFT method was tested on geometrically simple problems with a coarse representation of radiation energy dependence, and the performance of the method was found to be promising when compared to traditional weight windows–based variance-reduction techniques. In this work, the LIFT method is tested on a spatially complex benchmark test problem with a more realistic representation of energy dependence (50 energy groups) and heterogeneous materials. The performance of the method in comparison with a CADIS (Consistent Adjoint Driven Importance Sampling)–based weight windows method and an analog Monte Carlo simulation is studied. A multigroup Monte Carlo code that utilizes portions of the framework of the deterministic tool Attila has been developed such that the overhead time in implementing the variance-reduction techniques is minimal. The Monte Carlo simulations are performed on an arbitrary tetrahedral mesh created by the mesh generator in Attila. A method to transfer the deterministic solution generated on a finer mesh to a coarser mesh for implementing the hybrid simulations has been developed, and the results are quantified.

Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy.

The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. The authors present a detailed description of their new formalism and compare its accuracy to geant4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors' new formalism was determined using a gamma analysis with a 2%/2 mm criterion. Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against geant4, even in cases of strong magnetic field strengths and low density air.

Weight matrix analysis for back reflection continuous wave diffuse optical tomography (CWDOT) systems: translational method

Back reflection continuous wave diffuse optical tomography (CWDOT) systems use forward model photon fluence rate distributions for inverse problem solution to be able to reconstruct images. Forward model weight functions are also known as photon fluence rate distributions inside the homogenous media. The linearized equation systems are used for CWDOT imaging. To be able to recover the unknown delta absorption coefficients over background inside the homogenous media linearized equation system has to be solved. In this work the forward model weight matrix functions have been calculated according to the photon distribution of radiative transport equation in theoretical physics. After the forward model is set, the mathematical inverse problem solution methods have to be applied. In literature, the solution of linearized CWDOT equation systems are nonlinear methods but they have never been popular. The main goal of this study is to be able to show alternative weight matrix generation method. The weight matrix generation is very important for linearized CWDOT systems. The Monte Carlo (MC) simulations have been used to create the weight matrix by using the radiation transport problem solution via Rytov or Born approximation. The photon is sent into the tissue, the step distances of each photons are computed and the scattering angles of photons have to be known. It is calculated by occurrence probability for each voxel by the Henyey-Greenstein phase function. The generated MC simulation data is migrated from the simulation environment to the image reconstruction algorithm environment. The weight matrix is successively generated by explained translational method.

A GENERAL HYBRID RADIATION TRANSPORT SCHEME FOR STAR FORMATION SIMULATIONS ON AN ADAPTIVE GRID

Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate method for solving the radiation transfer problem. We describe the implementation of a hybrid radiation transport scheme in the adaptive grid-based FLASH general magnetohydrodynamics code. The hybrid scheme splits the radiative transport problem into a raytracing step and a diffusion step. The raytracer captures the first absorption event, as stars irradiate their environments, while the evolution of the diffuse component of the radiation field is handled by a flux-limited diffusion (FLD) solver. We demonstrate the accuracy of our method through a variety of benchmark tests including the irradiation of a static disk, subcritical and supercritical radiative shocks, and thermal energy equilibration. We also demonstrate the capability of our method for casting shadows and calculating gas and dust temperatures in the presence of multiple stellar sources. Our method enables radiation-hydrodynamic studies of young stellar objects, protostellar disks, and clustered star formation in magnetized, filamentary environments.

PRIZMA status

For more than thirty years the code PRIZMA has been used at RFNC-VNIITF for solving radiation transport problems with the Monte Carlo method. The code models the separate and coupled transport of neutrons, photons, electrons, positrons and ions in one-, two-, and three-dimensional geometry. For criticality calculations the code implements the method of generations with a constant number of fission sites in one generation. Now the code is extending its capabilities for nuclear reactor calculations. The paper describes the current status of the code and gives examples of its application to particle transport in nuclear reactors and other physical facilities.

Transient Radiation Coupled With Conduction Heat Transfer in a One Dimensional Slab

The present research work views over a solution of radiative transport problem along with conduction in one perspective piece and in the existence of participating media. The radiative transfer equations are developed for anisotropically scattering, absorbing, emitting medium and the equation is being discretized using finite volume method. Heat flux and the incident radiation effects have been computed at three different time step. Transient radiation along with transient conduction is solved and the radiative effect has been measured using radiative transfer equation while the conduction term has been measured using conduction equation.

Radiation Adhered with Conduction Heat Transfer Adopting Finite Volume Method

This article considers a radiative transport problem coupled with conduction in the one dimensional slab in the presence of participating media. The finite volume method of computation is presented to discretize the radiative transfer equation over the control volume and by using the error function, conduction term is being computed. In the mathematical derivation the RTE is integrated with respect to control volume and control angles with the freedom in choosing number of angular nodes. The results reveals that the proposed method is a promising alternative to the well-established practices like the discrete ordinates method (DOM), discrete transfer method (DTM), monte-carlo method and many more.

MO‐E‐18C‐04: Advanced Computer Simulation and Visualization Tools for Enhanced Understanding of Core Medical Physics Concepts

Purpose:Most medical physics programs emphasize proficiency in routine clinical calculations and QA. The formulaic aspect of these calculations and prescriptive nature of measurement protocols obviate the need to frequently apply basic physical principles, which, therefore, gradually decay away from memory. E.g. few students appreciate the role of electron transport in photon dose, making it difficult to understand key concepts such as dose buildup, electronic disequilibrium effects and Bragg‐Gray theory. These conceptual deficiencies manifest when the physicist encounters a new system, requiring knowledge beyond routine activities.Methods:Two interactive computer simulation tools are developed to facilitate deeper learning of physical principles. One is a Monte Carlo code written with a strong educational aspect. The code can “label” regions and interactions to highlight specific aspects of the physics, e.g., certain regions can be designated as “starters” or “crossers,” and any interaction type can be turned on and off. Full 3D tracks with specific portions highlighted further enhance the visualization of radiation transport problems. The second code calculates and displays trajectories of a collection electrons under arbitrary space/time dependent Lorentz force using relativistic kinematics.Results:Using the Monte Carlo code, the student can interactively study photon and electron transport through visualization of dose components, particle tracks, and interaction types. The code can, for instance, be used to study kerma‐dose relationship, explore electronic disequilibrium near interfaces, or visualize kernels by using interaction forcing. The electromagnetic simulator enables the student to explore accelerating mechanisms and particle optics in devices such as cyclotrons and linacs.Conclusion:The proposed tools are designed to enhance understanding of abstract concepts by highlighting various aspects of the physics. The simulations serve as virtual experiments that give deeper and long lasting understanding of core principles. The student can then make sound judgements in novel situations encountered beyond routine clinical activities.

Optical model of the atmosphere for problems of calculating the irradiance of the entrance pupils of optoelectronic systems

This paper describes an optical model of the atmosphere that fundamentally differs from the working models used to estimate how the atmosphere affects the operation of optoelectronic devices. The model includes concepts of typical aerosol situations (tropics, mid-latitude summer, etc.) and obtains its input parameters from standard weather reports. Molecular absorption is determined on the basis of the HITRAN spectral-line database; the concept of the transmission function is not used in this case, and accordingly the problem of an unresolved spectrum does not arise in problems of radiation transport in a medium with a complex structure of the absorption spectrum in the IR region. The latter problem is especially acute in determining the contrast of observed objects when the viewing paths have complex geometry. The approach used here is equivalent to line integration with an insignificant loss of accuracy and significant speed-up of the calculation. The model makes it possible to take into account diurnal and seasonal changes of the viewing conditions in the troposphere and especially in its lower layers with the maximum adequacy, both in clear weather and under low unbroken clouds, with and without precipitation.

A preliminary study on streaming effect through the gap of blanket modules for a K-DEMO fusion reactor

It is known that the blanket module in the fusion reactor is designed for slowing and absorbing neutrons, breeding tritium, and limiting radiation damage to other structures. These blankets are installed remotely at individual positions. In this process, gaps between the blanket modules can occur and the streaming effect through gaps has an effect on the performance of the fusion reactor. The streaming effect affects two aspects in the neutron transport problem: (1) activation of the fusion reactor structures and (2) radiation shielding. It is noted that the shape of the gap is locally different due to the specific shape of the fusion reactor. Also, the mechanical difference of the blanket modules changes the gap size. In this study, the streaming effect caused by different shape and size of the gap are evaluated for a K-DEMO fusion reactor. The blanket modules of the fusion reactor, which are the blanket, vacuum vessel, and water channel, were simply simulated. In each module, the neutron streaming effects were assessed by changing the gap size and shapes. The MCNP5 code was used for the evaluations with ENDF/B-VI cross-section library and SAB2002 thermal cross section library. It was noticed that the neutron flux was significantly changed due to the streaming effect. This study can give guidelines for the simplification of blanket modeling in radiation transport problems.

Implementation of the exponential directional weighted SN differencing scheme in RAPTOR-M3G for LWR radiation transport and dosimetry applications

A high-accuracy spatial differencing scheme is implemented in RAPTOR-M3G, a Westinghouse-developed three-dimensional parallel discrete ordinates (SN) radiation transport code. The exponential directional weighted (EDW) scheme offers enhanced accuracy and superior convergence properties compared to conventional differencing schemes at a relatively modest additional computing cost. This method enables complete convergence to typical industrial convergence thresholds on large commercial reactor problems where other differencing schemes fail. This paper explores the theoretical foundations of the EDW differencing scheme and discusses its implementation in LWR reactor problems to calculate exposure quantities of interest to the commercial reactor integrity analysis community. Comparisons to existing differencing schemes are included for several important characteristics. The computing requirements of EDW are quantified relative to the requirements of more conventional theta-weighted (TW) formulations. The convergence behavior of both methods is investigated with consideration given to spatial areas of non-convergence. Finally, the practical accuracy of both methods is assessed through comparisons of reactor dosimetry measurements to calculations from the operating fleet of commercial reactors. The EDW method and RAPTOR-M3G are demonstrated to be particularly powerful for solving the challenging three-dimensional radiation transport problems faced by today’s radiation analysis community, specifically in the extended beltline region. The EDW method enables accurate characterization of the total radiation environment in large LWR models on timescales conducive to commercial applications.

A Simple yet Elegant Expansion Method to Solve Radiative Transport Problems in Finite Media

Radiative heat transfer in one dimension is studied in a plane - parallel geometry for an absorbing and isotropically scattering medium subjected to azimuthally symmetric incident radiation at boundaries. The integral form of the transport equation, which is weakly singular Fredholm integral equation of the second kind, is used .The unknown function in the integral form is expanded in terms of truncated Chebyshev polynomials in the optical variable. The collocation method is applied to obtain a system of linear algebraic equations for the expansion coefficients. Numerical calculations are done for the transmissivctivity, and exit angular distributions of slabs with various values of single scattering albedo. Comparisons between the present and available results in references indicate that our results are accurate, as shown in the tables.

A Robust Multigrid Preconditioner for $S_N$DG Approximation of Monochromatic, Isotropic Radiation Transport Problems

We introduce a new stabilization for the $S_N$DG (discrete ordinate discontinuous Galerkin) approximation of monochromatic radiation transport, and argue that solutions converge to solutions to the LDG method of Cockburn and Shu in the thick diffusion limit. Then, we develop a multilevel scheme for this discretization. Nonoverlapping Schwarz smoothers are based on solving local radiation transport problems for each grid cell. The ideal version of the smoother uses sweeps forward and backward in the direction of the diagonal of each octant. A simplified version of the multilevel solver runs on each cell in parallel, but lacks robustness in vacuum. In extensive tests we verify that the number of iterations for a given gain in accuracy is independent of the mesh size and the scattering cross section.

Algorithm intended for space-energy parallelization in solving the criticality problem and implemented in the LUCKY_C multiprocessor program

The paper presents basic formulas for parallel solution in energy groups and spatial subdomains for solving the criticality problem of radiation transport on multiprocessor computers.