A two-component equilibrium-diffusion limit

The equilibrium-diffusion limit of the radiative transfer equations is characterized by a medium that is optically thick and diffusive for photons of all frequencies. In reality, this condition is almost never met because the transport medium tends to be optically thin for photons of sufficiently high frequency. Motivated by this fact, we derive a new asymptotic limit of the radiative transfer equations that is characterized by two photon components: one for which the medium is optically thick and diffusive, and the other for which the medium is optically thin. In this limit, the leading-order material temperature satisfies a time-dependent diffusion equation, and the leading-order radiation intensity for the optically thick photons is given by the Planck function evaluated at the leading-order material temperature, but the radiation intensity for the optically thin photons is zero through first order. The O(ϵ²) radiation intensity for the optically thin photons satisfies a quasi steady-state transport equation with zero interaction terms and a Planck emission term that depends upon the leading-order material temperature. We also discuss alternative scalings associated with the two-component limit that are characterized by a stronger coupling between the material and the optically thin component.     

Even-parity finite-element transport methods in the diffusion limit

We use an asymptotic analysis to investigate the behavior of continuous finite-element-method (CFEM) discretizations of the even-parity transport equation, in problems containing optically thick diffusive regions. Our first interesting result is that we can analyze the entire family of even-parity CFEMs, and can do so in three dimensions on an arbitrarily-connected grid. (Previous asymptotic analyses have been restricted to specific discretizations, either in slab geometry or in XY geometry on a rectangular grid.) We show that every even-parity CFEM transport solution satisfies a corresponding CFEM discretization of the correct diffusion equation in the diffusion limit, which is a highly desirable property. We further show that this solution is subject to a Dirichlet boundary condition given by a cosine (|n·Ω|) weighting of the incident intensity. We show that this boundary condition, which is less accurate than we would like, means that in certain problems the transport solution in a diffusive region can be more than a factor of two greater than the correct solution. We also show that the CFEM transport solution can be incorrect in non-diffusive regions that are adjacent to diffusive regions, no matter how fine the spatial grid is in the non-diffusive region. We give numerical results from slab geometry verifying the predictions of our analysis.     

Existence theory for a one-dimensional problem arising from the boundary layer analysis of radiative flows

We consider a simplified system of equations which models the transfer of energy with conductive, convective and radiative effects inside a convex region filled with a compressible fluid whose velocity field is known. The asymptotic analysis for positive but small distance from an optically thick medium leads to a one-dimensional system of differential equation which couples the temperature and the radiative intensity. We show that this system obeys a conservation law and this feature is explored in order to reduce the problem to a single one-dimension transport equation with anisotropic scattering. This equation admits a formulation in terms of integral operators in a suitable function space which allows us to establish the existence of a solution and infer its behavior far from the boundary. We also provide numerical simulations and comparison with the theoretical results which we have shown in order to validate our methodology.     

Existence theory for a one-dimensional problem arising from the boundary layer analysis of radiative flows

We consider a simplified system of equations which models the transfer of energy with conductive, convective and radiative effects inside a convex region filled with a compressible fluid whose velocity field is known. The asymptotic analysis for positive but small distance from an optically thick medium leads to a one-dimensional system of differential equation which couples the temperature and the radiative intensity. We show that this system obeys a conservation law and this feature is explored in order to reduce the problem to a single one-dimension transport equation with anisotropic scattering. This equation admits a formulation in terms of integral operators in a suitable function space which allows us to establish the existence of a solution and infer its behavior far from the boundary. We also provide numerical simulations and comparison with the theoretical results which we have shown in order to validate our methodology.     

强散射介质中子输运计算的角度相关附加再平衡加速算法

利用最小二乘有限元离散坐标方法,对一阶中子输运方程进行离散求解,给出了基于非结构网格的角度相关附加再平衡加速算法,采用附加修正量的办法达到再平衡的原理加速计算过程,同时也给出了其外推算法。将算法应用到强散射介质中子输运方程的计算中,一些基准问题的数值结果表明,计算速度可加速到原来的1.5～2倍。     

Energy distributions of multiple backscattered photons in materials

Backscattering of gamma photons from a material is of fundamental importance in radiation shielding,industrial and medical applications, radiation dosimetry,and non-destructive testing. In Compton scattering, incident photons undergo multiple scatterings within the material(target) before exiting. Gamma photons continue to soften in energy as the number of scatterings increases in a thick target; in other words, the energy of gamma photons decreases as the scatterings increase in case of a thick target and results in the generation of singly and multiply scattered events. In this work, the energy distribution of backscattered gamma photons with backscattering intensity and energy probabilities were calculated by using the Monte Carlo method for metallic, biological, and shielding materials with various thicknesses of slab geometry. The materials under study were targeted with gamma photons of 0.279, 0.662, 1.250, and 2.100 Me V energies. In addition, the energy distributions of multiply scattered gamma photons were studied for materials with infinite geometry.The results are presented and discussed in detail by comparing with other Monte Carlo calculations.     

Modelling of radiation transport

In the application of nuclear radiation, the problem of the transport of photons and neutral or charged particles through the matter is central for understanding the physics of the process, for a correct interpretation of the measurement and for a convenient choice of instrumental operating conditions. This paper, in the first part, is intended as a survey of the genesis of the transport equations, which describe the phenomenon of the diffusion of the particles. With a regressive procedure, it is possible to obtain the commonly used transport equations directly from Liouville equation; the approximations that must always been involved can be related to two dimensionless parameters if suitable dimesionless variables are introduced. In the second part, approximate solutions of Boltzmann and Fokker–Planck equations are given for particular physical situations of interest in X-ray spectroscopy and electron microprobe analysis.     

Emissivity of discretized diffusion problems

The numerical modeling of radiative transfer by the diffusion approximation can produce artificially damped radiation propagation if spatial cells are too optically thick. In this paper, we investigate this nonphysical behavior at external problem boundaries by examining the emissivity of the discretized diffusion approximation. We demonstrate that the standard cell-centered discretization produces an emissivity that is too low for optically thick cells, a situation that leads to the lack of radiation propagation. We then present a modified boundary condition that yields an accurate emissivity regardless of cell size. This modified boundary condition can be used with a deterministic calculation or as part of a hybrid transport-diffusion method for increasing the efficiency of Monte Carlo simulations. We also discuss the range of applicability, as a function of cell size and material properties, when this modified boundary condition is employed in a hybrid technique. With a set of numerical calculations, we demonstrate the accuracy and usefulness of this modified boundary condition.     

Radiation in systems with near zero dielectric constant

We discuss radiation effects in systems with near zero dielectric constant. An enhancement of intensity using the example of transition and diffusive radiation is demonstrated. A sharp peak in the transition radiation spectral-angular intensity is predicted. Numerical estimates for specific systems are made and possible applications are discussed.     

Diffusion of photons with arbitrary state of polarization: the Monte Carlo code MCSHAPE

When X-rays penetrate in the matter, they interact with the atoms, producing secondary radiation that carries important information about the composition of the target. The polarization state is one of the properties of the incoming photons which changes as a consequence of the number and the type of the undergone interaction. Therefore, to study properly the atomic properties of a material, it is necessary to consider the evolution of the polarization state of radiation. It is presented MCSHAPE, a Monte Carlo code developed to describe the evolution of the polarization state of X-ray photons as a consequence of the multiple scattering collisions undergone during the diffusion into the sample. In order to study properly the transport of photons with an arbitrary state of polarization, the model adopted in this code is derived from the so called ‘vector’ transport equation [Radiative Transfer, Chapter 1, Section 15, Clarendon, Oxford, 1950; Nucl. Instr. and Meth. B 73 (1993) 341]. Using the Stokes parameters I, Q, U and V, having the dimension of an intensity and containing all the physical information about the polarization state, MCSHAPE simulates the full state of polarization of the photons at any given position, wavelength and solid angle.     

Development of miniaturized SAF-LIBS with high repetition rate acousto-optic gating for quantitative analysis

The self-absorption effect in laser-induced breakdown spectroscopy(LIBS) reduces the accuracy of quantitative measurement results.The self-absorption-free LIBS(SAF-LIBS) has been proved to directly capture the optically thin plasma spectra by setting an appropriate exposure time.In this work,a novel SAF-LIBS technique with high repetition rate acousto-optic gating is developed,in which an acousto-optic modulator is used as the shutter to diffract the optically thin fluorescence,and a high repeti...     

Effects of Boundary Conditions on Thermal Response of a Cellulose Acetate Layer Using Hottel’s Zonal Method

Energy can transfer internally by radiation in addition to conduction in translucent polymers. Since radiant propagation is very rapid, it can provide energy within the layer more quickly than diffusion by heat conduction. Thus, the transient thermal response of a layer for combined radiative and conduction may be extremely different from that of conduction alone. In this paper, the behavior of a heat conducting, absorbing, and emitting layer of Cellulose Acetate layer is investigated during the transient interval when both conductive and radiative heat transfer are considered. Specifically, the effects of boundary conditions on the response of the layer are considered here. These boundary conditions include both conductive boundary conditions, such as convection coefficient and convective fluid temperature, and radiation boundary conditions, like radiation surrounding temperature and specular reflectivity. To this end, the governing differential equations including the equation of radiative heat transfer within the material coupled to the transient energy equation with radiative terms are presented. The solution procedure is based on nodal analysis and Hottel’s zonal method extended by the ray tracing method. The transient energy equation including the radiative internal energy source is solved using a time marching finite difference procedure with variable space and time increments.     

Ion beam characterization of advanced luminescent materials for application in radiation effects microscopy

The ion photon emission microscope (IPEM) is a technique developed at Sandia National Laboratories (SNL) to study radiation effects in integrated circuits with high energy, heavy ions, such as those produced by the 88” cyclotron at Lawrence Berkeley National Laboratory (LBNL). In this method, an ion-luminescent film is used to produce photons from the point of ion impact. The photons emitted due to an ion impact are imaged on a position-sensitive detector to determine the location of a single event effect (SEE). Due to stringent resolution, intensity, wavelength, decay time, and radiation tolerance demands, an engineered material with very specific properties is required to act as the luminescent film. The requirements for this material are extensive. It must produce a high enough induced luminescent intensity so at least one photon is detected per ion hit. The emission wavelength must match the sensitivity of the detector used, and the luminescent decay time must be short enough to limit accidental coincidences. In addition, the material must be easy to handle and its luminescent properties must be tolerant to radiation damage. Materials studied for this application include plastic scintillators, GaN and GaN/InGaN quantum well structures, and lanthanide-activated ceramic phosphors. Results from characterization studies on these materials will be presented; including photoluminescence, cathodoluminescence, ion beam induced luminescence, luminescent decay times, and radiation damage. Results indicate that the ceramic phosphors are currently proving to be the ideal material for IPEM investigations.     

Irradiation effects on fracture toughness of four nuclear reactor pressure vessel submerged-arc welds

This study applies statistical analyses to fracture toughness results for four irradiated “current practice” submerged-arc welds and an A533 grade B class 1 plate. Charpy V-notch, tensile, and 25 mm thick compact specimens were irradiated at 288°C to neutron fluences of 0.7 to 2.0 × 10²³ neutrons/m² (>1 MeV). The plate material contained 0.14% Cu and 0.67% Ni. The four submerged-arc welds contained 0.04 to 0.12% Cu and 0.10 to 0.63% Ni. The plate material showed a Charpy V-notch impact transition temperature increase of 68°C, and a Charpy V-notch upper-shelf energy drop of 16%. The four submerged-arc welds showed smaller changes than the plate material did. The fracture toughness results from the 25 mm thick compact specimens showed approximately the same temperature shift as the Charpy V-notch results. The results imply that submerged-arc welds with both low-copper and low-nickel contents can exhibit essentially zero radiation embrittlement and that nickel can contribute to radiation embrittlement even when the copper content is low.     

The linear Boltzmann equation in optically thick systems with forward-peaked scattering

The monoenergetic linear Boltzmann equation is approximated asymptotically in the limit as (i) the mean free path tends to zero, (ii) the mean scattering cosine tends to unity, and (iii) the transport cross section is held constant. Two differential scattering kernels, the Henyey-Greenstein and screened Rutherford kernels, are treated in this limit. In both cases, the leading and first-order terms in the approximations are described by the usual Fokker Planck operator and pseudodifferential operators that can be written in closed form. These pseudodifferential operators account for “large-angle” scattering effects that are not described by the standard “small-angle” Fokker-Planck operator.     

Thermal analysis of proposed transport cask for three advanced burner reactor used fuel assemblies

Abstract

Preliminary studies of used fuel generated in the US Department of Energy's Advanced Fuel Cycle Initiative have indicated that current used fuel transport casks may be insufficient for the transportation of said fuel. This work considers transport of three 5-year-cooled oxide advanced burner reactor used fuel assemblies with a burn-up of 160 MWD kg^–1. A transport cask designed to carry these assemblies is proposed. This design employs a 7-cm-thick lead gamma shield and a 20-cm-thick NS-4-FR composite neutron shield. The temperature profile within the cask, from its centre to its exterior surface, is determined by two-dimensional computational fluid dynamics simulations of conduction, convection and radiation within the cask. Simulations are performed for a cask with a smooth external surface and various neutron shield thicknesses. Separate simulations are performed for a cask with a corrugated external surface and a neutron shield thickness that satisfies shielding constraints. Resulting temperature profiles indicate that a three-assembly cask with a smooth external surface will meet fuel cladding temperature requirements but will cause outer surface temperatures to exceed the regulatory limit. A cask with a corrugated external surface will not exceed the limits for both the fuel cladding and outer surface temperatures.     

Radiation mean free path for non—LTE fully ionized medium

Radiation mean free path (RMFP) is the function of radiation temperature,electron temperature and material density,and needsto apply Planck mean and Rosseland mean,respectively,in the regions of rarefaction wave andshock wave.The analytical formulae for the two kinds of RMFP have been given,by which the RMFP have been calculated for the interesting small atomic number Z.The calculated results show that theRMFP in non-local-thermal-equilibrium (non-LTE) and in LTE are obviously different and PlanckRMFP is 30 times less than Rosseland one.     

CaS:Ce，Sm材料光致荧光辐射剂量相关性能测量

本工作对光致荧光材料CaS:Ce,Sm的辐射剂量特性进行研究。利用⁶⁰Coγ源对CaS:Ce,Sm/PMMA剂量片进行辐照，应用自行搭建的测试系统对剂量片发出的荧光信号进行测试。测试结果表明，CaS:Ce,Sm材料是短余辉材料，环境温度对材料性能影响显著，在0.1~100Gy内，荧光信号峰值强度与辐照剂量线性关系良好。     

Radiative Heat Deposition Analysis of Fusion Reactor First Wall by Monte Carlo Transport Code

Heat flux distribution on the first wall of a fusion reactor due to the thermal radiation from high temperature protection wall placed in front of the first wall was analyzed. With necessary modifications, a three-dimensional Monte Carlo transport code developed for neuronics calculation was successfully applied in the analysis. That is, reasonable results with sufficiently small statistical error were obtained with reasonable computational time. The heat flux distribution was found to be insensitive to the reflection characteristic of the radiation at the first wall i. e. diffusive or specular.     

An overview of the Boltzmann transport equation solution for neutrons,photons and electrons in Cartesian geometry

Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the P_N approximation, the S_N method (discrete ordinates method) and their variants. In the discrete ordinates (S_N) formulations of the transport equation, it is assumed that the linearised Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this paper, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we describe the recent advances in the class of deterministic methods applied to one and two dimensional transport problems for photons and electrons in Cartesian Geometry. First, we describe the Laplace transform technique applied to S_N two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker–Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a mono-energetic electron beam in a rectangular domain. The main idea relies on applying the P_N approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker–Planck equation and then applying the Laplace Transform in the spatial x variable. Numerical results are given to illustrate the accuracy of deterministic methods presented.