This bibliographical note presents a reference book which addresses the study of neutron transport in matter, the study of conditions for a chain reaction and the study of modifications of matter composition due to nuclear reactions. This book presents the main nuclear data, their measurement, assessment and processing, and the spallation. It proposes an overview of methods applied for the study of neutron transport: basic equations and their derived forms, deterministic methods and Monte Carlo method of resolution of the Boltzmann equation, methods of resolution of generalized Bateman equations, methods of time resolution of space kinetics coupled equations. It presents the main calculation codes, discusses the qualification and experimental aspects, and gives an overview of neutron transport applications: neutron transport calculation of reactors, neutron transport coupled with other disciplines, physics of fuel cycle, criticality
3-D neutron transport benchmarks
A set of 3-D neutron transport benchmark problems proposed by the Osaka University to NEACRP in 1988 has been calculated by many participants and the corresponding results are summarized in this report. The results of Keff, control rod worth and region-averaged fluxes for the four proposed core models, calculated by using various 3-D transport codes are compared and discussed. The calculational methods used were: Monte Carlo, Discrete Ordinates (Sn), Spherical Harmonics (Pn), Nodal Transport and others. The solutions of the four core models are quite useful as benchmarks for checking the validity of 3-D neutron transport codes
Linear stochastic neutron transport theory
A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)
Coupled neutron transport for HZETRN
Slaba, T.C., E-mail: Tony.C.Slaba@nasa.go [Old Dominion University, Norfolk, VA 23505 (United States); Blattnig, S.R. [NASA Langley Research Center, Hampton, VA 23681 (United States); Aghara, S.K. [Prairie View A and M University, Prairie View, TX 77446 (United States); Townsend, L.W.; Handler, T. [University of Tennessee, Knoxville, TN 37996 (United States); Gabriel, T.A. [Scientific Investigation and Development, Knoxville, TN 37922 (United States); Pinsky, L.S.; Reddell, B. [University of Houston, Houston, TX 77204 (United States)
2010-02-15
Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.
Coupled Neutron Transport for HZETRN
Slaba, Tony C.; Blattnig, Steve R.
2009-01-01
Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.
Neutron measurement by transportable spectrometer
Two levels of neutron spectrometry are in regular use at nuclear power plants: some techniques used in the laboratory produce detailed spectra but require specialist operators, while simple instruments used by non-specialists to measure the neutron dose-rate to operators provide little spectral information. The standard portable instruments are therefore of no use when anomalous readings are obtained which require further investigation. AEA Technology at Winfrith has developed a Transportable Neutron Spectrometer (TNS) which is designed to produce reasonable spectra in routine use by staff with no specialist skill in spectroscopy, and high-quality spectra in the hands of skilled staff. The TNS provides a level of information intermediate between those currently available, and is also designed to solve the problem of imperfect dose response which is common in portable dosimeters. The TNS system consists of a power supply, a probe and a signal processing and data acquisition unit. (author)
Neutron transport with periodic boundary conditions
Angelescu, N.; Marinescu, N.; Protopopescu, V.
1976-01-01
The initial value problem for monoenergetic neutron transport in homogeneous nonmultiplying, nonabsorbing medium with isotropic scattering and periodic boundary conditions. One completely determines the structure of the spectrum of the transport operator both in plane and parallelepipedic geometries.
Some improved methods in neutron transport theory
The methods described in this paper are: analytical approach to neutron spectra in case of energy dependent anisotropy of elastic scattering; Monte Carlo estimations of neutron absorption reaction rate during slowing down process; spherical harmonics treatment of space-angle-lethargy dependent slowing down transport equation; integral transport theory based on point-wise representation of variables
ANEMONA: multiassembly neutron transport modeling
Jevremovic, T.; Ito, T. E-mail: t-itoh@nfi.co.jp; Inaba, Y
2002-11-01
A new feature of the general geometry neutron transport code, ANEMONA, the modeling of multi-assembly geometries in 2D, is developed and presented in this paper. The new module is called the ANEMULT code. In addition, the two acceleration techniques are added: (a) the ANEMONA's original geometry independent ray tracer (GIT), now utilizes the, so called, virtual bounding volume concept that importantly speeds up the ray tracing, and (b) the flux solver is accelerated using the Chebyshev polynomials. A whole core configuration run by ANEMULT is generated linking assemblies through the boundary edges' flux. All geometrical data are prepared in advance running the ANEMONA code (independently for geometrically different assemblies only). In this paper, two numerical benchmarks are presented: a single BWR MOX fuel assembly and a 6x6 assembly geometry (each assembly is of BWR 9x9 type). The results compared with the Monte Carlo code, GMVP, show a very good agreement.
Neutron transport equation - indications on homogenization and neutron diffusion
In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks
Neutron stars - cooling and transport
Potekhin, A Y; Page, Dany
2015-01-01
Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of this theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.
Development of transient neutron transport calculation code
A transient neutron transport code for time-dependent analyses of neutronics systems, named DOT4-T, has been developed. The code is based on the Discrete Ordinates code DOT4.2, which solves the steady-state neutron transport equation in two dimensions. For the discretization of time variable, a direct method, the fully implicit and unconditionally stable time integration scheme, has been employed. The resulting code has been tested using several one-dimensional and two-dimensional benchmark problems, and the results obtained with DOT4-T shows very satisfactory agreement with the benchmark problem results. (authors)
Onsager equations and time dependent neutron transport
The diffusion of neutrons following an abrupt, localized temperature fluctuation can be conducted in the framework of Onsager-type transport equations. Considering Onsager equations as a generalized Fick's law, time-dependent particle and energy 'generalized diffusion equations' can be obtained. Aim of the present paper is to obtain the time-dependent diffusion Onsager-type equations for the diffusion of neutrons and to apply them to simple trial cases to gain a feeling for their behaviour. (author)
Study of a transportable neutron radiography system
This work presents a study a transportable neutron radiography system for a 185 GBq 241 Am-Be (α, η) source with a neutron yield roughly 1,25 x 107 n/s. Studies about moderation, collimation and shielding are showed. In these studies, a calculation using Transport Theory was carried out by means of transport codes ANISN and DOT (3.5). Objectives were: to obtain a maximum and more homogeneous thermal neutron flux in the collimator outlet to the image plain, and an adequate radiation shielding to attend radiological protection rules. With the presented collimator, it was possible to obtain for the thermal neutron flux, at the collimator outlet and next to the image plain, a L/D ratio of 14, for neutron fluxes up to 4,09 x 102 n.cm-2.s-1. Considering the low intensity of the source, it is a good value. Studies have also been carried out for L/D ratios of 22 and 30, giving thermal neutron fluxes at the image plain of 1,27 x 102 n.cm-2.s-1 and 2,65 x 102 n.cm-2.s-1, respectively. (author). 30 refs, 39 figs, 9 tabs
Uncertainty analysis of neutron transport calculation
A cross section sensitivity-uncertainty analysis code, SUSD was developed. The code calculates sensitivity coefficients for one and two-dimensional transport problems based on the first order perturbation theory. Variance and standard deviation of detector responses or design parameters can be obtained using cross section covariance matrix. The code is able to perform sensitivity-uncertainty analysis for secondary neutron angular distribution(SAD) and secondary neutron energy distribution(SED). Covariances of 6Li and 7Li neutron cross sections in JENDL-3PR1 were evaluated including SAD and SED. Covariances of Fe and Be were also evaluated. The uncertainty of tritium breeding ratio, fast neutron leakage flux and neutron heating was analysed on four types of blanket concepts for a commercial tokamak fusion reactor. The uncertainty of tritium breeding ratio was less than 6 percent. Contribution from SAD/SED uncertainties are significant for some parameters. Formulas to estimate the errors of numerical solution of the transport equation were derived based on the perturbation theory. This method enables us to deterministically estimate the numerical errors due to iterative solution, spacial discretization and Legendre polynomial expansion of transfer cross-sections. The calculational errors of the tritium breeding ratio and the fast neutron leakage flux of the fusion blankets were analysed. (author)
Hydrogen transport studies using neutron radiography
Neutron cross-sections and their angular and energy-dependence as characteristics of neutron interaction with hydrogen isotopes and compounds are presented. It is shown how deuteration and different molecular modifications (e.g. ortho and parahydrogen) affect the cross-sections and hence the beam attenuation. A comparison of neutron radiographic methods with other neutron techniques used for hydrogen detection is made and the necessary formalism to describe diffusion processes is given. The results obtained by neutron radiography on the measurement of hydrogen motion in various substances are reviewed, in particular diffusion measurements made on liquids (water, liquid hydrogen and methanol) and of hydrogen in metals (β-titanium, vanadium, niobium and tantalum). Finally, neutron-radiographic measurements of water transport in concrete and of carburetor icing are discussed. The advantages of the high detection efficiency of hydrogen by neutron radiography and the integral sample scan technique are simultaneously used for such measurements. Some typical results of this detection method in the field of physical and applied research are shown. (author)
Solving the equation of neutron transport
This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.
An Improved Neutron Transport Algorithm for HZETRN
Slaba, Tony C.; Blattnig, Steve R.; Clowdsley, Martha S.; Walker, Steven A.; Badavi, Francis F.
2010-01-01
Long term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures, and vehicles. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions, and that an extremely fine energy grid is required to resolve the problem under the current formulation. Two numerical methods are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. Convergence testing is completed by running the code for various environments and shielding materials with various energy grids to ensure stability of the newly implemented method.
Multi-group neutron transport theory
Multi-group neutron transport theory. In the paper the general theory of the application of the K. M. Case method to N-group neutron transport theory in plane geometry is given. The eigenfunctions (distributions) for the system of Boltzmann equations have been derived and the completeness theorem has been proved. By means of general solution two examples important for reactor and shielding calculations are given: the solution of a critical and albedo problem for a slab. In both cases the system of singular integral equations for expansion coefficients into a full set of eigenfunction distributions has been reduced to the system of Fredholm-type integral equations. Some results can be applied also to some spherical problems. (author)
Neutron transports in diffusing and thermalising media
Neutron transports in different diffusing and thermalising media were studied within one dimensional theory. Macroscopic cross section libraries for each medium or region were generated by one dimensional models that represent the geometry of the surrounding regions. Few group total and angular fluxes are computed. Especially, determination of angular fluxes at some points and directions are focused on. The results are compared with other computed and experimental values
AGENT code - neutron transport benchmark examples
The paper focuses on description of representative benchmark problems to demonstrate the versatility and accuracy of the AGENT (Arbitrary Geometry Neutron Transport) code. AGENT couples the method of characteristics and R-functions allowing true modeling of complex geometries. AGENT is optimized for robustness, accuracy, and computational efficiency for 2-D assembly configurations. The robustness of R-function based geometry generator is achieved through the hierarchical union of the simple primitives into more complex shapes. The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through true geometries. The computational efficiency is maintained through a set of acceleration techniques introduced in all important calculation levels. The selected assembly benchmark problems discussed in this paper are: the complex hexagonal modular high-temperature gas-cooled reactor, the Purdue University reactor and the well known C5G7 benchmark model. (author)
GEANT 4 simulation of neutron transport and scattering in media
GEANT 4 simulation toolkit and PhysList QGSP BIC HP for simulate neutron transport and scattering was used. Primary neutron spectrum was modeled similar spectrum of 239Pu - Be(alpha, n) neutron source. Spectra of neutron passing through the material and scattered were obtained. Number of thermal neutrons after passing various materials were calculated. Detector-dosimeter MKS-01R was used for measurements of the experimental thermal neutron flux from 239Pu - Be(alpha, n) neutron source. Satisfactory agreement between calculations and experiment was obtained.
Parallel Deterministic Neutron Transport with AMR
Clouse, C
2005-03-25
AMTRAN, a one, two and three dimensional Sn neutron transport code with adaptive mesh refinement (AMR) has been parallelized with MPI over spatial domains and energy groups and with threads over angles. Block refined AMR is used with linear finite element representations for the fluxes, which are node centered. AMR requirements are determined by minimum mean free path calculations throughout the problem and can provide an order of magnitude or more reduction in zoning requirements for the same level of accuracy, compared to a uniformly zoned problem.
Coupling of neutron transport equations. First results
To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs
Vector processing of the neutron transport codes
One of the large computations in JAERI is the neutron transport ones used for reactor shielding and criticality analyses. The adaptability of vector processings has been investigated on the neutron transport codes under the assumption of future use of super-computer. Five codes have been tested. They are DOT3.5, TWOTRAN and ANISN based on finite difference method, and PALLAS-2DCY and BERMUDA on the direct integration method. It has been found that the gain from vectorization depends upon the numerical methods, geometries, and problems types to be solved. That is, the direct integration is rather suited for vector processing. But in the conventional finite difference method, the difference equation has an unvectorizable recurrence form in (r, z) and (r, -)-geometries. But by altering the interative process, the equation can be vectorized and some gains have been found to be achieved in a criticality problem. For each code, described are some views on vectorization, program restructurings, speedup ratio on F75 APU, numerical studies on the interative process, and so forth. (author)
Asymptotic Behaviour of Neutron Transport Processes
reactor corresponds to strong mixing in the sense of ergodic theory; we define a reactor as critical if for all f and all g, positive almost everywhere, a positive limit (Ttf, g) exists for t --> ∞. This definition corresponds to the Fermi experiment. Boundedness of Tt can be demonstrated. Finally an attempt is made to define the mean entropy of a neutron transport process. (author)
Neutron transport on the connection machine
Monte Carlo methods are heavily used at CEA and account for a a large part of the total CPU time of industrial codes. In the present work (done in the frame of the Parallel Computing Project of the CEL-V Applied Mathematics Department) we study and implement on the Connection Machine an optimised Monte Carlo algorithm for solving the neutron transport equation. This allows us to investigate the suitability of such an architecture for this kind of problem. This report describes the chosen methodology, the algorithm and its performances. We found that programming the CM-2 in CM Fortran is relatively easy and we got interesting performances as, on a 16 k, CM-2 they are the same level as those obtained on one processor of a CRAY X-MP with a well optimized vector code
Generic programming for deterministic neutron transport codes
This paper discusses the implementation of neutron transport codes via generic programming techniques. Two different Boltzmann equation approximations have been implemented, namely the Sn and SPn methods. This implementation experiment shows that generic programming allows us to improve maintainability and readability of source codes with no performance penalties compared to classical approaches. In the present implementation, matrices and vectors as well as linear algebra algorithms are treated separately from the rest of source code and gathered in a tool library called 'Generic Linear Algebra Solver System' (GLASS). Such a code architecture, based on a linear algebra library, allows us to separate the three different scientific fields involved in transport codes design: numerical analysis, reactor physics and computer science. Our library handles matrices with optional storage policies and thus applies both to Sn code, where the matrix elements are computed on the fly, and to SPn code where stored matrices are used. Thus, using GLASS allows us to share a large fraction of source code between Sn and SPn implementations. Moreover, the GLASS high level of abstraction allows the writing of numerical algorithms in a form which is very close to their textbook descriptions. Hence the GLASS algorithms collection, disconnected from computer science considerations (e.g. storage policy), is very easy to read, to maintain and to extend. (authors)
Concise four-vector scheme for neutron transport calculations
An explicit Riemannian geometrical form or the vectorial Neutron Streaming Term is presented. The method applies the full Riemannian technique of general covariance. There are cases when the symmetry of the neutron flux must be smaller than that of the arrangement. However, in coordinate space there are always solutions of the Neutron Transport Equation as symmetric as the arrangement, if the latter's symmetry is at least an affine collineation of the Euclidian 3-space. (author). 7 refs
Design of a transportable high efficiency fast neutron spectrometer
Roecker, C.; Bernstein, A.; Bowden, N. S.; Cabrera-Palmer, B.; Dazeley, S.; Gerling, M.; Marleau, P.; Sweany, M. D.; Vetter, K.
2016-08-01
A transportable fast neutron detection system has been designed and constructed for measuring neutron energy spectra and flux ranging from tens to hundreds of MeV. The transportability of the spectrometer reduces the detector-related systematic bias between different neutron spectra and flux measurements, which allows for the comparison of measurements above or below ground. The spectrometer will measure neutron fluxes that are of prohibitively low intensity compared to the site-specific background rates targeted by other transportable fast neutron detection systems. To measure low intensity high-energy neutron fluxes, a conventional capture-gating technique is used for measuring neutron energies above 20 MeV and a novel multiplicity technique is used for measuring neutron energies above 100 MeV. The spectrometer is composed of two Gd containing plastic scintillator detectors arranged around a lead spallation target. To calibrate and characterize the position dependent response of the spectrometer, a Monte Carlo model was developed and used in conjunction with experimental data from gamma ray sources. Multiplicity event identification algorithms were developed and used with a Cf-252 neutron multiplicity source to validate the Monte Carlo model Gd concentration and secondary neutron capture efficiency. The validated Monte Carlo model was used to predict an effective area for the multiplicity and capture gating analyses. For incident neutron energies between 100 MeV and 1000 MeV with an isotropic angular distribution, the multiplicity analysis predicted an effective area of 500 cm2 rising to 5000 cm2. For neutron energies above 20 MeV, the capture-gating analysis predicted an effective area between 1800 cm2 and 2500 cm2. The multiplicity mode was found to be sensitive to the incident neutron angular distribution.
A transport optics for pulsed ultracold neutron sources
High-density ultracold neutron (UCN) is commonly desired for the improvement of the experimental sensitivity to measure the electric dipole moment of neutrons. We discuss a method to suppress the decrease of the UCN density in transporting UCNs to the spatially separated storage volume by changing the UCN velocity synchronizing to the UCN time-of-flight.
UPWIND DISCONTINUOUS GALERKIN METHODS FOR TWO DIMENSIONAL NEUTRON TRANSPORT EQUATIONS
袁光伟; 沈智军; 闫伟
2003-01-01
In this paper the upwind discontinuous Galerkin methods with triangle meshes for two dimensional neutron transport equations will be studied.The stability for both of the semi-discrete and full-discrete method will be proved.
Deterministic adjoint transport applications for He-3 neutron detector design
This work focuses on the determination of predicted neutron detector response accomplished using neutron importance derived from an adjoint discrete ordinates (SN) transport calculation. A hypothetical detector apparatus, intended to detect fast neutrons, was modeled using He-3 tubes with graphite moderation using the PENTRANTM 3-D multi-group discrete ordinates parallel transport code system. The detector geometry was modeled using z-axis symmetry and discretized into 30,280 3-D Cartesian cells. The material spatial mesh was generated using the PENMSHTM code in the PENTRAN system. The 47-group BUGLE-96 neutron cross section library was used for construction of macroscopic neutron cross sections. Results from an S8 angular quadrature using P3 anisotropy are presented. An adjoint transport source was established in the model using group dependent He-3 response cross sections. Each He-3 tube contained an adjoint source aliased to group He-3 absorption cross sections to permit assessment of detector performance. The spectrally dependent detector response from neutron capture in He-3 tubes from an arbitrary source can, therefore, be readily determined. This response comes from the complete integral of the actual source strength weighted by the adjoint function at the source location for any source distribution scenario. For selected neutron energies, an equivalent forward MCNP Monte Carlo model was used to demonstrate good agreement with the detector response determined from the adjoint calculation. The graphite used in this design has a large impact on detector performance due to the increasing sensitivity inherent in He-3 gas as neutrons thermalize. Computational adjoint results presented here predict a fast neutron detector design that yields efficiencies between 30 and 50% for neutron energies below 3 keV, and up to 30% efficiencies for neutron energies between 3 keV and 1 MeV. Overall, the methodology applied here highlights the elegant nature of an adjoint
Scattered Neutron Tomography Based on A Neutron Transport Inverse Problem
William Charlton
2007-07-01
Neutron radiography and computed tomography are commonly used techniques to non-destructively examine materials. Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions.
Transport coefficients in superfluid neutron stars
Tolos, Laura [Instituto de Ciencias del Espacio (IEEC/CSIC) Campus Universitat Autònoma de Barcelona, Facultat de Ciències, Torre C5, E-08193 Bellaterra (Barcelona) (Spain); Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Manuel, Cristina [Instituto de Ciencias del Espacio (IEEC/CSIC) Campus Universitat Autònoma de Barcelona, Facultat de Ciències, Torre C5, E-08193 Bellaterra (Barcelona) (Spain); Sarkar, Sreemoyee [Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai-400005 (India); Tarrus, Jaume [Physik Department, Technische Universität München, D-85748 Garching (Germany)
2016-01-22
We study the shear and bulk viscosity coefficients as well as the thermal conductivity as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state and the gap of the system. The shear viscosity due to phonon scattering is compared to calculations of that coming from electron collisions. We also comment on the possible consequences for r-mode damping in superfluid neutron stars. Moreover, we find that phonon collisions give the leading contribution to the bulk viscosities in the core of the neutron stars. We finally obtain a temperature-independent thermal conductivity from phonon collisions and compare it with the electron-muon thermal conductivity in superfluid neutron stars.
Solution of modified neutron transport equation in plane geometry
Neutron transport equation was formulated for universal anisotropic scattering function with integration over variable μ carried out segment (0,1) instead of segment (-1,1). A modified system of DPN equations was derived and solved by applying flux expansion in double Legendre polynomials over variable μ. As an example, case of neutron isotropic scattering was treated in detail and Green functions for infinitive medium were computed. The application of the eighth order analytical approximation achieved the accuracy to the unit on the sixth significant digit in the whole range of parameter c, angle cosine μ and distances x up ten optical lengths from the neutron source. 13 refs., 5 tabs
Considerations in the design of an improved transportable neutron spectrometer
Williams, A M; Brushwood, J M; Beeley, P A
2002-01-01
The Transportable Neutron Spectrometer (TNS) has been used by the Ministry of Defence for over 15 years to characterise neutron fields in workplace environments and provide local correction factors for both area and personal dosimeters. In light of advances in neutron spectrometry, a programme to evaluate and improve TNS has been initiated. This paper describes TNS, presents its operation in known radioisotope fields and in a reactor environment. Deficiencies in the operation of the instrument are highlighted, together with proposals for updating the response functions and spectrum unfolding methodologies.
Calculated characteristics of subcritical assembly with anisotropic transport of neutrons
Gorin, N.V.; Lipilina, E.N.; Lyutov, V.D.; Saukov, A.I. [Zababakhin Russian Federal Nuclear Center - All-Russian Scientific Researching Institute of Technical Physics (Russian Federation)
2003-07-01
There was considered possibility of creating enough sub-critical system that multiply neutron fluence from a primary source by many orders. For assemblies with high neutron tie between parts, it is impossible. That is why there was developed a construction consisting of many units (cascades) having weak feedback with preceding cascades. The feedback attenuation was obtained placing layers of slow neutron absorber and moderators between the cascades of fission material. Anisotropy of fast neutron transport through the layers was used. The system consisted of many identical cascades aligning one by another. Each cascade consists of layers of moderator, fissile material and absorber of slow neutrons. The calculations were carried out using the code MCNP.4a with nuclear data library ENDF/B5. In this construction neutrons spread predominantly in one direction multiplying in each next fissile layer, and they attenuate considerably in the opposite direction. In a calculated construction, multiplication factor of one cascade is about 1.5 and multiplication factor of whole construction composed of n cascades is 1.5{sup n}. Calculated keff value is 0.9 for one cascade and does not exceed 0.98 for a system containing any number of cascades. Therefore the assembly is always sub-critical and therefore it is safe in respect of criticality. There was considered using such a sub-critical assembly to create a powerful neutron fluence for neutron boron-capturing therapy. The system merits and demerits were discussed. (authors)
TRIPOLI-3: a neutron/photon Monte Carlo transport code
The present version of TRIPOLI-3 solves the transport equation for coupled neutron and gamma ray problems in three dimensional geometries by using the Monte Carlo method. This code is devoted both to shielding and criticality problems. The most important feature for particle transport equation solving is the fine treatment of the physical phenomena and sophisticated biasing technics useful for deep penetrations. The code is used either for shielding design studies or for reference and benchmark to validate cross sections. Neutronic studies are essentially cell or small core calculations and criticality problems. TRIPOLI-3 has been used as reference method, for example, for resonance self shielding qualification. (orig.)
Neutron transport study of a beam port based dynamic neutron radiography facility
Khaial, Anas M.
Neutron radiography has the ability to differentiate between gas and liquid in two-phase flow due both to the density difference and the high neutron scattering probability of hydrogen. Previous studies have used dynamic neutron radiography -- in both real-time and high-speed -- for air-water, steam-water and gas-liquid metal two-phase flow measurements. Radiography with thermal neutrons is straightforward and efficient as thermal neutrons are easier to detect with relatively higher efficiency and can be easily extracted from nuclear reactor beam ports. The quality of images obtained using neutron radiography and the imaging speed depend on the neutron beam intensity at the imaging plane. A high quality neutron beam, with thermal neutron intensity greater than 3.0x 10 6 n/cm2-s and a collimation ratio greater than 100 at the imaging plane, is required for effective dynamic neutron radiography up to 2000 frames per second. The primary objectives of this work are: (1) to optimize a neutron radiography facility for dynamic neutron radiography applications and (2) to investigate a new technique for three-dimensional neutron radiography using information obtained from neutron scattering. In this work, neutron transport analysis and experimental validation of a dynamic neutron radiography facility is studied with consideration of real-time and high-speed neutron radiography requirements. A beam port based dynamic neutron radiography facility, for a target thermal neutron flux of 1.0x107 n/cm2-s, has been analyzed, constructed and experimentally verified at the McMaster Nuclear Reactor. The neutron source strength at the beam tube entrance is evaluated experimentally by measuring the thermal and fast neutron fluxes using copper activation flux-mapping technique. The development of different facility components, such as beam tube liner, gamma ray filter, beam shutter and biological shield, is achieved analytically using neutron attenuation and divergence theories. Monte
Optimization study of a transportable neutron radiography unit based on a compact neutron generator
Fantidis, J.G. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece); Nicolaou, G.E., E-mail: nicolaou@ee.duth.g [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece); Tsagas, N.F. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece)
2010-06-21
A transportable fast and thermal neutron radiography system, incorporating a compact DD neutron generator, has been simulated using the MCNPX code. The materials considered were compatible with the European Union Directive on 'Restriction of Hazardous Substances'(RoHS) 2002/95/EC, hence excluding the use of cadmium and lead. Appropriate collimators were simulated for each of the radiography modes. With suitable aperture and collimator designs, it was possible to optimize the parameters for both fast and thermal neutron radiographies, for a wide range of values of the collimator ratio. The system simulated allows different object sizes to be studied with a wide range of radiography parameters.
Optimization study of a transportable neutron radiography unit based on a compact neutron generator
A transportable fast and thermal neutron radiography system, incorporating a compact DD neutron generator, has been simulated using the MCNPX code. The materials considered were compatible with the European Union Directive on 'Restriction of Hazardous Substances'(RoHS) 2002/95/EC, hence excluding the use of cadmium and lead. Appropriate collimators were simulated for each of the radiography modes. With suitable aperture and collimator designs, it was possible to optimize the parameters for both fast and thermal neutron radiographies, for a wide range of values of the collimator ratio. The system simulated allows different object sizes to be studied with a wide range of radiography parameters.
Neutron transport model based on the transmission probability method
Highlights: • One hexagonal assembly is divided into 6 triangular prisms in order to get accurate flux distributions. • Transmission probability method is applied to solve the integral neutron transport equation. • The neutron flux and source are expanded spatially by a set of second order orthogonal polynomials. • The neutron flux at the interface is approximated with simplified P1 approximation. - Abstract: A new project has been started recently at KIT to develop a code able to treat hexagonal-z geometries with low density regions. The mathematical method chosen for that purpose is the Transmission Probability Method (TPM) for solving the integral neutron transport equation. In this model, one hexagonal prism is divided into six or more triangular prisms in order to get accurate flux distributions. Within each triangular prism, the neutron source is assumed to be isotropic, the scalar flux and source being approximated in space with a set of second order orthogonal polynomials. The neutron flux at the interfaces is constant in space and approximated with the simplified P1 approximation in angle. A new code, TPM-HEXZ, based on the described model is developed and some benchmarks are used to verify the code, the results are in good agreement with reference ones
Thermal and transport properties of the neutron star inner crust
Page, Dany
2012-01-01
We review the nuclear and condensed matter physics underlying the thermal and transport properties of the neutron star inner crust. These properties play a key role in interpreting transient phenomena such as thermal relaxation in accreting neutron stars, superbursts, and magnetar flares. We emphasize simplifications that occur at low temperature where the inner crust can be described in terms of electrons and collective excitations. The heat conductivity and heat capacity of the solid and superfluid phase of matter is discussed in detail and we emphasize its role in interpreting observations of neutron stars in soft X-ray transients. We highlight recent theoretical and observational results, and identify future work needed to better understand a host of transient phenomena in neutron stars.
A new DPN formulation of neutron transport equation
Neutron transport equation where integration over variable μ was carried out in segment [0,1] instead of segment [-1,1] was formulated for anisotropic scattering function. A new system of DPN equations is obtained by applying flux expansion in double Legendre polynomial over variable μ. This procedure enables an approximate analytical solution of transport equation with high accuracy, even in low order approximation. (author). 6 refs., 2 tabs
A New Monte Carlo Neutron Transport Code at UNIST
Monte Carlo neutron transport code named MCS is under development at UNIST for the advanced reactor design and research purpose. This MC code can be used for fixed source calculation and criticality calculation. Continuous energy neutron cross section data and multi-group cross section data can be used for the MC calculation. This paper presents the overview of developed MC code and its calculation results. The real time fixed source calculation ability is also tested in this paper. The calculation results show good agreement with commercial code and experiment. A new Monte Carlo neutron transport code is being developed at UNIST. The MC codes are tested with several benchmark problems: ICSBEP, VENUS-2, and Hoogenboom-Martin benchmark. These benchmarks covers pin geometry to 3-dimensional whole core, and results shows good agreement with reference results
New developments in differencing the spherical geometry neutron transport equation
Early differencing methods due to Carlson, Lathrop, and others have continued to be used to approximate the spherical geometry neutron transport equations. Nonphysical depressions in the scalar flux profiles continue to cause problems when these early techniques are used. Recent developments, however, provide better understanding of the behavior of these methods and have led to a simple approach to improve numerical solutions
STABILITY OF P2 METHODS FOR NEUTRON TRANSPORT EQUATIONS
袁光伟; 沈智军; 沈隆钧; 周毓麟
2002-01-01
In this paper the P2 approximation to the one-group planar neutron transport theory is discussed. The stability of the solutions for P2 equations with general boundary conditions, including the Marshak boundary condition, is proved. Moreover,the stability of the up-wind difference scheme for the P2 equation is demonstrated.
Neutron transport calculations of some fast critical assemblies
To analyse the influence of the input variables of the transport codes upon the neutronic results (eigenvalues, generation times, . . . ) four Benchmark calculations have been performed. Sensitivity analysis have been applied to express these dependences in a useful way, and also to get an unavoidable experience to carry out calculations achieving the required accuracy and doing them in practical computing times. (Author) 29 refs
Projection and conservation methods for neutron transport
The solution of problems for large three-dimensional systems by conventional finite element methods is slow, even with the super-computer such as the CRAY. Projection and conservation methods can be used in conjunction to synthesis from a crude approximation a succession of more and more accurate approximations. The conservation method uses an extremum principle with two trial functions; but only one of these, the frame trial function, has to satisfy continuity conditions. When optimised the two trial functions ensure the satisfaction of the neutron conservation condition for each element. Having found a frame trial function the other trial function can be determined element by element. It is then transformed to provide another frame trial function. Extrapolation of these frame functions yields an improved frame trial function to initiate a fresh cycle of approximation. (author). 5 refs., 2 figs., 1 tab
Optimization of a neutron detector design using adjoint transport simulation
Yi, C.; Manalo, K.; Huang, M.; Chin, M.; Edgar, C.; Applegate, S.; Sjoden, G. [Georgia Inst. of Technology, Gilhouse Boggs Bldg., 770 State St, Atlanta, GA 30332-0745 (United States)
2012-07-01
A synthetic aperture approach has been developed and investigated for Special Nuclear Materials (SNM) detection in vehicles passing a checkpoint at highway speeds. SNM is postulated to be stored in a moving vehicle and detector assemblies are placed on the road-side or in chambers embedded below the road surface. Neutron and gamma spectral awareness is important for the detector assembly design besides high efficiencies, so that different SNMs can be detected and identified with various possible shielding settings. The detector assembly design is composed of a CsI gamma-ray detector block and five neutron detector blocks, with peak efficiencies targeting different energy ranges determined by adjoint simulations. In this study, formulations are derived using adjoint transport simulations to estimate detector efficiencies. The formulations is applied to investigate several neutron detector designs for Block IV, which has its peak efficiency in the thermal range, and Block V, designed to maximize the total neutron counts over the entire energy spectrum. Other Blocks detect different neutron energies. All five neutron detector blocks and the gamma-ray block are assembled in both MCNP and deterministic simulation models, with detector responses calculated to validate the fully assembled design using a 30-group library. The simulation results show that the 30-group library, collapsed from an 80-group library using an adjoint-weighting approach with the YGROUP code, significantly reduced the computational cost while maintaining accuracy. (authors)
Graphical User Interface for Simplified Neutron Transport Calculations
Schwarz, Randolph; Carter, Leland L
2011-07-18
A number of codes perform simple photon physics calculations. The nuclear industry is lacking in similar tools to perform simplified neutron physics shielding calculations. With the increased importance of performing neutron calculations for homeland security applications and defense nuclear nonproliferation tasks, having an efficient method for performing simple neutron transport calculations becomes increasingly important. Codes such as Monte Carlo N-particle (MCNP) can perform the transport calculations; however, the technical details in setting up, running, and interpreting the required simulations are quite complex and typically go beyond the abilities of most users who need a simple answer to a neutron transport calculation. The work documented in this report resulted in the development of the NucWiz program, which can create an MCNP input file for a set of simple geometries, source, and detector configurations. The user selects source, shield, and tally configurations from a set of pre-defined lists, and the software creates a complete MCNP input file that can be optionally run and the results viewed inside NucWiz.
A deterministic method for transient, three-dimensional neutron transport
A deterministic method for solving the time-dependent, three-dimensional Boltzmann transport equation with explicit representation of delayed neutrons has been developed and evaluated. The methodology used in this study for the time variable of the neutron flux is known as the improved quasi-static (IQS) method. The position, energy, and angle-dependent neutron flux is computed deterministically by using the three-dimensional discrete ordinates code TORT. This paper briefly describes the methodology and selected results. The code developed at the University of Tennessee based on this methodology is called TDTORT. TDTORT can be used to model transients involving voided and/or strongly absorbing regions that require transport theory for accuracy. This code can also be used to model either small high-leakage systems, such as space reactors, or asymmetric control rod movements. TDTORT can model step, ramp, step followed by another step, and step followed by ramp type perturbations. It can also model columnwise rod movement. A special case of columnwise rod movement in a three-dimensional model of a boiling water reactor (BWR) with simple adiabatic feedback is also included. TDTORT is verified through several transient one-dimensional, two-dimensional, and three-dimensional benchmark problems. The results show that the transport methodology and corresponding code developed in this work have sufficient accuracy and speed for computing the dynamic behavior of complex multi-dimensional neutronic systems
Coupled neutron and photon cross sections for transport calculations
A compact set of multigroup cross sections and transfer tables for use in neutron and photon transport calculations was prepared from ENDF/B-IV using the NJOY processing system. The library includes prompt and steady-state coupled sets for neutrons and photons in FIDO format, prompt and steady-state fission spectra (chi vectors) for the fissionable isotopes, and a table of useful response functions including heating and gas production. These multigroup constants should be useful for a wide variety of problems where self-shielding is not important. 15 references
Development of Library Processing System for Neutron Transport Calculation
Song, J. S.; Park, S. Y.; Kim, H. Y. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)] (and others)
2008-12-15
A system for library generation was developed for the lattice neutron transport program for pressurized water reactor core analysis. The system extracts multi energy group nuclear data for requested nuclides from ENDF/B whose data are based on continuous energy, generates hydrogen equivalent factor and resonance integral table as functions of temperature and background cross section for resonance nuclides, generates subgroup data for the lattice program to treat resonance exactly as possible, and generates multi-group neutron library file including nuclide depletion data for use of the lattice program.
Neutron shielding evaluation for a small fuel transport case
Coeck, M; Vanhavere, F
2002-01-01
We investigated the effectiveness of a small neutron shield configuration for the transportation of fresh MOX fuel rods in an experimental facility, this in order to reduce the dose received by the personnel. Monte Carlo simulations using the Tripoli and MCNP4B code were applied. Different configurations were studied, starting from the bare fuel rod positioned on an iron plate up to a fuel rod covered by a box-shaped shield made of different materials such as polyethylene, polyethylene with boron and polyethylene with a cadmium layer. We compared the neutron spectra for the different cases and calculated the corresponding ambient equivalent dose rate H*(10).
An adaptive finite element approach for neutron transport equation
Highlights: → Using uniform grid solution gives high local residuals errors. → Element refinement in the region where the flux gradient is large improves accuracy of results. → It is not necessary to use high density element throughout problem domain. → The method provides great geometrical flexibility. → Implementation of different density of elements lowers computational cost. - Abstract: In this paper, we develop an adaptive element refinement strategy that progressively refines the elements in appropriate regions of domain to solve even-parity Boltzmann transport equation. A posteriori error approach has been used for checking the approximation solutions for various sizes of elements. The local balance of neutrons in elements is utilized as an error assessment. To implement the adaptive approach a new neutron transport code FEMPT, finite element modeling of particle transport, for arbitrary geometry has been developed. This code is based on even-parity spherical harmonics and finite element method. A variational formulation is implemented for the even-parity neutron transport equation for the general case of anisotropic scattering and sources. High order spherical harmonic functions expansion for angle and finite element method in space is used as trial function. This code can be used to solve the multi-group neutron transport equation in highly complex X-Y geometries with arbitrary boundary condition. Due to powerful element generator tools of FEMPT, the description of desired and complicated 2D geometry becomes quite convenient. The numerical results show that the locally adaptive element refinement approach enhances the accuracy of solution in comparison with uniform meshing approach.
Computational benchmarking of fast neutron transport throughout large water thicknesses
Neutron dosimetry experiments seem to point our difficulties in the treatment of large water thickness like those encountered between the core baffle and the pressure vessel. This paper describes the theoretical benchmark undertaken by EDF, SCK/CEN and TRACTEBEL ENERGY ENGINEERING, concerning the transport of fast neutrons throughout a one meter cube of water, located after a U-235 fission sources plate. The results showed no major discrepancies between the calculations up to 50 cm from the source, accepting that a P3 development of the Legendre polynomials is necessary for the Sn calculations. The main differences occurred after 50 cm, reaching 20 % at the end of the water cube. This results lead us to consider an experimental benchmark, dedicated to the problem of fast neutron deep penetration in water, which has been launched at SCK/CEN. (authors)
Exact-to-precision generalized perturbation for neutron transport calculation
This manuscript extends the exact-to-precision generalized perturbation theory (EPGPT), introduced previously, to neutron transport calculation whereby previous developments focused on neutron diffusion calculation only. The EPGPT collectively denotes new developments in generalized perturbation theory (GPT) that place premium on computational efficiency and defendable accuracy in order to render GPT a standard analysis tool in routine design and safety reactor calculations. EPGPT constructs a surrogate model with quantifiable accuracy which can replace the original neutron transport model for subsequent engineering analysis, e.g. functionalization of the homogenized few-group cross sections in terms of various core conditions, sensitivity analysis and uncertainty quantification. This is achieved by reducing the effective dimensionality of the state variable (i.e. neutron angular flux) by projection onto an active subspace. Confining the state variations to the active subspace allows one to construct a small number of what is referred to as the 'active' responses which are solely dependent on the physics model rather than on the responses of interest, the number of input parameters, or the number of points in the state phase space. (authors)
Neutron imaging of ion transport in mesoporous carbon materials.
Sharma, Ketki; Bilheux, Hassina Z; Walker, Lakeisha M H; Voisin, Sophie; Mayes, Richard T; Kiggans, Jim O; Yiacoumi, Sotira; DePaoli, David W; Dai, Sheng; Tsouris, Costas
2013-07-28
Neutron imaging is presented as a tool for quantifying the diffusion of ions inside porous materials, such as carbon electrodes used in the desalination process via capacitive deionization and in electrochemical energy-storage devices. Monolithic mesoporous carbon electrodes of ∼10 nm pore size were synthesized based on a soft-template method. The electrodes were used with an aqueous solution of gadolinium nitrate in an electrochemical flow-through cell designed for neutron imaging studies. Sequences of neutron images were obtained under various conditions of applied potential between the electrodes. The images revealed information on the direction and magnitude of ion transport within the electrodes. From the time-dependent concentration profiles inside the electrodes, the average value of the effective diffusion coefficient for gadolinium ions was estimated to be 2.09 ± 0.17 × 10(-11) m(2) s(-1) at 0 V and 1.42 ± 0.06 × 10(-10) m(2) s(-1) at 1.2 V. The values of the effective diffusion coefficient obtained from neutron imaging experiments can be used to evaluate model predictions of the ion transport rate in capacitive deionization and electrochemical energy-storage devices. PMID:23756558
KAMCCO, a reactor physics Monte Carlo neutron transport code
KAMCCO is a 3-dimensional reactor Monte Carlo code for fast neutron physics problems. Two options are available for the solution of 1) the inhomogeneous time-dependent neutron transport equation (census time scheme), and 2) the homogeneous static neutron transport equation (generation cycle scheme). The user defines the desired output, e.g. estimates of reaction rates or neutron flux integrated over specified volumes in phase space and time intervals. Such primary quantities can be arbitrarily combined, also ratios of these quantities can be estimated with their errors. The Monte Carlo techniques are mostly analogue (exceptions: Importance sampling for collision processes, ELP/MELP, Russian roulette and splitting). Estimates are obtained from the collision and track length estimators. Elastic scattering takes into account first order anisotropy in the center of mass system. Inelastic scattering is processed via the evaporation model or via the excitation of discrete levels. For the calculation of cross sections, the energy is treated as a continuous variable. They are computed by a) linear interpolation, b) from optionally Doppler broadened single level Breit-Wigner resonances or c) from probability tables (in the region of statistically distributed resonances). (orig.)
Fast neutron transport through laminated iron-water shield
Reaction rates were measured in a laminated iron-water shield by threshold detectors, from which the neutron spectra were obtained with the aid of the SAND-II code. The error analysis for the unfolding of the spectra proved that the spectra obtained satisfactorily in the energy range of 1 -- 10.5 MeV. One-dimensional calculations were made by the discrete ordinates transport codes ANISN-JR and PALLAS in a spherical geometry. Agreements within a factor of 1.6 for the spectra and 1.31 for the reaction rates were obtained between the measurements and calculations, though rather large discrepancies were found in the spectra at the energy range of 3 -- 7 MeV. All experimental data in absolute value and detailed specifications for source, detector and the experimental geometry are given for a fast neutron transport benchmark calculation. (author)
Neutron transport in WIMS by the characteristics method
This report is the text of a Paper presented by the author at the American Nuclear Society meeting in San Diego, California in June 1993. It summarises the characteristics method known as CACTUS for solving the neutron transport equation, and describes its application to a benchmark problem with adjacent gadolinium pins. The new CACTUS options (a) to subdivide regions into computational meshes, and (b) to extend the method to allow for the spatial variation of source distributions are highlighted. (Author)
Deterministic methods to solve the integral transport equation in neutronic
We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs
Neutron transport calculations using Quasi-Monte Carlo methods
Moskowitz, B.S.
1997-07-01
This paper examines the use of quasirandom sequences of points in place of pseudorandom points in Monte Carlo neutron transport calculations. For two simple demonstration problems, the root mean square error, computed over a set of repeated runs, is found to be significantly less when quasirandom sequences are used ({open_quotes}Quasi-Monte Carlo Method{close_quotes}) than when a standard Monte Carlo calculation is performed using only pseudorandom points.
Transport of D-D fusion neutrons in thick concrete
By altering the collision mechanism in the numerical transport calculations, and by constructing an analytical model based on age-diffusion theory, the outstanding feature in the life history of D-D fusion neutrons penetrating deeply into ordinary concrete is shown to be the transport in the 2.3 MeV oxygen anti-resonance. This result is used to assess the impact of the cross-section uncertainties and the uncertainties due to variations in the D-D fusion spectrum and temperature
MAGGENTA: Multiassembly General Geometry Neutron Transport Theory Code
MAGGENTA solves the multigroup steady-state neutron integral transport equation in arbitrary two-dimensional multi-assembly geometries that can be described by combinatorial geometry. Given transport corrected macroscopic cross sections, MAGGENTA solves an eigenvalue problem and calculates the volumetric flux and incoming/outgoing current distributions. MAGGENTA utilizes the p4 Parallel Programming System on a network of workstations or other supercomputers to solve large multi-assembly problems. The solver is optimized for vectro processing on vector machines. A graphical interface has been developed to simplify the assembly layout construction and processor assignments
Solution of neutron transport equation by Method of Characteristics
Highlights: • A neutron transport theory code, based on Method of Characteristics (MOC), is developed. • The code is able to simulate square, circular, hexagonal geometries and their combinations. • Delaunay triangulation together with Bower–Watson algorithm is used for mesh generation. • The code is benchmarked against different geometry and boundary conditions. • Results corroborate well with the results available in literature. - Abstract: A computer code based on Method of Characteristics (MOC) is developed to solve neutron transport equation for mainly assembly level lattice calculation with reflective and periodic boundary conditions and to some extent core level calculation with vacuum boundary condition. The code is able to simulate square, circular and hexagonal geometries and their combinations. Delaunay triangulation together with the Bower–Watson algorithm is used to divide the problem geometry into triangular meshes. Ray tracing technique is developed to draw characteristics lines along different directions over the geometry and the transport equation is solved over these lines to obtain neutron flux distribution and multiplication factor for the geometry. A number of benchmark problems available in literature are analyzed to demonstrate the capability and validity of the code
Toward whole-core neutron transport without spatial homogenization
Full text of publication follows: A long-term goal of computational reactor physics is the deterministic analysis of power reactor core neutronics without incurring significant discretization errors in the energy, spatial or angular variables. In principle, given large enough parallel configurations with unlimited CPU time and memory, this goal could be achieved using existing three-dimensional neutron transport codes. In practice, however, solving the Boltzmann equation for neutrons over the six-dimensional phase space is made intractable by the nature of neutron cross-sections and the complexity and size of power reactor cores. Tens of thousands of energy groups would be required for faithful cross section representation. Likewise, the numerous material interfaces present in power reactor lattices require exceedingly fine spatial mesh structures; these ubiquitous interfaces preclude effective implementation of adaptive grid, mesh-less methods and related techniques that have been applied so successfully in other areas of engineering science. These challenges notwithstanding, substantial progress continues in the pursuit for more robust deterministic methods for whole-core neutronics analysis. This paper examines the progress over roughly the last decade, emphasizing the space-angle variables and the quest to eliminate errors attributable to spatial homogenization. As prolog we briefly assess 1990's methods used in light water reactor analysis and review the lessons learned from the C5G7 benchmark exercises which were originated in 1999 to appraise the ability of transport codes to perform core calculations without homogenization. We proceed by examining progress over the last decade much of which falls into three areas. These may be broadly characterized as reduced homogenization, dynamic homogenization and planar-axial synthesis. In the first, homogenization in three-dimensional calculations is reduced from the fuel assembly to the pin-cell level. In the second
Neutron transport benchmark examples with web-based AGENT
The AGENT (Arbitrary GEometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two- or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) mathematical theory of R-functions that is used to generate real three-dimensional geometries of square or hexagonal heterogeneous geometries, (2) the x-y method of characteristics (MOC) used to solve isotropic neutron transport in non-homogenized 2D reactor slices, and (3) the one-dimensional diffusion theory or MOC theory used to couple the x-y and z neutron tracks through the transverse leakage and angular mesh-wise flux values. The R-function geometrical module allows a sequential building of the layers of geometry and automatic submeshing based on the network of geometric domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). AGENT methodologies and numerical solutions are applicable in validating neutronic analysis for GenIV reactor designs while the effect of double heterogeneity in very high temperature reactors (VHTRs) is under development. The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: coarse mesh rebalancing (CMR) and coarse mesh finite difference
Direct measurement of lithium transport in graphite electrodes using neutrons
Highlights: ► Spatiotemporal measurements of lithium through the electrode thickness were quantified with high resolution neutron imaging. ► A nonuniform lithium distribution was observed early in the first intercalation cycle but relaxed as the electrode filled with lithium. ► Through-plane transport resistance in the bulk of the graphite composite electrode was measured. ► The distribution of lost capacity associated with trapped lithium was quantified and linked to regions with low intercalation rates. - Abstract: Lithium intercalation into graphite electrodes is widely studied, but few direct in situ diagnostic methods exist. Such diagnostic methods are desired to probe the influence of factors such as charge rate, electrode structure and solid electrolyte interphase layer transport resistance as they relate to lithium-ion battery performance and durability. In this work, we present a continuous measurement of through-plane lithium distributions in a composite graphite/lithium metal electrochemical cell. Capacity change in a thick graphite electrode was measured during several charge/discharge cycles with high resolution (14 μm) neutron imaging. A custom test fixture and a method for quantifying lithium are described. The measured lithium distribution within the graphite electrode is given as a function of state of charge. Bulk transport resistance is considered by comparing intercalation rates through the thickness of the electrode near the separator and current collector. The residual lithium content associated with irreversible capacity loss that results from cycling is also measured.
BERMUDA-2DN: a two-dimensional neutron transport code
A two-dimensional neutron transport code BERMUDA-2DN has been developed from the one-dimensional code PALLAS-TS (BERMUDA-1DN). The purpose of the present code is to analyze the fusion blanket neutronics experiments for plane or cylindrical assemblies, and to establish a basis of an accurate shielding analysis system for fusion and fission reactors. The time-independent transport equation is solved for two-dimensional, cylindrical, multi-regional geometry using the direct integration method in a multigroup model. In addition, group-angle transfer matrices are accurately obtained from the double-differential cross section data, without the Legendre polynomial expansion, but with the energy and scattering angle correlation. As to group constants, user is able to choose a 120-group or a 46-group library. For angular discrete ordinates, a set of 40 points is fixed over the hemisphere drawn by unit direction vectors. Not only latitudes but also longitudes (as the boundaries of the angular regions on the unit sphere) are taken into account for the calculation of the group-angle transfer matrices. For the fixed point source located at the origin of (r,z) coordinates, the uncollided flux is obtained at each spatial mesh point using the usual point kernel. The transport equation is solved for the first collision source from the uncollided flux plus the slowing down source from upper groups. Thus, the angular flux distribution is obtained as the sum of the solution and the uncollided flux values. At an intense D-T neutron source FNS, measurements were performed on the angular dependence of leakage spectra from Li2O slab assemblies. The present code has been tested by analyzing the measured spectra. The results have shown to represent fairly well the observed values. (author)
A transportable neutron radiography system based on a SbBe neutron source
Fantidis, J.G. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece); Nicolaou, G.E. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece)], E-mail: nicolaou@ee.duth.gr; Tsagas, N.F. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece)
2009-07-21
A transportable neutron radiography system, incorporating a SbBe neutron source, has been simulated using the MCNPX code. Design provisions have allowed two radiography systems to be utilised using the same SbBe neutron source. In this respect, neutron radiographies can be carried out using the photoneutrons produced when the {sup 124}Sb is surrounded by the Be target. Alternatively, {gamma}-radiography can be utilised with the photons from the {sup 124}Sb with the target removed. Appropriate collimators were simulated for each of the radiography modes. Apart from Be, the materials considered were compatible with the European Union Directive on 'Restriction of Hazardous Substances' (RoHS) 2002/95/EC, hence excluding the use of cadmium and lead. Bismuth was chosen as the material for {gamma}-radiation shielding and the proposed system allowed a maximum activity of the {sup 124}Sb up to 1.85x10{sup 13} Bq. The system simulated allows different object sizes to be studied with a wide range of radiography parameters.
A transportable neutron radiography system based on a SbBe neutron source
A transportable neutron radiography system, incorporating a SbBe neutron source, has been simulated using the MCNPX code. Design provisions have allowed two radiography systems to be utilised using the same SbBe neutron source. In this respect, neutron radiographies can be carried out using the photoneutrons produced when the 124Sb is surrounded by the Be target. Alternatively, γ-radiography can be utilised with the photons from the 124Sb with the target removed. Appropriate collimators were simulated for each of the radiography modes. Apart from Be, the materials considered were compatible with the European Union Directive on 'Restriction of Hazardous Substances' (RoHS) 2002/95/EC, hence excluding the use of cadmium and lead. Bismuth was chosen as the material for γ-radiation shielding and the proposed system allowed a maximum activity of the 124Sb up to 1.85x1013 Bq. The system simulated allows different object sizes to be studied with a wide range of radiography parameters.
Current status of the PSG Monte Carlo neutron transport code
PSG is a new Monte Carlo neutron transport code, developed at the Technical Research Centre of Finland (VTT). The code is mainly intended for fuel assembly-level reactor physics calculations, such as group constant generation for deterministic reactor simulator codes. This paper presents the current status of the project and the essential capabilities of the code. Although the main application of PSG is in lattice calculations, the geometry is not restricted in two dimensions. This paper presents the validation of PSG against the experimental results of the three-dimensional MOX fuelled VENUS-2 reactor dosimetry benchmark. (authors)
MINARET: Towards a time-dependent neutron transport parallel solver
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
On eigenvalue problems of the one-speed neutron transport equation for isotropic scattering
Highlights: • We consider isoperimetric inequalities for the one-speed neutron transport equation. • A ball will be a minimizer domain of the first eigenvalue. • We prove the Rayleigh–Faber–Krahn inequality for the neutron transport equation. - Abstract: In this paper, we consider eigenvalue problems of the one-speed neutron transport equation with isotropic scattering in a steady state and prove the Rayleigh–Faber–Krahn type inequality for the first eigenvalue
Structures of the fractional spaces generated by the difference neutron transport operator
The initial boundary value problem for the neutron transport equation is considered. The first, second and third order of accuracy difference schemes for the approximate solution of this problem are presented. Highly accurate difference schemes for neutron transport equation based on Padé approximation are constructed. In applications, stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained.The positivity of the neutron transport operator in Slobodeckij spaces is proved. Numerical techniques are developed and algorithms are tested on an example in MATLAB
It is shown that the combination of 3D neutron transport calculations and the results from activation foil measurements at a limited number of locations in a materials testing irradiation experiment can provide information at any position in the experiment for detailed neutron dosimetry and damage analysis. 4 refs
Benchmarking of neutron production of heavy-ion transport codes
Document available in abstract form only, full text of document follows: Accurate prediction of radiation fields generated by heavy ion interactions is important in medical applications, space missions, and in design and operation of rare isotope research facilities. In recent years, several well-established computer codes in widespread use for particle and radiation transport calculations have been equipped with the capability to simulate heavy ion transport and interactions. To assess and validate these capabilities, we performed simulations of a series of benchmark-quality heavy ion experiments with the computer codes FLUKA, MARS15, MCNPX, and PHITS. We focus on the comparisons of secondary neutron production. Results are encouraging; however, further improvements in models and codes and additional benchmarking are required. (authors)
Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport
Blattnig, S.R.; Slaba, T.C.; Heinbockel, J.H.
2008-01-01
Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.
Approximation theory and homogenization for neutron transport processes
In practical calculation of reactor systems homogenization is performed by some techniques mostly based on intuition and there is no uniquely accepted approach to this problem. In the first part of the paper an attempt is made to formulate mathematical basis of homogenization for the neutron diffusion and transport equations using recent developments in this field. The boundary value problems for both equations for non smooth H - periodic coefficients are related to appropriate variational problems stated in terms of bilinear forms. The behaviour of the solutions for H → 0 is investigated under various assumptions concerning a limit process to get the coefficients of homogenized equations. In the second part of the paper the assymptotic equivalence of the neutron diffusion to the transport equation is studied. The relation between homogenization procedures for both equations is also examined. As an example, the deriviation of the equations of homogenization in the case of hexagonal geometry typical for V.V.E.R. reactor is given. The obtained formulae for so called effective diffusion coefficient are analyzed for various types of lattices. (author)
Discontinuous finite element formulations for neutron transport in spherical geometry
Highlights: • We developed linear and quadratic discontinuous finite element methods in sphere. • We found that quadratic discontinuous finite element method is the best method. • Quadratic method has the desired convergence properties. • Smallest L2 error norms are obtained in scalar fluxes if quadratic method is used. - Abstract: We have developed the linear and quadratic Galerkin discontinuous finite element methods for the solution of both time-independent and time-dependent spherical geometry neutron transport problems. Discrete ordinates method is used for the angular discretization while the implicit method is utilized for temporal discretization in time-dependent problems. In order to assess the relative performance of the newly developed linear and quadratic discontinuous finite element spatial differencing methods relative to the previously developed linear discontinuous finite element and diamond difference discretizations, a computer code is developed and numerical solutions of the neutron transport equation for some benchmark problems are obtained. These numerical applications reveal that the newly developed quadratic discontinuous finite element method produces the most accurate results while the newly developed linear discontinuous finite element method follows as the second best discontinuous finite element method
PALLAS-TS: a one-dimensional neutron transport code for analyzing fusion blanket neutronics
The one-dimensional neutron transport code PALLAS-TS has been developed for solving the transport equation by direct numerical integration method. Group-transference kernels are accurately obtained from the double-differential cross section data using the energy and scattering angle correlation relation for elastic and inelastic (discrete levels) scattering. In addition, a usual multigroup model is adopted in calculation of spatial and angular flux distribution so as to make it possible to use iteration technique with neutron rebalancing in each group. This code uses a 120-group data library for 29 nuclides prepared temporarily by processing the ENDF/B-IV file, though the nuclear data file available now is incomplete for accounting fully the anisotropy of scattering. Results of test calculation for a 4-region system consisting of lithium and carbon were compared with the P5-S8 calculations by the ANISN code. The present code is the first trial of incorporating the multigroup to the direct integration method for solving the transport equation. It is observed that computing time by this code is shorter than that of the usual S sub(n) method by a factor of 2 or 3. (author)
Subroutines to Simulate Fission Neutrons for Monte Carlo Transport Codes
Lestone, J P
2014-01-01
Fortran subroutines have been written to simulate the production of fission neutrons from the spontaneous fission of 252Cf and 240Pu, and from the thermal neutron induced fission of 239Pu and 235U. The names of these four subroutines are getnv252, getnv240, getnv239, and getnv235, respectively. These subroutines reproduce measured first, second, and third moments of the neutron multiplicity distributions, measured neutron-fission correlation data for the spontaneous fission of 252Cf, and measured neutron-neutron correlation data for both the spontaneous fission of 252Cf and the thermal neutron induced fission of 235U. The codes presented here can be used to study the possible uses of neutron-neutron correlations in the area of transparency measurements and the uses of neutron-neutron correlations in coincidence neutron imaging.
Highlights: ► We have extended the KAERI library generation system to include gamma cross section generation capability. ► A gamma transport/diffusion calculation module has been implemented in KARMA 1.2. ► The computational results for benchmark problems show that the gamma library and gamma simulation in KARMA are reasonable. - Abstract: KAERI has developed a lattice transport calculation code KARMA (Kernel Analyzer by Ray-tracing Method for fuel Assembly) and its library generation system. Recently, the library generation system has been extended to include a gamma cross section generation capability and a gamma transport/diffusion calculation module has been implemented in KARMA 1.2. The method of characteristics for the neutron transport calculation to estimate eigenvalue has been utilized to predict gamma flux distribution and energy deposition. In addition, the coarse mesh finite difference method with diffusion approximation has also been utilized to estimate gamma flux distribution and energy depositions for each coarse mesh with homogenized pins as a computationally efficient alternative. This paper describes the procedure to generate neutron induced gamma production and gamma cross section data, and the methods to predict gamma flux distribution, gamma energy deposition and gamma smeared pin power distribution. The computational results for benchmark problems show that the gamma library and gamma simulation in KARMA are reasonable. And it is noted that gamma smeared power distributions predicted by coarse mesh diffusion calculation are very accurate compared to the results of transport calculation
Transport calculations for a 14.8 MeV neutron beam in a water phantom
A coupled neutron/photon Monte Carlo radiation transport code (MORSE-CG) has been used to calculate neutron and photon doses in a water phantom irradiated by 14.8 MeV neutrons from the Gas Target Neutron Source. The source-collimator-phantom geometry was carefully simulated. Results of calculations utilizing two different statistical estimators (next-collision and track-length) are presented
Birman-Schwinger principle and Nelkin conjecture theory of neutron transport
Stepin, S A
2001-01-01
The work is dedicated to studying the spectral properties of the operator model, appearing in the neutron transport theory. The operator L under the consideration, corresponds to the Boltzmann linearized equation, describing the neutron transport in the uniform medium with the isotopic distribution of the scattered neutrons. The effective evaluation of the number of the operator L eigenvalues, confirming and quantitatively supplementing the Nelkin hypothesis, is obtained
Parallel computing for homogeneous diffusion and transport equations in neutronics
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
Finite element based composite solution for neutron transport problems
A finite element treatment for solving neutron transport problems is presented. The employs region-wise discontinuous finite elements for the spatial representation of the neutron angular flux, while spherical harmonics are used for directional dependence. Composite solutions has been obtained by using different orders of angular approximations in different parts of a system. The method has been successfully implemented for one dimensional slab and two dimensional rectangular geometry problems. An overall reduction in the number of nodal coefficients (more than 60% in some cases as compared to conventional schemes) has been achieved without loss of accuracy with better utilization of computational resources. The method also provides an efficient way of handling physically difficult situations such as treatment of voids in duct problems and sharply changing angular flux. It is observed that a great wealth of information about the spatial and directional dependence of the angular flux is obtained much more quickly as compared to Monte Carlo method, where most of the information in restricted to the locality of immediate interest. (author)
Neutron transport and Montecarlo method: analysis and revision
The resolution of the neutron transport equation by the Montecarlo method is presented. Coming from an extensive discussion on the best formulation of that equation in order to be treated through the mentioned method, the theoretical bases of the estimator and random-walk generation is extensively explained. The most general expression for the estimators in different physical situations, each with a diverse random-walk, is included in this basical theoretical part. Furthemore, a large revision on the variance reduction methods is made. Its theoretical presentation is claimed to be in connection with the need for each one of them. The use of the adjoint equation, as a part of the importance sampling, Russian Roulette, splitting, exponential transform, conditional and correlated Montecarlo, and one-collision and next-event extimators, are discussed. Finally, come comments in the presentation of the last works on the theoretical prediction of errors in the generation of estimators-random walks are made. (author)
Tracking soil transport to sugarcane industry using neutron activation analysis
Soil as mineral impurity in sugarcane loads impacts the Brazilian sugar-ethanol industry with rising production and maintenance costs as well as decreased productivity. The mechanical harvesting of sugarcane was conceived as a technology with potential to increase the raw material quality thereby has been gradually replacing manual harvesting throughout the country. Instrumental neutron activation analysis was applied for determination of soil tracers in order to compare the performance of both harvesting systems in terms of mineral impurities. There were no significant differences in the amount of soil transported to sugarcane industry despite the technological progress aggregated to mechanical harvesting. However, for both harvesting systems there were significant differences on the amount of such mineral impurity between clay and sandy soils. (author)
Approximate solution to neutron transport equation with linear anisotropic scattering
A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)
Massively parallel performance of neutron transport response matrix algorithms
Massively parallel red/black response matrix algorithms for the solution of within-group neutron transport problems are implemented on the Connection Machines-2, 200 and 5. The response matrices are dericed from the diamond-differences and linear-linear nodal discrete ordinate and variational nodal P3 approximations. The unaccelerated performance of the iterative procedure is examined relative to the maximum rated performances of the machines. The effects of processor partitions size, of virtual processor ratio and of problems size are examined in detail. For the red/black algorithm, the ratio of inter-node communication to computing times is found to be quite small, normally of the order of ten percent or less. Performance increases with problems size and with virtual processor ratio, within the memeory per physical processor limitation. Algorithm adaptation to courser grain machines is straight-forward, with total computing time being virtually inversely proportional to the number of physical processors. (orig.)
Parallel processing of neutron transport in fuel assembly calculation
Group constants, which are used for reactor analyses by nodal method, are generated by fuel assembly calculations based on the neutron transport theory, since one or a quarter of the fuel assembly corresponds to a unit mesh in the current nodal calculation. The group constant calculation for a fuel assembly is performed through spectrum calculations, a two-dimensional fuel assembly calculation, and depletion calculations. The purpose of this study is to develop a parallel algorithm to be used in a parallel processor for the fuel assembly calculation and the depletion calculations of the group constant generation. A serial program, which solves the neutron integral transport equation using the transmission probability method and the linear depletion equation, was prepared and verified by a benchmark calculation. Small changes from the serial program was enough to parallelize the depletion calculation which has inherent parallel characteristics. In the fuel assembly calculation, however, efficient parallelization is not simple and easy because of the many coupling parameters in the calculation and data communications among CPU's. In this study, the group distribution method is introduced for the parallel processing of the fuel assembly calculation to minimize the data communications. The parallel processing was performed on Quadputer with 4 CPU's operating in NURAD Lab. at KAIST. Efficiencies of 54.3 % and 78.0 % were obtained in the fuel assembly calculation and depletion calculation, respectively, which lead to the overall speedup of about 2.5. As a result, it is concluded that the computing time consumed for the group constant generation can be easily reduced by parallel processing on the parallel computer with small size CPU's
Angular dependent rebalance method for solving the neutron transport equation
The behavior of neutrons in a medium is described mathematically by the Boltzmann transport equation. But the equation cannot be solved analytically even in one-dimensional geomerties. Therefore, for most realistic neutron transport problems and all production transport codes, the transport equation is numerically solved through discretization of the variables. To solve the discretized transport equation, the most widely used method is a form of Von Neumann's series solution referred to as iteration on the scattering source. It is simply called as the scattering source iteration (SI) method. However, it is well known that the scattering source iteration method converges arbitrary slowly for highly scattering dominant problems. Hence, many techniques for accelerating the scattering source iteration have been developed. Typically, the acceleration method consists of two equations. The first is the higher-order equation that is the general discretized transport equation and the second is the lower-order equation that improves the result of the higher-order equation. The most popular lower-order equation is the diffusion equation that is derived based on consistency with the higher-order equation. This type of methods are called as the diffusion synthetic acceleration method (DSA). Although this type of methods works very effectively, it is very difficult to devise diffusion acceleration equations that are both effective at reducing iteration counts and easy to solve computationally. Also, implementing the DSA method in an existing transport code usually requires a significant effort. The difficulty in solving the diffusion equation relative to that of the transport equation increases with additional spatial dimensions. This further complicates the task of devising efficient DSA methods for multidimensional problems. Also, development of new transport methods requires a complicated effort in deriving DSA equations or may be impossible to derive DSA equations. The
Neutron transport validation of variational nodal subelement methods
The properties of whole-core neutron transport computations are discussed and the shortcomings of present methods resulting from spatial homogenization at the fuel-pin cell and the fuel assembly levels examined. To eliminate spatial homogenization errors the variational nodal method implemented in the VARIANT code is generalized to perform full core transport calculations without spatial homogenization of cross sections at either the fuel-pin cell or fuel assembly level. The node size is chosen to correspond to one fuel-pin cell in the radial plane. Each node is divided into triangular finite subelements, with the interior spatial flux distribution represented by continuous, piecewise linear trial functions. The step change in the cross sections at the fuel-coolant interface can thus be represented explicitly in global calculations while retaining the full spherical harmonics capability of VARIANT. The resulting method is applied to a two-dimensional seven-group representation of a LWR containing MOX fuel assemblies. The accuracy of eigenvalues and peak pin powers and the CPU times are examined for various space-angle approximations. Monte Carlo reference solutions provide a basis for assessment. (author)
Experimental validation of a coupled neutron-photon inverse radiation transport solver
Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.
Subroutines to Simulate Fission Neutrons for Monte Carlo Transport Codes
Lestone, J. P.
2014-01-01
Fortran subroutines have been written to simulate the production of fission neutrons from the spontaneous fission of 252Cf and 240Pu, and from the thermal neutron induced fission of 239Pu and 235U. The names of these four subroutines are getnv252, getnv240, getnv239, and getnv235, respectively. These subroutines reproduce measured first, second, and third moments of the neutron multiplicity distributions, measured neutron-fission correlation data for the spontaneous fission of 252Cf, and meas...
Neutron and photon transport calculations in fusion system. 2
Sato, Satoshi [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
1998-03-01
On the application of MCNP to the neutron and {gamma}-ray transport calculations for fusion reactor system, the wide range design calculation has been carried out in the engineering design activities for the international thermonuclear fusion experimental reactor (ITER) being developed jointly by Japan, USA, EU and Russia. As the objects of shielding calculation for fusion reactors, there are the assessment of dose equivalent rate for living body shielding and the assessment of the nuclear response for the soundness of in-core structures. In the case that the detailed analysis of complicated three-dimensional shapes is required, the assessment using MCNP has been carried out. Also when the nuclear response of peripheral equipment due to the gap streaming between blanket modules is evaluated with good accuracy, the calculation with MCNP has been carried out. The analyses of the shieldings for blanket modules and NBI port are explained, and the examples of the results of analyses are shown. In the blanket modules, there are penetrating holes and continuous gap. In the case of the NBI port, shielding plug cannot be installed. These facts necessitate the MCNP analysis with high accuracy. (K.I.)
Cooperative learning of neutron diffusion and transport theories
A cooperative group instructional strategy is being used to teach a unit on neutron transport and diffusion theory in a first-year-graduate level, Reactor Theory course that was formerly presented in the traditional lecture/discussion style. Students are divided into groups of two or three for the duration of the unit. Class meetings are divided into traditional lecture/discussion segments punctuated by cooperative group exercises. The group exercises were designed to require the students to elaborate, summarize, or practice the material presented in the lecture/discussion segments. Both positive interdependence and individual accountability are fostered by adjusting individual grades on the unit exam by a factor dependent upon group achievement. Group collaboration was also encouraged on homework assignments by assigning each group a single grade on each assignment. The results of the unit exam have been above average in the two classes in which the cooperative group method was employed. In particular, the problem solving ability of the students has shown particular improvement. Further,the students felt that the cooperative group format was both more educationally effective and more enjoyable than the lecture/discussion format
Neutron spectrum obtained with Monte Carlo and transport theory
The development of the computer, resulting in increasing memory capacity and processing speed, has enabled the application of Monte Carlo method to estimate the fluxes in thousands of fine bin energy structure. Usually the MC calculation is made using continuous energy nuclear data and exact geometry. Self shielding and interference of nuclides resonances are properly considered. Therefore, the fluxes obtained by this method may be a good estimation of the neutron energy distribution (spectrum) for the problem. In an early work it was proposed to use these fluxes as weighting spectrum to generate multigroup cross section for fast reactor analysis using deterministic codes. This non-traditional use of MC calculation needs a validation to gain confidence in the results. The work presented here is the validation start step of this scheme. The spectra of the JOYO first core fuel assembly MK-I and the benchmark Godiva were calculated using the tally flux estimator of the MCNP code and compared with the reference. Also, the two problems were solved with the multigroup transport theory code XSDRN of the AMPX system using the 171 energy groups VITAMIN-C library. The spectra differences arising from the utilization of these codes, the influence of evaluated data file and the application to fast reactor calculation are discussed. (author)
Adjacent-cell preconditioners for accelerating multidimensional neutron transport methods
The Adjacent-cell Preconditioner (AP) is derived for accelerating generic fixed-weight, Weighted Diamond Difference (WDD) neutron transport methods in multidimensional Cartesian geometry. The AP is determined by requiring: (a) the eigenvalue of the combined mesh sweep-AP iterations to vanish in the vicinity of the origin in Fourier space; and (b) the diagonal and off-diagonal elements of the preconditioner to satisfy a diffusion-like condition. The spectra of the resulting iterations for a wide range of problem parameters exhibit a spectral radius smaller than .25, that vanishes implying immediate convergence for very large computational cells. More importantly, unlike other unconditionally stable acceleration schemes, the AP is cell-centered and its spectral radius remains small when the cell aspect ratio approaches 0 or ∞. Testing of the AP and comparison of its rate of convergence to the standard Source Iterations (SI) for Burre's Suite of Test Problems (BSTeP) demonstrates its high efficiency in reducing the number of iterations required to achieve convergence, especially for optically thick cells where acceleration is most needed
Transport calculation of neutron flux distribution in reflector of PW reactor
Two-dimensional transport calculation of the neutron flux and spectrum in the equatorial plain of PW reactor, using computer program DOT 3, is presented. Results show significant differences between neutron fields in which test samples and reactor vessel are exposed. (author)
MCNP, a general Monte Carlo code for neutron and photon transport: a summary
The general-purpose Monte Carlo code MCNP can be used for neutron, photon, or coupled neutron-photon transport, including the capability to calculate eigenvalues for critical systems. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and some special fourth-degree surfaces
D. W. Nigg; J. K. Hartwell; J. R. Venhuizen; C. A. Wemple; R. Risler; G. E. Laramore; W. Sauerwein; G. Hudepohl; A. Lennox
2006-06-01
The Idaho National Laboratory (INL), the University of Washington (UW) Neutron Therapy Center, the University of Essen (Germany) Neutron Therapy Clinic, and the Northern Illinois University(NIU) Institute for Neutron Therapy at Fermilab have been collaborating in the development of fast-neutron therapy (FNT) with concurrent neutron capture (NCT) augmentation [1,2]. As part of this effort, we have conducted measurements to produce suitable benchmark data as an aid in validation of advanced three-dimensional treatment planning methodologies required for successful administration of FNT/NCT. Free-beam spectral measurements as well as phantom measurements with Lucite{trademark} cylinders using thermal, resonance, and threshold activation foil techniques have now been completed at all three clinical accelerator facilities. The same protocol was used for all measurements to facilitate intercomparison of data. The results will be useful for further detailed characterization of the neutron beams of interest as well as for validation of various charged particle and neutron transport codes and methodologies for FNT/NCT computational dosimetry, such as MCNP [3], LAHET [4], and MINERVA [5].
Calculation of neutron transport in plane geometry by invariant imbedding method
A practical combination of invariant imbedding and transfer matrix methods was displayed in this paper. A very simple scheme for neutron transport analysis was obtained for slab materials and some results of numerical calculations are presented. (author)
The LTSN formulation is extended to the neutron transport equation in slab geometry is anisotropic scattering of second order and one group of energy. The procedure consists in the LTSN matrix decomposition. Numerical results are presented. (author)
Extension of the high charge and energy (HZE) transport computer program HZETRN for angular transport of neutrons is considered. For this paper, only light ion transport, He4 and lighter, will be analyzed using a pure solar proton source. The angular transport calculator is the ANISN/PC program which is being controlled by the HZETRN program. The neutron flux values are compared for straight-ahead transport and angular transport in one dimension. The shield material is aluminum and the target material is water. The thickness of these materials is varied; however, only the largest model calculated is reported which is 50 gm/cm2 of aluminum and 100 gm/cm2 of water. The flux from the ANISN/PC calculation is about two orders of magnitude lower than the flux from HZETRN for very low energy neutrons. It is only a magnitude lower for the neutrons in the 10 to 20 MeV range in the aluminum and two orders lower in the water. The major reason for this difference is in the transport modes: straight-ahead versus angular. The angular treatment allows a longer path length than the straight-ahead approximation. Another reason is the different cross section sets used by the ANISN/PC-BUGLE-80 mode and the HZETRN mode. The next step is to investigate further the differences between the two codes and isolate the differences to just the angular versus straight-ahead transport mode. Then, create a better coupling between the angular neutron transport and the charged particle transport
PHISICS multi-group transport neutronic capabilities for RELAP5
Epiney, A.; Rabiti, C.; Alfonsi, A.; Wang, Y.; Cogliati, J.; Strydom, G. [Idaho National Laboratory (INL), 2525 N. Fremont Ave., Idaho Falls, ID 83402 (United States)
2012-07-01
PHISICS is a neutronic code system currently under development at INL. Its goal is to provide state of the art simulation capability to reactor designers. This paper reports on the effort of coupling this package to the thermal hydraulic system code RELAP5. This will enable full prismatic core and system modeling and the possibility to model coupled (thermal-hydraulics and neutronics) problems with more options for 3D neutron kinetics, compared to the existing diffusion theory neutron kinetics module in RELAP5 (NESTLE). The paper describes the capabilities of the coupling and illustrates them with a set of sample problems. (authors)
Measurements of neutron pulse time-width and intensity have been carried out on grids of small moderators placed side by side and decoupled by cadmium strips; a moderator concept introduced by the authors through previous publications. Transport calculations are based on the standard reactor code DOT 3.5 with the ENDF-B IV nuclear data library. (orig.)
Transport calculation of thermal and cold neutrons using NMTC/JAERI-MCNP4A code system
Iga, Kiminori [Kyushu Univ., Fukuoka (Japan); Takada, Hiroshi; Nagao, Tadashi
1998-01-01
In order to investigate the applicability of the NMTC/JAERI-MCNP4A code system to the neutronics design study in the neutron science research project of JAERI, transport calculations of thermal and cold neutrons are performed with the code system on a spallation neutron source composed of light water cooled tantalum target with a moderator and a reflector system. The following neutronic characteristics are studied in the calculation : the variation of the intensity of neutrons emitted from a light water moderator or a liquid hydrogen with/without the B{sub 4}C decoupler, which are installed to produce sharp pulse, and that dependent on the position of external source neutrons in the tantalum target. The calculated neutron energy spectra are reproduced well by the semi-empirical formula with the parameter values reliable in physical meanings. It is found to be necessary to employ proper importance sampling technique in the statistics. It is confirmed from this work that the NMTC/JAERI-MCNP4A code system is applicable to the neutronics design study of spallation neutron sources proposed for the neutron science research project. (author)
On the neutron-noise transmission studies for non-multiplying media using transport theory
This paper reports the results of our investigations on the neutron-noise transmission characteristics of non-multiplying media using transport theory. The study has been carried out systematically by first considering the infinite medium case for monoenergetic neutrons and then extending it to the finite media, multigroup and anisotropic scattering cases. The results are particularly related with the problems and prospects of the neutron-noise studies by excore detectors in fast reactors and would be particularly useful in developing the technology of malfunction detection by neutron-noise methods. (author)
Monte Carlo method is widely used for solving neutron transport equation. Basically Monte Carlo method treats continuous angle, space and energy. It gives very accurate solution when enough many particle histories are used, but it takes too long computation time. To reduce computation time, discrete Monte Carlo method was proposed. It is called Discrete Transport Monte Carlo (DTMC) method. It uses discrete space but continuous angle in mono energy one dimension problem and uses lump, linear-discontinuous (LLD) equation to make probabilities of leakage, scattering, and absorption. LLD may cause negative angular fluxes in highly scattering problem, so two scatter variance reduction method is applied to DTMC and shows very accurate solution in various problems. In transport Monte Carlo calculation, the particle history does not end for scattering event. So it also takes much computation time in highly scattering problem. To further reduce computation time, Discrete Diffusion Monte Carlo (DDMC) method is implemented. DDMC uses diffusion equation to make probabilities and has no scattering events. So DDMC takes very short computation time comparing with DTMC and shows very well-agreed results with cell-centered diffusion results. It is known that diffusion result may not be good in boundaries. So in hybrid method of DTMC and DDMC, boundary regions are calculated by DTMC and the other regions are calculated by DDMC. In this thesis, DTMC, DDMC and hybrid methods and their results of several problems are presented. The results show that DDMC and DTMC are well agreed with deterministic diffusion and transport results, respectively. The hybrid method shows transport-like results in problems where diffusion results are poor. The computation time of hybrid method is between DDMC and DTMC, as expected
Analytical benchmarks for nuclear engineering applications. Case studies in neutron transport theory
Preservation of know-how in the nuclear field is promoted through the activities of the OECD Nuclear Energy Agency Data Bank. One area of importance concerns methods for solving radiation transport problems, especially with regard to neutrons. This handbook (in the form of a case study), prepared by Barry D Ganapol, is the result of such an initiative. It is a compilation of solutions to the transport equation for which analytical representations can be found. It is designed for educational use in courses on analytical transport methods and numerical methods with application to reactor physics. In addition, it contains elements for the continuous improvement of transport methods and for computer code verification. The areas of neutron slowing down, thermalization and one-, two- and three-dimensional neutron transport theory are covered. A series of training courses, based on this compilation of solutions has recently begun. (author)
Cosmic ray heliospheric transport study with neutron monitor data
Ahluwalia, H. S.; Ygbuhay, R. C.; Modzelewska, R.; Dorman, L. I.; Alania, M. V.
2015-10-01
Determining transport coefficients for galactic cosmic ray (GCR) propagation in the turbulent interplanetary magnetic field (IMF) poses a fundamental challenge in modeling cosmic ray modulation processes. GCR scattering in the solar wind involves wave-particle interaction, the waves being Alfven waves which propagate along the ambient field (B). Empirical values at 1 AU are determined for the components of the diffusion tensor for GCR propagation in the heliosphere using neutron monitor (NM) data. At high rigidities, particle density gradients and mean free paths at 1 AU in B can only be computed from the solar diurnal anisotropy (SDA) represented by a vector A (components Ar, Aϕ, and Aθ) in a heliospherical polar coordinate system. Long-term changes in SDA components of NMs (with long track record and the median rigidity of response Rm ~ 20 GV) are used to compute yearly values of the transport coefficients for 1963-2013. We confirm the previously reported result that the product of the parallel (to B) mean free path (λ||) and radial density gradient (Gr) computed from NM data exhibits a weak Schwabe cycle (11y) but strong Hale magnetic cycle (22y) dependence. Its value is most depressed in solar activity minima for positive (p) polarity intervals (solar magnetic field in the Northern Hemisphere points outward from the Sun) when GCRs drift from the polar regions toward the helioequatorial plane and out along the heliospheric current sheet (HCS), setting up a symmetric gradient Gθs pointing away from HCS. Gr drives all SDA components and λ|| Gr contributes to the diffusive component (Ad) of the ecliptic plane anisotropy (A). GCR transport is commonly discussed in terms of an isotropic hard sphere scattering (also known as billiard-ball scattering) in the solar wind plasma. We use it with a flat HCS model and the Ahluwalia-Dorman master equations to compute the coefficients α (=λ⊥/λ∥) and ωτ (a measure of turbulence in the solar wind) and transport
VVER-440 Ex-Core Neutron Transport Calculations by MCNP-5 Code and Comparison with Experiment
Ex-core neutron transport calculations are needed to evaluate radiation loading parameters (neutron fluence, fluence rate and spectra) on the in-vessel equipment, reactor pressure vessel (RPV) and support constructions of VVER type reactors. Due to these parameters are used for reactor equipment life-time assessment, neutron transport calculations should be carried out by precise and reliable calculation methods. In case of RPVs, especially, of first generation VVER-440s, the neutron fluence plays a key role in the prediction of RPV lifetime. Main part of VVER ex-core neutron transport calculations are performed by deterministic and Monte-Carlo methods. This paper deals with precise calculations of the Russian first generation VVER-440 by MCNP-5 code. The purpose of this work was an application of this code for expert calculations, verification of results by comparison with deterministic calculations and validation by neutron activation measured data. Deterministic discrete ordinates DORT code, widely used for RPV neutron dosimetry and many times tested by experiments, was used for comparison analyses. Ex-vessel neutron activation measurements at the VVER-440 NPP have provided space (in azimuth and height directions) and neutron energy (different activation reactions) distributions data for experimental (E) validation of calculated results. Calculational intercomparison (DORT vs. MCNP-5) and comparison with measured values (MCNP-5 and DORT vs. E) have shown agreement within 10-15% for different space points and reaction rates. The paper submits a discussion of results and makes conclusions about practice use of MCNP-5 code for ex-core neutron transport calculations in expert analysis. (authors)
Realistic simulations of the passage of fast neutrons through tissue require a large quantity of cross-sectional data. What are needed are differential (in particle type, energy and angle) cross sections. A computer code is described which produces such spectra for neutrons above ∼14 MeV incident on light nuclei such as carbon and oxygen. Comparisons have been made with experimental measurements of double-differential secondary charged-particle production on carbon and oxygen at energies from 27 to 60 MeV; they indicate that the model is adequate in this energy range. In order to utilize fully the results of these calculations, they should be incorporated into a neutron transport code. This requires defining a generalized format for describing charged-particle production, putting the calculated results in this format, interfacing the neutron transport code with these data, and charged-particle transport. The design and development of such a program is described. 13 refs., 3 figs
Spin diffusive modes and thermal transport in neutron star crusts
Sedrakian, Armen
2015-01-01
In this contribution we first review a method for obtaining the collective modes of pair-correlated neutron matter as found in a neutron star inner crust. We discuss two classes of modes corresponding to density and spin perturbations with energy spectra $\\omega = \\omega_0 + \\alpha q^2$, where $\\omega_0 = 2\\Delta$ is the threshold frequency and $\\Delta$ is the gap in the neutron fluid spectrum. For characteristic values of Landau parameters in neutron star crusts the exitonic density modes have $\\alpha 0$ and they exist above $\\omega_0$ which implies that these modes are damped. As an application of these findings we compute the thermal conductivity due to spin diffusive modes and show that it scales as $T^{1/2} \\exp(-2\\omega_0/T)$ in the case where their two-by-two scattering cross-section is weakly dependent on temperature.
Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media
2014-01-01
We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.
Resolution of the neutron transport equation by massively parallel computer in the Cronos code
The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)
The infinite medium Green's function for neutron transport in plane geometry 40 years later
In 1953, the first of what was supposed to be two volumes on neutron transport theory was published. The monograph, entitled open-quotes Introduction to the Theory of Neutron Diffusionclose quotes by Case et al., appeared as a Los Alamos National Laboratory report and was to be followed by a second volume, which never appeared as intended because of the death of Placzek. Instead, Case and Zweifel collaborated on the now classic work entitled Linear Transport Theory 2 in which the underlying mathematical theory of linear transport was presented. The initial monograph, however, represented the coming of age of neutron transport theory, which had its roots in radiative transfer and kinetic theory. In addition, it provided the first benchmark results along with the mathematical development for several fundamental neutron transport problems. In particular, one-dimensional infinite medium Green's functions for the monoenergetic transport equation in plane and spherical geometries were considered complete with numerical results to be used as standards to guide code development for applications. Unfortunately, because of the limited computational resources of the day, some numerical results were incorrect. Also, only conventional mathematics and numerical methods were used because the transport theorists of the day were just becoming acquainted with more modern mathematical approaches. In this paper, Green's function solution is revisited in light of modern numerical benchmarking methods with an emphasis on evaluation rather than theoretical results. The primary motivation for considering the Green's function at this time is its emerging use in solving finite and heterogeneous media transport problems
Application of neutron/gamma transport codes for the design of explosive detection systems
Applications of neutron and gamma transport codes to the design of nuclear techniques for detecting concealed explosives material are discussed. The methodology of integrating radiation transport computations in the development, optimization and analysis phases of these new technologies is discussed. Transport and Monte Carlo codes are used for proof of concepts, guide the system integration, reduce the extend of experimental program and provide insight into the physical problem involved. The paper concentrates on detection techniques based on thermal and fast neutron interactions in the interrogated object. (authors). 6 refs., 1 tab., 5 figs
2008-01-01
A discrete ordinates method for a threedimensional first-order neutron transport equation based on unstructured-meshes that avoids the singularity of the second-order neutron transport equation in void regions was derived.The finite element variation equation was obtained using the least-squares method.A three-dimensional transport calculation code was developed.Both the triangular-z and the tetrahedron elements were included.The numerical results of some benchmark problems demonstrated that this method can solve neutron transport problems in unstructuredmeshes very well.For most problems,the error of the eigenvalue and the angular flux is less than 0.3% and 3.0% respectively.
Transport synthetic acceleration scheme for multi-dimensional neutron transport problems
The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)
TDTORT: Time-Dependent, 3-D, Discrete Ordinates, Neutron Transport Code System with Delayed Neutrons
1 - Description of program or function: TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation. TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. TDTORT reads ANISN-format cross-section libraries, which are not included in the package. Users may choose from several available in RSICC's data library collection which can be identified by the keyword 'ANISN FORMAT'. 2 - Methods:The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function. The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal
Experimental validation of a coupled neutron-photon inverse radiation transport solver
Forward radiation transport is the problem of calculating the radiation field given a description of the radiation source and transport medium. In contrast, inverse transport is the problem of inferring the configuration of the radiation source and transport medium from measurements of the radiation field. As such, the identification and characterization of special nuclear materials (SNM) is a problem of inverse radiation transport, and numerous techniques to solve this problem have been previously developed. The authors have developed a solver based on nonlinear regression applied to deterministic coupled neutron-photon transport calculations. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5-kg sphere of alpha-phase, weapons-grade plutonium. The source was measured in six different configurations: bare, and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses of 1.27, 2.54, 3.81, 7.62, and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to characterize the solver's ability to correctly infer the configuration of the source from its measured signatures.
In situ studies of mass transport in liquid alloys by means of neutron radiography.
Kargl, F; Engelhardt, M; Yang, F; Weis, H; Schmakat, P; Schillinger, B; Griesche, A; Meyer, A
2011-06-29
When in situ techniques became available in recent years this led to a breakthrough in accurately determining diffusion coefficients for liquid alloys. Here we discuss how neutron radiography can be used to measure chemical diffusion in a ternary AlCuAg alloy. Neutron radiography hereby gives complementary information to x-ray radiography used for measuring chemical diffusion and to quasielastic neutron scattering used mainly for determining self-diffusion. A novel Al(2)O(3) based furnace that enables one to study diffusion processes by means of neutron radiography is discussed. A chemical diffusion coefficient of Ag against Al around the eutectic composition Al(68.6)Cu(13.8)Ag(17.6) at.% was obtained. It is demonstrated that the in situ technique of neutron radiography is a powerful means to study mass transport properties in situ in binary and ternary alloys that show poor x-ray contrast. PMID:21654050
A study of a transportable thermal neutron radiography unit based on a compact RFI linac
A transportable thermal neutron radiography system, incorporating a compact proton accelerator as neutron source has been simulated using the MCNP4B code. The neutron source will be produced via the 7Li(p,n)7Be reactions by a 2.5 MeV, 10 mA proton beam into a thick lithium target. Variable values for the collimator ratio were calculated. Thermal neutron radiography parameters are comparable to the research nuclear reactors. Sapphire filter was treated in order to improve the results. Simple and advanced neutron shielding materials considered which was further enhanced with layers of bismuth. The system was compatible with the European Union Directive on 'Restriction of Hazardous Substances' (RoHS) 2002/95/EC, hence excluding the use of cadmium and lead. (author)
Risch, P.; Dekens, O.; Ait Abderrahim, H. [SCK-CEN, Fuel Research Department, (Belgium); Wouters, R. de [Tractebel, Energy Engineering, (Belgium)
1997-10-01
Neutron dosimetry experiments seem to point our difficulties in the treatment of large water thickness like those encountered between the core baffle and the pressure vessel. This paper describes the theoretical benchmark undertaken by EDF, SCK/CEN and TRACTEBEL ENERGY ENGINEERING, concerning the transport of fast neutrons throughout a one meter cube of water, located after a U-235 fission sources plate. The results showed no major discrepancies between the calculations up to 50 cm from the source, accepting that a P3 development of the Legendre polynomials is necessary for the Sn calculations. The main differences occurred after 50 cm, reaching 20 % at the end of the water cube. This results lead us to consider an experimental benchmark, dedicated to the problem of fast neutron deep penetration in water, which has been launched at SCK/CEN. (authors). 7 refs.
Development of deterministic transport methods for low energy neutrons for shielding in space
Ganapol, Barry
1993-01-01
Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in
Poveschenko, T.; Poveschenko, O. [RRC Kurchatov Inst., Kurchatov square, 1, 123182, Moscow (Russian Federation)
2012-07-01
This paper presents the new approach to creation of geometrical module for nuclear reactor neutron transport computer simulation analysis so called the differential cross method. It is elaborated for detecting boards between physical zones. It is proposed to use GMSH open source mesh editor extended by some features: a special option and a special kind of mesh (cubic background mesh).This method is aimed into Monte Carlo Method as well as for deterministic neutron transport methods. Special attention is attended for reactor core composed of a set of material zones with complicate geometrical boundaries. The idea of this approach is described. In general case method works for 3-D space. Algorithm of creation of the geometrical module is given. 2-D neutron transport benchmark-test for RBMK reactor cluster cell is described. It demonstrates the ability of this approach to provide flexible definition of geometrical meshing with preservation of curved surface or any level of heterogeneity. (authors)
This paper presents the new approach to creation of geometrical module for nuclear reactor neutron transport computer simulation analysis so called the differential cross method. It is elaborated for detecting boards between physical zones. It is proposed to use GMSH open source mesh editor extended by some features: a special option and a special kind of mesh (cubic background mesh).This method is aimed into Monte Carlo Method as well as for deterministic neutron transport methods. Special attention is attended for reactor core composed of a set of material zones with complicate geometrical boundaries. The idea of this approach is described. In general case method works for 3-D space. Algorithm of creation of the geometrical module is given. 2-D neutron transport benchmark-test for RBMK reactor cluster cell is described. It demonstrates the ability of this approach to provide flexible definition of geometrical meshing with preservation of curved surface or any level of heterogeneity. (authors)
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)
1996-12-31
The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
Improved Algorithms and Coupled Neutron-Photon Transport for Auto-Importance Sampling Method
Wang, Xin; Qiu, Rui; Li, Chun-Yan; Liang, Man-Chun; Zhang, Hui; Li, Jun-Li
2016-01-01
Auto-Importance Sampling (AIS) method is a Monte Carlo variance reduction technique proposed by Tsinghua University for deep penetration problem, which can improve computational efficiency significantly without pre-calculations for importance distribution. However AIS method is only validated with several basic deep penetration problems of simple geometries and cannot be used for coupled neutron-photon transport. This paper firstly presented the latest algorithm improvements for AIS method including particle transport, fictitious particles creation and adjustment, fictitious surface geometry, random number allocation and calculation of estimated relative error, which made AIS method applicable to complicated deep penetration problem. Then, a coupled Neutron-Photon Auto-Importance Sampling (NP-AIS) method was proposed to apply AIS method with the improved algorithms in coupled neutron-photon Monte Carlo transport. Finally, the NUREG/CR-6115 PWR benchmark model was calculated with the method of geometry splitti...
Analytical benchmarks for nuclear engineering applications. Case studies in neutron transport theory
The developers of computer codes involving neutron transport theory for nuclear engineering applications seldom apply analytical benchmarking strategies to ensure the quality of their programs. A major reason for this is the lack of analytical benchmarks and their documentation in the literature. The few such benchmarks that do exist are difficult to locate, as they are scattered throughout the neutron transport and radiative transfer literature. The motivation for this benchmark compendium, therefore, is to gather several analytical benchmarks appropriate for nuclear engineering applications under one cover. We consider the following three subject areas: neutron slowing down and thermalization without spatial dependence, one-dimensional neutron transport in infinite and finite media, and multidimensional neutron transport in a half-space and an infinite medium. Each benchmark is briefly described, followed by a detailed derivation of the analytical solution representation. Finally, a demonstration of the evaluation of the solution representation includes qualified numerical benchmark results. All accompanying computer codes are suitable for the PC computational environment and can serve as educational tools for courses in nuclear engineering. While this benchmark compilation does not contain all possible benchmarks, by any means, it does include some of the most prominent ones and should serve as a valuable reference. (author)
Computational Transport Modeling of High-Energy Neutrons Found in the Space Environment
Cox, Brad; Theriot, Corey A.; Rohde, Larry H.; Wu, Honglu
2012-01-01
The high charge and high energy (HZE) particle radiation environment in space interacts with spacecraft materials and the human body to create a population of neutrons encompassing a broad kinetic energy spectrum. As an HZE ion penetrates matter, there is an increasing chance of fragmentation as penetration depth increases. When an ion fragments, secondary neutrons are released with velocities up to that of the primary ion, giving some neutrons very long penetration ranges. These secondary neutrons have a high relative biological effectiveness, are difficult to effectively shield, and can cause more biological damage than the primary ions in some scenarios. Ground-based irradiation experiments that simulate the space radiation environment must account for this spectrum of neutrons. Using the Particle and Heavy Ion Transport Code System (PHITS), it is possible to simulate a neutron environment that is characteristic of that found in spaceflight. Considering neutron dosimetry, the focus lies on the broad spectrum of recoil protons that are produced in biological targets. In a biological target, dose at a certain penetration depth is primarily dependent upon recoil proton tracks. The PHITS code can be used to simulate a broad-energy neutron spectrum traversing biological targets, and it account for the recoil particle population. This project focuses on modeling a neutron beamline irradiation scenario for determining dose at increasing depth in water targets. Energy-deposition events and particle fluence can be simulated by establishing cross-sectional scoring routines at different depths in a target. This type of model is useful for correlating theoretical data with actual beamline radiobiology experiments. Other work exposed human fibroblast cells to a high-energy neutron source to study micronuclei induction in cells at increasing depth behind water shielding. Those findings provide supporting data describing dose vs. depth across a water-equivalent medium. This
Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes
Possibility of neutron transport cross section measurement in a sphere surrounded by moderation
The possibility of an estimation of the neutron macroscopic transport cross section for a medium with known adsorption cross section is presented. A two-region spherical system is used with the sample of interest as the inner sphere. The fundamental decay constant of the thermal neutron flux is calculated on the basis of diffusion theory for such a system as a function of the dimensions of the external sphere and/or the macroscopic absorption cross section of the inner medium. The influence of the diffusion cooling coefficient and the hydrogen content in the inner sphere on the transport cross section estimation is discussed. (author)
Multigroup neutron transport equation in the diffusion and P1 approximation
Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P1 approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P1 approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)
Effects of fuel particle size distributions on neutron transport in stochastic media
Highlights: • Effects of fuel particle size distributions on neutron transport are evaluated. • Neutron channeling is identified as the fundamental reason for the effects. • The effects are noticeable at low packing and low optical thickness systems. • Unit cells of realistic reactor designs are studied for different size particles. • Fuel particle size distribution effects are not negligible in realistic designs. - Abstract: This paper presents a study of the fuel particle size distribution effects on neutron transport in three-dimensional stochastic media. Particle fuel is used in gas-cooled nuclear reactor designs and innovative light water reactor designs loaded with accident tolerant fuel. Due to the design requirements and fuel fabrication limits, the size of fuel particles may not be perfectly constant but instead follows a certain distribution. This brings a fundamental question to the radiation transport computation community: how does the fuel particle size distribution affect the neutron transport in particle fuel systems? To answer this question, size distribution effects and their physical interpretations are investigated by performing a series of neutron transport simulations at different fuel particle size distributions. An eigenvalue problem is simulated in a cylindrical container consisting of fissile fuel particles with five different size distributions: constant, uniform, power, exponential and Gaussian. A total of 15 parametric cases are constructed by altering the fissile particle volume packing fraction and its optical thickness, but keeping the mean chord length of the spherical fuel particle the same at different size distributions. The tallied effective multiplication factor (keff) and the spatial distribution of fission power density along axial and radial directions are compared between different size distributions. At low packing fraction and low optical thickness, the size distribution shows a noticeable effect on neutron
A Monte Carlo Green's function method for three-dimensional neutron transport
This paper describes a Monte Carlo transport kernel capability, which has recently been incorporated into the RACER continuous-energy Monte Carlo code. The kernels represent a Green's function method for neutron transport from a fixed-source volume out to a particular volume of interest. This method is very powerful transport technique. Also, since kernels are evaluated numerically by Monte Carlo, the problem geometry can be arbitrarily complex, yet exact. This method is intended for problems where an ex-core neutron response must be determined for a variety of reactor conditions. Two examples are ex-core neutron detector response and vessel critical weld fast flux. The response is expressed in terms of neutron transport kernels weighted by a core fission source distribution. In these types of calculations, the response must be computed for hundreds of source distributions, but the kernels only need to be calculated once. The advance described in this paper is that the kernels are generated with a highly accurate three-dimensional Monte Carlo transport calculation instead of an approximate method such as line-of-sight attenuation theory or a synthesized three-dimensional discrete ordinates solution
Highlights: → Meyer's sub-space iteration method is used to evaluate dominant prompt time eigenvalues of neutron transport equation. → Mono-energetic 1-D benchmark problems are analysed. → The method is found to correctly compute complex eigenvalues also. - Abstract: The aim of this paper is to explore the use of Meyer's sub-space iteration (SSI) method for the evaluation of dominant prompt time-eigenvalues of the neutron transport equation. The integro-differential form of the transport equation is considered. The SSI method is known to be an efficient technique to find the dominant eigenvalues of a non-symmetric matrix. It has been earlier used for eigenvalue problems in neutron diffusion theory. However, it does not seem to be tried in the transport theory case. Here, the use of SSI has been tested in transport theory for some 1-D mono-energetic homogeneous and heterogeneous benchmark problems. The space variable is discretised by finite differencing while neutron directions are discretised by discrete ordinates (Sn-) method. The SSI method needs frequent multiplication of the relevant matrix operator with vectors. As known from earlier works in this area, this can be achieved in terms of external source calculations for which a 1-D programme was developed and used. With the availability of more versatile Sn-method codes, it may perhaps be possible to extend use of SSI to more realistic cases.
Flexible polyvinyl chloride neutron guides for transporting ultracold and very cold neutrons
Arzumanov, S. S., E-mail: sarzumanov@yandex.ru; Bondarenko, L. N. [Russian Research Center Kurchatov Institute (Russian Federation); Geltenbort, P. [Institut Laue-Langevin (France); Morozov, V. I. [Russian Research Center Kurchatov Institute (Russian Federation); Nesvizhevsky, V. V. [Institut Laue-Langevin (France); Panin, Yu. N.; Strepetov, A. N.; Chuvilin, D. Yu. [Russian Research Center Kurchatov Institute (Russian Federation)
2011-12-15
The transmission of ultracold neutrons (UCNs) through flexible polyvinyl chloride (PVC) tubes with lengths of up to 3 m and an internal diameter of 6-8 mm has been studied. High UCN transmission is found even for arbitrarily bent tubes (single bend, double bend, triple bend, figure eight, etc.). The transmission can be improved significantly by coating the inner surface of the tube with a thin layer of liquid fluorine polymer. The prospects of these neutron guides in fundamental and applied research are discussed.
Flexible polyvinyl chloride neutron guides for transporting ultracold and very cold neutrons
The transmission of ultracold neutrons (UCNs) through flexible polyvinyl chloride (PVC) tubes with lengths of up to 3 m and an internal diameter of 6–8 mm has been studied. High UCN transmission is found even for arbitrarily bent tubes (single bend, double bend, triple bend, figure eight, etc.). The transmission can be improved significantly by coating the inner surface of the tube with a thin layer of liquid fluorine polymer. The prospects of these neutron guides in fundamental and applied research are discussed.
PELAN - a transportable, neutron-based UXO identification technique
An elemental characterization method is used to differentiate between inert projectiles and UXO's. This method identifies in a non-intrusive, nondestructive manner, the elemental composition of the projectile contents. Most major and minor chemical elements within the interrogated object (hydrogen, carbon, nitrogen, oxygen, fluorine, phosphorus, chlorine, arsenic, etc.) are identified and quantified. The method is based on PELAN - Pulsed Elemental Analysis with Neutrons. PELAN uses pulsed neutrons produced from a compact, sealed tube neutron generator. Using an automatic analysis computer program, the quantities of each major and minor chemical element are determined. A decision-making tree identifies the object by comparing its elemental composition with stored elemental composition libraries of substances that could be contained within the projectile. In a series of blind tests, PELAN was able to identify without failure, the contents of each shell placed in front of it. The PELAN probe does not need to be in contact with the interrogated projectile. If the object is buried, the interrogation can take place in situ provided the probe can be inserted a few centimeters from the object's surface. (author)
Neutron absorber plate and radioactive material transportation cask
Aluminum alloy flame-coating layers are formed at the outer surface of a neutron absorber plate in order to prevent corrosion due to potential difference. However, pin holes of micron order are sometimes formed on the flame-coating membranes, which are hard to be found by usual inspection. Then, ferrous flame-coating membranes are formed at the outer surface of boron carbide and aluminum alloy flame-coating membranes are formed at the outer surface thereof. The outer surface of a boron carbide plate is coated with the ferrous flame-coating membranes instead of being coated with an external plate made of neutron cells, and an aluminum alloy flame-coating membranes or mixed flame-coating layers of aluminum oxide and titania are coated thereover in order to prevent rusts. Whether the pin holes are present or not can be confirmed easily by a ferroxyl test. If there are pin holes, flame-coating is applied again to form complete membranes. Then, since it is no more necessary to fix a neutron absorbing cell at the outer surface of a fuel cell by means of welding, production cost can be reduced. (N.H.)
A standard numerical procedure for the solution of singular integral equations is applied to the one-dimensional transport equation for monoenergetic neutrons. As is usual in quadrature methods, the procedure yields an Eigen system whose solution provide, for the critical slab, both the eigenvalue which is proportional to the number of secondary neutrons per collision, and the density as a function of position. The results obtained with two versions of the procedure, differing only in the extent of the basic region to which they are applied, are compared with analytically derived results available for benchmarking. The procedures considered yield consistent results for the calculated neutron densities and eigenvalues. Since the one-dimensional transport kernel and its spatial moments are integrable and their integrals can be put in terms of exponential integral functions, the resulting approximations to the neutron density yield somewhat lengthy but closed, forms. These approximate expressions of the neutron density can be used to render, after they are operated on, closed-form formulas for build-up factors, extrapolation distances or angular densities or employed for other purposes that require an analytical expression of the neutron density. As an example of this latter capability, the results of the calculation of the angular density at the surface of the slab are provided. (Author)
This work concerns calculation of a neutron response, caused by a neutron field perturbed by materials surrounding the source or the detector. Solution of a problem is obtained using coupling of the Monte Carlo radiation transport computation for the perturbed region and the discrete ordinates transport computation for the unperturbed system. (author). 62 refs
Quantifying moisture transport in cementitious materials using neutron radiography
Lucero, Catherine L.
A portion of the concrete pavements in the US have recently been observed to have premature joint deterioration. This damage is caused in part by the ingress of fluids, like water, salt water, or deicing salts. The ingress of these fluids can damage concrete when they freeze and expand or can react with the cementitious matrix causing damage. To determine the quality of concrete for assessing potential service life it is often necessary to measure the rate of fluid ingress, or sorptivity. Neutron imaging is a powerful method for quantifying fluid penetration since it can describe where water has penetrated, how quickly it has penetrated and the volume of water in the concrete or mortar. Neutrons are sensitive to light atoms such as hydrogen and thus clearly detect water at high spatial and temporal resolution. It can be used to detect small changes in moisture content and is ideal for monitoring wetting and drying in mortar exposed to various fluids. This study aimed at developing a method to accurately estimate moisture content in mortar. The common practice is to image the material dry as a reference before exposing to fluid and normalizing subsequent images to the reference. The volume of water can then be computed using the Beer-Lambert law. This method can be limiting because it requires exact image alignment between the reference image and all subsequent images. A model of neutron attenuation in a multi-phase cementitious composite was developed to be used in cases where a reference image is not available. The attenuation coefficients for water, un-hydrated cement, and sand were directly calculated from the neutron images. The attenuation coefficient for the hydration products was then back-calculated. The model can estimate the degree of saturation in a mortar with known mixture proportions without using a reference image for calculation. Absorption in mortars exposed to various fluids (i.e., deionized water and calcium chloride solutions) were investigated
For almost 20 yr, the main thrust of the author's research has been the generation of as many benchmark solutions to the time-dependent monoenergetic neutron transport equation as possible. The major motivation behind this effort has been to provide code developers with highly accurate numerical solutions to serve as standards in the assessment of numerical transport algorithms. In addition, these solutions provide excellent educational tools since the important physical features of neutron transport are still present even though the problems solved are idealized. A secondary motivation, though of equal importance, is the intellectual stimulation and understanding provided by the combination of the analytical, numerical, and computational techniques required to obtain these solutions. Therefore, to further the benchmark development, the added complication of time-dependent cross sections in the one-group transport equation is considered here
Monte Carlo simulations of the particle transport in semiconductor detectors of fast neutrons
Several Monte Carlo all-particle transport codes are under active development around the world. In this paper we focused on the capabilities of the MCNPX code (Monte Carlo N-Particle eXtended) to follow the particle transport in semiconductor detector of fast neutrons. Semiconductor detector based on semi-insulating GaAs was the object of our investigation. As converter material capable to produce charged particles from the (n, p) interaction, a high-density polyethylene (HDPE) was employed. As the source of fast neutrons, the 239Pu–Be neutron source was used in the model. The simulations were performed using the MCNPX code which makes possible to track not only neutrons but also recoiled protons at all interesting energies. Hence, the MCNPX code enables seamless particle transport and no other computer program is needed to process the particle transport. The determination of the optimal thickness of the conversion layer and the minimum thickness of the active region of semiconductor detector as well as the energy spectra simulation were the principal goals of the computer modeling. Theoretical detector responses showed that the best detection efficiency can be achieved for 500 μm thick HDPE converter layer. The minimum detector active region thickness has been estimated to be about 400 μm. -- Highlights: ► Application of the MCNPX code for fast neutron detector design is demonstrated. ► Simulations of the particle transport through conversion film of HDPE are presented. ► Simulations of the particle transport through detector active region are presented. ► The optimal thickness of the HDPE conversion film has been calculated. ► Detection efficiency of 0.135% was reached for 500 μm thick HDPE conversion film
For the treatment of anisotropic elastic neutron scattering in Ssub(N) reactor calculations extended transport approximations are widely used, which in the simplest case describe the elastic anisotropy by the mean elastic-scattering cosine anti μ in the transport cross section Σsub(tr) = Σsub(t) - anti μΣsub(s). In the present paper this approximation is improved by higher-order transport approximations with transport cross sections that consistently take into account anisotropic neutron inscattering. The quality of different weighting procedures for the generation of anisotropic group constants in the resonance region is assessed. Elastic anisotropy increasing with neutron energy on one hand and weighting functions with resonance structure up to about 3 MeV on the other hand are connected by the use of numerically advantageous energy-dependent higher-order transport approximations. With the application of the usual heavy material weighting procedure a consistent transition from the structural-material resonance region to the heavy-material resonance region is achieved. It is shown: in a fine group structure of 208 energy groups the macroscopic shape of the weighting functions may be neglected, this shape however, is important in case of collapsing to coarse groups in different spatial zones. For the critical assembly ZPRIII-56B the above-mentioned methods together with consistently improved transport cross sections of the KFKINR group constant set yield ksub(eff) = 1.0066. The prediction of directional neutron spectra in a small lithium sphere with a 14 MeV neutron source is successful within an accuracy of 20% with respect to experimental measurements. (orig.)
On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions
Song, Degong
2000-01-01
This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of L^p including L^1. Some aspects of the spectral properties of the transport operator A and the strongly continuous semigroup T(t) generated by A are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas...
One-speed neutron transport eigenvalues review and some new results
The eigenvalue problem for one-speed neutron transport in stationary and time-dependent systems is stated. Various types of anisotropic scattering and boundary conditions are discussed. The calculation methods used for solving the transport equation in its differential or integral form are described. A review is given of the work done at our institute on homogenous and heterogenous systems. Preliminary results from some recent investigations are also presented. (44 refs.)
MC++: A parallel, portable, Monte Carlo neutron transport code in C++
MC++ is an implicit multi-group Monte Carlo neutron transport code written in C++ and based on the Parallel Object-Oriented Methods and Applications (POOMA) class library. MC++ runs in parallel on and is portable to a wide variety of platforms, including MPPs, SMPs, and clusters of UNIX workstations. MC++ is being developed to provide transport capabilities to the Accelerated Strategic Computing Initiative (ASCI). It is also intended to form the basis of the first transport physics framework (TPF), which is a C++ class library containing appropriate abstractions, objects, and methods for the particle transport problem. The transport problem is briefly described, as well as the current status and algorithms in MC++ for solving the transport equation. The alpha version of the POOMA class library is also discussed, along with the implementation of the transport solution algorithms using POOMA. Finally, a simple test problem is defined and performance and physics results from this problem are discussed on a variety of platforms
Guideline of Monte Carlo calculation. Neutron/gamma ray transport simulation by Monte Carlo method
2002-01-01
This report condenses basic theories and advanced applications of neutron/gamma ray transport calculations in many fields of nuclear energy research. Chapters 1 through 5 treat historical progress of Monte Carlo methods, general issues of variance reduction technique, cross section libraries used in continuous energy Monte Carlo codes. In chapter 6, the following issues are discussed: fusion benchmark experiments, design of ITER, experiment analyses of fast critical assembly, core analyses of JMTR, simulation of pulsed neutron experiment, core analyses of HTTR, duct streaming calculations, bulk shielding calculations, neutron/gamma ray transport calculations of the Hiroshima atomic bomb. Chapters 8 and 9 treat function enhancements of MCNP and MVP codes, and a parallel processing of Monte Carlo calculation, respectively. An important references are attached at the end of this report.
In this work we developed a software to model and generate results in tables and graphs of one-dimensional neutron transport problems in multi-group formulation of energy. The numerical method we use to solve the problem of neutron diffusion is analytic, thus eliminating the truncation errors that appear in classical numerical methods, e.g., the method of finite differences. This numerical analytical method increases the computational efficiency, since they are not refined spatial discretization necessary because for any spatial discretization grids used, the numerical result generated for the same point of the domain remains unchanged unless the rounding errors of computational finite arithmetic. We chose to develop a computational application in MatLab platform for numerical computation and program interface is simple and easy with knobs. We consider important to model this neutron transport problem with a fixed source in the context of shielding calculations of radiation that protects the biosphere, and could be sensitive to ionizing radiation
DIAMANT2 - A multigroup neutron transport program for triangular and hexagonal geometry
DIAMANT2 evolved out of the DIAMANT-code. DIAMANT2 solves the multigroup neutron transport equation in planar geometry using the Ssub(N) method. Spatial discretization is accomplished by taking finite differences on a meshgrid composed of equilateral triangles. This report contains a detailed documentation of the program and the input description. (orig./HJ)
Quadrature sums of highest algebraic degree of precision for neutron transport integrals
A Gaussian-type quadrature formula for neutron transport integrals is here re-established according to the orthogonal-polynomial method. Limit properties of the asymptotic and nonasymptotic parts of the quadrature sum are also obtained, together with another quadrature formula of the highest algebraic degree of precision, for purely scattering media. Numerical-application examples are given in the appendix. (author)
Existence result for the kinetic neutron transport problem with a general albedo boundary condition
We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied. (authors)
Two-group neutron transport theory in adjacent space with lineary anisotropic scattering
A solution method for two-group neutron transport theory with anisotropic scattering is introduced by the combination of case method (expansion method of self singular function) and the invariant imbedding (invariance principle). The numerical results for the Milne problem in light water and borated water is presented to demonstrate the avalibility of the method
Development of a 3D neutron transport code and benchmark tests
Results are reported of NEACRP '3D Neutron Transport Benchmarks' proposed from Osaka UNiversity, and of recent progress in the development of a 3D neutron transport code. Takeda et al. proposed four problems to NEACRP as 3D neutron transport benchmarks, and 22 results from 20 organizations were submitted. A variety of methods have been used, such as the Monte Carlo, Sn, Pn, synthetic, and nodal method. The results for k-eff, control-rod worths, and region-averaged fluxes are summarized with the conclusions that (1) in XYZ geometry the Sn method with n=8 shows a good agreement with the Monte-Carlo method, and gives even better results in some cases, (2) the Pn method has significant spatial mesh effects, and (3) the Sn method is not satisfactory in hexagonal-Z geometry, and improvements in accuracy are desirable. Improvement of a 3D neutron transport code is in progress to resolve the problem in the hexagonal-Z geometry by considering new diamond difference schemes and an improved coarse-mesh method, and also by applying the nodal method. (author)
The neutron transport code DTF-Traca users manual and input data
This is a users manual of the neutron transport code DTF-TRACA, which is a version of the original DTF-IV with some modifications made at JEN. A detailed input data descriptions is given. The new options developed at JEN are included too. (Author) 18 refs
Monte Carlo neutron transport simulation of the Ghana Research Reactor-1
Stochastic Monte Carlo neutron particle transport methods have been applied to successfully model in 3-D, the HEU-fueled Ghana Research Reactor-1 (GHARR-1), a commercial version of the Miniature Neutron Source Reactor (MNSR) using the MCNP version 4c3 particle transport code. The preliminary multigroup neutronic criticality calculations yielded a keff is contained in 1.00449 with a corresponding cold clean excess reactivity of 4.47mk (447pcm) compared with experimental values of keff is contained in 1.00402 and excess reactivity of 4.00mk (400pcm). The Monte Carlo simulations also show comparable results in the neutron fluxes in the HEU core and some regions of interest. The observed trends in the radial and axial flux distributions in the core, beryllium annular reflector and the water region in the top shim reflector tray were reproduced, indicating consistency of the results, accuracy of the model, precision of the MCNP transport code and the comparability of the Monte Carlo simulations. The results further illustrate the close agreement between stochastic transport theory and the experimental measurements conducted during off-site zero power cold tests. (author)
Remarkable moments in the history of neutron transport Monte Carlo methods
I highlight a few results from the past of the neutron and photon transport Monte Carlo methods which have caused me a great pleasure for their ingenuity and wittiness and which certainly merit to be remembered even when tricky methods are not needed anymore. (orig.)
Dumazert, Jonathan; Coulon, Romain; Carrel, Frédérick; Corre, Gwenolé; Normand, Stéphane; Méchin, Laurence; Hamel, Matthieu
2016-08-01
Neutron detection forms a critical branch of nuclear-related issues, currently driven by the search for competitive alternative technologies to neutron counters based on the helium-3 isotope. The deployment of plastic scintillators shows a high potential for efficient detectors, safer and more reliable than liquids, more easily scalable and cost-effective than inorganic. In the meantime, natural gadolinium, through its 155 and mostly 157 isotopes, presents an exceptionally high interaction probability with thermal neutrons. This paper introduces a dual system including a metal gadolinium core inserted at the center of a high-scale plastic scintillator sphere. Incident fast neutrons are thermalized by the scintillator shell and then may be captured with a significant probability by gadolinium 155 and 157 nuclei in the core. The deposition of a sufficient fraction of the capture high-energy prompt gamma signature inside the scintillator shell will then allow discrimination from background radiations by energy threshold, and therefore neutron detection. The scaling of the system with the Monte Carlo MCNPX2.7 code was carried out according to a tradeoff between the moderation of incident fast neutrons and the probability of slow neutron capture by a moderate-cost metal gadolinium core. Based on the parameters extracted from simulation, a first laboratory prototype for the assessment of the detection method principle has been synthetized. The robustness and sensitivity of the neutron detection principle are then assessed by counting measurement experiments. Experimental results confirm the potential for a stable, highly sensitive, transportable and cost-efficient neutron detector and orientate future investigation toward promising axes.
Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) point source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green's function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade
Development and benchmarking of higher energy neutron transport data libraries
Neutron cross-section evaluations covering the energy range from 10/sup /minus/11/ to 100 MeV have been prepared for several materials. The principal method used to generate this data base has employed statistical-preequilibrium nuclear models, sophisticated phase shift analyses, and R-matrix techniques. The library takes advantage of formats developed for Version 6 of the Evaluated Nuclear Data File, ENDF. Methods to efficiently utilize the ENDF/B-VI representation of this library in the MCNP Monte Carlo code have been developed. MCNP results using the new library have been compared with calculated results using codes or data based upon intranuclear cascade models. 7 refs., 8 figs
A design-oriented three dimensional stochastic neutron transport code was made with a new lattice model for shielding analysis. The basic assumption of this lattice model is that neutron motion may be sampled at predetermined points. A medium is considered to be filled with a cubic lattice. The number of allowed directions of motion is revised from 26 in the old lattice model to 98 in the new one. By using the lattice model, a computer code named DIMOS has been developed on the basis of a stochastic approach. In addition, this code has an option coupling the two-dimensional discrete ordinates code PALLAS with the DIMOS code. In order to demonstrate the ability of this code, three neutron streaming problems were calculated with the option of coupling in the DIMOS: a cylindrical air duct in water, a straight annular duct in an unsymmetrical configuration and an annular duct with the one bend. Results obtained are in good agreement experimental ones. (author)
Numerical solution of neutron transport equations in discrete ordinates and slab geometry
An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used
Post-merger evolution of a neutron star-black hole binary with neutrino transport
Foucart, Francois; Roberts, Luke; Duez, Matthew D; Haas, Roland; Kidder, Lawrence E; Ott, Christian D; Pfeiffer, Harald P; Scheel, Mark A; Szilagyi, Bela
2015-01-01
We present a first simulation of the post-merger evolution of a black hole-neutron star binary in full general relativity using an energy-integrated general relativistic truncated moment formalism for neutrino transport. We describe our implementation of the moment formalism and important tests of our code, before studying the formation phase of a disk after a black hole-neutron star merger. We use as initial data an existing general relativistic simulation of the merger of a neutron star of 1.4 solar mass with a black hole of 7 solar mass and dimensionless spin a/M=0.8. Comparing with a simpler leakage scheme for the treatment of the neutrinos, we find noticeable differences in the neutron to proton ratio in and around the disk, and in the neutrino luminosity. We find that the electron neutrino luminosity is much lower in the transport simulations, and that the remnant is less neutron-rich. The spatial distribution of the neutrinos is significantly affected by relativistic effects. Over the short timescale e...
Advanced method of solution of neutron transport equation in nuclear reactor cell - 361
Method of solution of neutron transport integral equation has been developed. It is aimed into calculation analysis of neutron flux in nuclear reactor cell with complicated geometry and different boundary conditions. On this stage of nuclear reactor calculation it is important to take into account special futures of neutron flux behavior included anisotropy scattering. Modern computational strategy requires the ability to accurately solution of Boltzmann transport equation in the shortest possible time. This approach is based on neutron flux expansion with orthogonal polynomial system in every uniform mesh of the cell. As result of this approximation the system of linear integral equation is reduced to algebraic system with coefficients that are the six-fold integrals over the cell area in general case. In this paper formulae for calculation of these values are given. The algorithm of computer code for neutron flux calculation is described. The results obtained with general version of collision probabilities method code are given. The advantage of above described approach has been demonstrated. (authors)
Highlights: • Powerful hp-SEM refinement approach for PN neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks
Development of a CAD-based neutron transport code with the method of characteristics
The main problem determining whether the method of characteristics (MOC) can be used in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. In this study, a new idea making use of MCAM, which is a Mutlti-Calculation Automatic Modeling for Neutronics and Radiation Transport program developed by FDS Team, for geometry description and ray tracing of particle transport was brought forward to solve the geometry problem mentioned above. Based on the theory and approach as the foregoing statement, a two dimensional neutron transport code was developed which had been integrated into VisualBUS, developed by FDS Team. Several benchmarks were used to verify the validity of the code and the numerical results were coincident with the reference values very well, which indicated the accuracy and feasibility of the method and the MOC code. (authors)
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed
Radiative or neutron transport modeling using a lattice Boltzmann equation framework
Bindra, H.; Patil, D. V.
2012-07-01
In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.
Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.
2014-10-15
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.
Transport simulation and image reconstruction for fast-neutron detection of explosives and narcotics
Micklich, B.J.; Fink, C.L.; Sagalovsky, L.
1995-07-01
Fast-neutron inspection techniques show considerable promise for explosive and narcotics detection. A key advantage of using fast neutrons is their sensitivity to low-Z elements (carbon, nitrogen, and oxygen), which are the primary constituents of these materials. We are currently investigating two interrogation methods in detail: Fast-Neutron Transmission Spectroscopy (FNTS) and Pulsed Fast-Neutron Analysis (PFNA). FNTS is being studied for explosives and narcotics detection in luggage and small containers for which the transmission ratio is greater than about 0.01. The Monte-Carlo radiation transport code MCNP is being used to simulate neutron transmission through a series of phantoms for a few (3-5) projection angles and modest (2 cm) resolution. Areal densities along projection rays are unfolded from the transmission data. Elemental abundances are obtained for individual voxels by tomographic reconstruction, and these reconstructed elemental images are combined to provide indications of the presence or absence of explosives or narcotics. PFNA techniques are being investigated for detection of narcotics in cargo containers because of the good penetration of the fast neutrons and the low attenuation of the resulting high-energy gamma-ray signatures. Analytic models and Monte-Carlo simulations are being used to explore the range of capabilities of PFNA techniques and to provide insight into systems engineering issues. Results of studies from both FNTS and PFNA techniques are presented.
In today's society acts of terrorism must involve in some stages the illicit trafficking either of explosives, chemical agents and/or nuclear materials. Therefore society must rely on an anti-trafficking infrastructure which encompasses responsible authorities, field personnel and adequate instrumental networks. Modern inspection systems for personnel, parcel, vehicle and cargo, as noninvasive imaging techniques, are based on the use of nuclear analytical methods. The inspection systems make use of penetrating radiation (neutrons, gamma and x-rays) in a scanning geometry, with the detection of radiation either transmitted or produced in the interrogated object. Explosives and chemical agent detection systems are based on the fact that the problem of identification can be reduced to the measurement of elemental concentrations. Different nuclear analytical techniques could be used for this purpose; however the use of neutrons has some specific advantages due to the high penetrability in large payloads. Of special interest is the design and use of a transportable neutron system coupled to a gamma-ray radiographic device for inspecting large containers searching for contraband, explosives, weapons etc. The use of neutron induced reactions for non-destructive bulk elemental analysis is well documented. All neutrons, in particular fast neutrons, are well suited to explore large volume samples because of their high penetration in bulk material. Fast neutrons can be produced efficiently and economically by natural radioactive sources, small accelerators or compact electronic neutron generators, making possible the use of neutron based techniques in field applications. Gamma-rays produced by irradiating the sample with neutrons gives the elemental composition of the material, moreover, knowing the nuclear cross-sections and estimating the absorption factors in the different materials, it is possible to perform a quantitative analysis of elements in the sample even in depth
The spectral element method for static neutron transport in AN approximation. Part I
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, AN formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the AN (i.e. SP2N−1) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
Development of a 1D neutron transport code employing the method of characteristics
To investigate the 2D/1D fusion core analysis method, a 1D neutron transport problem solver, PEACH-ID, is developed. It is a code of method of characteristics (MOC), both the usual fiat-source step characteristics (SC) scheme and linear source (LS) approximation scheme are adopted for tracking calculation along the neutron flying trajectory. Exponential function interpolation table and fission source extrapolation are adopted as two major methods to accelerate the computational process. Numerical results demonstrate that PEACH-1D is accurate and efficient, and the proposed LS scheme is able to handle quite larger mesh division and deserves much more application in the MOC codes. (authors)
Interface software package for generating the source for neutron transport discrete ordinates code
The safe operation of the reactors imposes heightened requirements toward the quality of the calculated values of the irradiation for the life-time limit assessment of the reactor vessel. The organisation of the calculations has to assure maximum authenticity of the input data, possibility for control and revision of the initial conditions. That's why the whole calculating process has to be computerised. This work presents the software package by means of which the distribution of the primary neutron source in the reactor core, calculated with the,help of diffusion codes is transformed to the source suitable for the codes calculating the neutron transport out of the core by discrete ordinates method
Comparison of neutronic transport equation resolution nodal methods
In this work, some transport equation resolution nodal methods are comparatively studied: the constant-constant (CC), linear-nodal (LN) and the constant-quadratic (CQ). A nodal scheme equivalent to finite differences has been used for its programming, permitting its inclusion in existing codes. Some bidimensional problems have been solved, showing that linear-nodal (LN) are, in general, obtained with accuracy in CPU shorter times. (Author)
Methodology for coupling computational fluid dynamics and integral transport neutronics
The CFD code STAR-CD was coupled to the integral transport code DeCART in order to provide high-fidelity, full physics reactor simulations. An interface program was developed to perform the tasks of mapping the STAR-CD mesh to the DeCART mesh, managing all communication between STAR-CD and DeCART, and monitoring the convergence of the coupled calculations. The interface software was validated by comparing coupled calculation results with those obtained using an independently developed interface program. An investigation into the convergence characteristics of coupled calculations was performed using several test models on a multiprocessor LINUX cluster. The results indicate that the optimal convergence of the coupled field calculation depends on several factors, to include the tolerance of the STAR-CD solution and the number of DeCART transport sweeps performed before exchanging data between codes. Results for a 3D, multi-assembly PWR problem on 12 PEs of the LINUX cluster indicate the best performance is achieved when the STAR-CD tolerance and number of DeCART transport sweeps are chosen such that the two fields converge at approximately the same rate. (authors)
Assessment of the performance of the spectral element method applied to neutron transport problems
Highlights: • The spectral element method (SEM) is applied to various transport models. • The results allow to assess the performance of SEM when applied to neutron transport problems in reactor physics. • The method is validated against benchmark results and manufactured solutions. • The results presented prove the effectiveness of the method and the high level of accuracy that can be attained. - Abstract: The spectral element method can be used to deal with the spatial operators of neutron transport problems with high efficiency, as shown recently in the framework of the second-order AN transport approximation. The results highlight interesting computational features and show the appeal of the scheme for reactor physics applications. In this paper we investigate the numerical performance of the method in detail. In order to carry out an accurate monitoring of the error behavior to levels close to numerical round-off, we use benchmark problems with known analytical solutions, or with manufactured solutions. Manufactured solutions can easily be obtained for source-injected problems, by tailoring the external neutron source and the boundary conditions to a pre-established analytical solution for a given system. The results presented prove the effectiveness of the method and the high level of accuracy that can be attained
A time-dependent neutron transport model and its coupling to thermal-hydraulics
A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code system is based on the well-known Discrete Ordinates code DORT, which solves the steady-state neutron/photon transport equation in two dimensions for an arbitrary number of energy groups and the most common regular geometries. For the implementation of time-dependence a fully implicit first-order scheme was employed to minimize errors due to temporal discretization. This requires various modifications to the transport equation as well as the extensive use of elaborated acceleration mechanisms. The convergence criteria for fluxes, fission rates etc. had to be strongly tightened to ensure the reliability of results. To perform coupled analyses, an interface to the GRS system code ATHLET has been developed. The nodal power densities from the neutron transport code are passed to ATHLET to calculate thermal-hydraulic system parameters, e.g. fuel and coolant temperatures. These are in turn used to generate appropriate nuclear cross sections by interpolation of pre-calculated data sets for each time step. Finally, to demonstrate the transient capabilities of the coupled code system, the research reactor FRM-II has been analysed. Several design basis accidents were modelled, like the loss of off site power, loss of secondary heat sink and unintended control rod withdrawal. (author)
Numerical solution of the neutron transport equation using cellular neural networks
Various methods have been used for solving the neutron transport equation in the past, and a number of computer codes have been developed based on these solution methods. This paper describes a novel method for the solution of the steady-state and time-dependent neutron transport equation using the duality between neutronic parameters in the method of characteristic (MOC) and the electrical parameters in the cellular neural networks (CNN). The relevant electrical circuit can be simulated by professional electrical circuit simulator software, HSPICE. This software is used for numerical solution of the transport equation only by preparation of appropriate inputs. This method does not need inner and outer iterations, which is a necessary step in the other deterministic methods. One of the main applications of the proposed method may be the development of a new hardware by VLSI technology for online spatio-temporal calculations of the transport equation for nuclear reactor core. The accuracy and capability of this method are examined in a 2D steady-state problem for a BWR fuel assembly, and a 2D time-dependent TWIGL seed/blanket problem
Neutron transport through semi-infinite continuous stochastic media using Gaussian statistics
The stationary solution of the one-speed neutron transport equation in a semi-infinite stochastic medium with linear anisotropic scattering is considered. The cross-section function of the medium is assumed to be a continuous random function of position with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as radiant neutron energy and net neutron flux, for an arbitrary correlation function. The problem is solved at first in the deterministic case, then the solution is averaged using Gaussian joint probability distribution function. A modified Gaussian probability distribution function is also used to average the solution. Numerical results are given for the sake of comparison
Benchmark calculations of neutron dose rates at transport and storage casks
The application of numerical calculations methods for demonstration of sufficient radiation shielding of radioactive waste transport and storage casks requires a validation based on appropriate measurements of gamma and neutron sources. The results of the comparison of measured data and calculations using the Monte Carlo program MCNP show deviations dependent on the loading of the cask within the standard deviation which is dominated by the measuring method. Considering the neutrons scattered at the salt MCNP (in case of disposal in the salt) tends to underestimate the nominal values, but still within the double standard deviation. This accuracy is not reached with MAVRIC. Based on AHE (active handling experiments) data benchmark calculations were performed that can be used as reference value. The total accuracy results from the accuracy of the source term and the measurement of the neutron dose rate with a deviation of 15%.
A Monte Carlo tool RSMC (Reaction Sequence Monte Carlo) was developed to simulate deuteron/triton transportation and reaction coupled problem. The 'Forced particle production' variance reduction technique was used to improve the simulation speed, which made the secondary product play a major role. The mono-energy 14 MeV fusion neutron source was employed as a validation. Then the thermal-to-fusion neutron convertor was studied with our tool. Moreover, an in-core conversion efficiency measurement experiment was performed with 6LiD and 6LiH converters. Threshold activation foils was used to indicate the fast and fusion neutron flux. Besides, two other pivotal parameters were calculated theoretically. Finally, the conversion efficiency of 6LiD is obtained as 1.97x10-4, which matches well with the theoretical result. (authors)
The neutron transport in a solid cylinder that contains an inhomogeneous medium with anisotropic scattering is considered. The medium has diffuse reflecting boundary with an external incidence and contains an internal neutron source. This general problem can be solved in terms of the solution of the corresponding source-free problem with transparent boundary and isotropic external incidence. The source-free problem is solved in its integral form using the variationai method. Trial functions of the solution are assumed in terms of the asymptotic solution of the Pomraning-Eddington approximation of the source-free problem. The variational technique is used to determine the constants of the trial functions. The partial flux at the boundary, the neutron density and the net flux of the general problem are calculated
NOTRAN/3D, 3-D Neutron Transport in X-Y-Z Geometry by Discrete Nodal Transport Method
1 - Description of program or function: NOTRAN/3D solves the neutron transport equation in three-dimensional XYZ geometry by the discrete nodal transport method. Source and eigenvalue problems can be solved. The input format for cross sections is the same as for ANISN. Multigroup cross section libraries such as DLC-37 and DLC75/BUGLE-80 can be used. 2 - Method of solution: NOTRAN/3D uses the discrete nodal transport method. Anisotropic scattering is treated using Legendre expansion. The order of interior flux approximation is two. Plane or linear leakage approximation of surface flux is used. 3 - Restrictions on the complexity of the problem: Maximum order of: anisotropic scattering = 3; material compositions = 20; energy groups = 2; angular quadrature = 8; zones = 20. When coarse-mesh re-balancing is used, the maximum number of course meshes is 5 in each direction. If computer memory permits, some arrays can be enlarged to reduce the above restrictions
A new paradigm for whole core neutron transport without homogenization
A new paradigm is introduced which allows the performance of whole core transport calculations without lattice homogenization. Quasi-reflected interface conditions are formulated to partially decouple periodic lattice effects from the pin-cell to pin-cell flux variation in the finite sub-element form of the variational nodal code VARIANT. With fuel-coolant homogenization eliminated, the interface variables that couple pin-cell sized nodes are divided into low-order and high-order spherical harmonic terms. Reflected interface conditions are subsequently applied to the high-order terms to remove them from the system of unknowns. Combined with an integral transport treatment within the node, the new approach dramatically reduces both the formation time and the size of the response matrices and leads to sharply reduced memory and CPU requirements. The method is applied to the two-dimensional C5-G7 problem, an OECD/NEA PWR benchmark containing MOX and UO2 fuel assemblies. Results indicate the new approach results in very little loss of accuracy relative to the corresponding full spherical harmonics expansions while reducing CPU times by well over an order of magnitude. (authors)
Neutron transport by collision probability method in complicated geometries
Constantin, Marin [Institute for Nuclear Research, Pitesti (Romania)
2000-09-01
For the first flight collision probability (FFCP) method a rapidly increasing of the memory requirements and execution time with the number of discrete regions occurs. Generally, the use of the method is restricted at cell/supercell level. However, the amazing developments both in computer hardware and computer architecture allow a real extending of the problems' domain and a more detailed treatment of the geometry. Two ways are discussed into the paper: the direct design of new codes and the improving of the mainframe old versions. The author's experience is focused on the performances' improving of the 3D integral transport code PIJXYZ (from an old version to a modern one) and on the design and developing of the 2D transport code CP{sub 2}D in the last years. In the first case an optimization process have been performed before the parallelization. In the second a modular design and the newest techniques (factorization of the geometry, the macrobands method, the mobile set of chords, the automatic calculation of the integration error, optimal algorithms for the innermost programming level, the mixed method for tracking process and CPs calculation, etc.) were adopted. In both cases the parallelization uses a PCs network system. Some short examples for CP{sub 2}D and PIJXYZ calculation are presented: reactivity void effect in typical CANDU cells using a multistratified coolant model, a problem of some adjacent fuel assemblies, CANDU reactivity devices 3D simulation. (author)
Morel, J.E.
1981-01-01
A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field. The method is easily extended to other geometries and higher dimensions. Applications exist in the areas of neutron transport with highly anisotropic scattering (such as that associated with hydrogenous media), charged-particle transport, and particle transport in controlled-fusion plasmas. 23 figures, 6 tables.
1 - Nature of physical problem solved: TDA (Time-Dependent ANISN) solves the one-dimensional time- dependent Boltzmann transport equation for neutrons and/or gamma- rays in slab, sphere or cylindrical geometries. Delayed neutron and other time-dependent effects are not considered in the present version. A choice of two types of sources and one initial condition specification is given (A. Space and energy distributed source with a step function time distribution. B. Analytical first collision source). 2 - Method of solution: TDA is based on the steady-state SN code ANISN for reasons of stability and generality. The weighted difference equations are used. 3 - Restrictions on the complexity of the problem: Limited only by available main storage
Anisotropic kernel p(μ → μ') for transport calculations of elastically scattered neutrons
Literature in the area of anisotropic neutron scattering is by no means lacking. Attention, however, is usually devoted to solution of some particular neutron transport problem and the model employed is at best approximate. The present approach to the problem in general is classically exact and may be of some particular value to individuals seeking exact numerical results in transport calculations. For attempts neutrons originally directed toward the unit vector Omega, it attempts the evaluation of p(theta'), defined such that p(theta') d theta' is that fraction of scattered neutrons that emerges in the vicinity of a cone i.e., having been scattered to between angles theta' and theta' + d theta' with the axis of preferred orientation i; Omega makes an angle theta with i. The relative simplicity of the final form of the solution for hydrogen, in spite of the complicated nature of the limits involved, is a trade-off that truly is not necessary. The exact general solution presented here in integral form, has exceedingly simple limits, i.e., 0 ≤ theta' ≤ π regardless of the material involved; but the form of the final solution is extraordinarily complicated
High performance parallel Monte Carlo transport computations for ITER fusion neutronics applications
Large scale neutronics calculations for radiation safety and machine reliability are required to support design activities for the ITER fusion reactor which is currently in phase of construction. Its large size and complexity of diagnostics, control and heating systems and ports, and also channel penetrations inside the thick blanket shielding surrounding the 14 MeV D-T neutron source are essential challenges for neutronics calculations. In the ITER tokamak geometry, the Monte Carlo (MC) method is the preferred one for radiation transport calculations. This method allows describing neutrons interactions with matter by tracking individual particle histories. The precision of the MC method depends on number of sampled particles according to statistical laws and on systematic uncertainties introduced by modeling assumptions. Due to the independence of particle histories, their tracks can be processed in parallel. Parallel computations on high performance cluster computers substantially increase number of sampled particles and therefore allow reaching the desired statistical precision of the MC results. Use of CAD-based approach with high spatial resolution improves systematic adequacy of the MC geometry modeling. These achievements are demonstrated on radiation transport calculations for designing the Blanket Shield Module and Auxiliary Shield of the ITER Electron Cyclotron Heating (ECH) upper launcher. (author)
Neutron transport solver parallelization using a Domain Decomposition method
A domain decomposition (DD) method is investigated for the parallel solution of the second-order even-parity form of the time-independent Boltzmann transport equation. The spatial discretization is performed using finite elements, and the angular discretization using spherical harmonic expansions (PN method). The main idea developed here is due to P.L. Lions. It consists in having sub-domains exchanging not only interface point flux values, but also interface flux 'derivative' values. (The word 'derivative' is here used with quotes, because in the case considered here, it in fact consists in the Ω.∇ operator, with Ω the angular variable vector and ∇ the spatial gradient operator.) A parameter α is introduced, as proportionality coefficient between point flux and 'derivative' values. This parameter can be tuned - so far heuristically - to optimize the method. (authors)
Deterministic methods to solve the differential transport equation in neutronic
We present a synthesis of the methods used to solve the integro-differential form of the transport equation. This form is used above all to achieve whole core calculations in 2 and 3D. First, we discretize the equation in energy and it leads us to an one group energy equation. For each of these groups, the scope of the calculation is so big that we have to calculate our solution on homogenized cells. On this homogenized medium, we describe different angular and spatial discretizations with acceleration methods. Finally we select some promising schemes to test: - SN Linear Nodal method with a Diffusion Synthetic Acceleration method; - Variational Nodal Method. These methods could be compared with more classical ones. To say, finite element or finite difference methods. (author). 65 refs., 3 annexes
Neutron- and proton-induced evaluated transport library up to 150 MeV
A new evaluated nuclear data library has been created. The library consists of two sub-libraries for neutron and proton incident particles. The neutron sub-library contains nuclear data for transport, heating and shielding applications for 242 nuclides with atomic numbers ranging from 8 to 82 in the energy region of primary neutrons from 10-5 eV to 150 MeV. Data below 20 MeV are taken mainly from ENDF/B-VI (revision 8) and for some nuclides, from the JENDL-3.3 and JEFF-3.0 libraries. The proton sub-library should contain data for the same range of target nuclides and energies. Proton-induced evaluated cross-section files are available for 15 nuclides at the moment. The evaluation of emitted particle energy and angular distributions at energies above 20 MeV (for incident neutrons) and above the reaction threshold (for incident protons) was performed with the help of the ALICE/ASH code and the analysis of available experimental data. The total cross-sections, elastic cross-sections and elastic scattering angular distributions were calculated with the help of the coupled channel model. The results of the calculation were adjusted to the data from ENDF/B-VI, JENDL-3.3, or JEFF-3.0 at the neutron energy equal to 20 MeV. The library is written in ENDF-6 format using the MF=3/MT=5 and MF=6/MT=5 representations
Transport coefficients of relativistic nuclear and neutron matter with in-medium effects
The transport coefficients (thermal conductivity, shear and bulk viscosities) of symmetric nuclear matter and neutron matter are calculated in the Walecka model with a Boltzmann-Uehling-Uhlenbeck (BUU) collision term by means of a Chapman-Enskog expansion in first order. The order of magnitude of the influence of in-medium effects induced by the presence of the mean σ and ω fields on these coefficients is evaluated. It is found that the transport coefficients can be modified by a factor up to 4 in the range of interest for heavy-ion collisions hydrodynamics or for neutron stars. The results obtained from the BUU collision term are in agreement with those of a previous calculation (R. Hakim and L. Mornas, Phys. Rev. C47 (1993) 2846) in the relaxation-time approximation. ((orig.))
Monte Carlo method for neutron transport calculations in graphics processing units (GPUs)
Monte Carlo simulation is well suited for solving the Boltzmann neutron transport equation in an inhomogeneous media for complicated geometries. However, routine applications require the computation time to be reduced to hours and even minutes in a desktop PC. The interest in adopting Graphics Processing Units (GPUs) for Monte Carlo acceleration is rapidly growing. This is due to the massive parallelism provided by the latest GPU technologies which is the most promising solution to the challenge of performing full-size reactor core analysis on a routine basis. In this study, Monte Carlo codes for a fixed-source neutron transport problem were developed for GPU environments in order to evaluate issues associated with computational speedup using GPUs. Results obtained in this work suggest that a speedup of several orders of magnitude is possible using the state-of-the-art GPU technologies. (author)
Monte Carlo Neutrino Transport Through Remnant Disks from Neutron Star Mergers
Richers, S; O'Connor, Evan; Fernandez, Rodrigo; Ott, Christian
2015-01-01
We present Sedonu, a new open source, steady-state, special relativistic Monte Carlo (MC) neutrino transport code, available at bitbucket.org/srichers/sedonu. The code calculates the energy- and angle-dependent neutrino distribution function on fluid backgrounds of any number of spatial dimensions, calculates the rates of change of fluid internal energy and electron fraction, and solves for the equilibrium fluid temperature and electron fraction. We apply this method to snapshots from two dimensional simulations of accretion disks left behind by binary neutron star mergers, varying the input physics and comparing to the results obtained with a leakage scheme for the case of a central black hole and a central hypermassive neutron star. Neutrinos are guided away from the densest regions of the disk and escape preferentially around 45 degrees from the equatorial plane. Neutrino heating is strengthened by MC transport a few scale heights above the disk midplane near the innermost stable circular orbit, potentiall...
The light transport properties of scintillator light inside alternative He-3 neutron detectors using scintillator sheets have been investigated by a ray-tracing simulation code. The detector consists of a light-reflecting tube, a thin rectangular ceramic scintillator sheet laminated on a glass plate, and two photo-multiplier tubes (PMTs) mounted at both ends of the detector tube. The flashes of light induced on the surface of the scintillator sheet via nuclear interaction between the scintillator and neutrons are detected by the two PMTs. The light output at both ends of various detectors in which the scintillator sheets are installed with several different arrangements were examined and evaluated in comparison with experimental results. The results derived from the simulation reveal that the light transport property is strongly dependent on the arrangement of the scintillator sheet inside the tube and the shape of the tube
Ohzu, A., E-mail: ohzu.akira@jaea.go.jp [Nuclear Science and Engineering Center, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195 (Japan); Takase, M.; Haruyama, M.; Kurata, N.; Kobayashi, N.; Kureta, M. [Nuclear Science and Engineering Center, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195 (Japan); Nakamura, T.; Toh, K.; Sakasai, K.; Suzuki, H.; Soyama, K. [J-PARC, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195 (Japan); Seya, M. [Integrated Support Center for Nuclear Nonproliferation and Nuclear Security, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195 (Japan)
2015-10-21
The light transport properties of scintillator light inside alternative He-3 neutron detectors using scintillator sheets have been investigated by a ray-tracing simulation code. The detector consists of a light-reflecting tube, a thin rectangular ceramic scintillator sheet laminated on a glass plate, and two photo-multiplier tubes (PMTs) mounted at both ends of the detector tube. The flashes of light induced on the surface of the scintillator sheet via nuclear interaction between the scintillator and neutrons are detected by the two PMTs. The light output at both ends of various detectors in which the scintillator sheets are installed with several different arrangements were examined and evaluated in comparison with experimental results. The results derived from the simulation reveal that the light transport property is strongly dependent on the arrangement of the scintillator sheet inside the tube and the shape of the tube.
The polynomial interpolation of neutron flux between the chosen space and energy variables enabled transformation of the integral transport equation into a system of linear equations with constant coefficients. Solutions of this system are the needed values of flux for chosen values of space and energy variables. The proposed improved method for solving the neutron transport problem including the mathematical formalism is simple and efficient since the number of needed input data is decreased both in treating the spatial and energy variables. Mathematical method based on this approach gives more stable solutions with significantly decreased probability of numerical errors. Computer code based on the proposed method was used for calculations of one heavy water and one light water reactor cell, and the results were compared to results of other very precise calculations. The proposed method was better concerning convergence rate, decreased computing time and needed computer memory. Discretization of variables enabled direct comparison of theoretical and experimental results
A transportable fast neutron and dual gamma-ray system for the detection of illicit materials
A transportable FNGR radiography system has been simulated using the MCNPX Monte Carlo code. The system is envisaged to be applied to the material characterisation of a suspicious bulky object, in view of identifying illegal materials. The system combines a neutron and two gamma-ray sources achieving characterisation of the material of the object through two ratios, namely 137Cs/DD and 60Co/DD. Hence, the system discriminates materials of similar or even the same of either of the two ratios. The proposed unit complies with radiation protection requirements achieving a safe occupational environment. - Highlights: → Transportable radiography system. → Neutron- and dual energy photon-beams available. → Discrimination of materials. → Detection of illicit materials.
A transportable fast neutron and dual gamma-ray system for the detection of illicit materials
Fantidis, J.G. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Vas. Sofias 12, Xanthi 67100 (Greece); Nicolaou, G.E., E-mail: nicolaou@ee.duth.gr [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Vas. Sofias 12, Xanthi 67100 (Greece)
2011-08-21
A transportable FNGR radiography system has been simulated using the MCNPX Monte Carlo code. The system is envisaged to be applied to the material characterisation of a suspicious bulky object, in view of identifying illegal materials. The system combines a neutron and two gamma-ray sources achieving characterisation of the material of the object through two ratios, namely {sup 137}Cs/DD and {sup 60}Co/DD. Hence, the system discriminates materials of similar or even the same of either of the two ratios. The proposed unit complies with radiation protection requirements achieving a safe occupational environment. - Highlights: > Transportable radiography system. > Neutron- and dual energy photon-beams available. > Discrimination of materials. > Detection of illicit materials.
New contributions to neutron stochastic transport theory in the time and in the frequency domain
The authors generalize the stochastic transport theory of Pal and Munoz-Cobo and Perez methodology, to include the delayed neutron effects. They apply this theory to interpret several experiments measuring the cross power spectral density G12(W), G13(W), G23(W) of three detectors 1, 2 and 3, located in and out of a tank containing a UO2F2 solution in water. (Auth.)
Transient Neutron Transport in Semi-Infinite Media for Pure-Triplet Scattering
The transient neutron transport in a semi-infinite medium with pure-triplet scattering is presented. Case s eigenfunctions for this problem can be obtained for this high order anisotropic scattering and orthogonality relations of these eigenfunctions can be derived mathematically. The reflectivity at the boundary, radiant energy and net heat flux are computed for specular-reflecting boundary with angular-dependent externally-incident flux. For the sake of comparison, we use two different weight functions in our calculations
Wang, Weiwei
2013-01-01
High pressure, high magnetic field and low temperature techniques are required to investigate magnetic transitions and quantum critical behaviour in different ferromagnetic materials to elucidate how novel forms of superconductivity and other new states are brought about. In this project, several instruments for magneto-transport and neutron scattering measurements have been designed and built. They include inserts for a dilution refrigerator and pressure cells for resistivity,...
Neutron, electron and photon transport in ICF tragets in direct and fast ignition
A. Parvazian; A. Okhovat
2005-01-01
Fusion energy due to inertial confinement has progressed in the last few decades. In order to increase energy efficiency in this method various designs have been presented. The standard scheme for direct ignition and fast ignition fuel targets are considered. Neutrons, electrons and photons transport in targets containing different combinations of Li and Be are calculated in both direct and fast ignition schemes. To compress spherical multilayer targets having fuel in the central part, they a...
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2
Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)
Typical half-space problems in two-group neutron transport theory are solved numerically using the singular-eigenfunction-expansion technique, considering isotropic-and linearly anisotropic scattering. Numerical results are reported for the Albedo, Milne and Constant-Source problems in a half-space pure light-water medium using isotropic scattering data set of Metacalf and Zweifel and considering various degrees of anisotropy
The first-order neutron transport equation is solved by the least-squares finite element method based on the discrete ordinates discretization. The angular dependent rebalance (ADR) acceleration arithmetic and its extrapolate method are given. The numerical results of some benchmark problems demonstrate that the arithmetic can shorten the CPU time to 34% ∼ 50% and it is effective even for the strong scattering problem. (authors)
Analysis of two different benchmark problems using one-dimensional neutron transport theory code
This paper focuses on the application of method of characteristics (MOC) for the solution of neutron transport equation in one-dimensional geometries. The paper discusses the results obtained for two different benchmark problems. The results compared well with the benchmark results. An interesting result is that, in case of MOC the unphysical flux dip at the centre of sphere (commonly found with SN - method) is absent. (author)
Modular, object-oriented redesign of a large-scale Monte Carlo neutron transport program
This paper describes the modular, object-oriented redesign of a large-scale Monte Carlo neutron transport program. This effort represents a complete 'white sheet of paper' rewrite of the code. In this paper, the motivation driving this project, the design objectives for the new version of the program, and the design choices and their consequences will be discussed. The design itself will also be described, including the important subsystems as well as the key classes within those subsystems
A new coarse-mesh rebalance method is developed and tested to accelerate one-dimensional discrete ordinates neutron transport equation. The method is based on the use of angular dependent rebalance factors. Unlike the original Coarse-Mesh Rebalance method, Fourier analysis and numerical results show that this Angular Dependent Coarse-Mesh Rebalance(ADCMR) method is unconditionally stable for any optical thickness and that the acceleration effect is significant
Systems guide to MCNP (Monte Carlo Neutron and Photon Transport Code)
The subject of this report is the implementation of the Los Alamos National Laboratory Monte Carlo Neutron and Photon Transport Code - Version 3 (MCNP) on the different types of computer systems, especially the IBM MVS system. The report supplements the documentation of the RSIC computer code package CCC-200/MCNP. Details of the procedure to follow in executing MCNP on the IBM computers, either in batch mode or interactive mode, are provided
Kara, Ayahn [Sinop Univ. (Turkey). Dept. of Nuclear Energy Engineering; Anli, Fikret [Univ. Kahramanmaras (Turkey). Dept of Physics
2015-03-15
PN approximation is known as a proper method to solve neutron transport equation when literature is taken into consideration. Generally, conventional scattering function is used to solve criticality and diffusion problems in Legendre polynomial approximation. In this study, instead of conventional scattering function, Henyey-Greenstein (HG) and Anli-Gungor phase functions (AG) are used in slab geometry transport equation and some critical thicknesses of the slab are calculated as an application with Legendre polynomial (PN) approximation and Marshak boundary condition. Results obtained from HG and AG scattering functions are compared and the correlations and discrepancies between the two functions are presented in the tables.
Hybrid method of deterministic and probabilistic approaches for multigroup neutron transport problem
A hybrid method of deterministic and probabilistic methods is proposed to solve Boltzmann transport equation. The new method uses a deterministic method, Method of Characteristics (MOC), for the fast and thermal neutron energy ranges and a probabilistic method, Monte Carlo (MC), for the intermediate resonance energy range. The hybrid method, in case of continuous energy problem, will be able to take advantage of fast MOC calculation and accurate resonance self shielding treatment of MC method. As a proof of principle, this paper presents the hybrid methodology applied to a multigroup form of Boltzmann transport equation and confirms that the hybrid method can produce consistent results with MC and MOC methods. (authors)
Synergism of the method of characteristics and CAD technology for neutron transport calculation
The method of characteristics (MOC) is a very popular methodology in neutron transport calculation and numerical simulation in recent decades for its unique advantages. One of the key problems determining whether the MOC can be applied in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. Most of the existing MOC codes describe the geometry by lines and arcs with extensive input data, such as circles, ellipses, regular polygons and combination of them. Thus they have difficulty in geometry modeling, background meshing and ray tracing for complicated geometry domains. In this study, a new idea making use of a CAD solid modeler MCAM which is a CAD/Image-based Automatic Modeling Program for Neutronics and Radiation Transport developed by FDS Team in China was introduced for geometry modeling and ray tracing of particle transport to remove these geometrical limitations mentioned above. The diamond-difference scheme was applied to MOC to reduce the spatial discretization error of the flat flux approximation in theory. Based on MCAM and MOC, a new MOC code was developed and integrated into SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical testing results demonstrated the feasibility and effectiveness of the new idea for geometry treatment in SuperMC. (authors)
A new generation transport in TNR is characterized by substantially higher level of requirements on the accuracy of cross-sections (1--3% for total and 10--20% for double differential ones). This is true in the first place for the breeder and coolant materials in the blanket as well as for shielding materials. However, the experience of integral experiments calculation analysis convinces that the increase in accuracy of single microscopic data ensures not always in achievement of sufficient accuracy of single microscopic data ensures not always in achievement of sufficient accuracy in an integral result in the calculation with concrete nuclide data. The natural criterion of the data quality is an integral experiment which enables for the data producer to obtain information on advantages and disadvantages of a file, and for the user -- to determine the level of confidence in his calculation results. This paper provides a short review of experimental and calculated works on testing neutronic data for neutron multiplying materials, such as 238U, Th, Be and Pb
Neutron and gamma ray transport calculations in shielding system
Masukawa, Fumihiro; Sakamoto, Hiroki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
In the shields for radiation in nuclear facilities, the penetrating holes of various kinds and irregular shapes are made for the reasons of operation, control and others. These penetrating holes and gaps are filled with air or the substances with relatively small shielding performance, and radiation flows out through them, which is called streaming. As the calculation techniques for the shielding design or analysis related to the streaming problem, there are the calculations by simplified evaluation, transport calculation and Monte Carlo method. In this report, the example of calculation by Monte Carlo method which is represented by MCNP code is discussed. A number of variance reduction techniques which seem effective for the analysis of streaming problem were tried. As to the investigation of the applicability of MCNP code to streaming analysis, the object of analysis which are the concrete walls without hole and with horizontal hole, oblique hole and bent oblique hole, the analysis procedure, the composition of concrete, and the conversion coefficient of dose equivalent, and the results of analysis are reported. As for variance reduction technique, cell importance was adopted. (K.I.)
A portable, parallel, object-oriented Monte Carlo neutron transport code in C++
We have developed a multi-group Monte Carlo neutron transport code using C++ and the Parallel Object-Oriented Methods and Applications (POOMA) class library. This transport code, called MC++, currently computes k and α-eigenvalues and is portable to and runs parallel on a wide variety of platforms, including MPPs, clustered SMPs, and individual workstations. It contains appropriate classes and abstractions for particle transport and, through the use of POOMA, for portable parallelism. Current capabilities of MC++ are discussed, along with physics and performance results on a variety of hardware, including all Accelerated Strategic Computing Initiative (ASCI) hardware. Current parallel performance indicates the ability to compute α-eigenvalues in seconds to minutes rather than hours to days. Future plans and the implementation of a general transport physics framework are also discussed
Yong Wang; Wenzheng Yue; Mo Zhang
2016-01-01
The anisotropic transport of thermal neutron in heterogeneous porous media is of great research interests in many fields. In this paper, it is the first time that a new model based on micron X-ray computed tomography (CT) has been proposed to simultaneously consider both the separation of matrix and pore and the distribution of mineral components. We apply the Monte Carlo method to simulate thermal neutrons transporting through the model along different directions, and meanwhile detect those ...
Some results on the neutron transport and the coupling of equations
Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)
Žukauskaite, A; Plukiene, R; Plukis, A
2007-01-01
Particle accelerators and other high energy facilities produce penetrating ionizing radiation (neutrons and γ-rays) that must be shielded. The objective of this work was to model photon and neutron transport in various materials, usually used as shielding, such as concrete, iron or graphite. Monte Carlo method allows obtaining answers by simulating individual particles and recording some aspects of their average behavior. In this work several nuclear experiments were modeled: AVF 65 – γ-ray beams (1-10 MeV), HIMAC and ISIS-800 – high energy neutrons (20-800 MeV) transport in iron and concrete. The results were then compared with experimental data.
This report documents the research and development goals reached within the reactor safety research project RS1503 ''Development and Application of Neutron Transport Methods and Uncertainty Analyses for Reactor Core Calculations''. The superordinate goal of the project is the development, validation, and application of neutron transport methods and uncertainty analyses for reactor core calculations. These calculation methods will mainly be applied to problems related to the core behaviour of light water reactors and innovative reactor concepts. The contributions of this project towards achieving this goal are the further development, validation, and application of deterministic and stochastic calculation programmes and of methods for uncertainty and sensitivity analyses, as well as the assessment of artificial neutral networks, for providing a complete nuclear calculation chain. This comprises processing nuclear basis data, creating multi-group data for diffusion and transport codes, obtaining reference solutions for stationary states with Monte Carlo codes, performing coupled 3D full core analyses in diffusion approximation and with other deterministic and also Monte Carlo transport codes, and implementing uncertainty and sensitivity analyses with the aim of propagating uncertainties through the whole calculation chain from fuel assembly, spectral and depletion calculations to coupled transient analyses. This calculation chain shall be applicable to light water reactors and also to innovative reactor concepts, and therefore has to be extensively validated with the help of benchmarks and critical experiments.
Time step control for solving the transient even-parity neutron transport equation
Recently a discretization (in time) scheme for the transient even-parity neutron transport equation was successfully developed and implemented in the VARIANT/KIN3D code. Starting from this result we have first more thoroughly investigated the order of approximation, with respect to the time variable, arising from such a scheme especially having in mind the use of a variable time step. Based on the results of this analysis we have then introduced a time discretization scheme capable of keeping the mathematical structure of the equation also in the framework of a variable time step. Starting from this new scheme we have also introduced an automatic time step control option based on the estimation of the third order time derivative by comparing the backward and centered Euler schemes. In the paper, the developed theoretical background is presented and results for a small size fast reactor are shown. We have investigated the time step control option and find its behavior being in agreement with the physical phenomena. In particular the increase of the delayed neutron fraction changes the behavior in the expected manner. The time step control was, in fact, able to detect the presence of additional time scales introduced by two families of delayed neutrons in comparison with the case with almost no delayed neutrons. (authors)
In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) δ (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) δ (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring and nuclear properties is used to obtain stable and unstable harmonics and to verify if these exist. It is found that the solution does not present instability in the conditions stated in the new concept of annular pulsed reactor. (author)
1 - Description of problem or function: FOCUS enables the calculation of any quantity related to neutron transport in reactor or shielding problems, but was especially designed to calculate differential quantities, such as point values at one or more of the space, energy, direction and time variables of quantities like neutron flux, detector response, reaction rate, etc. or averages of such quantities over a small volume of the phase space. Different types of problems can be treated: systems with a fixed neutron source which may be a mono-directional source located out- side the system, and Eigen function problems in which the neutron source distribution is given by the (unknown) fundamental mode Eigen function distribution. Using Monte Carlo methods complex 3- dimensional geometries and detailed cross section information can be treated. Cross section data are derived from ENDF/B, with anisotropic scattering and discrete or continuous inelastic scattering taken into account. Energy is treated as a continuous variable and time dependence may also be included. 2 - Method of solution: A transformed form of the adjoint Boltzmann equation in integral representation is solved for the space, energy, direction and time variables by Monte Carlo methods. Adjoint particles are defined with properties in some respects contrary to those of neutrons. Adjoint particle histories are constructed from which estimates are obtained of the desired quantity. Adjoint cross sections are defined with which the nuclide and reaction type are selected in a collision. The energy after a collision is selected from adjoint energy distributions calculated together with the adjoint cross sections in advance of the actual Monte Carlo calculation. For multiplying systems successive generations of adjoint particles are obtained which will die out for subcritical systems with a fixed neutron source and will be kept approximately stationary for Eigen function problems. Completely arbitrary problems can
In this work a comparative analysis of the results for the neutrons dispersion in a not multiplicative semi-infinite medium is presented. One of the frontiers of this medium is located in the origin of coordinates, where a neutrons source in beam form, i.e., μο=1 is also. The neutrons dispersion is studied on the statistical method of Monte Carlo and through the unidimensional transport theory and for an energy group. The application of transport theory gives a semi-analytic solution for this problem while the statistical solution for the flow was obtained applying the MCNPX code. The dispersion in light water and heavy water was studied. A first remarkable result is that both methods locate the maximum of the neutrons distribution to less than two mean free trajectories of transport for heavy water, while for the light water is less than ten mean free trajectories of transport; the differences between both methods is major for the light water case. A second remarkable result is that the tendency of both distributions is similar in small mean free trajectories, while in big mean free trajectories the transport theory spreads to an asymptote value and the solution in base statistical method spreads to zero. The existence of a neutron current of low energy and toward the source is demonstrated, in contrary sense to the neutron current of high energy coming from the own source. (Author)
Seubert, A.; Langenbuch, S.; Velkov, K.; Zwermann, W. [Gesellschaft fuer Anlagen- und Reaktorsicherheit mbH (GRS), Garching (Germany). Forschungsinstitute
2007-07-01
An overview is given of the recent progress at GRS concerning deterministic transport and Monte Carlo methods with thermal-hydraulic feedback. The development of the time-dependent 3D discrete ordinates transport code TORT-TD is described which has also been coupled with ATHLET. TORT-TD/ATHLET allows 3D pin-by-pin coupled analyses of transients using few energy groups and anisotropic scattering. As a step towards Monte Carlo steady-state calculations with nuclear point data and thermal-hydraulic feedback, MCNP has been prepared to incorporate thermal-hydraulic parameters. Results obtained for selected test cases demonstrate the applicability of deterministic and Monte Carlo neutron transport models coupled with thermo-fluiddynamics. (orig.)
The behavior of neutrons and gamma rays in a nuclear reactor or configuration of fissile material can be represented as a stochastic process. The observation of this stochastic process is usually achieved by measuring the fluctuations of the neutron and gamma ray population on the system. The general theory of the stochastic neutron field has been developed to a high degree. However, the theory of the stochastic nature of the gamma rays and neutrons couples the two processes. The generalized probability balances are developed from which the first and higher moments of the neutron and gamma rays fields are obtained. The paper also provides a description of the probability generating functions for both photon and neutron detectors that are the foundations for measurements of the fluctuations. The formalism developed in this paper for the representation of the statistical descriptors of the neutron-photon coupled field is applicable for many neutron noise analysis measurements
Application of ENDF nuclear data for testing a Monte-Carlo neutron and photon transport code
A Monte-Carlo photon and neutron transport code was developed at OAEP. The code was written in C and C++ languages in an object-oriented programming style. Constructive solid geometry (CSG), rather than combinatorial, was used such that making its input file more readable and recognizable. As the first stage of code validation, data from some ENDF files, in the MCNP's specific format, were used and compared with experimental data. The neutron (from a 300 mCi Am/Be source) attenuation by water was chosen to compare the results. The agreement of the quantity 1/Σ among the calculation from SIPHON and MCNP, and the experiment - which are 10.39 cm, 9.71 cm and 10.25 cm respectively - was satisfactorily well within the experimental uncertainties. These results also agree with the 10.8 cm result of N.M., Mirza, et al. (author)
Transport equations and linear response of superfluid Fermi mixtures in neutron stars
Gusakov, M E
2010-01-01
We study transport properties of a strongly interacting superfluid mixture of two Fermi-liquids. A typical example of such matter is the neutron-proton liquid in the cores of neutron stars. To describe the mixture, we employ the Landau theory of Fermi-liquids, generalized to allow for the effects of superfluidity. We formulate the kinetic equation and analyze linear response of the system to vector (e.g., electromagnetic) perturbation. In particular, we calculate the transverse and longitudinal polarization functions for both liquid components. We demonstrate, that they can be expressed through the Landau parameters of the mixture and polarization functions of noninteracting matter (when the Landau quasiparticle interaction is neglected). Our results can be used, e.g., for studies of the kinetic coefficients and low-frequency long-wavelength collective modes in superfluid Fermi-mixtures.
MCNP: a general Monte Carlo code for neutron and photon transport
The general-purpose Monte Carlo code MCNP ca be used for neutron, photon, or coupled neutron-photon transport, including the capability to calculate eigenvalues for critical systems. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and some special fourth-degree surfaces (elliptical tori). Pointwise cross-section data are used. For neutrons, all reactions given in a particular cross-section evaluation are accounted for. Thermal neutrons are described by both the free-gas and S(α,β) models. For photons, the code takes account of incoherent and coherent scattering, the possibility of fluorescent emission following photoelectric absorption, and absorption in pair production with local emission of annihilation radiation. MCNP includes an elaborate, interactive plotting capability that allows the user to view his input geometry to help check for setup errors. Standard features which are available to improve computational efficiency include geometry splitting and Russian roulette, weight cutoff with Russian roulette, correlated sampling, analog capture or capture by weight reduction, the exponential transformation, energy splitting, forced collisions in designated cells, flux estimates at point or ring detectors, deterministically transporting pseudo-particles to designated regions, track-length estimators, source biasing, and several parameter cutoffs. Extensive summary information is provided to help the user better understand the physics and Monte Carlo simulation of his problem. The standard, user-defined output of MCNP includes two-way current as a function of direction across any set of surfaces or surface segments in the problem. Flux across any set of surfaces or surface segments is available. 58 figures, 28 tables
1 - Nature of physical problem solved: The function of the AIRTRANS system is to calculate by Monte Carlo methods the radiation field produced by neutron and/or gamma-ray sources which are located in the atmosphere. The radiation field is expressed as the time - and energy-dependent flux at a maximum of 50 point detectors in the atmosphere. The system calculates un-collided fluxes analytically and collided fluxes by the 'once-more collided' flux-at-a-point technique. Energy-dependent response functions can be applied to the fluxes to obtain desired flux functionals, such as doses, at the detector point. AIRTRANS also can be employed to generate sources of secondary gamma radiation. 2 - Method of solution - Neutron interactions treated in the calculational scheme include elastic (isotropic and anisotropic) scattering, inelastic (discrete level and continuum) scattering, and absorption. Charged particle reactions, e.g, (n,p) are treated as absorptions. A built-in kernel option can be employed to take neutrons from the 150 keV to thermal energy, thus eliminating the need for particle tracking in this energy range. Another option used in conjunction with the neutron transport problem creates an 'interaction tape' which describes all the collision events that can lead to the production of secondary gamma-rays. This interaction tape subsequently can be used to generate a source of secondary gamma rays. The gamma-ray interactions considered include Compton scattering, pair production, and the photoelectric effect; the latter two processes are treated as absorption events. Incorporated in the system is an option to use a simple importance sampling technique for detectors that are many mean free paths from the source. In essence, particles which fly far from the source are split into fragments, the degree of fragmentation being proportional to the penetration distance from the source. Each fragment is tracked separately, thus increasing the percentage of computer time spent
One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)
Hybrid parallel programming models for AMR neutron Monte-Carlo transport
This paper deals with High Performance Computing (HPC) applied to neutron transport theory on complex geometries, thanks to both an Adaptive Mesh Refinement (AMR) algorithm and a Monte-Carlo (MC) solver. Several Parallelism models are presented and analyzed in this context, among them shared memory and distributed memory ones such as Domain Replication and Domain Decomposition, together with Hybrid strategies. The study is illustrated by weak and strong scalability tests on complex benchmarks on several thousands of cores thanks to the peta-flop supercomputer Tera100. (authors)
A vectorized Monte Carlo method with pseudo-scattering for neutron transport analysis
A vectorized Monte Carlo method has been developed for the neutron transport analysis on the vector supercomputer HITAC S810. In this method, a multi-particle tracking algorithm is adopted and fundamental processing such as pseudo-random number generation is modified to use the vector processor effectively. The flight analysis of this method is characterized by the new algorithm with pseudo-scattering. This algorithm was verified by comparing its results with those of the conventional one. The method realized a speed-up of factor 10; about 7 times by vectorization and 1.5 times by the new algorithm for flight analysis
Benchmark results for the critical slab and sphere problem in one-speed neutron transport theory
Research highlights: → The critical slab and sphere problem in neutron transport under Case eigenfunction formalism is considered. → These equations reduce to integral expressions involving X functions. → Gauss quadrature is not ideal but DE quadrature is well-suited. → Several fold decrease in computational effort with improved accuracy is realisable. - Abstract: In this paper benchmark numerical results for the one-speed criticality problem with isotropic scattering for the slab and sphere are reported. The Fredholm integral equations of the second kind based on the Case eigenfunction formalism are numerically solved by Neumann iterations with the Double Exponential quadrature.
Simulation of neutron transport process, photons and charged particles within the Monte Carlo method
Description is given to the program system BRAND designed for the accurate solution of non-stationary transport equation of neutrons, photons and charged particles in the conditions of real three-dimensional geometry. An extensive set of local and non-local estimates provides an opportunity of calculating a great set of linear functionals normally being of interest in the calculation of reactors, radiation protection and experiment simulation. The process of particle interaction with substance is simulated on the basis of individual non-group data on each isotope of the composition. 24 refs
Domain decomposition and terabyte tallies with the OpenMC Monte Carlo neutron transport code
Memory limitations are a key obstacle to applying Monte Carlo neutron transport methods to high-fidelity full-core reactor analysis. Billions of unique regions are needed to carry out full-core depletion and fuel performance analyses, equating to terabytes of memory for isotopic abundances and tally scores - far more than can fit on a single computational node in modern architectures. This work introduces an implementation of domain decomposition that addresses this problem, demonstrating excellent scaling up to a 2.39TB mesh-tally distributed across 512 compute nodes running a full-core reactor benchmark on the Mira Blue Gene/Q supercomputer at Argonne National Laboratory. (author)
3-D Monte Carlo neutron-photon transport code JMCT and its algorithms
JMCT Monte Carlo neutron and photon transport code has been developed which is based on the JCOGIN toolbox. JCOGIN includes the geometry operation, tally, the domain decomposition and the parallel computation about particle (MPI) and spatial domain (OpenMP) etc. The viewdata of CAD is equipped in JMCT preprocessor. The full-core pin-mode, which is from Chinese Qinshan-II nuclear power station, is design and simulated by JMCT. The detail pin-power distribution and keff results are shown in this paper. (author)
Adjacent-cell Preconditioners for solving optically thick neutron transport problems
We develop, analyze, and test a new acceleration scheme for neutron transport methods, the Adjacent-cell Preconditioner (AP) that is particularly suited for solving optically thick problems. Our method goes beyond Diffusion Synthetic Acceleration (DSA) methods in that it's spectral radius vanishes with increasing cell thickness. In particular, for the ID case the AP method converges immediately, i.e. in one iteration, to 10-4 pointwise relative criterion in problems with dominant cell size of 10 mfp or thicker. Also the AP has a simple formalism and is cell-centered hence, multidimensional and high order extensions are easier to develop, and more efficient to implement
A Space-Point Energy-Group integral transport theory method (SPEG) is developed and applied to the local and global calculations of the Yugoslav RA reactor. Compared to other integral transport theory methods, the SPEG distinguishes by (1) the arbitrary order of the polynomial, (2) the effective determination of integral parameters through point flux values, (3) the use of neutron balance condition. as a posterior measure of the accuracy of the calculation and (4) the elimination of the subdivisions- into zones, in realistic cases. In addition, different direct (collision probability) and indirect (Monte Carlo) approaches to integral transport theory have been investigated and Some effective acceleration procedures introduced. The study was performed on three test problems in plane and cylindrical geometry, as well as on the nine-region cell of the RA reactor. In particular, the limitations of the integral transport theory including its non-applicability to optically large material regions and to global reactor calculations were examined. The proposed strictly multipoint approach, avoiding the subdivision into zones and groups, seems to provide a good starting point to overcome these limitations of the integral transport theory. (author)
Coarse mesh transport method for whole-core neutronics analysis in cylindrical geometry
In this paper, a coarse mesh transport (Comet) method has been developed to predict neutronics behaviors in reactor cores with 2-dimensional cylindrical (r, θ) geometry. Based on neutron balance in each coarse mesh, the outgoing partial current (or flux) from a coarse mesh is calculated as the sum of the local responses to all incoming partial currents/fluxes via pre-computed incident response expansion functions. These local functions essentially represents the probabilities that the incoming neutrons and their progenies contributes to the quantities of interest such as outgoing partial currents/fluxes and fission densities. The Comet code was benchmark against the Monte Carlo Code MCNP in a test problem representative of a simplified Pebble Bed reactor core in (r, θ) geometry, consisting of an inner reflector, an annular fuel region, and a controlled outer reflector. With 4th order expansion in space and 2nd expansion order in the polar and azimuthal angles, the Comet calculation agrees very well with the MCNP reference solution. (Author)
The stationary solution of the one-speed neutron transport equation in a semi infinite stochastic medium with pure-triplet scattering is considered. The cross section function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged solution for an arbitrary correlation function. The problem is solved at first in the deterministic case, then the solution is averaged using Gaussian joint probability distribution function. Numerical results are given for the radiant neutron energy and net neutron flux. Keywords: Neutron transport, Stochastic media, Gaussian statistics, Pure triplet scattering
Žukauskaitėa, A; Plukienė, R; Ridikas, D
2007-01-01
Particle accelerators and other high energy facilities produce penetrating ionizing radiation (neutrons and γ-rays) that must be shielded. The objective of this work was to model photon and neutron transport in various materials, usually used as shielding, such as concrete, iron or graphite. Monte Carlo method allows obtaining answers by simulating individual particles and recording some aspects of their average behavior. In this work several nuclear experiments were modeled: AVF 65 (AVF cyclotron of Research Center of Nuclear Physics, Osaka University, Japan) – γ-ray beams (1-10 MeV), HIMAC (heavy-ion synchrotron of the National Institute of Radiological Sciences in Chiba, Japan) and ISIS-800 (ISIS intensive spallation neutron source facility of the Rutherford Appleton laboratory, UK) – high energy neutron (20-800 MeV) transport in iron and concrete. The calculation results were then compared with experimental data.compared with experimental data.
OMEGA, Subcritical and Critical Neutron Transport in General 3-D Geometry by Monte-Carlo
1 - Description of problem or function: OMEGA is a Monte Carlo code for the solution of the stationary neutron transport equation with k-eff as the Eigenvalue. A three-dimensional geometry is permitted consisting of a very general arrangement of three basic shapes (columns with circular, rectangular, or hexagonal cross section with a finite height and different material layers along their axes). The main restriction is that all the basic shapes must have parallel axes. Most real arrangements of fissile material inside and outside a reactor (e.g., in a fuel storage or transport container) can be described without approximation. The main field of application is the estimation of criticality safety. Many years of experience and comparison with reference cases have shown that the code together with the built-in cross section libraries gives reliable results. The following results can be calculated: - the effective multiplication factor k-eff; - the flux distribution; - reaction rates; - spatially and energetically condensed cross sections for later use in a subsequent OMEGA run. A running job may be interrupted and continued later, possibly with an increased number of batches for an improved statistical accuracy. The geometry as well as the k-eff results may be visualized. The use of the code is demonstrated by many illustrating examples. 2 - Method of solution: The Monte Carlo method is used with neutrons starting from an initial source distribution. The histories of a generation (or batch) of neutrons are followed from collision to collision until the histories are terminated by capture, fission, or leakage. For the solution of the Eigenvalue problem, the starting positions of the neutrons for a given generation are determined by the fission points of the preceding generation. The summation of the results starts only after some initial generations when the spatial part of the fission source has converged. At present the code uses the BNAB-78 subgroup library of the
System of constants to calculate neutron transport with energy 10-2-4x108 eV
A description of the library of nuclear data to calculate neutron transport in the energy range 10-2 eV-4x102 MeV (BND-400) is presented. The library contains a seven-group system of data for neutrons of E>10.5 MeV and a standard 26-group system for neutrons with E10.5 MeV, and those for matching with the file of data for neutrons with E<10.5 MeV are briefly described. In the BND-400 complex there are subroutines, which allow one to calculate the cross sections for neutron interaction with nuclei of matter with the help of various methods and models as well as to calculate group cross sections. It also provides output files in the form convenient for work. A brief instruction for BND-400 explotation on the computer BESM-6 is given
The impact of fuel particle size distribution on neutron transport in stochastic media
This paper presents a study of the particle size distribution impact on neutron transport in three-dimensional stochastic media. An eigenvalue problem is simulated in a cylindrical container consisting of fissile fuel particles with five different size distributions: constant, uniform, power, exponential and Gaussian. We construct 15 cases by altering the fissile particle volume packing fraction and its optical thickness, but keeping the mean chord length of the spherical fuel particle the same at different size distributions. The tallied effective multiplication factor (keff) and flux distribution along axial and radial directions are compared between different size distributions. At low packing fraction and low optical thickness, the size distribution has a significant impact on radiation transport in stochastic media, which can cause as high as ∼270 pcm difference in keff value and ∼2.6% relative error difference in peak flux. As the packing fraction and optical thickness increase, the impact gradually dissipates. (authors)
The first-order neutron transport equation was solved by the least-squares finite element method based on the discrete ordinates discretization. For the traditional source iteration method is very slowly for the optically thick diffusive medium, sometime even divergent especially for the scattering ratio is close to unity, so the acceleration method should be proposed. There is only diffusive synthetical acceleration (DSA) for the discontinuous finite element method (DFEM) and almost no one for the least- squares finite element method. The additive angular dependent rebalance (AADR) acceleration arithmetic and its extrapolate method were given, in which the additive modification was used. It was applied to solve the transport equation with fixed source, fission source, in optically thick diffusive regions and with unstructured-mesh. The numerical results of benchmark problems demonstrate that the arithmetic can shorten the CPU time about 1.5-2 times and give high precise. (authors)
CACTUS, a characteristics solution to the neutron transport equations in complicated geometries
CACTUS has been written to solve the multigroup neutron transport equation in a general two-dimensional geometry. The method is based upon a characteristics formulation for the problem in which the transport equation is integrated explicitly along straight line tracks that are suitably distributed throughout the problem. Source distributions and scattering are assumed to be isotropic, but the only restriction on geometry is that the outer boundary should be rectangular. Within this rectangular boundary the user is free to build his problem geometry using any combination of intersecting straight lines and circular arcs. The theory of the method is described, followed by some details of a coding, a sensitivity study on the number of tracks required to integrate fluxes in a particular problem, a user's guide, and a few test cases. (author)
On the use of the conjugate gradient method for the solution of the neutron transport equation
The possibility of using the standard conjugate gradient (CG) method to directly solve the Sn equations based on the diamond difference scheme is studied for mono-energetic neutron transport problems with isotropic scattering. It is shown that such a direct use is possible for practical heterogeneous problems with a significant speed-up over the conventional source iteration (SI) method except for the problems that are prone to unphysical negative fluxes. Some recipes are suggested to make use of the CG-method even in those cases which need negative flux fix-up in the SI-method. The transport synthetic acceleration scheme, recently developed by Ramone [Nucl. Sci. Eng. 125 (1997) 257] and others, is shown to be useful in such cases. A symmetrisation scheme for the coefficient matrix has also been presented to enable the use of the CG-method. This scheme is compared with another approach of using weighted inner products
Deterministic numerical methods for eigenvalue problems in neutron linear transport theory
Conventional deterministic numerical methods applied to eigenvalue problems in neutron transport theory in the discrete ordinates (SN) formulation are described. In order to architect an efficient time-dependent simulator for thermal reactor cores, for the cases where diffusion theory fails to give good results, the accuracy of a spectral nodal method applied to a simplified time-dependent transport model is investigated. Moreover, in order to generate the initial conditions for the one-dimensional kinetics problems, considered in the CINUNI section section of the simulator, a numerical method for SN eigenvalue problems with no spatial truncation errors is introduced. The convergence of the outer iterations with the Tchebycheff technique and implemented the option of albedo boundary conditions has been accelerated. These albedo boundary exactly substitute the top and bottom reflector regions. (author)
The reliability of calculation tools to evaluate and calculate dose rates appearing behind multi-layered shields is important with regard to the certification of transport and storage casks. Actual benchmark databases like SINBAD do not offer such configurations because they were developed for reactor and accelerator purposes. Due to this, a bench-mark-suite based on own experiments that contain dose rates measured in different distances and levels from a transport and storage cask and on a public benchmark to validate Monte-Carlo-transport-codes has been developed. The analysed and summarised experiments include a 60Co point-source located in a cylindrical cask, a 252Cf line-source shielded by iron and polyethylene (PE) and a bare 252Cf source moderated by PE in a concrete-labyrinth with different inserted shielding materials to quantify neutron streaming effects on measured dose rates. In detail not only MCNPTM (version 5.1.6) but also MAVRIC, included in the SCALE 6.1 package, have been compared for photon and neutron transport. Aiming at low deviations between calculation and measurement requires precise source term specification and exact measurements of the dose rates which have been evaluated carefully including known uncertainties. In MAVRIC different source-descriptions with respect to the group-structure of the nuclear data library are analysed for the calculation of gamma dose rates because the energy lines of 60Co can only be modelled in groups. In total the comparison shows that MCNPTM fits very wall to the measurements within up to two standard deviations and that MAVRIC behaves similarly under the prerequisite that the source-model can be optimized. (author)
Large-scale Monte Carlo neutron transport calculations with thermal hydraulic feedback
Highlights: • Method of internal coupling, based on dynamic material distribution, is presented. • The Wielandt shift method is implemented to accelerate Mote Carlo calculations. • The Uniform Fission Site method is introduced for tallies with large numbers of bins. • The stochastic approximation scheme is used to stabilize coupled code convergence. - Abstract: The Monte Carlo method provides the most accurate description of the particle transport problem. The criticality problem is simulated by following the histories of individual particles without approximating the energy, angle or the coordinate dependence. These calculations are usually done using homogeneous thermal hydraulic conditions. This is a very crude approximation in the general case. In this paper, the method of internal coupling between neutron transport and thermal hydraulics is presented. The method is based on dynamic material distribution, where coordinate dependent temperature and density information is supplied on the fly during the transport calculation. This method does not suffer from the deficiencies characteristic of the external coupling via the input files. In latter case, the geometry is split into multiple cells having distinct temperatures and densities to supply the feedback. The possibility to efficiently simulate large scale geometries at pin-by-pin and subchannel level resolution was investigated. The Wielandt shift method for reducing the dominance ratio of the system and accelerating the fission source convergence was implemented. During the coupled iteration a detailed distribution of the fission heat deposition is required by the thermal hydraulics calculation. Providing reasonable statistical uncertainties for tallies having large numbers of bins, is a complicated task. This problem was resolved by applying the Uniform Fission Site method. Previous investigations showed that the convergence of the coupled neutron transport/thermal hydraulics calculation is limited by
Nelson, Adam
Multi-group scattering moment matrices are critical to the solution of the multi-group form of the neutron transport equation, as they are responsible for describing the change in direction and energy of neutrons. These matrices, however, are difficult to correctly calculate from the measured nuclear data with both deterministic and stochastic methods. Calculating these parameters when using deterministic methods requires a set of assumptions which do not hold true in all conditions. These quantities can be calculated accurately with stochastic methods, however doing so is computationally expensive due to the poor efficiency of tallying scattering moment matrices. This work presents an improved method of obtaining multi-group scattering moment matrices from a Monte Carlo neutron transport code. This improved method of tallying the scattering moment matrices is based on recognizing that all of the outgoing particle information is known a priori and can be taken advantage of to increase the tallying efficiency (therefore reducing the uncertainty) of the stochastically integrated tallies. In this scheme, the complete outgoing probability distribution is tallied, supplying every one of the scattering moment matrices elements with its share of data. In addition to reducing the uncertainty, this method allows for the use of a track-length estimation process potentially offering even further improvement to the tallying efficiency. Unfortunately, to produce the needed distributions, the probability functions themselves must undergo an integration over the outgoing energy and scattering angle dimensions. This integration is too costly to perform during the Monte Carlo simulation itself and therefore must be performed in advance by way of a pre-processing code. The new method increases the information obtained from tally events and therefore has a significantly higher efficiency than the currently used techniques. The improved method has been implemented in a code system
TIMOC-72, 3-D Time-Dependent Homogeneous or Inhomogeneous Neutron Transport by Monte-Carlo
1 - Nature of physical problem solved: TIMOC solves the energy and time dependent (or stationary) homogeneous or inhomogeneous neutron transport equation in three-dimensional geometries. The program can treat all commonly used scattering kernels, such as absorption, fission, isotropic and anisotropic elastic scattering, level excitation, the evaporation model, and the energy transfer matrix model, which includes (n,2n) reactions. The exchangeable geometry routines consist at present of (a) periodical multilayer slab, spherical and cylindrical lattices, (b) an elaborate three-dimensional cylindrical geometry which allows all kinds of subdivisions, (c) the very flexible O5R geometry routine which is able to describe any body combinations with surfaces of second order. The program samples the stationary or time-energy-region dependent fluxes as well as the transmission ratios between geometrical regions and the following integral quantities or eigenvalues, the leakage rate, the slowing down density, the production to source ratio, the multiplication factor based on flux and collision estimator, the mean production time, the mean destruction time, time distribution of production and destruction, the fission rates, the energy dependent absorption rates, the energy deposition due to elastic scattering for the different geometrical regions. 2 - Method of solution: TIMOC is a Monte Carlo program and uses several, partially optional variance reducing techniques, such as the method of expected values (weight factor), Russian roulette, the method of fractional generated neutrons, double sampling, semi-systematic sampling and the method of expected leakage probability. Within the neutron lifetime a discrete energy value is given after each collision process. The nuclear data input is however done by group averaged cross sections. The program can generate the neutron fluxes either resulting from an external source or in the form of fundamental mode distributions by a special
Agent code: Neutron transport benchmark example and extension to 3D lattice geometry
Hursin Mathieu
2005-01-01
Full Text Available The general methodology be hind 2D arbitrary geometry neutron transport AGENT code is the theory of R-functions, which al lows for simple modeling of complex geometries, and the method of characteristics, which solves the integral transport equation along characteristic neutron trajectories. This paper focuses on the extension of the methodology to ac count for 3D lattice geometries. Since the direct application of method of characteristics to 3D non-homogenized core con figuration may re quire a tremendous amount of memory and computing time, an alternative approximate solution based on coupling 2D method of characteristics and 1D diffusion solution is developed. The planar 2D method of characteristics and axial 1D diffusion solutions are coupled through the trans verse leak age. The use of a lower order 1D solution in the axial direction is justified by the fact that more heterogeneity in current PWR and BWR reactor cores occurs in the radial direction than in the axial one. In order to demonstrate the versatility and accuracy of the AGENT code, a 2D heterogeneous lattice problem, C5G7 is described in details. A theoretical description of the coupling methodology for 3D method of characteristics solution is followed by preliminary validation in comparison to the DeCART code.
The purpose of this work is to solve the neutron transport equation in discrete-ordinates and X-Y geometry by developing and using the strong discontinuous and strong modified discontinuous nodal finite element schemes. The strong discontinuous and modified strong discontinuous nodal finite element schemes go from two to ten interpolation parameters per cell. They are describing giving a set Dc and polynomial space Sc corresponding for each scheme BDMO, RTO, BL, BDM1, HdV, BDFM1, RT1, BQ and BDM2. The solution is obtained solving the neutron transport equation moments for each nodal scheme by developing the basis functions defined by Pascal triangle and the Legendre moments giving in the polynomial space Sc and, finally, looking for the non singularity of the resulting linear system. The linear system is numerically solved using a computer program for each scheme mentioned . It uses the LU method and forward and backward substitution and makes a partition of the domain in cells. The source terms and angular flux are calculated, using the directions and weights associated to the SN approximation and solving the angular flux moments to find the effective multiplication constant. The programs are written in Fortran language, using the dynamic allocation of memory to increase efficiently the available memory of the computing equipment. (Author)
The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P1) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P1) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1977-11-01
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.
Background: Working under extreme conditions, nuclear fuel rods, the key component of nuclear plants and reactors, are easy to be broken. In order to be safe in operation, lots of testing methods on the fuel rods have to be carried out from fabrication to operation. Purpose: Neutron radiography is a unique non-destructive testing technique which can be used to test samples with radioactivity. As the essential equipment, the nuclear fuel rod transport container has to shield the radioactivity of fuel rod and control its movement during testing and transporting. Methods: The shielding simulation of the transport container was performed using the MCNP4C code, which is a general purpose Monte Carlo code for calculating the time dependent multi-group energy transport equation for neutrons, photons and electrons in three dimensional geometries. Results: The material and dimension of the transport container used for neutron radiography testing fuel rods at Chinese Advanced Research Reactor (CARR) were optimally designed by MCNP, and the mechanical devices used to control fuel rods' movement were also described. Conclusion: The 2-m long fuel rod can be tested at CARR's neutron radiography facility (under construction) with this transport container. (authors)
Bernnat, W.; Keinert, J.; Mattes, M. [Inst. for Nuclear Energy and Energy Systems, Univ. of Stuttgart, Stuttgart (Germany)
2004-03-01
For the calculation of neutron spectra in cold and super thermal sources scattering laws for a variety of liquid and solid cyrogenic materials were evaluated and prepared for use in deterministic and Monte Carlo transport calculations. For moderator materials like liquid and solid H{sub 2}O, liquid He, liquid D{sub 2}O, liquid and solid H{sub 2} and D{sub 2}, solid CH{sub 4} and structure materials such as Al, Bi, Pb, ZrHx, and graphite scattering law data and cross sections are available. The evaluated data were validated by comparison with measured cross sections and comparison of measured and calculated neutron spectra as far as available. Further applications are the calculation of production and transport and storing of ultra cold neutrons (UCN) in different UCN sources. The data structures of the evaluated data are prepared for the common S{sub N}-transport codes and the Monte Carlo Code MCNP. (orig.)
For the calculation of neutron spectra in cold and super thermal sources scattering laws for a variety of liquid and solid cyrogenic materials were evaluated and prepared for use in deterministic and Monte Carlo transport calculations. For moderator materials like liquid and solid H2O, liquid He, liquid D2O, liquid and solid H2 and D2, solid CH4 and structure materials such as Al, Bi, Pb, ZrHx, and graphite scattering law data and cross sections are available. The evaluated data were validated by comparison with measured cross sections and comparison of measured and calculated neutron spectra as far as available. Further applications are the calculation of production and transport and storing of ultra cold neutrons (UCN) in different UCN sources. The data structures of the evaluated data are prepared for the common SN-transport codes and the Monte Carlo Code MCNP. (orig.)
Stochastic time-dependent one-speed neutron transport problem in a participating semi-infinite medium is studied for anisotropic scattering, namely, pure-triplet scattering. This anisotropic scattering higher order is beneficial for the collision treatment in neutron transport to calculate the effective multiplication constant. The medium is assumed to be discrete random with binary Markovian mixtures (e.g. neutron transport in boiling water reactor, and pebble bed reactor) described by Markovian statistics. The specular reflectivity of the boundary is angular-dependent described by the Fresnel's reflection probability function, which depends mainly on the refractive index of the medium boundary. The problem is solved first in the deterministic case after transforming the problem into a stationary-like problem. Then the solution is averaged using the formalism developed by Levermore and Pomraning, to treat particle transport problems in statistical mixtures. Some physical quantities of interest such as the reflectivity of the boundary, average neutron energy, and average net neutron flux are computed at different times for various values of refractive index of the nuclear materials used as the boundary of the medium under consideration. (authors)
Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.
TRANSX-2.15, Neutron Gamma Particle Transport Tables from MATXS Format Cross-Sections
1 - Description of program or function: TRANSX is a computer code that reads nuclear data from a library in MATXS format and produces transport tables compatible with many discrete-ordinates (SN) and diffusion codes. Tables can be produced for neutron, photon, charged-particle, or coupled transport. Options include adjoint tables, mixtures, homogeneous or heterogeneous self-shielding, group collapse, homogenization, thermal up-scatter, prompt or steady-state fission, transport corrections, elastic removal corrections, and flexible response function edits. 2 - Method of solution: TRANSX reads through the materials in a MATXS library and accumulates the cross sections into a transport table using the user's mix instructions. At the same time, response function edit cross sections are accumulated using the user's edit instructions. They can thus be any linear combination of the cross sections available in the library. When the table is complete, it is written out in the desired format. Output options include DTF-style card images, FIDO, ISOTXS, and the binary group-ordered GOXS format. Self-shielding is handled using the background cross section method. Heterogeneity options include homogeneous mixtures, escape using mean chord, lattices of cylinders by the Bell or Sauer approximations, and reflected or periodic slab cell by the bell or E3 approximations. 3 - Restrictions on the complexity of the problem: Only narrow- resonance self-shielding is available in this version. This may affect accuracy for thermal problems
Radiation exposure of the police forces accompanying transports of spent fuel elements and high-active waste form reprocessing (HAW) is determined by means of albedo dosemeters. The official dosimetry services use this type of dosemeter to mesure the personal dose in mixed gamma/neutron radiation fields above all for routine monitoring of workers occupationally exposed to radiation. The present report describes the detailed set-up and functioning of the albedo dosemeter, the process of obtaining the photon and neutron personal dose from the detector indications as well as the determination of the detection limit of the total personal dose of the albedo dosemeter according to the methods specified in the valid standards. Determination of the detection limit is based on the experience gained during previous transports, on measurements performed at transport casks, on results of type tests at PTB (Federal Physical and Technical Authority), on the measurement uncertainties obtained from the annual intercomparison measurements of the PTB as well as on the test irradiation specially performed in the range of small neutron and photon doses under laboratory conditions. For the dosimetry systems of the dosimetry services and the specific transport conditions, a reference level of 100 μSv was specified with regard to the dose detection limit. (orig.)
Library McSUB is a package of easy-to-use subroutines and functions treating neutron transport in two different kind of media by Monte Carlo calculations. The first medium, D0, contains deuterium and natural carbon while the second medium, D1, contains hydrogen and natural carbon. In the neutron energy interval 0.1-20 MeV eight different kinds of interactions are considered: Elastic and (n,2n) interactions with deuterium, elastic interactions with hydrogen and elastic and inelastic interactions with natural carbon. The inelastic interaction with carbon are subdivided into four different interaction classes, one for each excited state of the recoiled carbon nucleus. The neutron cross sections and Legendre coefficients (expressing differential cross sections) have been supplied by NEA Data Bank in France. (author)
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used: TFQMR (transpose free quasi-minimal residual algorithm) CGS (conjugate gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These subroutines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. The reasons to choose the generalized conjugate gradient methods are that the methods have better residual (equivalent to error) control procedures in the computation and have better convergent rate. The pointwise incomplete LU factorization ILU, modified pointwise incomplete LU factorization MILU, block incomplete factorization BILU and modified blockwise incomplete LU factorization MBILU are the preconditioning techniques used in the several testing problems. In Bi-CGSTAB, CGS, TFQMR and QMRCGSTAB method, we find that either CGS or Bi-CGSTAB method combined with preconditioner MBILU is the most efficient algorithm in these methods in the several testing problems. The numerical solution of flux by preconditioned CGS and Bi-CGSTAB methods has the same result as those from Cray computer, obtained by either the point successive relaxation method or the line successive relaxation method combined with Gaussian elimination
MCNP: a general Monte Carlo code for neutron and photon transport
The general-purpose Monte Carlo code MCNP can be used for neutron, photon, or coupled neutron--photon transport. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and some special fourth-degree surfaces (elliptical tori). Pointwise cross-section data are used. For neutrons, all reactions given in a particular cross-section evaluation (such as ENDF/B-IV) are accounted for. For photons, the code takes account of incoherent and coherent scattering, the possibility of fluorescent emission following photoelectric absorption, and absorption in pair production with local emission of annihilation radiation. Standard optional variance reduction schemes include geometry splitting and Russian roulette, the exponential transformation, energy splitting, forced collisions in designated cells, flux estimates at point detectors, track-length estimators, and source biasing. The standard output of MCNP includes two-way current as a function of energy, time, and angle with the normal, across any subset of bounding surfaces in the problem. Fluxes across any set of bounding surfaces are available as a function of time and energy. Similarly, the flux at designated points and the average flux in a cell (track length per unit volume) are standard tallies. Reactions such as fissions or absorptions may be obtained in a subset of geometric cells. The heating tallies give the energy deposition per starting particle. In addition, particles may be flagged when they cross specified surfaces or enter designated cells, and the contributions of these flagged particles to certain of the tallies are listed separately. All quantities printed out have their relative errors listed also. 11 figures, 27 tables
The use of neutron radiography for visualization of fluid flow through flow visualization modules has been very successful. Current experiments at the Penn State Breazeale Reactor serve to verify the mixing and transport of soluble boron under natural flow conditions as would be experienced in a pressurized water reactor. Different flow geometries have been modeled including holes, slots, and baffles. Flow modules are constructed of aluminum box material 1 1/2 inches by 4 inches in varying lengths. An experimental flow system was built which pumps fluid to a head tank and natural circulation flow occurs from the head tank through the flow visualization module to be radiographed. The entire flow system is mounted on a portable assembly to allow placement of the flow visualization module in front of the neutron beam port. A neutron-transparent fluorinert fluid is used to simulate water at different densities. Boron is modeled by gadolinium oxide powder as a tracer element, which is placed in a mixing assembly and injected into the system by remote operated electric valve, once the reactor is at power. The entire sequence is recorded on real-time video. Still photographs are made frame-by-frame from the video tape. Computers are used to digitally enhance the video and still photographs. The data obtained from the enhancement will be used for verification of simple geometry predictions using the TRAC and RELAP thermal-hydraulic codes. A detailed model of a reactor vessel inlet plenum, downcomer region, flow distribution area and core inlet is being constructed to model the AP600 plenum. Successive radiography experiments of each section of the model under identical conditions will provide a complete vessel/core model for comparison with the thermal-hydraulic codes
Thomas, Justin W.
2006-12-01
The Numerical Nuclear Reactor (NNR) is a code suite that is being developed to provide high-fidelity multi-physics capability for the analysis of light water nuclear reactors. The focus of the work here is to extend the capability of the NNR by incorporation of the neutronics module, DeCART, for Boiling Water Reactor (BWR) applications. The DeCART code has been coupled to the NNR fluid mechanics and heat transfer module STAR-CD for light water reactor applications. The coupling has been accomplished via an interface program, which is responsible for mapping the STAR-CD and DeCART meshes, managing communication, and monitoring convergence. DeCART obtains the solution of the 3-D Boltzmann transport equation by performing a series of 2-D modular ray tracing-based method of characteristics problems that are coupled within the framework of 3-D coarse-mesh finite difference. The relatively complex geometry and increased axial heterogeneity found in BWRs are beyond the modeling capability of the original version of DeCART. In this work, DeCART is extended in three primary areas. First, the geometric capability is generalized by extending the modular ray tracing scheme and permitting an unstructured mesh in the global finite difference kernel. Second, numerical instabilities, which arose as a result of the severe axial heterogeneity found in BWR cores, have been resolved. Third, an advanced nodal method has been implemented to improve the accuracy of the axial flux distribution. In this semi-analytic nodal method, the analytic solution to the transverse-integrated neutron diffusion equation is obtained, where the nonhomogeneous neutron source was first approximated by a quartic polynomial. The successful completion of these three tasks has allowed the application of the coupled DeCART/STAR-CD code to practical BWR problems.
A POD reduced order model for resolving angular direction in neutron/photon transport problems
Buchan, A.G., E-mail: andrew.buchan@imperial.ac.uk [Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, SW7 2AZ (United Kingdom); Calloo, A.A.; Goffin, M.G.; Dargaville, S.; Fang, F.; Pain, C.C. [Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, SW7 2AZ (United Kingdom); Navon, I.M. [Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120 (United States)
2015-09-01
This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead they are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.
Krylov sub-space methods for K-eigenvalue problem in 3-D multigroup neutron transport
The K-eigenvalue problem in nuclear reactor physics is often formulated in the framework of Neutron Transport Theory. The fundamental mode solution of this problem is usually obtained by the Power Iteration method. The present report is concerned with the use of a Krylov Sub-Space method. called ORTHOMIN, to obtain a more efficient solution of the K-eigenvalue problem. A matrix-free approach is proposed which can be easily implemented by using a transport code which can perform fixed source calculations. The Power Iteration and ORTHOMIN schemes are compared for two realistic 3-D multi-group cases: an LWR benchmark and the AHWR Critical Facility. The within-group iterations over self-scattering source are required in the solution of K-eigenvalue problem. They are also accelerated using another Krylov method called Conjugate Gradient method. In this work, the discretisation of Transport Equation is based on fmite-differencing and Sn-method and isotropic scattering is considered. (author)
A comparison of acceleration methods for solving the neutron transport k-eigenvalue problem
Over the past several years a number of papers have been written describing modern techniques for numerically computing the dominant eigenvalue of the neutron transport criticality problem. These methods fall into two distinct categories. The first category of methods rewrite the multi-group k-eigenvalue problem as a nonlinear system of equations and solve the resulting system using either a Jacobian-Free Newton–Krylov (JFNK) method or Nonlinear Krylov Acceleration (NKA), a variant of Anderson Acceleration. These methods are generally successful in significantly reducing the number of transport sweeps required to compute the dominant eigenvalue. The second category of methods utilize Moment-Based Acceleration (or High-Order/Low-Order (HOLO) Acceleration). These methods solve a sequence of modified diffusion eigenvalue problems whose solutions converge to the solution of the original transport eigenvalue problem. This second class of methods is, in our experience, always superior to the first, as most of the computational work is eliminated by the acceleration from the LO diffusion system. In this paper, we review each of these methods. Our computational results support our claim that the choice of which nonlinear solver to use, JFNK or NKA, should be secondary. The primary computational savings result from the implementation of a HOLO algorithm. We display computational results for a series of challenging multi-dimensional test problems
A POD reduced order model for resolving angular direction in neutron/photon transport problems
This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead they are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures
A new assembly-level Monte Carlo neutron transport code for reactor physics calculations
This paper presents a new assembly-level Monte Carlo neutron transport code, specifically intended for diffusion code group-constant generation and other reactor physics calculations. The code is being developed at the Technical Research Centre of Finland (VTT), under the working title 'Probabilistic Scattering Game', or PSG. The PSG code uses a method known as Woodcock tracking to simulate neutron histories. The advantages of the method include fast simulation in complex geometries and relatively simple handling of complicated geometrical objects. The main drawback is the inability to calculate reaction rates in optically thin volumes. This narrows the field of application to calculations involving parameters integrated over large volumes. The main features of the PSG code and the Woodcock tracking method are introduced. The code is applied in three example cases, involving infinite lattices of two-dimensional LWR fuel assemblies. Comparison calculations are carried out using MCNP4C and CASMO-4E. The results reveal that the code performs quite well in the calculation cases of this study, especially when compared to MCNP. The PSG code is still under extensive development and there are both flaws in the simulation of the interaction physics and programming errors in the source code. The results presented here, however, seem very encouraging, especially considering the early development stage of the code. (author)
Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation
Chang, B; Brown, P; Greenbaum, A; Machorro, E
2005-01-21
In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L{sup 2} norm at the rate of h{sup 2}. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.
Exhaustive treatment is presented for the analytical and numerical evaluation of elementary spatial and angular interaction matrix elements arising in transport problems with anisotropic scattering when plane and spherical geometries in order. Their use concern mainly projected FP∞N-BN Fourier generalized transform method adopted to face anisotropic scattering neutron transport in spectral calculation for fast reactors and in multilayer plane systems for shielding problems. Their application extend to radioactive transfer and to high energy charged particles sputtering problems
Duerigen, Susan
2013-01-01
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal mesh...
Cortesi, M.; Zboray, R.; Adams, R.; Dangendorf, V.; Breskin, A.; Mayer, S.; Hoedlmoser, H.; Prasser, H.-M.
2012-01-01
Novel high efficiency fast-neutron detectors were suggested for fan-beam tomography applications. They combine multi-layer polymer converters in gas medium, coupled to thick gaseous electron multipliers (THGEM). In this work we discuss the results of a systematic study of the electron transport inside a narrow gap between successive converter foils, which affects the performance of the detector, both in terms of detection efficiency and localization properties. The efficiency of transporting ...
Milne problem in two adjacent half-spaces in neutron transport theory in two energy groups
Case's method, combined with invariance principle, is used to obtain exact solutions of neutron transport problems in two adjacent half-spaces, in the two-group isotropic scattering model. The continuity condition and the invariance principle are used to obtain a set of coupled regular integral equations for the angular distribution at the interface. The expansion coefficients can be obtained from the solutions of these integral equations using the orthogonality properties of the eigen functions. Numerical results are presented for the Milne and the Constant Source problems for pure and borated light water media. The results show the feasibility of the proposed method to provide exact numerical results which can be used as standards of comparison for various approximate methods
GPU-based high performance Monte Carlo simulation in neutron transport
Heimlich, Adino; Mol, Antonio C.A.; Pereira, Claudio M.N.A. [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil). Lab. de Inteligencia Artificial Aplicada], e-mail: cmnap@ien.gov.br
2009-07-01
Graphics Processing Units (GPU) are high performance co-processors intended, originally, to improve the use and quality of computer graphics applications. Since researchers and practitioners realized the potential of using GPU for general purpose, their application has been extended to other fields out of computer graphics scope. The main objective of this work is to evaluate the impact of using GPU in neutron transport simulation by Monte Carlo method. To accomplish that, GPU- and CPU-based (single and multicore) approaches were developed and applied to a simple, but time-consuming problem. Comparisons demonstrated that the GPU-based approach is about 15 times faster than a parallel 8-core CPU-based approach also developed in this work. (author)
Design of the Prototype Low Energy Beam Transport Line for the Spallation Neutron Source
The design of the Spallation Neutron Source (SNS) prototype low-energy beam transport (LEBT) system is discussed. This LEBT must transfer 35 mA of H- current from the ion source outlet aperture to the entrance of the radio-frequency quadrupole (RFQ). The plasma generator is a radio frequency-driven multicusp source, operated at 6% duty factor (1 ms, 60 Hz). The entire LEBT configuration is electrostatic, with a high-voltage extraction gap followed by two sets of einzel lenses. The second einzel lens will be split into four quadrants to permit the application of transverse steering and beam chopping fields. The H- ion source emits a gas flow into the LEBT that must be efficiently pumped to reduce stripping losses of the H- ions. Therefore, an efficient electrode design is incorporated to reduce the gas pressure between the electrodes. Alignment requirements and related issues will also be discussed
Annealing study of electron transport in slightly neutron-irradiated graphite
A study has been made on the recovery of transport properties of synthetic single-crystal graphite irradiated with fast neutrons to a total dose of 3 x 1036 nvt. Isochronal annealing was conducted stepwise between 100 0C and 1600 0C. An analysis based on the rigid two-band model gives a consistent account of the diffusion thermoelectricity and the galvanomagnetic effect. In addition to the major normal recovery between 200 0C and 300 0C, a reverse recovery in the carrier constitution is found to take place in the annealing range from 300 0C to 350 0C. This seems explicable by considering that divacancies are intermediately transformed to single vacancies during their annihilation process. The phonon-drag thermoelectric power vs. acceptor concentration relationship implies that positive holes are more strongly scattered than electrons by radiation-induced vacancies negatively charged by accepting electrons within the basal plane. (author)
The solution of the multigroup neutron transport equation using spherical harmonics
A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW)
A massively parallel discrete ordinates response matrix method for neutron transport
In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S8 and S16 solutions are obtained for fixed-source benchmark problems in x-y geometry
An approximate method to study the one-velocity neutron integral transport equation
An approximate method to study the monokinetic linear transport equation is outlined, starting from its integral form, rather than the integro-differential one. The approximate solution may be deduced either analytically, in simple cases, or numerically by means of typical space discretization techniques, through a system of second-order differential equations, associated with proper boundary conditions. Both the system and the boundary conditions may be matched with the standard neutron diffusion multigroup ones, by means of a proper correspondence of the coefficients and of the unknowns. The slab and the radially-symmetric sphere are then analysed in detail. It is shown how, in the plane case, the present approximation is perfectly equivalent to the well-known discrete ordinate one. For curved geometries no such equivalence exists, and it is in these cases that the application of the method at hand looks promising, in order to avoid complications and numerical problems in practical applications. (author)
The present article focuses on the application of the SPH factor method to the integro-differential neutron transport equation. While leakage-related parameters are arbitrarily corrected by the SPH factors, the correction procedure for these parameters affects the calculation accuracy. We treat two correction procedures named the simultaneous correction and the direct correction, and compare them with each other in one-dimensional colorset assembly problems. Through numerical testing, we find that the simultaneous SPH correction gives better accuracy than the direct SPH correction, and the higher-order SPH-corrected calculations show better accuracy than the low-order ones. Furthermore, to consider the flux discontinuity between different types of assemblies, the improved SPH method proposed by Yamamoto and the SPH method with the Selengut normalization condition are also tested. Numerical results reveal that the both methods significantly improve the calculation accuracy and that the latter method is more robust than the former method. (author)
Multi-domain/multi-method numerical approach for neutron transport equation
A new methodology for the solution of the neutron transport equation, based on domain decomposition has been developed. This approach allows us to employ different numerical methods together for a whole core calculation: a variational nodal method, a discrete ordinate nodal method and a method of characteristics. These new developments authorize the use of independent spatial and angular expansion, non-conformal Cartesian and unstructured meshes for each sub-domain, introducing a flexibility of modeling which is not allowed in today available codes. The effectiveness of our multi-domain/multi-method approach has been tested on several configurations. Among them, one particular application: the benchmark model of the Phebus experimental facility at Cea-Cadarache, shows why this new methodology is relevant to problems with strong local heterogeneities. This comparison has showed that the decomposition method brings more accuracy all along with an important reduction of the computer time
GPU-based high performance Monte Carlo simulation in neutron transport
Graphics Processing Units (GPU) are high performance co-processors intended, originally, to improve the use and quality of computer graphics applications. Since researchers and practitioners realized the potential of using GPU for general purpose, their application has been extended to other fields out of computer graphics scope. The main objective of this work is to evaluate the impact of using GPU in neutron transport simulation by Monte Carlo method. To accomplish that, GPU- and CPU-based (single and multicore) approaches were developed and applied to a simple, but time-consuming problem. Comparisons demonstrated that the GPU-based approach is about 15 times faster than a parallel 8-core CPU-based approach also developed in this work. (author)
A new proposed method for solving the space-energy dependent spherical harmonics equations represents a methodological contribution to neutron transport theory. The proposed method was applied for solving the problem of spec-energy transport of fast and resonance neutrons in multi-zone, cylindrical y symmetric infinite reactor cell and is related to previously developed procedure for treating the thermal energy region. The advantages of this method are as follows: a unique algorithm was obtained for detailed determination of spatial and energy distribution of neutrons (from thermal to fast) in the reactor cell; these detailed distributions enable more precise calculations of criticality conditions, obtaining adequate multigroup data and better interpretation of experimental data; computing time is rather short
1 - Description of program or function: TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system. TORT is used in two- or three- dimensional geometric systems, and DORT is used in one- or two- dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Certain reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. Note that the PC release is 2.7.3. 2 - Method of solution: The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and finite-difference methods to treat spatial variables. Energy dependence is treated using a multigroup formulation. Time dependence is not treated. Starting in one corner of a mesh, at the highest energy, and with starting guesses for implicit sources, boundary conditions and recursion relationships are used to sweep into the mesh for each discrete direction independently. Integral quantities such as scalar flux are obtained from weighted sums over the directional results. The calculation then proceeds to lower energy groups, one at a time. Iterations are used to resolve implicitness caused by scattering between directions within a single energy group, by scattering from an energy group to another group previously calculated, by fission, and by certain boundary conditions. Methods are available to accelerate convergence. Anisotropic scattering is represented by a Legendre expansion of arbitrary order, and methods are available to mitigate the effect of negative scattering estimates resulting from finite truncation of the expansion. Direction sets can be biased, concentrating work into directions of particular interest. Fixed sources can be specified at either external or internal mesh
Coupled full core neutron transport/CFD simulations of pressurized water reactors
Recently as part of the CASL project, a capability to perform 3D whole-core coupled neutron transport and computational fluid dynamics (CFD) calculations was demonstrated. This work uses the 2D/1D transport code DeCART and the commercial CFD code STAR-CCM+. It builds on previous CASL work demonstrating coupling for smaller spatial domains. The coupling methodology is described along with the problem simulated and results are presented for fresh hot full power conditions. An additional comparison is made to an equivalent model that uses lower order T/H feedback to assess the importance and cost of high fidelity feedback to the neutronics problem. A simulation of a quarter core Combustion Engineering (CE) PWR core was performed with the coupled codes using a Fixed Point Gauss-Seidel iteration technique. The total approximate calculation requirements are nearly 10,000 CPU hours and 1 TB of memory. The problem took 6 coupled iterations to converge. The CFD coupled model and low order T/H feedback model compared well for global solution parameters, with a difference in the critical boron concentration and average outlet temperature of 14 ppm B and 0.94 deg. C, respectively. Differences in the power distribution were more significant with maximum relative differences in the core-wide pin peaking factor (Fq) of 5.37% and average relative differences in flat flux region power of 11.54%. Future work will focus on analyzing problems more relevant to CASL using models with less approximations. (authors)
Coupled full core neutron transport/CFD simulations of pressurized water reactors
Kochunas, B.; Stimpson, S.; Collins, B.; Downar, T. [Dept. of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, 2200 Bonisteel Blvd, Ann Arbor, MI 48104 (United States); Brewster, R.; Baglietto, E. [CD-adapco, 60 Broadhollow Road, Melville, NY 11747 (United States); Yan, J. [Westinghouse Electric Company LLC, Columbia, SC (United States)
2012-07-01
Recently as part of the CASL project, a capability to perform 3D whole-core coupled neutron transport and computational fluid dynamics (CFD) calculations was demonstrated. This work uses the 2D/1D transport code DeCART and the commercial CFD code STAR-CCM+. It builds on previous CASL work demonstrating coupling for smaller spatial domains. The coupling methodology is described along with the problem simulated and results are presented for fresh hot full power conditions. An additional comparison is made to an equivalent model that uses lower order T/H feedback to assess the importance and cost of high fidelity feedback to the neutronics problem. A simulation of a quarter core Combustion Engineering (CE) PWR core was performed with the coupled codes using a Fixed Point Gauss-Seidel iteration technique. The total approximate calculation requirements are nearly 10,000 CPU hours and 1 TB of memory. The problem took 6 coupled iterations to converge. The CFD coupled model and low order T/H feedback model compared well for global solution parameters, with a difference in the critical boron concentration and average outlet temperature of 14 ppm B and 0.94 deg. C, respectively. Differences in the power distribution were more significant with maximum relative differences in the core-wide pin peaking factor (Fq) of 5.37% and average relative differences in flat flux region power of 11.54%. Future work will focus on analyzing problems more relevant to CASL using models with less approximations. (authors)
This report gives an account of the DSN method for simulating neutron transport, together with methods of solution developed to deal with problems in the physics of thermal reactors, for which previously available computer programmes were unsatisfactory. The methods described are those incorporated in the programmes WINFRITH DSN written in FORTRAN language for the IBM 7090 and STRETCH computers. (author)
This Is a users manual of the neutron transport code TWOTRAN-TRACA, which is a version of the original TWOTRAN-GG from the Los Alamos Laboratory, with some modifications made at JEN. A detailed input data description is given as well as the new modifications developed at JEN. (Author) 8 refs
Development of new multigrid schemes for the method of characteristics in neutron transport theory
This dissertation is based upon our doctoral research that dealt with the conception and development of new non-linear multigrid techniques for the Method of the Characteristics (MOC) within the TDT code. Here we focus upon a two-level scheme consisting of a fine level on which the neutron transport equation is iteratively solved using the MOC algorithm, and a coarse level defined by a more coarsely discretized phase space on which a low-order problem is considered. The solution of this problem is then used in order to correct the angular flux moments resulting from the previous transport iteration. A flux-volume homogenization procedure is employed to evaluate the coarse-level material properties after each transport iteration. This entails the non-linearity of the methods. According to the Generalised Equivalence Theory (GET), additional degrees of freedom are introduced for the low-order problem so that the convergence of the acceleration scheme can be ensured. We present two classes of non-linear methods: transport-like methods and discussion-like methods. Transport-like methods consider a homogenized low-order transport problem on the coarse level. This problem is iteratively solved using the same MOC algorithm as for the transport problem on the fine level. Discontinuity factors are then employed, per region or per surface, in order to reconstruct the currents evaluated by the low-order operator, which ensure the convergence of the acceleration scheme. On the other hand, discussion-like methods consider a low-order problem inspired by diffusion. We studied the non-linear Coarse Mesh Finite Difference (CMFD) method, already present in literature, in the perspective of integrating it into TDT code. Then, we developed a new non-linear method on the model of CMFD. From the latter, we borrowed the idea to establish a simple relation between currents and fluxes in order to obtain a problem involving only coarse fluxes. Finally, those non-linear methods have been
Wang, Yong; Yue, Wenzheng; Zhang, Mo
2016-06-01
The anisotropic transport of thermal neutron in heterogeneous porous media is of great research interests in many fields. In this paper, it is the first time that a new model based on micron X-ray computed tomography (CT) has been proposed to simultaneously consider both the separation of matrix and pore and the distribution of mineral components. We apply the Monte Carlo method to simulate thermal neutrons transporting through the model along different directions, and meanwhile detect those unreacted thermal neutrons by an array detector on the other side of the model. Therefore, the anisotropy of pore structure can be imaged by the amount of received thermal neutrons, due to the difference of rock matrix and pore-filling fluids in the macroscopic reaction cross section (MRCS). The new model has been verified by the consistent between the simulated data and the pore distribution from X-ray CT. The results show that the evaluation of porosity can be affected by the anisotropy of media. Based on the research, a new formula is developed to describe the correlation between the resolution of array detectors and the quality of imaging. The formula can be further used to analyze the critical resolution and the suitable number of thermal neutrons emitted in each simulation. Unconventionally, we find that a higher resolution cannot always lead to a better image.
The TORT three-dimensional discrete ordinates neutron/photon transport code (TORT version 3)
Rhoades, W.A.; Simpson, D.B.
1997-10-01
TORT calculates the flux or fluence of neutrons and/or photons throughout three-dimensional systems due to particles incident upon the system`s external boundaries, due to fixed internal sources, or due to sources generated by interaction with the system materials. The transport process is represented by the Boltzman transport equation. The method of discrete ordinates is used to treat the directional variable, and a multigroup formulation treats the energy dependence. Anisotropic scattering is treated using a Legendre expansion. Various methods are used to treat spatial dependence, including nodal and characteristic procedures that have been especially adapted to resist numerical distortion. A method of body overlay assists in material zone specification, or the specification can be generated by an external code supplied by the user. Several special features are designed to concentrate machine resources where they are most needed. The directional quadrature and Legendre expansion can vary with energy group. A discontinuous mesh capability has been shown to reduce the size of large problems by a factor of roughly three in some cases. The emphasis in this code is a robust, adaptable application of time-tested methods, together with a few well-tested extensions.
A priori efficiency calculations for Monte Carlo applications in neutron transport
In this paper a general derivation is given of equations describing the variance of an arbitrary detector response in a Monte Carlo simulation and the average number of collisions a particle will suffer until its history ends. The theory is validated for a simple slab system using the two-direction transport model and for a two-group infinite system, which both allow analytical solutions. Numerical results from the analytical solutions are compared with actual Monte Carlo calculations, showing excellent agreement. These analytical solutions demonstrate the possibilities for optimizing the weight window settings with respect to variance. Using the average number of collisions as a measure for the simulation time a cost function inversely proportional to the usual figure of merit is defined, which allows optimization with respect to overall efficiency of the Monte Carlo calculation. For practical applications it is outlined how the equations for the variance and average number of collisions can be solved using a suitable existing deterministic neutron transport code with adapted number of energy groups and scattering matrices. (author)
In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD5,3 and WD12,8 (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD5,3 and WD12,8 were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD3 and SD8 (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)
Lattice design of medium energy beam transport line for n spallation neutron source
A 1 GeV H- injector linac is being designed at RRCAT for the proposed Indian Spallation Neutron Source (ISNS). The front-end of the injector linac will consist of Radiofrequency Quadrupole (RFQ) linac, which will accelerate the H- beam from 50 keV to 3 MeV. The beam will be further accelerated in superconducting Single Spoke Resonators (SSRs). A Medium Energy Beam Transport (MEBT) line will be used to transport the beam from the exit of RFQ to the input of SSR. The main purpose of MEBT is to carry out beam matching from RFQ to SSR, and beam chopping. In this paper, we describe the optimization criteria for the lattice design of MEBT. The optimized lattice element parameters are presented for zero and full (15 mA) current case. Beam dynamics studies have been carried out using an envelope tracing code Trace-3D. Required beam deflection angle due to the chopper housed inside the MEBT for beam chopping has also been estimated. (author)
MCNP: a general Monte Carlo code for neutron and photon transport
MCNP is a very general Monte Carlo neutron photon transport code system with approximately 250 person years of Group X-6 code development invested. It is extremely portable, user-oriented, and a true production code as it is used about 60 Cray hours per month by about 150 Los Alamos users. It has as its data base the best cross-section evaluations available. MCNP contains state-of-the-art traditional and adaptive Monte Carlo techniques to be applied to the solution of an ever-increasing number of problems. Excellent user-oriented documentation is available for all facets of the MCNP code system. Many useful and important variants of MCNP exist for special applications. The Radiation Shielding Information Center (RSIC) in Oak Ridge, Tennessee is the contact point for worldwide MCNP code and documentation distribution. A much improved MCNP Version 3A will be available in the fall of 1985, along with new and improved documentation. Future directions in MCNP development will change the meaning of MCNP to Monte Carlo N Particle where N particle varieties will be transported
Computation of continuous-energy neutron spectra with discrete ordinates transport theory
A procedure is presented to obtain a continuous-energy representation of the neutron spectrum using one-dimensional discrete ordinates calculations with a combination of multigroup (MG) and pointwise (PW) nuclear data. This provides the capability of determining the fine-structure energy distribution of the angular flux and flux moments within the resonance range as well as the smoother spectrum in the high- and thermal-energy ranges. A new method called a submoment expansion is developed to accurately calculate the Legendre moments of the elastic scatter source for the PW transport calculation, and the coupling between the MG and PW calculations is discussed in detail. The continuous-energy flux spectra can be utilized as problem-dependent weighting functions to process self-shielded MG cross sections for reactor physics and/or criticality safety analysis. This calculational method has been implemented in a new PW transport code called CENTRM that can be executed as a module in the AMPX and SCALE computer code packages. An example application using ENDF/B-VI cross-section data to analyze critical benchmarks is presented
Finite moments approach to the time-dependent neutron transport equation
Currently, nodal techniques are widely used in solving the multidimensional diffusion equation because of savings in computing time and storage. Thanks to the development of computer technology, one can now solve the transport equation instead of the diffusion equation to obtain more accurate solution. The finite moments method, one of the nodal methods, attempts to represent the fluxes in the cell and on cell surfaces more rigorously by retaining additional spatial moments. Generally, there are two finite moments schemes to solve the time-dependent transport equation. In one, the time variable is treated implicitly with finite moments method in space variable (implicit finite moments method), the other method uses finite moments method in both space and time (space-time finite moments method). In this study, these two schemes are applied to two types of time-dependent neutron transport problems. One is a fixed source problem, the other a heterogeneous fast reactor problem with delayed neutrons. From the results, it is observed that the two finite moments methods give almost the same solutions in both benchmark problems. However, the space-time finite moments method requires a little longer computing time than that of the implicit finite moments method. In order to reduce the longer computing time in the space-time finite moments method, a new iteration strategy is exploited, where a few time-stepwise calculation, in which original time steps are grouped into several coarse time divisions, is performed sequentially instead of performing iterations over the entire time steps. This strategy results in significant reduction of the computing time and we observe that 2-or 3-stepwise calculation is preferable. In addition, we propose a new finite moments method which is called mixed finite moments method in this thesis. Asymptotic analysis for the finite moments method shows that accuracy of the solution in a heterogeneous problem mainly depends on the accuracy of the
The primary goal of this task is to provide the capabilities in the activation code RACC, to treat pulsed operation modes. In addition, it is required that the code utilizes the same spatial mesh and geometrical models as employed in the one or multidimensional neutron transport codes used in ITER design. This would ensure the use of the same neutron flux generated by those codes to calculate the different activation parameters. It is also required to have the capabilities for generating graphical outputs for the calculated activation parameters
Buelbuel, Ahmet [Osmaniye Korkut Ata Univ. (Turkey). Dept. of Physics
2015-11-15
The steady-state one speed neutron transport equation without sources is studied in slab geometry using Henyey-Greenstein scattering function. The critical thicknesses are calculated for various c (mean number of secondary neutrons per collision) and t scattering parameters using U{sub N} method and obtained values are compared with P{sub N} method. All the numerical results for different collision scattering functions and t parameters of U{sub N} and P{sub N} methods are presented in the tables.
Azmy, Yousry
2014-06-10
We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. However, as presently formulated, it is both restricted to orthogonal geometries and susceptible to producing ray effects. In this work, a finite element formulation, utilizing a canonical form of the transport equation, is developed to obtain both integral and pointwise solutions to neutron transport problems. To facilitate its application to nonorthogonal planar geometries, the formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included in the formulation by employing discrete ordinates like approximations. In addition, multigroup source outer iteration techniques are employed to perform group dependent calculations. The ability of the formulation to substantially reduce ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal type lattice. A small high leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation
Neutron scattering and neutron physics using low energy neutrons are very prominent utilization fields of research reactors. Though thermal and cold neutrons are used mainly until now, the trend of user needs is going to lower energy. It shows that importance of very cold neutron (VCN) and ultracold neutron (UCN) source is growing. To have more lower energy neutron at the experimental facilities, not only development of CNS but the extraction of VCN and the generation of UCN is also very important. The trial fabrication of replica supermirrors for VCN guide tubes and the new concept of the mechanical neutron decelerator for UCN generation using multilayer monochromators are reported. As for the VCN extraction, the neutron guide tube must be inserted closely to CNS. So it must be tough against irradiation and heat cycle. The replica Ni-mirror guide was developed by Garching grope and installed in the vertical guide tube in ILL. It showed the effectiveness of the close approach of guide tube to the source for such very low energy neutrons. To enhance the extraction efficiency of VCN replica supermirrors are developing. They are Ni-Ti multilayers and Cu is electroplated. The measured neutron reflectivity shows the god accordance with the calculated result. The multistage neutron turbine using multilayer monochromator is proposed as a new mechanical neutron decelerator. the incident angle of neutrons to the reflection blade is perpendicular, and it enables to let neutron go straight through three stages. The incident neutron velocity is about 150 m/s. The velocity change in one stage is much smaller than the Doppler shifter. It makes monochromators much easier to be fabricated. The deceleration efficiency with the monochromator reflectivity of unity in this three stage turbine is about 0.47 from 150 m/s to UCN (5-7 m/s), and that of the final stage is about 0.6 from 50 m/s. (author)
Analysis and development of spatial hp-refinement methods for solving the neutron transport equation
The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4. generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called SN approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of hp-refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into sub-cells, or by order refinement (p-refinement), by increasing the order of the polynomial basis. In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores. These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the
The first part discusses the design and results of a 252Cf-neutron and a 14-MeV neutron benchmark experiment for verifying previously developed theoretical methods for use in the design of a neutron logging tool for uranium borehole exploration. The second part discusses the Science Applications, Inc. (SAI) development of a fast fission monitor for measuring 14-MeV neutrons for a D-T borehole sonde in a high neutron moderating and absorbing environment. The 14-MeV pulsed neutron monitor was used in carrying out the 14-MeV neutron benchmark experiment, and a variation on the method of quantitatively counting many events in one burst of pileup counts, developed for the 14-MeV-pulsed neutron monitor, was employed in successfully counting the epithermal neutrons produced by a short (2 μs) burst of 14-MeV neutrons. Thus, the development of the 14-MeV-neutron monitor and the measurements with 14-MeV neutrons were intimately related
The effect of ion cyclotron resonance heating (ICRH) on (3He)D plasmas at JET was studied with the time of flight optimized rate (TOFOR) spectrometer dedicated to 2.5 MeV dd neutron measurements. In internal transport barrier (ITB) plasma experiments with large 3He concentrations (X(3He)>15%) an increase in neutron yield was observed after the ITB disappeared but with the auxiliary neutral beam injection and ICRH power still applied. The analysis of the TOFOR data revealed the formation of a high energy (fast) D population in this regime. The results were compared to other mode conversion experiments with similar X(3He) but slightly different heating conditions. In this study we report on the high energy neutron tails originating from the fast D ions and their correlation with X(3He) and discuss the light it can shed on ICRH-plasma power coupling mechanisms.
Sunil, C.; Tyagi, Mohit; Biju, K.; Shanbhag, A. A.; Bandyopadhyay, T.
2015-12-01
The scarcity and the high cost of 3He has spurred the use of various detectors for neutron monitoring. A new lithium yttrium borate scintillator developed in BARC has been studied for its use in a neutron rem counter. The scintillator is made of natural lithium and boron, and the yield of reaction products that will generate a signal in a real time detector has been studied by FLUKA Monte Carlo radiation transport code. A 2 cm lead introduced to enhance the gamma rejection shows no appreciable change in the shape of the fluence response or in the yield of reaction products. The fluence response when normalized at the average energy of an Am-Be neutron source shows promise of being used as rem counter.
We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide
This study was conducted to investigate the methodology and feasibility of developing a transportable neutron activation analysis (NAA) system to quantify manganese (Mn) in bone using a portable deuterium–deuterium (DD) neutron generator as the neutron source. Since a DD neutron generator was not available in our laboratory, a deuterium–tritium (DT) neutron generator was used to obtain experimental data and validate the results from Monte Carlo (MC) simulations. After validation, MC simulations using a DD generator as the neutron source were then conducted. Different types of moderators and reflectors were simulated, and the optimal thicknesses for the moderator and reflector were determined. To estimate the detection limit (DL) of the system, and to observe the interference of the magnesium (Mg) γ line at 844 keV to the Mn γ line at 847 keV, three hand phantoms with Mn concentrations of 30 parts per million (ppm), 150 ppm, and 500 ppm were made and irradiated by the DT generator system. The Mn signals in these phantoms were then measured using a 50% high-efficiency high-purity germanium (HPGe) detector. The DL was calculated to be about 4.4 ppm for the chosen irradiation, decay, and measurement time. This was calculated to be equivalent to a DL of about 3.3 ppm for the DD generator system. To achieve this DL with one 50% high-efficiency HPGe detector, the dose to the hand was simulated to be about 37 mSv, with the total body equivalent dose being about 23µSv. In conclusion, it is feasible to develop a transportable NAA system to quantify Mn in bone in vivo with an acceptable radiation exposure to the subject. (paper)
This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (TN) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the TN moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state TN moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations
MORSE-EMP, Monte-Carlo Neutron and Gamma Multigroup Transport with Array Geometry, for PC
A - Description of program or function: MORSE-CGA was developed to add the capability of modeling rectangular lattices for nuclear reactor cores or for multi-partitioned structures. It thus enhances the capability of the MORSE code system. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. It has been designed as a tool for solving most shielding problems. Through the use of multigroup cross sections, the solution of neutron, gamma-ray, or coupled neutron-gamma-ray problems may be obtained in either the forward or adjoint mode. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. Isotropic or anisotropic scattering up to a P16 expansion of the angular distribution is allowed. B - Method of solution: Monte Carlo methods are used to solve the forward and the adjoint transport equations. Quantities of interest are then obtained by summing the contributions over all collisions, and frequently over most of phase space. Standard multigroup cross sections, such as those used in discrete ordinates codes, may be used as input; either CCC-254/ANISN, CCC-42/DTF-IV, or CCC-89/DOT cross section formats are acceptable. Anisotropic scattering is treated for each group-to-group transfer by utilizing a generalized Gaussian quadrature technique. The Morse code is organised into functional modules with simplified interfaces such that new modules may be incorporated with reasonable ease. The modules are (1) random walk, (2) cross section, (3) geometry, (4) analysis, and (5) diagnostic. The MARS module allows the efficient modeling of complex lattice geometries. Computer memory requirements are minimized because fewer body specifications are needed and nesting and repetition of arrays is allowed. While the basic MORSE code assumes the analysis module is user-written, a general analysis package, SAMBO is included. SAMBO handles some
Inversion of Source and Transport Parameters of Relativistic SEPs from Neutron Monitor Data
Agueda, Neus; Bütikofer, Rolf; Vainio, Rami; Heber, Bernd; Afanasiev, Alexander; Malandraki, Olga E.
2016-04-01
We present a new methodology to study the release processes of relativistic solar energetic particles (SEPs) based on the direct inversion of Ground Level Enhancements (GLEs) observed by the worldwide network of neutron monitors (NMs). The new approach makes use of several models, including: the propagation of relativistic SEPs from the Sun to the Earth, their transport in the Earth's magnetosphere and atmosphere, as well as the detection of the nucleon component of the secondary cosmic rays by ground based NMs. The combination of these models allows us to compute the expected ground-level NM counting rates for a series of instantaneous releases from the Sun. The amplitudes of the source components are then inferred by fitting the NM observations with the modeled NM counting rate increases. Within the HESPERIA project, we will develop the first software package for the direct inversion of GLEs and we will make it freely available for the solar and heliospheric communities. Acknowledgement: This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 637324.
On some one-speed neutron transport problems revisited and reformulated
The solution of a number of one-speed neutron transport problems involving infinite media have been re-considered in the light of a transformation first used by Wallace (Wallace, P.R., 1944a. Boundary Conditions at Thin Absorbing Shells and Plates I. Canadian National Research Council Report MT-34; Wallace, P.R., 1944b. On the Thermal Utilisation of Plates in the Presence of Linear Anisotropic Scattering. Canadian National Research Council Report MT-63). The outcome of this transformation is that the infinite medium problem can be reduced to one in terms of an integral equation involving finite regions only. For example, in the case of an infinitely reflected slab, the infinite reflector is removed and its presence transferred to the kernel of a new integral equation. These kernels turn out to be the point or plane kernels of the corresponding infinite medium problem in the pure reflector material. In this paper the method is extended to slabs with arbitrary anisotropic scattering in slab and reflector; it is also applied to reflected spheres. In this case however, there is a limitation that the total mean free path in sphere and reflector be the same. Finally, we comment on the physical meaning of the standard anisotropic formalism and show that a more realistic eigenvalue exists which is directly related to the isotropic fission source. Some numerical results are given to illustrate our conclusions
Hoffman, Adam J.; Lee, John C.
2016-02-01
A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Source Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.
This paper summarized two improvements of a real production code by using vectorization and multitasking techniques. After a short description of Monte Carlo algorithms employed in our neutron transport problems, we briefly describe the work we have done in order to get a vector code. Vectorization principles will be presented and measured performances on the CRAY 1S, CYBER 205 and CRAY X-MP compared in terms of vector lengths. The second part of this work is an adaptation to multitasking on the CRAY X-MP using exclusively standard multitasking tools available with FORTRAN under the COS 1.13 system. Two examples will be presented. The goal of the first one is to measure the overhead inherent to multitasking when tasks become too small and to define a granularity threshold, that is to say a minimum size for a task. With the second example we propose a method that is very X-MP oriented in order to get the best speedup factor on such a computer. In conclusion we prove that Monte Carlo algorithms are very well suited to future vector and parallel computers. (orig.)
Highlights: ► The general theory for the stochastic method of characteristics is given. ► Stochastic space is discretised using the polynomial chaos technique. ► Stochastic Galerkin and collocation methods are used to solve the working equations. ► Fixed source and multiplying problems are used to illustrate the theory. ► For increased compute time, Galerkin methods show little benefit over collocation. - Abstract: The polynomial chaos expansion has been used to solve the mono-energetic stochastic neutron transport equation with the spatial and angular components discretised using the step characteristics method. Uncertainties were assumed to arise purely from the material cross sections and a novel method for treating uncertainties in discrete, uncorrelated, material regions has been proposed. The method is illustrated by numerical and Monte Carlo simulation of the mean, variance and probability density of the scalar flux for the fixed source Reed cell problem and a critical benchmark in one dimension. For the case of the critical benchmark we compare the results from the Newton–Krylov root finding method to that of the stochastic collocation method. We find that there is no benefit in the extra computation of using the Newton–Krylov method.
Transport and mixing of r-process elements in neutron star binary merger blast waves
Montes, Gabriela; Naiman, Jill; Shen, Sijing; Lee, William H
2016-01-01
The r-process nuclei are robustly synthesized in the material ejected during a neutron star binary merger (NSBM), as tidal torques transport angular momentum and energy through the outer Lagrange point in the form of a vast tidal tail. If NSBM are indeed solely responsible for the solar system r- process abundances, a galaxy like our own would require to host a few NSBM per million years, with each event ejecting, on average, about 5x10^{-2} M_sun of r-process material. Because the ejecta velocities in the tidal tail are significantly larger than in ordinary supernovae, NSBM deposit a comparable amount of energy into the interstellar medium (ISM). In contrast to extensive efforts studying spherical models for supernova remnant evolution, calculations quantifying the impact of NSBM ejecta in the ISM have been lacking. To better understand their evolution in a cosmological context, we perform a suite of three-dimensional hydrodynamic simulations with optically-thin radiative cooling of isolated NSBM ejecta expa...
Resonance self-shielding methodology of new neutron transport code STREAM
This paper reports on the development and verification of three new resonance self-shielding methods. The verifications were performed using the new neutron transport code, STREAM. The new methodologies encompass the extension of energy range for resonance treatment, the development of optimum rational approximation, and the application of resonance treatment to isotopes in the cladding region. (1) The extended resonance energy range treatment has been developed to treat the resonances below 4 eV of three resonance isotopes and shows significant improvements in the accuracy of effective cross sections (XSs) in that energy range. (2) The optimum rational approximation can eliminate the geometric limitations of the conventional approach of equivalence theory and can also improve the accuracy of fuel escape probability. (3) The cladding resonance treatment method makes it possible to treat resonances in cladding material which have not been treated explicitly in the conventional methods. These three new methods have been implemented in the new lattice physics code STREAM and the improvement in the accuracy of effective XSs is demonstrated through detailed verification calculations. (author)
Palmer, T S
2003-01-01
In this NEER project, researchers from Oregon State University have investigated the limitations of the treatment of two-phase coolants as a homogeneous mixture in neutron transport calculations. Improved methods of calculating the neutron distribution in binary stochastic mixtures have been developed over the past 10-15 years and are readily available in the transport literature. These methods are computationally more expensive than the homogeneous (or atomic mix) models, but can give much more accurate estimates of ensemble average fluxes and reaction rates provided statistical descriptions of the distributions of the two materials are know. A thorough review of the two-phase flow literature has been completed and the relevant mixture distributions have been identified. Using these distributions, we have performed Monte Carlo criticality calculations of fuel assemblies to assess the accuracy of the atomic mix approximation when compared to a resolved treatment of the two-phase coolant. To understand the ben...
The basket of transport/storage cask must have a structural strength at any temperature expected during storage and transport condition, and must satisfy each function of sub-criticality and heat removal. It is also preferable to increase the number of fuel assemblies in the cask and to reduce the manufacturing cost. The use of aluminium alloy for the basket is preferable because of its high thermal conductivity in order to improve heat removal. Aluminium alloy is lightweight and it is more effective to improve the capacity. The conventional design of aluminium basket had a combination of square tubes, which have structural strength and heat removal function, and the neutron absorption material with high concentration of boron. The developed basket has square tube shape containing neutron absorption materials that has both functions of heat removal and sub-criticality. It is an effective way to improve the storage capacity of fuel assemblies and it is also easy to be assembled
Duerigen, Susan
2013-05-15
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP3 and diffusion equations, which guarantees high accuracy. The SP3 equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP3 transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP3 transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
Time-eigenvalues of the one-speed neutron transport equation in two-medium slabs and spheres
The transport of monoenergetic neutrons with isotropic scattering and vacuum boundary conditions is studied in two-medium spherical and plane systems. The mean-free-path is assumed to be the same in the two media. The two coupled intergral equations that are obtained are numerically solved using the spatial Legendre expansion method (Carlvik's method). Tables and curves of the fundamental and higher time-eigenvalues for various dimensions of the bodies are given
In this work we report an analytical solution for the time-dependent one-dimensional neutron transport equation in cartesian geometry for bounded and unbounded domain. The main idea consists in the application of the Laplace transform technique in time variable, solution of the resulting equation by the LTSN method and reconstruction of the angular flux in time-variable by numerical inversion scheme. We report numerical simulations and results validations with the ones of literature. (author)
A Gaussian-type quadrature formula is derived for Lebesgue-Stieltjes integrals pertaining to the neutron transport theory (one-velocity, isotropic scattering, plane geometry). The quadrature formula originates from an orthogonality property satisfied by the well-known gsub(n)(c, ν) functions which appear in the solution by Legendre expansion of the transport equation. The quadrature formula thus obtained reduces to the classical Gaussian one in the case of a purely capturing medium. An application to the Milne problem is given. Examples of numerical quadratures are carried out in the appendix
Derluyn, Hannelore; Griffa, Michele; Mannes, David; Jerjen, Iwan; Dewanckele, Jan; Vontobel, Peter; Derome, Dominique; Cnudde, Veerle; Lehmann, Eberhard; Carmeliet, Jan
2011-01-01
This article presents coupled data on saline transport, pore filling due to salt crystallization and resulting salt damage in Savonnières limestone. This is achieved by combining the non-destructive techniques of neutron radiography - for transport imaging - and X-ray microtomography - for pore structure and fracture visualization – applied to the same sample when subjecting it to consecutive wetting-drying cycles. Capillary uptake of water, 1.4m sodium sulfate and 5.8m sodium chloride soluti...
Novel high-efficiency fast-neutron detectors were suggested for fan-beam tomography applications. They combine multi-layer polymer converters in gas medium, coupled to thick gaseous electron multipliers (THGEM). Neutron-induced scattering on the converter's hydrogen nuclei results in gas ionization by the escaping recoil-protons between two successive converters. The electrons drift under the action of a homogeneous electric field, parallel to the converter-foil surfaces, towards a position-sensitive THGEM multiplying element. In this work we discuss the results of a systematic study of the electron transport inside a narrow gap between successive converter foils, which affects the performance of the detector, both in terms of detection efficiency and localization properties. The efficiency of transporting ionization electrons was measured along a 0.6 mm wide gas gap in 6 and 10 mm wide polymer converters. Computer simulations provided conceptual understanding of the observations. For drift lengths of 6 mm, electrons were efficiently transported along the narrow gas gap with minimal diffusion-induced losses; an average collection efficiency of 95% was achieved for ionization electrons induced by few keV photoelectrons. The 10 mm height converter yielded considerably lower efficiency due to electrical and mechanical flaws of the converter foils. The results indicate that detection efficiencies of ∼ 7% can be expected for 2.5 MeV neutrons with 300-foils converters, of 6 mm height, 0.4 mm thick foils and 0.6 mm gas gap.
Niranjan, Ram; Rout, R K; Srivastava, R; Kaushik, T C; Gupta, Satish C
2016-03-01
A 17 kJ transportable plasma focus (PF) device with flexible transmission lines is developed and is characterized. Six custom made capacitors are used for the capacitor bank (CB). The common high voltage plate of the CB is fixed to a centrally triggered spark gap switch. The output of the switch is coupled to the PF head through forty-eight 5 m long RG213 cables. The CB has a quarter time-period of 4 μs and an estimated current of 506 kA is delivered to the PF device at 17 kJ (60 μF, 24 kV) energy. The average neutron yield measured using silver activation detector in the radial direction is (7.1 ± 1.4) × 10(8) neutrons/shot over 4π sr at 5 mbar optimum D2 pressure. The average neutron yield is more in the axial direction with an anisotropy factor of 1.33 ± 0.18. The average neutron energies estimated in the axial as well as in the radial directions are (2.90 ± 0.20) MeV and (2.58 ± 0.20) MeV, respectively. The flexibility of the PF head makes it useful for many applications where the source orientation and the location are important factors. The influence of electromagnetic interferences from the CB as well as from the spark gap on applications area can be avoided by putting a suitable barrier between the bank and the PF head. PMID:27036774
The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.)
Teixeira, Paulo Cleber Mendonca
2002-12-01
In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) {delta} (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) {delta} (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring and nuclear properties is used to obtain stable and unstable harmonics and to verify if these exist. It is found that the solution does not present instability in the conditions stated in the new concept of annular pulsed reactor. (author)
Numerical solutions of the monoenergetic neutron transport equation with anisotropic scattering
The Boltzmann equation for monoenergetic neutrons has been solved numerically with high accuracy for homogeneous slabs and spheres with various degree of linear anisotropy. Vacuum boundary conditions are used. The numerical method is based on previous work by Carlvik. Benchmark values of the criticality factor and higher order eigenvalues are given for multiplying systems of thickness or diameter from 10 -5 to 20 mean free paths and with anisotropy coefficients from 0.0 to 0.3. For slab geometry, both even and odd mode eigenvalues are treated. With increasing anisotropy, an increasing number of complex eigenvalues is observer. The total flux is calculated from the eigenvector and tables of the fundamental mode flux are given. Accurate extrapolation distances are derived for various dimensions and anisotropy coefficients from our eigenvalue results on slabs and spheres and from the work by Sanchez on infinite cylinders.The time eigenvalue spectrum in subcritical systems has also been studied. First, the connection between the eigenvalues arising from the time dependent and stationary transport equation is established. Based on this, the spectrum of real time eigenvalues in slabs and spheres is calculated. For spheres, the existence of complex time eigenvalues in the region beyond the value corresponding to the Corngold limit is numerically established. The presence of such eigenvalues has earlier not been proved. It is further shown that the Boltzmann equation for a sphere is significantly simplified when the decay constant is at the Corngold limit. The spectrum of sphere diameters corresponding to this decay constant is calculated for various linear anisotropies, and detailed numerical results are given. (Author)
American Society for Testing and Materials. Philadelphia
2011-01-01
1.1 Need for Neutronics Calculations—An accurate calculation of the neutron fluence and fluence rate at several locations is essential for the analysis of integral dosimetry measurements and for predicting irradiation damage exposure parameter values in the pressure vessel. Exposure parameter values may be obtained directly from calculations or indirectly from calculations that are adjusted with dosimetry measurements; Guide E944 and Practice E853 define appropriate computational procedures. 1.2 Methodology—Neutronics calculations for application to reactor vessel surveillance encompass three essential areas: (1) validation of methods by comparison of calculations with dosimetry measurements in a benchmark experiment, (2) determination of the neutron source distribution in the reactor core, and (3) calculation of neutron fluence rate at the surveillance position and in the pressure vessel. 1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is th...
The activities of the Radiation Shielding Information Center (RSIC) of the Oak Ridge National Laboratory are being utilized in support of fusion reactor technology. The major activities of RSIC include the operation of a computer-based information storage and retrieval system, the collection, packaging, and distribution of large computer codes, and the compilation and dissemination of processed and evaluated data libraries, with particular emphasis on neutron and gamma-ray cross-section data. The Center has acquired thirteen years of experience in serving fission reactor, weapons, and accelerator shielding research communities, and the extension of its technical base to fusion reactor research represents a logical progression. RSIC is currently working with fusion reactor researchers and contractors in computer code development to provide tested radiation transport and shielding codes and data library packages. Of significant interest to the CTR community are the 100 energy group neutron and 21 energy group gamma-ray coupled cross-section data package (DLC-37) for neutronics studies, a comprehensive 171 energy group neutron and 36 energy group gamma-ray coupled cross-section data base with retrieval programs, including resonance self-shielding, that are tailored to CTR application, and a data base for the generation of energy-dependent atomic displacement and gas production cross sections and heavy-particle-recoil spectra for estimating radiation damage to CTR structural components
TN trademark Resin Vyal, a patent pending composite, is a new neutron shielding material developed by COGEMA LOGISTICS for transport/storage casks of radioactive materials (spent fuel, reprocessed fuel,..). This material is composed of a thermosetting resin (vinylester resin in solution of styrene) and two mineral fillers (alumine hydrate and zinc borate). Its shielding ability for neutron radiation is related to a high hydrogen content (for slowing down neutrons) and a high boron content (for absorbing neutrons). Source of hydrogen is organic matrix (resin) and alumine hydrate; source of boron is zinc borate. Atomic concentrations are equal to 5.1022 at/cm3 for hydrogen and 9.1020 at/cm3 for boron. Due to the flame retardant character of components, the final material has a good fire resistance (it is auto-extinguishable). Its density is equal to 1,8. The manufacturing process of these material is easy: it consists in mixing the fillers and pouring in-situ (in cask); so, the curing of this composite, which leads to a three-dimensional structure, takes place at ambient temperature. Temperature resistance of this material was evaluated by performing exposition tests of samples at different temperatures (150 C to 170 C). According to tests results, its maximal temperature of use was confirmed equal to 160 C
Bergmann, Ryan
Graphics processing units, or GPUs, have gradually increased in computational power from the small, job-specific boards of the early 1990s to the programmable powerhouses of today. Compared to more common central processing units, or CPUs, GPUs have a higher aggregate memory bandwidth, much higher floating-point operations per second (FLOPS), and lower energy consumption per FLOP. Because one of the main obstacles in exascale computing is power consumption, many new supercomputing platforms are gaining much of their computational capacity by incorporating GPUs into their compute nodes. Since CPU-optimized parallel algorithms are not directly portable to GPU architectures (or at least not without losing substantial performance), transport codes need to be rewritten to execute efficiently on GPUs. Unless this is done, reactor simulations cannot take full advantage of these new supercomputers. WARP, which can stand for ``Weaving All the Random Particles,'' is a three-dimensional (3D) continuous energy Monte Carlo neutron transport code developed in this work as to efficiently implement a continuous energy Monte Carlo neutron transport algorithm on a GPU. WARP accelerates Monte Carlo simulations while preserving the benefits of using the Monte Carlo Method, namely, very few physical and geometrical simplifications. WARP is able to calculate multiplication factors, flux tallies, and fission source distributions for time-independent problems, and can run in both criticality or fixed source modes. WARP can transport neutrons in unrestricted arrangements of parallelepipeds, hexagonal prisms, cylinders, and spheres. WARP uses an event-based algorithm, but with some important differences. Moving data is expensive, so WARP uses a remapping vector of pointer/index pairs to direct GPU threads to the data they need to access. The remapping vector is sorted by reaction type after every transport iteration using a high-efficiency parallel radix sort, which serves to keep the
Zarebanadkouki, Mohsen; Kroener, Eva; Kaestner, Anders; Carminati, Andrea
2014-10-01
Our understanding of soil and plant water relations is limited by the lack of experimental methods to measure water fluxes in soil and plants. Here, we describe a new method to noninvasively quantify water fluxes in roots. To this end, neutron radiography was used to trace the transport of deuterated water (D2O) into roots. The results showed that (1) the radial transport of D2O from soil to the roots depended similarly on diffusive and convective transport and (2) the axial transport of D2O along the root xylem was largely dominated by convection. To quantify the convective fluxes from the radiographs, we introduced a convection-diffusion model to simulate the D2O transport in roots. The model takes into account different pathways of water across the root tissue, the endodermis as a layer with distinct transport properties, and the axial transport of D2O in the xylem. The diffusion coefficients of the root tissues were inversely estimated by simulating the experiments at night under the assumption that the convective fluxes were negligible. Inverse modeling of the experiment at day gave the profile of water fluxes into the roots. For a 24-d-old lupine (Lupinus albus) grown in a soil with uniform water content, root water uptake was higher in the proximal parts of lateral roots and decreased toward the distal parts. The method allows the quantification of the root properties and the regions of root water uptake along the root systems. PMID:25189533
A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods
Zhang, H.; Zheng, Y.; Wu, H.; Cao, L. [School of Nuclear Science and Technology, Xi' an Jiaotong University, No. 28, Xianning West Road, Xi' an, Shaanxi 710049 (China)
2013-07-01
A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)
A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods
A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)
Report on the repair of the OPAL neutron beam transport system
The OPAL research reactor commenced operation early in 2007, and has been in continuous operation for most of the time since then. Initial characterization measurements of the cold and thermal neutron beams that feed the neutron guide hall confirmed the high fluxes that had been predicted in the design process. However, by 2011 it was clear that the performance of the neutron guide system had degraded substantially. Investigation revealed that the degradation resulted from delamination of the guides. The root cause was build-up of mechanical stress in the glass substrates due to alpha radiation produced during neutron capture by boron in the glass. Remediation involved replacement of 72 metres of the neutron guide system with guides that use glass substrates which have higher radiation resistance. Neutron flux and spectrum measurements have since verified that the performance of the system has largely been restored. Preliminary measurements at the neutron spectrometers since repair reveal flux increases in the range of 40 % to 90 % relative to 2011
Cortesi, M; Adams, R; Dangendorf, V; Breskin, A; Mayer, S; Hoedlmoser, H; Prasser, H -M
2012-01-01
Novel high efficiency fast-neutron detectors were suggested for fan-beam tomography applications. They combine multi-layer polymer converters in gas medium, coupled to thick gaseous electron multipliers (THGEM). In this work we discuss the results of a systematic study of the electron transport inside a narrow gap between successive converter foils, which affects the performance of the detector, both in terms of detection efficiency and localization properties. The efficiency of transporting ionization electrons was measured along a 0.6 mm wide gas gap in 6 and 10 mm wide polymer converters Computer simulations provided conceptual understanding of the observations. For a drift lengths of 6 mm electrons were efficiently transported along the narrow gas gap, with minimal diffusion-induced losses; an average collection efficiency of 95% was achieved for the ionization electrons induced by a primary electron of a few keV initial energy. The 10 mm height converter yielded considerably lower efficiency due to elect...
Radiation transport in earth for neutron and gamma ray point sources above an air-ground interface
Two-dimensional discrete ordinates methods were used to calculate the instantaneous dose rate in silicon and neutron and gamma ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 meters) above an air--ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth--concrete model containing 0.9 meters of borated concrete beginning 0.5 meters below the earth's surface to obtain fluence distributions to a depth of 3.0 meters. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon and, in all cases, the secondary gamma ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths greater than 0.6 meter. 4 figures, 4 tables
Questions, related to Monte-Carlo method for solution of neutron and photon transport equation, are discussed in the work concerned. Problems dealing with direct utilization of information from evaluated nuclear data files in run-time calculations are considered. ENDF-6 format libraries have been used for calculations. Approaches provided by the rules of ENDF-6 files 2, 3-6, 12-15, 23, 27 and algorithms for reconstruction of resolved and unresolved resonance region cross sections under preset energy are described. The comparison results of calculations made by NJOY and GRUCON programs and computed cross sections data are represented. Test computation data of neutron leakage spectra for spherical benchmark-experiments are also represented. (authors)
Radiation transport in earth for neutron and gamma ray point sources above an air-ground interface
Lillie, R.A.; Santoro, R.T.
1979-03-01
Two-dimensional discrete ordinates methods were used to calculate the instantaneous dose rate in silicon and neutron and gamma ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 meters) above an air--ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth--concrete model containing 0.9 meters of borated concrete beginning 0.5 meters below the earth's surface to obtain fluence distributions to a depth of 3.0 meters. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon and, in all cases, the secondary gamma ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths greater than 0.6 meter. 4 figures, 4 tables.
Radiation transport in earth for neutron and gamma-ray point sources above an air-ground interface
Two-dimensional discrete-ordinates methods have been used to calculate the instantaneous dose rate in silicon and neutron and gamma-ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 m) above an air-ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth-concrete model containing 0.9 m of borated concrete beginning 0.5 m below the earth's surface to obtain fluence distributions to a depth of 3.0 m. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon, and in all cases, the secondary gamma-ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths > 0.6 m
Radiation transport in earth for neutron and gamma-ray point sources above an air-ground interface
Lillie, R.A.; Santoro, R.T.
1980-01-01
Two-dimensional discrete-ordinates methods have been used to calculate the instantaneous dose rate in silicon and neutron and gamma-ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 m) above an air-ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth-concrete model containing 0.9 m of borated concrete beginning 0.5 m below the earth's surface to obtain fluence distributions to a depth of 3.0 m. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon, and in all cases, the secondary gamma-ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths > 0.6 m.
Full Core, Heterogeneous, Time Dependent Neutron Transport Calculations with the 3D Code DeCART
Hursin, Mathieu
2010-01-01
The current state of the art in reactor physics methods to assess safety, fuel failure, and operability margins for Design Basis Accidents (DBAs) for Light Water Reactors (LWRs) rely upon the coupling of nodal neutronics and one-dimensional thermal hydraulic system codes. The neutronic calculations use a multi-step approach in which the assembly homogenized macroscopic cross sections and kinetic parameters are first calculated using a lattice code for the range of conditions (temperatures, bu...
The MOOSE based reactor physics tool MAMMOTH provides the capability to seamlessly couple the neutron transport application RATTLESNAKE to the fuels performance application BISON to produce a higher fidelity tool for fuel performance simulations. The ultimate purpose of this coupling is to provide a tool with the predictive capabilities to gain new knowledge and help resolve fundamental questions in the fuel performance arena, i.e. high-burnup structures, pellet-cladding interaction, missing pellet surface, etc. RATTLESNAKE solves the self-adjoint angular flux transport equation, derived from the linearized Boltzmann transport equation, and provides a sub-pin level resolution of the multigroup neutron flux. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. The coupling within the MOOSE framework allows both applications to solve their respective systems on aligned and unaligned unstructured finite element meshes. MAMMOTH uses the power density calculated by RATTLESNAKE to compute the local burnup evolution. Subsequently, MAMMOTH transfers the power density and burnup distribution to BISON with the MOOSE Multiapp transfer system. BISON in turn is able to provide sub-pin level temperature for cross section feed back effects. Multiple depletion cases were run with one-way and two-way data transfer in MAMMOTH for RATTLESNAKE-BISON. The one-way eigenvalues obtained show good agreement with the reference values obtained from the lattice physics code DRAGON4 while the two-way eigenvalue show expected differences. The power distributions obtained are consistent with both DRAGON4 and the SERPENT Monte Carlo code. The one-way and two-way calculations produce power density results that are comparable with those of the internal, static, Lassmannstyle model in BISON. Differences in the power densities arise from the use of better neutron energy deposition parameters obtained from the DRAGON4 tabulations, and differences in the fuel
A specialized moments-method computer code was constructed for the calculation of the even spatial moments of the scalar flux, phi/sub 2n/, through 2n = 80. Neutron slowing-down and transport in a medium with constant cross sections was examined and the effect of a superimposed square-well cross section minimum on the penetrating flux was studied. In the constant cross section case, for nuclei that are not too light, the scalar flux is essentially independent of the nuclide mass. The numerical results obtained were used to test the validity of existing analytic approximations to the flux at both small and large lethargies relative to the source energy. As a result it was possible to define the regions in the lethargy--distance plane where these analytic solutions apply with reasonable accuracy. A parametric study was made of the effect of a square-well cross section minimum on neutron fluxes at energies below the minimum. It was shown that the flux at energies well below the minimum is essentially independent of the position of the minimum in lethargy. The results can be described by a convolution-of-sources model involving only the lethargy separation between detector and source, the width and the relative depth of the minimum. On the basis of the computations and the corresponding model, it is possible to predict, e.g., the conditions under which transport in the region of minimum completely determines the penetrating flux. At the other extreme, the model describes when the transport in the minimum can be treated in the same manner as in any comparable lethargy interval. With the aid of these criteria it is possible to understand the apparent paradoxical effects of certain minima in neutron penetration through such media as iron and sodium
The fundamental motivation for the research presented in this dissertation was the need to development a more accurate prediction method for characterization of mixed radiation fields around medical electron accelerators (MEAs). Specifically, a model is developed for simulation of neutron and other particle production from photonuclear reactions and incorporated in the Monte Carlo N-Particle (MCNP) radiation transport code. This extension of the capability within the MCNP code provides for the more accurate assessment of the mixed radiation fields. The Nuclear Theory and Applications group of the Los Alamos National Laboratory has recently provided first-of-a-kind evaluated photonuclear data for a select group of isotopes. These data provide the reaction probabilities as functions of incident photon energy with angular and energy distribution information for all reaction products. The availability of these data is the cornerstone of the new methodology for state-of-the-art mutually coupled photon-neutron transport simulations. The dissertation includes details of the model development and implementation necessary to use the new photonuclear data within MCNP simulations. A new data format has been developed to include tabular photonuclear data. Data are processed from the Evaluated Nuclear Data Format (ENDF) to the new class ''u'' A Compact ENDF (ACE) format using a standalone processing code. MCNP modifications have been completed to enable Monte Carlo sampling of photonuclear reactions. Note that both neutron and gamma production are included in the present model. The new capability has been subjected to extensive verification and validation (V and V) testing. Verification testing has established the expected basic functionality. Two validation projects were undertaken. First, comparisons were made to benchmark data from literature. These calculations demonstrate the accuracy of the new data and transport routines to better than 25 percent. Second, the ability to
Morgan C. White
2000-07-01
The fundamental motivation for the research presented in this dissertation was the need to development a more accurate prediction method for characterization of mixed radiation fields around medical electron accelerators (MEAs). Specifically, a model is developed for simulation of neutron and other particle production from photonuclear reactions and incorporated in the Monte Carlo N-Particle (MCNP) radiation transport code. This extension of the capability within the MCNP code provides for the more accurate assessment of the mixed radiation fields. The Nuclear Theory and Applications group of the Los Alamos National Laboratory has recently provided first-of-a-kind evaluated photonuclear data for a select group of isotopes. These data provide the reaction probabilities as functions of incident photon energy with angular and energy distribution information for all reaction products. The availability of these data is the cornerstone of the new methodology for state-of-the-art mutually coupled photon-neutron transport simulations. The dissertation includes details of the model development and implementation necessary to use the new photonuclear data within MCNP simulations. A new data format has been developed to include tabular photonuclear data. Data are processed from the Evaluated Nuclear Data Format (ENDF) to the new class ''u'' A Compact ENDF (ACE) format using a standalone processing code. MCNP modifications have been completed to enable Monte Carlo sampling of photonuclear reactions. Note that both neutron and gamma production are included in the present model. The new capability has been subjected to extensive verification and validation (V&V) testing. Verification testing has established the expected basic functionality. Two validation projects were undertaken. First, comparisons were made to benchmark data from literature. These calculations demonstrate the accuracy of the new data and transport routines to better than 25 percent. Second
This report describes a major revision of the DIAMANT2 code, which evolved from the DIAMANT-code. DIAMANT2 solves the static multigroup neutron transport equation in planar geometry using the SN-method. Spatial discretization is accomplished by taking finite differences on a meshgrid composed of equilateral triangles. This new version of DIAMANT2 is written in FORTRAN 77 and designed to run on scalar and vector computers. This report contains a detailed documentation of the program and the input description as well as some experiences gained with the code on several vector computers. (orig.)
FEM-RZ, 2-D Multigroup Neutron Transport in R-Z Geometry, Eigenvalue and Fixed Source Problems
1 - Nature of the physical problem solved: FEM-RZ is a computer program for solving multi-group neutron transport problems in two-dimensional cylindrical (r,z) geometry. It can solve not only eigenvalue problems but also other problems, such as fixed source problems. 2 - Method of solution: The method of higher order finite elements is used for the spatial variables. It is based on the discontinuous method with Galerkin-type scheme. The discrete ordinate Sn method is used for the angular variables. 3 - Restrictions on the complexity of the problem: No restrictions except for computer size
The pulsed neutron experiments rest, as is well known, on the assumption that the neutron transport equation, in a finite bare body, possesses at least one discrete eigenvalue. Nelkin and then Corngold pointed out that this assumption could no longer be true if the sample is very small. Their arguments, however, were based on certain simplifying assumptions about the scattering kernel or the spatial dependence of the neutron density, which could, in principle, greatly restrict the validity of their results when dealing with realistic problems. We have thus preferred to attack the problem from a quite general point of view, which resembles, in many aspects, the approach of Lehner and Wing’s paper, ''On the spectrum of an asymmetric operator arising in the transport theory of neutron'', relating to the one-velocity theory. We have considered the integro-differential transport equation in a finite homogeneous convex body of an arbitrary shape, surrounded by vacuum. The free gas-scattering kernel (averaged over the angles, so that the scattering is isotropic) has been adopted, and then the absorption has been assumed to follow the ''1/v'' law. Let then lim vΣs(v) = h0, where h0 results in a positive constant. v->0 The eigenvalue spectrum of the transport equation can be shown to have the following structure: the half-plane Re λ ≤ -h0 is occupied by a densely distributed spectrum (let us say ''continuous spectrum''), while the remaining half-plane Re λ > - h0 contains at most a finite number of real eigenvalues λi. It has been shown that the number of the discrete eigenvalues can reduce to zero if the body is small enough (of the order of a mean free path). Thus we see that Nelkin’s idea on the disappearing of the decay modes for samples of very small size is correct also within our general assumptions. As far as we know the experimental results do not seem to provide an unambiguous answer pro or contra this theoretical assertion. We are now developing a
The flux limited diffusion theory is able to determine the fast neutron flux density in regions outside the reactor core, especially in the pressure vessel. Only transport calculations predict the flux distribution with sufficient accuracy in this field. Diffusion coefficients are adjusted by the use of a sophisticated theory. There is no need for preceeding transport calculations as compared to other methods. Originally this theory is limited to one-dimensional geometry and isotropic scattering. Fundamental investigations and a calculation of a Benchmark experiment have been carried out to verify the method. A P1-approximation of the scattering source was introduced additionally, resulting in good agreement between diffusion and corresponding transport flux distributions. The procedure was generalized to two-dimensional geometries. In connection with a diffusion code the method was implemented and tested. Flux distributions, calculated in this way, indicate negligible deviations in the pressure vessel compared with transport results. The required computing time was reduced to about one half of the corresponding transport calculation. (orig./HP)
The use of universal neutron transport codes in order to calculate the parameters of well-logging probes presents a new approach first tried in U.S.A. and UK in the eighties. This paper deals with first such an attempt in Poland. The work is based on the use of MORSE code developed in Oak Ridge National Laboratory in U.S.A.. Using CG MORSE code we calculated neutron detector response when surrounded with sandstone of porosities 19% and 38%. During the work it come out that it was necessary to investigate different methods of estimation of the neutron flux. The stochastic estimation method as used currently in the original MORSE code (next collision approximation) can not be used because of slow convergence of its variance. Using the analog type of estimation (calculation of the sum of track lengths inside detector) we obtained results of acceptable variance (∼ 20%) for source-detector spacing smaller than 40 cm. The influence of porosity on detector response is correctly described for detector positioned at 27 cm from the source. At the moment the variances are quite large. (author). 33 refs, 8 figs, 8 tabs
Further development of semigroup method for modeling the time dependent neutron transport
By using semi groups generated by linear Boltzmann transport operator, an equivalent transport equation, having analytical solution, has been derived. A direct relation between the Case stationary eigenfunctions and eigenvalues and the corresponding quantities for the proposed transformed transport operator, has been shown. A generalization to heterogeneous system including arbitrary scattering anisotropy is shown as well. (author)
A Monte Carlo code (MORSE-SGC) from the Radiation Shielding Information Centre at Oak Ridge National Laboratory, USA, has been adapted and used to model radiation transport in the Auckland prompt gamma in vivo neutron activation analysis facility. Preliminary results are presented for the slow neutron flux in an anthropomorphic phantom which are in broad agreement with those obtained by measurement via activation foils. Since experimental optimization is not logistically feasible and since theoretical optimization of neutron activation facilities has not previously been attempted, it is hoped that the Monte Carlo calculations can be used to provide a basis for improved system design
Gleicher, Frederick N.; Williamson, Richard L.; Ortensi, Javier; Wang, Yaqi; Spencer, Benjamin W.; Novascone, Stephen R.; Hales, Jason D.; Martineau, Richard C.
2014-10-01
The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.
In this paper, the accuracy and computational efficiency of the efficient consistent spatial homogenization method (ECSH) in neutron transport theory is assessed in a 1D benchmark problem characteristic of gas cooled thermal systems that are extremely challenging for conventional homogenization methods because of their longer neutron mean free path than water-based thermal reactors. The ECSH method is an extension of the consistent spatial homogenization method by using: (1) B-spline instead of Fourier series for the expansion of the spatial domain in the auxiliary cross section term and (2) a source iteration scheme instead of local fixed-source calculations in the re-homogenization procedure. Furthermore, the effect of the angular expansion order in the definition of the auxiliary cross section is studied. This method can be viewed as a significant improvement in accuracy of standard homogenization methods used for VHTR whole core analysis in which core environment effects are pronounced. It is shown that the ECSH method can reproduce the heterogeneous transport solution with up to 4 times faster computational speed, depending on the configuration of the control rods while maintaining reasonable accuracy and robust re-homogenization procedure. (author)
A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the Keff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for Keff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)
3-D Deep Penetration Neutron Imaging of Thick Absorgin and Diffusive Objects Using Transport Theory
Ragusa, Jean; Bangerth, Wolfgang
2011-08-01
here explores the inverse problem of optical tomography applied to heterogeneous domains. The neutral particle transport equation was used as the forward model for how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newtons method served as the basis of the inverse problem. Optical tomography aims at reconstructing the material properties using (a) illuminating sources and (b) detector readings. However, accurate simulations for radiation transport require that the particle (gamma and/or neutron) energy be appropriate discretize in the multigroup approximation. This, in turns, yields optical tomography problems where the number of unknowns grows (1) about quadratically with respect to the number of energy groups, G, (notably to reconstruct the scattering matrix) and (2) linearly with respect to the number of unknown material regions. As pointed out, a promising approach could rely on algorithms to appropriately select a material type per material zone rather than G2 values. This approach, though promising, still requires further investigation: (a) when switching from cross-section values unknowns to material type indices (discrete integer unknowns), integer programming techniques are needed since derivative information is no longer available; and (b) the issue of selecting the initial material zoning remains. The work reported here proposes an approach to solve the latter item, whereby a material zoning is proposed using one-group or few-groups transport approximations. The capabilities and limitations of the presented method were explored; they are briefly summarized next and later described in fuller details in the Appendices. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the
Approximate high-order eigenvalues in two-medium, one-speed neutron transport
Earlier work on high-order criticality eigenvalues in homogeneous systems with neutrons of one speed has been extended to two-medium systems. Reflected spheres as well as reflected infinite slabs and cylinders have been studied. Values from the derived formulae have been compared with numerical results obtained recently by Garis for spheres and slabs. The agreement is generally good. (author)
Bergmann, Ryan
Graphics processing units, or GPUs, have gradually increased in computational power from the small, job-specific boards of the early 1990s to the programmable powerhouses of today. Compared to more common central processing units, or CPUs, GPUs have a higher aggregate memory bandwidth, much higher floating-point operations per second (FLOPS), and lower energy consumption per FLOP. Because one of the main obstacles in exascale computing is power consumption, many new supercomputing platforms are gaining much of their computational capacity by incorporating GPUs into their compute nodes. Since CPU-optimized parallel algorithms are not directly portable to GPU architectures (or at least not without losing substantial performance), transport codes need to be rewritten to execute efficiently on GPUs. Unless this is done, reactor simulations cannot take full advantage of these new supercomputers. WARP, which can stand for ``Weaving All the Random Particles,'' is a three-dimensional (3D) continuous energy Monte Carlo neutron transport code developed in this work as to efficiently implement a continuous energy Monte Carlo neutron transport algorithm on a GPU. WARP accelerates Monte Carlo simulations while preserving the benefits of using the Monte Carlo Method, namely, very few physical and geometrical simplifications. WARP is able to calculate multiplication factors, flux tallies, and fission source distributions for time-independent problems, and can run in both criticality or fixed source modes. WARP can transport neutrons in unrestricted arrangements of parallelepipeds, hexagonal prisms, cylinders, and spheres. WARP uses an event-based algorithm, but with some important differences. Moving data is expensive, so WARP uses a remapping vector of pointer/index pairs to direct GPU threads to the data they need to access. The remapping vector is sorted by reaction type after every transport iteration using a high-efficiency parallel radix sort, which serves to keep the
High-energy neutron transport file for the 209Bi isotope
The simulation of the nuclear processes, occurring in media irradiated with high-energy particles, promote the elaboration of high-energy transport files. These files being used in versatile computer codes, such as MCNP, allow to simulate with high accuracy particle transport. High-energy transport files are very important for the investigation of accelerator-driven systems. The detailed description of the methods and codes used for the elaboration of the file for 209Bi is presented in this paper. (orig.)
Pinchedez, K
1999-06-01
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
Arreola V, G. [IPN, Escuela Superior de Fisica y Matematicas, Posgrado en Ciencias Fisicomatematicas, area en Ingenieria Nuclear, Unidad Profesional Adolfo Lopez Mateos, Edificio 9, Col. San Pedro Zacatenco, 07730 Mexico D. F. (Mexico); Vazquez R, R.; Guzman A, J. R., E-mail: energia.arreola.uam@gmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 Mexico D. F. (Mexico)
2012-10-15
In this work a comparative analysis of the results for the neutrons dispersion in a not multiplicative semi-infinite medium is presented. One of the frontiers of this medium is located in the origin of coordinates, where a neutrons source in beam form, i.e., {mu}{omicron}=1 is also. The neutrons dispersion is studied on the statistical method of Monte Carlo and through the unidimensional transport theory and for an energy group. The application of transport theory gives a semi-analytic solution for this problem while the statistical solution for the flow was obtained applying the MCNPX code. The dispersion in light water and heavy water was studied. A first remarkable result is that both methods locate the maximum of the neutrons distribution to less than two mean free trajectories of transport for heavy water, while for the light water is less than ten mean free trajectories of transport; the differences between both methods is major for the light water case. A second remarkable result is that the tendency of both distributions is similar in small mean free trajectories, while in big mean free trajectories the transport theory spreads to an asymptote value and the solution in base statistical method spreads to zero. The existence of a neutron current of low energy and toward the source is demonstrated, in contrary sense to the neutron current of high energy coming from the own source. (Author)
Megavoltage photons above 10 MeV used in external beam radiotherapy lead to a significant photo-neutron fluence, which must be taken into account in bunker design (IPEM, 1997, Report 75, The design of radiotherapy treatment room facilities). This work describes Monte-Carlo simulations of such neutrons for a proposed bunker, which is to house a 15 MV accelerator. Neutron fluence spectra and absorbed dose due to neutrons and neutron-capture photons were scored at the accelerator iso centre and at the maze entrance for mono-energetic neutron sources of 0.5, 3 and 6 MeV. The reduction in neutron and photon dose at the maze entrance, achieved by cladding concrete maze walls with either wood, polyethylene or a commercially available plastic, was determined.
Analysis and evaluation of critical experiments for validation of neutron transport calculations
The calculation schemes, computational codes and nuclear data used in neutronic design require validation to obtain reliable results. In the nuclear criticality safety field this reliability also translates into a higher level of safety in procedures involving fissile material. The International Criticality Safety Benchmark Evaluation Project is an OECD/NEA activity led by the United States, in which participants from over 20 countries evaluate and publish criticality safety benchmarks. The product of this project is a set of benchmark experiment evaluations that are published annually in the International Handbook of Evaluated Criticality Safety Benchmark Experiments. With the recent participation of Argentina, this information is now available for use by the neutron calculation and criticality safety groups in Argentina. This work presents the methodology used for the evaluation of experimental data, some results obtained by the application of these methods, and some examples of the data available in the Handbook.
Milgram, Michael S. [P.O. Box 1484, Deep River, Ont., K0J 1P0 (Canada)]. E-mail: mike@geometrics-unlimited.com
2005-07-15
Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.
VIM4.0, Stead-State 3-D Neutron Transport Using ENDF/B or Multigroup Cross Sections
1 - Description of program or function: VIM solves the steady-state neutron or photon transport problem in any detailed three-dimensional geometry using either continuous energy-dependent ENDF nuclear data or multigroup cross sections. Neutron transport is carried out in a criticality mode, or in a fixed source mode (optionally incorporating subcritical multiplication). Photon transport is simulated in the fixed source mode. The geometry options are infinite medium, combinatorial geometry, and hexagonal or rectangular lattices of combinatorial geometry unit cells, and rectangular lattices of cells of assembled plates. Boundary conditions include vacuum, specular and white reflection, and periodic boundaries for reactor cell calculations. The VIM 4.0 distribution includes data from ENDF/B-IV, ENDF/B-V, ENDF/B-VI and JEF2.2. Binary sequential data libraries for use with the code system on IBM or Sun workstations are included. ASCII data libraries and a convenient means to convert them to binary on a target machine are included for users on other systems. In addition to be included in the RSICC distribution files, the VIM User Guide is available on the developer's web site http://www.ra.anl.gov/vimguide/. 2 - Methods:VIM uses standard Monte Carlo methods for particle tracking with several optional variance-reduction techniques. These include splitting/Russian roulette, non-terminating absorption with non-analog weight cutoff energy. The keff is determined by the optimum linear combinations of two of the three eigenvalue estimates - analog, collision, and track length. Resonance and smooth cross sections are specified pointwise with linear-linear interpolation, frequently with many thousands of energy points. Unresolved resonances are described by the probability table method, which allows the statistical nature of the evaluated resonance cross sections to be incorporated naturally into self-shielding. Neutron interactions are elastic, inelastic and thermal scattering
Boillat, P; Oberholzer, P; Seyfang, B C; Kästner, A; Perego, R; Scherer, G G; Lehmann, E H; Wokaun, A
2011-06-15
A method combining (2)H labeling of different sources of H atoms (hydrogen, water vapor) with neutron imaging for the analysis of transport parameters in the bulk and at the interfaces of Nafion polymer electrolyte membranes is proposed. The use of different isotope compositions in the steady state allows evaluation of the relation between bulk and interface transport parameters, but relies on literature data for evaluating absolute values. By using transients of isotope composition, absolute values of these parameters including the self-diffusion coefficient of H can be extracted, making this method an attractive alternative to self-diffusion measurements using nuclear magnetic resonance (NMR), allowing measurements in precisely controlled conditions in real fuel cell structures. First measurements were realized on samples with and without electrodes and we report values of the self-diffusion coefficient of the same order of magnitude as values measured using NMR, although with slightly higher numbers. In our particular case, lower interfacial exchange rates for water transport were observed for samples with an electrode. PMID:21613688
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution
Biondo, Elliott D [ORNL; Ibrahim, Ahmad M [ORNL; Mosher, Scott W [ORNL; Grove, Robert E [ORNL
2015-01-01
Detailed radiation transport calculations are necessary for many aspects of the design of fusion energy systems (FES) such as ensuring occupational safety, assessing the activation of system components for waste disposal, and maintaining cryogenic temperatures within superconducting magnets. Hybrid Monte Carlo (MC)/deterministic techniques are necessary for this analysis because FES are large, heavily shielded, and contain streaming paths that can only be resolved with MC. The tremendous complexity of FES necessitates the use of CAD geometry for design and analysis. Previous ITER analysis has required the translation of CAD geometry to MCNP5 form in order to use the AutomateD VAriaNce reducTion Generator (ADVANTG) for hybrid MC/deterministic transport. In this work, ADVANTG was modified to support CAD geometry, allowing hybrid (MC)/deterministic transport to be done automatically and eliminating the need for this translation step. This was done by adding a new ray tracing routine to ADVANTG for CAD geometries using the Direct Accelerated Geometry Monte Carlo (DAGMC) software library. This new capability is demonstrated with a prompt dose rate calculation for an ITER computational benchmark problem using both the Consistent Adjoint Driven Importance Sampling (CADIS) method an the Forward Weighted (FW)-CADIS method. The variance reduction parameters produced by ADVANTG are shown to be the same using CAD geometry and standard MCNP5 geometry. Significant speedups were observed for both neutrons (as high as a factor of 7.1) and photons (as high as a factor of 59.6).
Today neutron transport in PWR's core is routinely computed through the transport-diffusion(2 groups) scheme. This method gives satisfactory results for reactors operating in normal conditions but the 2 group diffusion approximation is unable to take into account interface effects or anisotropy. The improvement of this scheme is logically possible through the use of a simplified PN method (SPN) for the modeling of the core. The comparison between SN calculations and SPN calculations shows an excellent agreement on eigenvalues as well as on power maps. We can notice that: -) it is no use extending the development beyond P3, there is no effect; -) the P1 development is adequate; and -) the P0 development is totally inappropriate. Calculations performed on the N4 core of the Chooz power plant have enabled us to compare diffusion operators with transport operators (SP1, SP3, SP5 and SP7). These calculations show that the implementation of the SPN method is feasible but the extra-costs in computation times and memory are important. We recommend: SP5P1 calculations for heterogeneous 2-dimension geometry and SP3P1 calculations for the homogeneous 3-dimension geometry. (A.C.)
Hayashi, Masatoshi
1988-12-01
The reactivity effects of neutron beam tubes in a research reactor were investigated with the two-dimensional transport code DORT. The core model for the calculation was a two-dimensional cylinder. The reactivity effects of one radial and two tangential beam tubes were estimated through the results of the two-dimensional calculation using the space-dependent weight function which is as defined a product of the macroscopic scattering cross section, the forward neutron flux, the adjoint neutron flux and the volume. The reactivity effect of the tangential beam tube is larger than that of the radial tube. An aluminum wall of a beam tube decreases the reactivity of the core due to the neutron absorption.
Košťál, Michal; Milčák, Ján; Cvachovec, František; Jánský, Bohumil; Rypar, Vojtěch; Juříček, Vlastimil; Novák, Evžen; Egorov, Alexander; Zaritskiy, Sergey
2016-02-01
A set of benchmark experiments was carried out in the full scale VVER-1000 mock-up on the reactor LR-0 in order to validate neutron transport calculation methodologies and to perform the optimization of the shape and locations of neutron flux operation monitors channels inside the shielding of the new VVER-1000 type reactors. Compared with previous experiments on the VVER-1000 mock-up on the reactor LR-0, the fast neutron spectra were measured in the extended neutron energy interval (0.1-10 MeV) and new calculations were carried out with the MCNPX code using various nuclear data libraries (ENDF/B VII.0, JEFF 3.1, JENDL 3.3, JENDL 4, ROSFOND 2009, and CENDL 3.1). Measurements and calculations were carried out at different points in the mock-up. The calculation and experimental data are compared.
American Society for Testing and Materials. Philadelphia
2007-01-01
1.1 This practice provides procedures for qualification and acceptance of neutron absorber materials used to provide criticality control by absorbing thermal neutrons in systems designed for nuclear fuel storage, transportation, or both. 1.2 This practice is limited to neutron absorber materials consisting of metal alloys, metal matrix composites (MMCs), and cermets, clad or unclad, containing the neutron absorber boron-10 (10B). 1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
Ghorai, S. K.
1983-01-01
The purpose of this project was to use a one-dimensional discrete coordinates transport code called ANISN in order to determine the energy-angle-spatial distribution of neutrons in a 6-feet cube rock box which houses a D-T neutron generator at its center. The project was two-fold. The first phase of the project involved adaptation of the ANISN code written for an IBM 360/75/91 computer to the UNIVAC system at JSC. The second phase of the project was to use the code with proper geometry, source function and rock material composition in order to determine the neutron flux distribution around the rock box when a 14.1 MeV neutron generator placed at its center is activated.
McClanahan, Timothy; Mirofanov, Igor; Boynton, William; Chin, Gordon; Livengood, Timothy; Su, Jiao Jang; Sagdeev, Raold; Parsons, Ann; Evans, Larry; Starr, Richard; Hamara, Dave; Bodnarik, Julia; Williams, Jeane-Pierre; Mazarico, Erwan; Litvak, Maxim; Sanin, Anton; Murray, Joseph
2016-04-01
We report evidence that the Moon's diurnally modulating neutron flux is being forced by a latitude dependent mix of 1) transient hydrogen-bearing volatiles near the surface in the upper latitudes and 2) regolith temperature variation in lower latitudes. In this study we investigate diurnally varying neutron flux measurements from the Lunar Reconnaissance Orbiter's (LRO) Lunar Exploration Neutron Detector's Collimated Sensor for Epithermal Neutrons (LEND CSETN) and surface temperature observations from the Diviner radiometer poleward of >±45°. Our presentation shows that the modulating neutron flux is not consistent with a regolith temperature control for latitudes >70°. The anticorrelation may be evidence for transported lunar hydrogen volatiles or highly non-uniform regolith compositional dynamics. Observational evidence is consistent with regolith temperature being the source of the neutron flux modulation in the northern mare (45° to 60°) and may be related to its mafic composition and fast neutron contributions. Predictions for hypothesized regolith temperature effects are evaluated using insolation inferred from the Lunar Observing Laser Altimeter (LOLA) topography.
A discrete nodal method for three-dimensional neutron transport numerical calculations
A coarse-mesh, discrete nodal transport method (DNTM) has been developed for efficient numerical solution of the 3-D-transport equation in Cartesian geometry, and it has been encoded in a 3-D nodal transport code, NOTRAND/3C, using quadratic node-interior flux and constant surface foux expansions. It is a logical extension of the previously developed 2-D DNTM. A series of 3-D calculations for the test problems has been performed to verify the code. The numerical results demonstrate that it has very high precision on coarse spatial meshes and superior computational efficiency over the discrete SN method
An additive angular-dependent re-balance (AADR) factor acceleration method is described to accelerate the source iteration of discrete ordinates transport calculation. The formulation of the AADR method follows that of the angular-dependent re-balance (ADR) method in that the re-balance factor is defined only on the cell interface and in that the low-order equation is derived by integrating the transport equation (high-order equation) over angular subspaces. But, the re-balance factor is applied additively. While the AADR method is similar to the boundary projection acceleration and the alpha-weighted linear acceleration, it is more general and does have distinct features. The method is easily extendible to DPN and low-order SN re-balancing, and it does not require consistent discretizations between the high- and low-order equations as in diffusion synthetic acceleration. We find by Fourier analysis and numerical results that the AADR method with a chosen form of weighting functions is unconditionally stable and very effective. There also exists an optimal weighting parameter that leads to the smallest spectral radius. The AADR acceleration method described in this paper is simple to implement, unconditionally stable, and very effective. It uses a physically based weighting function with an optimal parameter, leading to the best spectral radius of ρ<0.1865, compared to ρ<0.2247 of DSA. The application of the AADR acceleration method with the LMB scheme on a test problem shows encouraging results
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
TART2000 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo radiation transport code. This code can run on any modern computer. It is a complete system to assist you with input Preparation, running Monte Carlo calculations, and analysis of output results. TART2000 is also incredibly FAST; if you have used similar codes, you will be amazed at how fast this code is compared to other similar codes. Use of the entire system can save you a great deal of time and energy. TART2000 is distributed on CD. This CD contains on-line documentation for all codes included in the system, the codes configured to run on a variety of computers, and many example problems that you can use to familiarize yourself with the system. TART2000 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART2000 and its data files
In order to improve the accuracy and calculating speed of shielding analyses, MCNP 4, a Monte Carlo neutron and photon transport code system, has been parallelized and measured of its efficiency in the highly parallel distributed memory type computer, AP1000. The code has been analyzed statically and dynamically, then the suitable algorithm for parallelization has been determined for the shielding analysis functions of MCNP 4. This includes a strategy where a new history is assigned to the idling processor element dynamically during the execution. Furthermore, to avoid the congestion of communicative processing, the batch concept, processing multi-histories by a unit, has been introduced. By analyzing a sample cask problem with 2,000,000 histories by the AP1000 with 512 processor elements, the 82 % of parallelization efficiency is achieved, and the calculational speed has been estimated to be around 50 times as fast as that of FACOM M-780. (author)
Cullen, D E
1998-11-22
TART98 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo radiation transport code. This code can run on any modern computer. It is a complete system to assist you with input preparation, running Monte Carlo calculations, and analysis of output results. TART98 is also incredibly FAST; if you have used similar codes, you will be amazed at how fast this code is compared to other similar codes. Use of the entire system can save you a great deal of time and energy. TART98 is distributed on CD. This CD contains on-line documentation for all codes included in the system, the codes configured to run on a variety of computers, and many example problems that you can use to familiarize yourself with the system. TART98 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART98 and its data files.
Performance tests on PNL's transportable neutron/gamma waste waste assay system
Battelle Pacific Northwest Laboratory, in conjunction with Canberra Industries, has implemented a 55-gallon drum waste assay system. The single system unit consists of a combined segmented gamma assay system and a neutron assay system. The unit is designed to function either in the laboratory or in a mobile trailer. The system is on wheels and can be moved through standard double doors. The gamma system uses an HPGe detector with a Se-75 source for transmission corrections. The neutron detector uses 40 He-3 detectors connected to a JSR-12 neutron coincidence counter. The system's software is unique and is interactive with the user; it features a menu driven operator screen from which all functions regarding operations and calibrations can be selected. Single or combined assays with various setups, including containers smaller than 55 gallons, may be performed. The software and analysis is designed for unknown waste contents, but allows input of waste stream information prior to assay. The system was originally designed for safeguards' MC ampersand A requirements and has enough sensitivity to determine whether a drum is TRU or LLW in one assay pass. Typical counting times are approximately 1800 seconds for a dual pass. Preliminary testing of the system with the available Pu standards has shown the system will perform to the required levels stated in the Data Quality Objectives of the WIPP Performance Demonstration program. An overall study of the system is underway to determine the lower limit of detection (LLD) for different isotopes, to best utilize the combined assay results, and to apply the appropriate data corrections for more complete answers, such as corrections for the end effects. Results from these developments will be presented at the conference
The main objective of this work is to create a neutronic calculations system for the SILOE-SILOETTE reactors, adaptable to other types of plate reactors. The author presents the methodology and the development of the APOLLO 1D (99 gr.) calculations for the creation of cross sections libraries. After a recall of the Discrete Ordinate Method (DOT), the method accuracy is studied in order to optimize the spatial discretization of the calculations; calculations of DOT 3.5 and of SILOETTE core are conducted and their convergence and costs are examined. DOT calculations of SILOETTE and experimental tests results are then compared
Assessing the impact of increased transport time between failed fuel and delayed neutron detectors
A typical DN monitoring system in use in CANDU reactors is discussed and a mathematical model is developed to simulate the transport from a fuel defect location to the DN detectors. This model will be used to determine the impact of an increased transport time to the DN monitors due to pipe fouling and to quantify the contribution from tramp uranium to the total background activity in the PHTS. The model may be applied to CANDU-6 designs with minor modifications. (author)
Chang, B
2004-03-22
This paper contains three analytical solutions of transport problems which can be used to test ray-effect errors in the numerical solutions of the Boltzmann Transport Equation (BTE). We derived the first two solutions and the third was shown to us by M. Prasad. Since this paper is intended to be an internal LLNL report, no attempt was made to find the original derivations of the solutions in the literature in order to cite the authors for their work.
A new 2D neutron transport code AutoMOC for arbitrary geometry has been developed. This code is based on the method of characteristics (MOCs) and the customization of AutoCAD. The MOC solves the neutron transport equation along characteristic lines. It is independent of the geometric shape of boundaries and regions. So theoretically, this method can be used to solve the neutron transport equation in highly complex geometries. However, it is important to describe the geometry and calculate intersection points of each characteristic line with every boundary and region in advance. In complex geometries, due to the complications of treating the arbitrary domain, the selection of geometric shapes and efficiency of ray tracing are generally limited. The geometry treatment through the customization of AutoCAD, a widely used computer-aided design software package, is given in this paper. Thanks to the powerful capability of AutoCAD, the description of arbitrary geometry becomes quite convenient. Moreover, with the language Visual Basic for Applications (VBAs), AutoCAD can be customized to carry out the ray tracing procedure with a high flexibility in geometry. The numerical results show that AutoMOC can solve 2D neutron transport problems in a complex geometry accurately and effectively
Within the frame of an ongoing project to develop a folded Tandem-Electrostatic-Quadrupole (TESQ) accelerator facility for Accelerator-Based Boron Neutron Capture Therapy (AB-BNCT), we discuss here the electrostatic design of the machine, including the accelerator tubes with electrostatic quadrupoles and the simulations for the transport and acceleration of a high intensity beam.
A - Nature of problem or function: DOT solves the Boltzmann transport equation in two-dimensional geometries. Principal applications are to neutron and/or photon transport, although the code can be applied to transport problems for any particles not subject to external force fields. Both homogeneous and external-source problems can be solved. Searches on multiplication factor, time absorption, nuclide concentration, and zone thickness are available for reactor problems. Numerous edits and output data sets for subsequent use are available. DOT-3.5 improves the space-scaling algorithm. DOT-3.5/CAB contains group by group UPSCATTER scaling method. DUCT calculates perturbations to the scalar flux caused by the presence of ducts filled with coolant. VIP is a program for cross section sensitivity analysis using two- dimensional discrete ordinates transport calculations. DGRAD calculates the directional flux gradients from DOT-3 diffusion theory flux tapes. In conjunction with VIP and TPERT, it allows the use of diffusion theory fluxes to obtain exact and first-order perturbation reactivity changes. In order to calculate the reactivity associated with changes in reactor compositions using diffusion theory, it is necessary to fold not only the scalar fluxes with the appropriate cross sections, but also the average flux gradients with the diffusion coefficients. Since DOT diffusion theory does not directly calculate these gradients, it was necessary to calculate the needed quantities external to the DOT code. TPERT is a perturbation code to obtain exact and first-order reactivity changes. TPERT is coupled to VIP which generates adjoint forward flux tables using DOT-3 scalar flux tape information. GRTUNCL calculates an analytical first-collision source for subsequent use in DOT. B - Method of solution: The method of discrete ordinates is used. Balance equations are solved for the density of particles moving along discrete directions in each cell of a two-dimensional spatial
Monte Carlo transport calculations and analysis for reactor pressure vessel neutron fluence
The application of Monte Carlo methods for reactor pressure vessel (RPV) neutron fluence calculations is examined. As many commercial nuclear light water reactors approach the end of their design lifetime, it is of great consequence that reactor operators and regulators be able to characterize the structural integrity of the RPV accurately for financial reasons, as well as safety reasons, due to the possibility of plant life extensions. The Monte Carlo method, which offers explicit three-dimensional geometric representation and continuous energy and angular simulation, is well suited for this task. A model of the Three Mile Island unit 1 reactor is presented for determination of RPV fluence; Monte Carlo (MCNP) and deterministic (DORT) results are compared for this application; and numerous issues related to performing these calculations are examined. Synthesized three-dimensional deterministic models are observed to produce results that are comparable to those of Monte Carlo methods, provided the two methods utilize the same cross-section libraries. Continuous energy Monte Carlo methods are shown to predict more (15 to 20%) high-energy neutrons in the RPV than deterministic methods
GNES-R: Global nuclear energy simulator for reactors task 1: High-fidelity neutron transport
A multi-laboratory, multi-university collaboration has formed to advance the state-of-the-art in high-fidelity, coupled-physics simulation of nuclear energy systems. We are embarking on the first-phase in the development of a new suite of simulation tools dedicated to the advancement of nuclear science and engineering technologies. We seek to develop and demonstrate a new generation of multi-physics simulation tools that will explore the scientific phenomena of tightly coupled physics parameters within nuclear systems, support the design and licensing of advanced nuclear reactors, and provide benchmark quality solutions for code validation. In this paper, we have presented the general scope of the collaborative project and discuss the specific challenges of high-fidelity neutronics for nuclear reactor simulation and the inroads we have made along this path. The high-performance computing neutronics code system utilizes the latest version of SCALE to generate accurate, problem-dependent cross sections, which are used in NEWTRNX - a new 3-D, general-geometry, discrete-ordinates solver based on the Slice-Balance Approach. The Global Nuclear Energy Simulator for Reactors (GNES-R) team is embarking on a long-term simulation development project that encompasses multiple laboratories and universities for the expansion of high-fidelity coupled-physics simulation of nuclear energy systems. (authors)
Mugica R, C.A.; Valle G, E. del [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx
2005-07-01
In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD{sub 5,3} and WD{sub 12,8} (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD{sub 5,3} and WD{sub 12,8} were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD{sub 3} and SD{sub 8} (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)
In this thesis, we have first developed a time dependent 3D neutron transport solver on unstructured meshes with discontinuous Galerkin finite elements spatial discretization. The solver (called MINARET) represents in itself an important contribution in reactor physics thanks to the accuracy that it can provide in the knowledge of the state of the core during severe accidents. It will also play an important role on vessel fluence calculations. From a mathematical point of view, the most important contribution has consisted in the implementation of modern algorithms that are well adapted for modern parallel architectures and that significantly decrease the computing times. A special effort has been done in order to efficiently parallelize the time variable by the use of the parareal in time algorithm. For this, we have first analyzed the performances that the classical scheme of parareal can provide when applied to the resolution of the neutron transport equation in a reactor core. Then, with the purpose of improving these performances, a parareal scheme that takes more efficiently into account the presence of other iterative schemes in the resolution of each time step has been proposed. The main idea consists in limiting the number of internal iterations for each time step and to reach convergence across the parareal iterations. A second phase of our work has been motivated by the following question: given the high degree of accuracy that MINARET can provide in the modeling of the neutron population, could we somehow use it as a tool to monitor in real time the population of neutrons on the purpose of helping in the operation of the reactor? And, what is more, how to make such a tool be coherent in some sense with the measurements taken in situ? One of the main challenges of this problem is the real time aspect of the simulations. Indeed, despite all of our efforts to speed-up the calculations, the discretization methods used in MINARET do not provide simulations
1 - Nature of physical problem solved: The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. It has been designed as a tool for solving most shielding problems. Through the use of multigroup cross sections, the solution of neutron, gamma-ray, or coupled neutron-gamma-ray problems may be obtained in either the forward or adjoint mode. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry, as well as specialized one-dimensional geometry descriptions, may be used with an albedo option available at any material surface. Isotropic or anisotropic scattering up to a P16 expansion of the angular distribution is allowed. MORSE-E1 - This is a new analysis package written by ESIS at Ispra. It can be used with the O5R geometry or with the combinatorial geometry as with any other geometry compatible with MORSE. It contains a flexible set of subprograms tailored to solve a variety of shielding problems. It provides uniform source distributions of several geometrical shapes, and calculates particle fluxes and reaction rates integrated over the volumes defined by the user. Currents of particles through surfaces may be calculated. MORSE-H has been developed from MORSE-CG (CCC-0203) and MORSE-E. The special features of this version are: 1) Track-length (volume integrated flux) or next event (point flux) estimates; 2) multiple source region specification; 3) flexible source direction options; 4) restartable in all classes of problems; 5) eigenvalue (keff) solution obtainable even if keff is significantly different from unity. 2 - Method of solution: Monte Carlo methods are used to solve the forward and the adjoint transport equations. Quantities of interest are then obtained by summing the contributions over all collisions, and frequently over most of phase space. Standard multigroup cross sections such as those used in discrete ordinates codes may be used as input; either ANISN, DTF-4 or DOT cross
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 PN approximation, the SN method (discrete ordinates method) and their variants. In the discrete ordinates (SN) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to SN 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 monoenergetic electron beam in a rectangular domain. The main idea relies on applying the PN 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. (author)
Highlights: • WARP, a GPU-accelerated Monte Carlo neutron transport code, has been developed. • The NVIDIA OptiX high-performance ray tracing library is used to process geometric data. • The unionized cross section representation is modified for higher performance. • Reference remapping is used to keep the GPU busy as neutron batch population reduces. • Reference remapping is done using a key-value radix sort on neutron reaction type. - Abstract: In recent supercomputers, general purpose graphics processing units (GPGPUs) are a significant faction of the supercomputer’s total computational power. GPGPUs have different architectures compared to central processing units (CPUs), and for Monte Carlo neutron transport codes used in nuclear engineering to take advantage of these coprocessor cards, transport algorithms must be changed to execute efficiently on them. WARP is a continuous energy Monte Carlo neutron transport code that has been written to do this. The main thrust of WARP is to adapt previous event-based transport algorithms to the new GPU hardware; the algorithmic choices for all parts of which are presented in this paper. It is found that remapping history data references increases the GPU processing rate when histories start to complete. The main reason for this is that completed data are eliminated from the address space, threads are kept busy, and memory bandwidth is not wasted on checking completed data. Remapping also allows the interaction kernels to be launched concurrently, improving efficiency. The OptiX ray tracing framework and CUDPP library are used for geometry representation and parallel dataset-side operations, ensuring high performance and reliability
Ahnert, C.; Aragones, J. M.
1981-07-01
This Is a users manual of the neutron transport code TWOTRAN-TRACA, which is a version of the original TWOTRAN-GG from the Los Alamos Laboratory, with some modifications made at JEN. A detailed input data description is given as well as the new modifications developed at JEN. (Author) 8 refs.
An accurate determination of damage fluence accumulated by reactor pressure vessels (RPV) as a function of time is essential in order to evaluate the vessel integrity for both pressurized thermal shock (PTS) transients and end-of-life considerations. The desired accuracy for neutron exposure parameters such as displacements per atom or fluence (E > 1 MeV) is of the order of 20 to 30%. However, these types of accuracies can only be obtained realistically by validation of nuclear data and calculational methods in benchmark facilities. The purposes of this paper are to review the needs and requirements for benchmark experiments, to discuss the status of current benchmark experiments, to summarize results and conclusions obtained so far, and to suggest areas where further benchmarking is needed
Neutron wave reflexions in interface media with transport equation P1 approximation
The propagation of neutron waves in non multiplying media is investigated employing the Telegrapher's equation obtained from the P1 approximation of the time, space and energy dependent Boltzmann equation. Solution of the problem of propagation of sinusoidally modulated source incident on one face of the medium is obtained by analysing the Fourier component of a pulsed source introduced, for the corresponding frequency. The amplitude and the phase of the flux are computed as a function of frequency in media consisting of one, two and three regions in order to study the effects of reflection at the interfaces. The results are compared with those from the Diffusion approximation obtained by neglecting the term involving the second order time derivative. (author)
Applying the response matrix method for solving coupled neutron diffusion and transport problems
The numerical determination of the flux and power distribution in the design of large power reactors is quite a time-consuming procedure if the space under consideration is to be subdivided into very fine weshes. Many computing methods applied in reactor physics (such as the finite-difference method) require considerable computing time. In this thesis it is shown that the response matrix method can be successfully used as an alternative approach to solving the two-dimension diffusion equation. Furthermore it is shown that sufficient accuracy of the method is achieved by assuming a linear space dependence of the neutron currents on the boundaries of the geometries defined for the given space. (orig.)
Aerosol samples were collected to study the characteristics of marine aerosols in the different western Pacific ocean areas. During the first cruise from 15 October to 25 November 1989, aerosol samples were collected with a kA-200 Andersen cascade impactor and a kB-120 sampler. Instrumental neutron activation analysis was used to determine the elemental composition of the aerosols. The concentrations of crustal and pollution elements in aerosols were higher over the ocean area close to the China coast and decreased very rapidly with increasing distance from land. The morphology and elemental composition of aerosol particles showed that the seasalt particles may conglomerate with small crustal and pollution particles from land to form large particles. (author). 4 refs, 1 fig., 1 tab
Numerical solutions of the one-speed neutron transport equation in two-medium slabs and spheres
The monoenergetic neutron transport equation with isotropic scattering has been applied to two-medium spherical and plane critical systems. The plane system has been considered both with vacuum boundary conditions and with repeated multiplying and non-multiplying material. The mean-free-path is assumed to be the same even though the multiplication factors are different in both media. The two coupled integral equations that are obtained are numerically solved using the spatial Legendre polynomial method (Carlvik's method). Benchmark values of the fundamental and higher eigenvalues are given for various dimensions of the bodies. The total flux is calculated from the eigenvector and the first 4 or 5 flux modes are plotted for some typical cases. The time-eigenvalue spectrum in subcritical two-medium systems has also been studied for vacuum boundary conditions. Using the close relation between the eigenvalues arising from the time-dependent and stationary transport equation the results for the stationary, critical case have been transformed to those for the time-dependent one. Further, the decay constants have been calculated by an iterative process when some parameter are fixed. In addition, simple approximation formulae for very high-order eigenvalues have been derived for both homogeneous and two-medium systems. The formulae were tested against available and new numerical results. (au)
Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author)
The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)
Matsumoto, T. (Musashi Inst. of Tech., Kawasaki, Kanagawa (Japan). Atomic Energy Research Lab.)
1990-07-01
Distributions of thermal neutron fluence and capture {gamma} ray absorbed dose rates were evaluated, taking into consideration various physical factors relevant to boron neutron capture therapy. The use of a larger neutron irradiation aperture was associated with an increase in thermal neutron fluence and capture {gamma} ray absorbed dose rates. Radiation leakage was more significant with smaller phantoms. Attenuation of thermal neutron fluence rates by {sup 10}B suggested that there was an optimal {sup 10}B concentration (<100 PPM) for a given tumour. Deuteration of water allowed better penetration of thermal neutrons with less capture {gamma} rays and is potentially applicable for the treatment of deep-seated brain tumours. (author).
Design of a high-current low-energy beam transport line for an intense D-T/D-D neutron generator
Lu, Xiaolong; Wang, Junrun; Zhang, Yu; Li, Jianyi; Xia, Li; Zhang, Jie; Ding, Yanyan; Jiang, Bing; Huang, Zhiwu; Ma, Zhanwen; Wei, Zheng; Qian, Xiangping; Xu, Dapeng; Lan, Changlin; Yao, Zeen
2016-03-01
An intense D-T/D-D neutron generator is currently being developed at the Lanzhou University. The Cockcroft-Walton accelerator, as a part of the neutron generator, will be used to accelerate and transport the high-current low-energy beam from the duoplasmatron ion source to the rotating target. The design of a high-current low-energy beam transport (LEBT) line and the dynamics simulations of the mixed beam were carried out using the TRACK code. The results illustrate that the designed beam line facilitates smooth transportation of a deuteron beam of 40 mA, and the number of undesired ions can be reduced effectively using two apertures.
This investigation used sysmbolic manipulation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular integral and integro-differential equations which appear in radiative and mixed-mode energy transport. Contained in this report are seven papers which present the technical results as individual modules
The analysis by several neutron transport methods of a small PWR model problem
A small model problem in x-y co-ordinate geometry is specified in detail to permit readers to make their own calculations. The problem is analysed using diffusion theory, differential and integral transport methods and a Monte Carlo code, and a best estimate eigenvalue is deduced. (author)
A fast calculation program ''BRIDGE'' was developed for the calculation of a Cold Neutron Source (CNS) at a radial beam tube of the FRG-I reactor, which couples a total assembly diffusion calculation to a transport calculation for a certain subregion. For the coupling flux and current boundary values at the common surfaces are taken from the diffusion calculation and are used as driving conditions in the transport calculation. 'Equivalence Theorie' is used for the transport feedback effect on the diffusion calculation to improve the consistency of the boundary values. The optimization of a CNS for maximizing the subthermal flux in the wavelength range 4 - 6 A is discussed. (orig.)
Megavoltage photons above 10 MeV used in external beam radiotherapy lead to a significant photoneutron fluence, which must be taken into account in bunker design. This work describes Monte-Carlo simulations of such neutrons for a proposed bunker which is to house a 15 MV accelerator. Of particular interest was the effect on the neutron dose at the maze entrance, of cladding maze walls with various materials. Simulations were performed using the MCNP4B Monte-Carlo code. Mean photo-neutron energies of 0.5, 3 and 6 MeV were assumed to be produced isotropically from the accelerator head. Neutron fluence spectra and absorbed dose due to neutrons and neutron-capture photons were scored at the machine isocentre and at the maze entrance in a 30 cm diameter sphere of tissue. Absorbed dose at the maze entrance was then determined relative to isocentre dose. The reduction in neutron dose at the maze entrance, achieved by cladding concrete maze walls with either wood, polystyrene or a commercially available plastic, was determined. A comparison of materials has been made in terms of efficiency and cost implications. (author)
Codes complex for quick transport 3D neutron calculations of WWER
Complex Surface Values System that capable to carry out the all stages of neutron physical stationary calculations for reactors WWER and PWR is presented. This complex based oneself on using the Surface Values Methods. The approach consists in maximum possible account of specific features in reactor calculations. There is a certain amount of specific features in reactor problems due attention to which is crucial for attaining the main goal-organizing of reactor code.s complexes those provide economical and safe reactors' operating. It is important for the estimation of a code quality to fix of the methodical component but it is necessary to have in view of scale of other ones of result uncertainties. We mention in passing it afterwards. Complex Surface Values System present the approach of building computational reactor models that account for the specifics of reactor problems outlined above. This approach is called the methods of surface values. It utilizes method of surface pseudo-sources for calculating cells within active cores and method of surface harmonics for calculating the whole core or certain sub-assemblies that contain several cells. The part of total complex - the complex Surface Values Lattices - is destined for cells, assembly and sub-assembly calculations of thermal water reactors. The complex Surface Values Lattices use micro constant libraries prepared in the format WIMS. There are libraries in such format based on different initial files of valued data (ENDBF, JEFF, UKNDL, JENDL) on site IAEA. We used these libraries for comparing and choused the one similar to recommended IAEA library. The code Surface Values Core is contained in the total complex Surface Values System besides the complex Surface Values Lattice. This code provide the total scale calculations of reactor's cores. The equations of the Surface Harmonics Method are suitable well for inside reactor core. Other approximations are necessary for neutron description inside reflector
Calculations of Neutron Flux Distributions by Means of Integral Transport Methods
Flux distributions have been calculated mainly in one energy group, for a number of systems representing geometries interesting for reactor calculations. Integral transport methods of two kinds were utilised, collision probabilities (CP) and the discrete method (DIT). The geometries considered comprise the three one-dimensional geometries, planes, sphericals and annular, and further a square cell with a circular fuel rod and a rod cluster cell with a circular outer boundary. For the annular cells both methods (CP and DIT) were used and the results were compared. The purpose of the work is twofold, firstly to demonstrate the versatility and efficacy of integral transport methods and secondly to serve as a guide for anybody who wants to use the methods
Updated version of the DOT 4 one- and two-dimensional neutron/photon transport code
Rhoades, W.A.; Childs, R.L.
1982-07-01
DOT 4 is designed to allow very large transport problems to be solved on a wide range of computers and memory arrangements. Unusual flexibilty in both space-mesh and directional-quadrature specification is allowed. For example, the radial mesh in an R-Z problem can vary with axial position. The directional quadrature can vary with both space and energy group. Several features improve performance on both deep penetration and criticality problems. The program has been checked and used extensively.
Updated version of the DOT 4 one- and two-dimensional neutron/photon transport code
DOT 4 is designed to allow very large transport problems to be solved on a wide range of computers and memory arrangements. Unusual flexibilty in both space-mesh and directional-quadrature specification is allowed. For example, the radial mesh in an R-Z problem can vary with axial position. The directional quadrature can vary with both space and energy group. Several features improve performance on both deep penetration and criticality problems. The program has been checked and used extensively
2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons
In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)
Neutron transport in spatially random media: An assessment of the accuracy of first order smoothing
A formalism has been developed for studying the transmission of neutrons through a spatially stochastic medium. The stochastic components are represented by absorbing plates of randomly varying strength and random position. This type of geometry enables the Feinberg-Galanin-Horning method to be employed and leads to the solution of a coupled set of linear equations for the flux at the plate positions. The matrix of the coefficients contains members that are random and these are solved by simulation. That is, the strength and plate positions are sampled from uniform distributions and the equations solved many times (in this case 105 simulations are carried out). Probability distributions for the plate transmission and reflection factors are constructed from which the mean and variance can be computed. These essentially exact solutions enable closure approximations to be assessed for accuracy. To this end, the author has compared the mean and variance obtained from the first order smoothing approximation of Keller with the exact results and have found excellent agreement for the mean values but note deviations of up to 40% for the variance. Nevertheless, for the problems considered here, first order smoothing appears to be of practical value and is very efficient numerically in comparison with simulation
This thesis is a blend of neutron transport theory and numerical analysis. We start with the study of the problem of the Mika/Case eigenexpansion used in the solution process of the homogeneous one-speed Boltzmann neutron transport equation with anisotropic scattering for plane symmetry. The anisotropic scattering is expressed as a finite Legendre series in which the coefficients are the scattering coefficients'. This eigenexpansion consists of a discrete spectrum of eigenvalues with its corresponding eigenfunctions and the continuous spectrum [-1,+1] with its corresponding eigendistributions. In the general case where the anisotropic scattering can be of any (finite) order, multiple discrete eigenvalues exist and these have to be located to have the complete spectrum. We have devised a stable and robust method that locates all these discrete eigenvalues. The method is a two-step process: first the number of discrete eigenvalues is calculated and this is followed by the calculation of the discrete eigenvalues themselves, now being able to count them down and make sure none are forgotten. During our numerical experiments, we came across what we called near-singular eigenvalues: discrete eigenvalues that are located extremely close to the continuum and hence lead to near-singular behaviour in the eigenfunction. Our solution method has been adapted and allows for the automatic detection of such a near-singular eigenvalue. For the elements of the continuous spectrum [-1,+1], there is no non-zero function satisfying the associated eigenequation but there is a non-zero distribution that does satisfy it. It is not feasible to compute a distribution as such but one can evaluate integrals in which this distribution appears. The continuum part of the eigenexpansion can hence only be characterised by its (angular) moments. Accurate and fast numerical quadrature is needed to evaluate these integrals. Several quadrature methods have been evaluated on a representative test
A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code system is based on the well-known discrete ordinates code DORT, which solves the steady-state neutron transport equation for an arbitrary number of energy groups and the most common regular 2D-geometries. For the implementation of time-dependence a fully implicit first-order time-integration scheme was employed to minimise errors due to temporal discretisation. This requires various modifications to the transport equation, the extensive use of sophisticated acceleration mechanisms and strongly tightened convergence criteria. To perform coupled analyses, an interface to the GRS (Gesellschaft fuer Reaktorsicherheit) system code ATHLET was developed. From the nodal power densities ATHLET calculates thermal-hydraulic system parameters, which are in turn used to generate appropriate nuclear cross sections. The code system has been applied to analyse the reactor dynamics of the research reactor FRM-II. After extensive steady-state analyses, several design basis accidents have been simulated: Loss of offsite power, loss of secondary heat sink and unintended withdrawl of control rod. Results from applying neutron transport theory were compared to diffusion theory and point kinetics calculations. Additionally, two hypothetical transients with large reactivity insertions of 3$ and 12% were considered to show the capability of the code system to cope with inhomogeneous reactivity insertions and strong flux distortions. (orig.)
One-speed neutron transport eigenvalues for reflected slabs and spheres
The monoenergetic transport equation with isotropic scattering and vacuum boundary conditions is applied to two-medium spherical and plane systems. The mean-free-path is assumed to be the same even though the multiplication factors are different in both media. The two coupled integral equations that are obtained are numerically solved using Carlvik's method. Tables of seven or more eigenvalues for various dimensions of the bodies are given and the first 5 flux modes for some cases are plotted. In addition, for homogeneous systems we present more accurate and high order c-eigenvalues than those known so far. (author)
One-speed neutron transport eigenvalues for an infinite, two-medium slab lattice
The monoenergetic transport equation with isotropic scattering is applied to an infinite, two-medium slab lattice. One of the media is assumed to have a multiplication factor larger than unity and the other smaller than unity. The two coupled integral equations that are derived are numerically solved using the spatial Legendre expansion method (Carlvik's method). Tables of seven eigenvalues for various dimensions of the bodies are given and the first four flux modes for some cases are plotted. In addition, simple formulae for very high-order eigenvalues are given. (author)
A new multidimensional semi-analytical benchmark capability is developed. The key feature in the solution is the point kernel formulation. The 3D nature of the source is inherited in the flux making this a true multidimensional test. In addition, an efficient numerical scheme, called iterative interpolation, is used to evaluate the required point kernel solution and maintain benchmark accuracy. The EVENT finite element transport algorithm is compared to the point source solution as the first step of embedding the benchmark directly with the EVENT code. Additional code comparisons will be presented. (authors)
Four calculational benchmarks have been selected to compare various nuclear data libraries based on both ENDF/B-IV and V, and to compare results from various transport codes. Discrepancies up to 20% in tritium production from 7Li were found and have been attributed mainly to differences in current ENDF/B-IV and V evaluations, while approx.4% is attributed to differences in the group structure of the libraries used. Results from MCNP and VIP Monte Carlo codes are in good agreement, but MORSE calculations show good agreement only for high threshold reactions
The principal goal of this manuscript is devoted to the investigation of a new type of heterogeneous mesh adapted to the shape of the fuel pins (fuel-clad-moderator). The new heterogeneous mesh guarantees the spatial modelling of the pin-cell with a minimum of regions. Two methods are investigated for the spatial discretization of the transport equation: the discontinuous finite element method and the method of characteristics for structured cells. These methods together with the new representation of the pin-cell result in an appreciable reduction of calculation points. They allow an exact modelling of the fuel pin-cell without spatial homogenization. A new synthetic acceleration technique based on an angular multigrid is also presented for the speed up of the inner iterations. These methods are good candidates for transport calculations for a nuclear reactor core. A second objective of this work is the application of method of characteristics for non-structured geometries to the study of double heterogeneity problem. The letters is characterized by fuel material with a stochastic dispersion of heterogeneous grains, and until now was solved with a model based on collision probabilities. We propose a new statistical model based on renewal-Markovian theory, which makes possible to take into account the stochastic nature of the problem and to avoid the approximations of the collision probability model. The numerical solution of this model is guaranteed by the method of characteristics. (author)
2D/1D approximations to the 3D neutron transport equation. I: Theory
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
Whole-core neutron transport calculations without fuel-coolant homogenization
The variational nodal method implemented in the VARIANT code is generalized to perform full core transport calculations without spatial homogenization of cross sections at either the fuel-pin cell or fuel assembly level. The node size is chosen to correspond to one fuel-pin cell in the radial plane. Each node is divided into triangular finite subelements, with the interior spatial flux distribution represented by piecewise linear trial functions. The step change in the cross sections at the fuel-coolant interface can thus be represented explicitly in global calculations while retaining the fill spherical harmonics capability of VARIANT. The resulting method is applied to a two-dimensional seven-group representation of a LWR containing MOX fuel assemblies. Comparisons are made of the accuracy of various space-angle approximations and of the corresponding CPU times
Parallel PENTRAN solutions of the 'TIEL' steady state neutron transport benchmark problems
The TIEL benchmarks include a set of analytical benchmark solutions to the transport equation in infinite media. In this paper, we present solutions for the infinite planar, point, spherical shell, and solid spherical sources solved using the PENTRAN 3-D Parallel SN code compared to reference solutions of the TIEL benchmark problems. Excellent agreement (less than 0.7% difference) was achieved when comparing reference solutions with PENTRAN scalar fluxes in the case of planar, shell and solid sphere sources. Depending on the scattering properties and the geometry of the system, Legendre-Chebychev quadratures as high as S34 for the planar or S54 for the spherical symmetry sources, with appropriate spatial discretization, were needed to properly represent the flux. Inherent numerical difficulties were encountered when finding the solution in the very close proximity (< 0.1 mfp) of the sources. (authors)
Computer-aided design of nuclear shielding and irradiation facilities is characterized by studies of different design variants in order to determine which facilities are safe and still economicol. The design engineer has a very complex task including the formulation of calculation models, data linking of programs and data, and the management of large data stores. Integrated modular program systems with centralized module and data management make it possible to treat these problems in a more simplified and automatic manner. The paper describes a system of this type for the field of radiation transport and radiation shielding. The basis is the modular system RSYST II which has a dynamic hierarchical scheme for the structuring of problem data in a central data base. (orig./RW)
In order to calculate the in-medium neutron–neutron (nn) differential cross section and the transport properties of the pure neutron matter, the lowest order constrained variational (LOCV) method is applied to obtain the effective nucleon–nucleon (NN) interactions from the various bare realistic phenomenological NN interaction. The wide range of potentials, such as the Reid68, the Δ-Reid68, the V8′ and the Av18 are used as the input phenomenological interactions. The approach, based on the effective NN interaction, allows for a consistent description of the neutron matter and the nucleon–nucleon scattering in the nuclear medium. In this work, by using the above LOCV effective NN interactions, beside the nn differential cross section, the related quantities such as the shear viscosity and the thermal conductivity of the pure neutron matter, which are the important gradient for the stellar structure, are calculated within the Landau–Abrikosov–Khalatnikov (LAK) formalism. It is shown that, while the density dependence of effective mass are not important, the choice of in-medium effective interaction has crucial rule on the resulting nn differential cross section as well as the shear viscosity and the thermal conductivity of pure neutron matter. Finally, our above LOCV calculations are compared with those predicted by the other theoretical methods
The method of characteristics (MOC) is gaining increased popularity in the reactor physics community all over the world because it gives a new degree of freedom in nuclear reactor analysis. The MARIKO code solves the neutron transport equation by the MOC in two-dimensional real geometry. The domain of solution can be a rectangle or right hexagon with periodic boundary conditions on the outer boundary. Any reasonable symmetry inside the domain can be fully accounted for. The geometry is described in three levels-macro-cells, cells, and regions. The macro-cells and cells can be any polygon. The outer boundary of a region can be any combination of straight line and circular arc segments. Any level of embedded regions is allowed. Procedures for automatic geometry description of hexagonal fuel assemblies and reflector macro-cells have been developed. The initial ray tracing procedure is performed for the full rectangular or hexagonal domain, but only azimuthal angles in the smallest symmetry interval are tracked. (Authors)
This report is a kind of audit report on a research laboratory whose activity is organized in three departments: neutron transport and criticality (themes: numerical methods, maths and statistics related to the simulation of neutral particle propagation, nuclear data, uncertainty propagation and bias estimation, code qualification and associated experimental programs, neutron transport in reactors and fuel cycle, criticality accidents), radionuclide transfer in radioactive waste disposals (site identification strategy, hydro-mechanical phenomena affecting storage performance, physical-chemical evolution factors, storage modelling), and metrology and confinement of radioactive gases and aerosols. The authors discuss an assessment of the unit activities in terms of strengths and opportunities, aspects to be improved and recommendations, productions and publications. A more detailed assessment is presented for each department in terms of scientific quality, influence and attractiveness (awards, recruitment capacity, capacity to obtain financing and to tender, participation to international programs), strategy and governance, and project
The criticality problem is studied based on one-speed time-dependent neutron transport theory, for a uniform and finite slab, using the Marshak boundary condition. The time-dependent neutron transport equation is reduced to a stationary equation. The variation of the critical thickness of the time-dependent system is investigated by using the linear anisotropic scattering kernel together with the combination of forward and backward scattering. Numerical calculations for various combinations of the scattering parameters and selected values of the time decay constant and the reflection coefficient are performed by using the Chebyshev polynomials approximation method. The results are compared with those previously obtained by other methods which are available in the literature.
We describe a number of alternative iterative schemes to sweep the spatial grid in order to numerically solve one-speed X,Y-geometry neutron transport problems in the discrete ordinates (SN) formulation. We perform numerical experiments with the one-node block inversion iterative schemes to solve the discretized equations on the linear nodal method and we illustrate the computational performance of each iterative scheme for typical steady-state model problems. (author)
In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law using Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy respectively). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with non-zero values for a very small range of the cosine of the scattering angle. Besides, the finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of this cross section. As such, the Legendre expansion is less suited to represent the scattering law. Furthermore, this model induces negative values which are non-physical. In this work, various scattering laws are briefly described and the limitations of the existing model are pointed out. Hence, piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. The discrete ordinates method which is widely employed to solve the transport equation has been adapted. Thus, the finite volume method for angular discretization has been developed and implemented in Paris environment which hosts the Sn solver, Snatch. The angular finite volume method has been compared to the collocation method with Legendre moments to ensure its proper performance. Moreover, unlike the latter, this method is adapted for both the Legendre moments and the piecewise-constant functions representations of the scattering cross section. This hybrid-source method has been validated for different cases: fuel cell in infinite lattice
Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with PN method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (PN) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.
1 - Description of program or function: The DOORS3.2a discrete ordinates transport code system includes the most recent versions of CCC-0543/TORT-DORT, CCC-0254/ANISN-ORNL, CCC-0628/GBANISN and CCC-0351/FALSTF. It also includes the ISOPLOT code from the PSR-0155/DOGS package and various utility programs listed below which were previously included in the TORT-DORT package. In this release each module is a separate executable file. Several modules, as needed, can be run in a single job by using 'jdos' to call the 'drv' module which interprets the sequence specified in the input. TORT calculates the flux of fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two-or three-dimensional geometric systems, and DORT is used in one- or two-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. ANISN solves the one-dimensional Boltzmann transport equation for neutrons or gamma rays in slab, spherical, or cylindrical geometry. GBANISN is based on ANISN but was modified to allow randomizing of multi-bank fluxes within a group at all interfaces between dissimilar materials and a reduction in the number of outer iterations for problems involving neutron up-scatter into higher energy groups. GBANISN requires fewer outer iterations than ANISN by performing 'inner iterations' over energy groups within a 'band' and converging those groups before moving to the next band. These 'inner' iterations slightly resemble outer iterations in ANISN. Thus, a calculation with up-scatter and no fission can be solved with one traditional outer iteration. GBANISN, like ANISN, includes a technique for handling general anisotropic scattering, pointwise convergence
Solution of the neutron transport equation by the collision probability method for 3D geometries
The TDT code solves the multigroup transport equation by the interface-current method for unstructured 2D geometries. This works presents the extension of TDT to the treatment of 3D geometries obtained by axial displacement of unstructured 2D geometries. Three-dimensional trajectories are obtained by lifting the 2D trajectories. The code allows for the definition of macro-domains in the axial direction to be used in interface-current method. Specular and isotropic reflection or translations boundary conditions can be applied to the horizontal boundaries of the domain. Numerical studies have shown the need for longer trajectory cutoffs for trajectories intersecting horizontal boundaries. Numerical applications to the calculation of local power peaks are given in a second part for: the local destruction of a Pyrex absorbent, inter-assembly (U02-MOX) power distortion due to pellet collapsing at the top of the core. Calculations with 16 groups were performed by coupling TDT to the spectral code APOLLO2. One-group comparisons with the Monte Carlo code TRIMARAN2 are also given. (author)
Solution of the neutron transport equation by the collision probability for 3D geometries
The TDT code solves the multigroup transport equation by the interface current method for unstructured 2D geometries. This works presents the extension of TDT to the treatment of 3D geometries obtained by axial displacement of unstructured 2D geometries. Three-dimensional trajectories are obtained by lifting the 2D trajectories. The code allows for the definition of macro-domains in the axial direction to be used in the interface-current method. Specular and isotropic reflection or translations boundary conditions can be applied to the horizontal boundaries of the domain. Numerical studies have shown the need for longer trajectory cutoffs for trajectories intersecting horizontal boundaries. Numerical applications to the calculation of local power peaks are given in a second part for: the local destruction of a Pyrex absorbent and inter-assembly (UO2-MOX) power distortion due to pellet collapsing at the top of the core. Calculations with 16 groups were performed by coupling TDT to the spectral code APOLLO2. One-group comparisons with the Monte Carlo code TRIMARAN2 are also given. (author)
GANTRAS is a system of codes for neutron transport calculations in which the anisotropy of elastic and inelastic (including (n,n'x)-reactions) scattering is fully taken into account. This is achieved by employing a rigorous method, so-called I*-method, to represent the scattering term of the transport equation and with the use of double-differential cross-sections for the description of the emission of secondary neutrons. The I*-method was incorporated into the conventional transport code ONETRAN. The ONETRAN subroutines were modified for the new purpose. An implementation of the updated version ANTRA1 was accomplished for plane and spherical geometry. ANTRA1 was included in GANTRAS and linked to another modules which prepare angle-dependent transfer matrices. The GANTRAS code consists of three modules: 1. The CROMIX code which calculates the macroscopic transfer matrices for mixtures on the base of microscopic nuclide-dependent data. 2. The ATP code which generates discretized angular transfer probabilities (i.e. discretizes the I*-function). 3. The ANTRA1 code to perform SN transport calculations in one-dimensional plane and spherical geometries. This structure of GANTRAS allows to accommodate the system to various transport problems. (orig.)
In order to investigate the neutron transportation from a beam-line tunnel to an access maze at a 12-GeV proton accelerator, we measured the spatial distribution of thermal and epithermal neutrons by using the Au activation method in detail. Gold foils were placed at about 70 positions in the maze in the case of the insertion (or extraction) of a copper target of 1 mm thickness into (or from) the beam axis in front of the maze. After the end of accelerator operation, relative activities of the Au foils were simultaneously measured by using an imaging plate technique and the radioactivity of one reference foil was also measured with a HPGe detector to convert to the absolute activities of all foils. It was found that the neutrons reach to the depth of the maze in the case of the insertion of the copper target. This result reflects higher proportion of high-energy particles from the copper target to that from other beam loss points and high-energy particles become the successive source of low-energy neutrons. Furthermore, it was found that several circumstances such as door walls and electric wire cables obviously affect the absorption effect of thermal neutrons. The reaction rates obtained in this study were also used for the benchmark of the Monte Carlo simulation code, MARS15 (version of February 2008). The results of the MARS15 calculations precisely reproduced experimental results and significant effects of the electric wire cables and door walls
Spatial homogenization methods for pin-by-pin neutron transport calculations
Kozlowski, Tomasz
For practical reactor core applications low-order transport approximations such as SP3 have been shown to provide sufficient accuracy for both static and transient calculations with considerably less computational expense than the discrete ordinate or the full spherical harmonics methods. These methods have been applied in several core simulators where homogenization was performed at the level of the pin cell. One of the principal problems has been to recover the error introduced by pin-cell homogenization. Two basic approaches to treat pin-cell homogenization error have been proposed: Superhomogenization (SPH) factors and Pin-Cell Discontinuity Factors (PDF). These methods are based on well established Equivalence Theory and Generalized Equivalence Theory to generate appropriate group constants. These methods are able to treat all sources of error together, allowing even few-group diffusion with one mesh per cell to reproduce the reference solution. A detailed investigation and consistent comparison of both homogenization techniques showed potential of PDF approach to improve accuracy of core calculation, but also reveal its limitation. In principle, the method is applicable only for the boundary conditions at which it was created, i.e. for boundary conditions considered during the homogenization process---normally zero current. Therefore, there exists a need to improve this method, making it more general and environment independent. The goal of proposed general homogenization technique is to create a function that is able to correctly predict the appropriate correction factor with only homogeneous information available, i.e. a function based on heterogeneous solution that could approximate PDFs using homogeneous solution. It has been shown that the PDF can be well approximated by least-square polynomial fit of non-dimensional heterogeneous solution and later used for PDF prediction using homogeneous solution. This shows a promise for PDF prediction for off
1 - Description of program or function: specified on ORNL-RSIC-25, shielding benchmark problems. - BP-3 (Neutron cross sections): Format: ANISN, DOT and MORSE; Number of groups: 22 neutron / 18 gamma-ray; Nuclides: air; Origin: ENDF/B; Weighting spectrum: 1/E; - BP-6 (neutron and gamma-ray cross sections): Format: ANISN, DOT and MORSE; Number of groups: 22 neutron / 18 gamma-ray; Nuclides: Borated Polyethylene (C-12, H, and B-10); Origin: ENDF/B-II. The cross section data can be used to repeat the Shielding Benchmark Problems 3.0 and 6.0 for testing against the results published in ORNL-RSIC-25. 2 - Method of solution: ZZ-BP-3 neutron cross sections from the CCC-17/05R library were processed into 104 neutron groups using the PSR-9/CSP code. The fine-group neutron cross sections were collapsed to 22 broad groups using CCC-254/ANISN with an equilibrium fission spectrum source. The resulting multigroup cross sections are P5 coefficients punched on cards in format suitable for input to ANISN, DOT, and MORSE. ZZ-BP-6 neutron and gamma-ray cross sections for 12C, H, and 10B were from ENDF/B-II data. The neutron multigroup cross sections were generated into 104 neutron groups using the PSR-13/SUPERTOG code. The fine-group neutron cross sections were collapsed to 22 broad groups using CCC-254/ANISN with an equilibrium fission spectrum source. The gamma-ray multigroup cross sections were generated using PSR-7/MUG. The neutron-gamma-ray coupling utilized yield data from the DLC-12/POPOP4 library (data sets 010101, 060101, 060301, and 05100201). The neutron-gamma-ray coupled multigroup cross-section set was generated using the SAMPLE COUPLING CODE (ASCC). The multigroup cross sections are in a 22-18 group structure with P3 coefficients punched on cards in format suitable for input to ANISN, DOT, and MORSE
Japan Spallation Neutron Source (JSNS) is one of major experimental facilities in Japan Proton Accelerator Research Complex (J-PARC). JSNS operated by 3-GeV and 1-MW pulsed proton beams has the highest class neutron intensity in the world. In the design stage, aiming to the best neutronic performance, the PHITS code was fully applied to JSNS neutronics designs and several thousands calculation cases were done with complicated models. Not only optimization of neutronic performance, but also shielding calculation, nuclear heat estimation for the engineering design, residual radioactivity estimation for the cask design and radiation damage estimation for the life and maintenance design were done with the PHITS code. JSNS is one of the first facilities in the world fully adapted such a simulation code to the neutronics design. In these calculations, note that the particle energy change from GeV to meV (12 decades) and neutron fluxes reduce by 10 decades or more. To confirm the reliability of these calculations, neutron spectral intensities were measured. As a result, the measured values were good agreement with the calculated values. We could confirm that the PHITS were reliable for such a design calculation. (author)
Burns, Kimberly A. [Georgia Inst. of Technology, Atlanta, GA (United States)
2009-08-01
The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples.
In order to present credible results in nuclear design and safety analysis, computer codes must adhere to stringent qualification procedures imposed by nuclear licensing authorities. Such procedures form the basis for a quality assured verification and validation process. This is particularly true for advanced nuclear systems of Generation IV type, where little licensing experience exists as well as little or no plant data is available. Qualification of nuclear design and analysis codes can be achieved in various ways, namely: comparison of results from a code with results from another code i.e. code to code benchmarking; comparison of results from a given code with experimental results, i.e. code to experiment benchmarking; comparison of results from a given code with operational plant data; and finally, comparison of the results of a given code with known analytical solutions. In this paper, a systematic qualification of the coupled neutron transport and thermal hydraulics code DORT-TD/THERMIX is presented. As part of developing this coupled code to the level where it can be used as an independent tool by both designers of pebble-bed High-Temperature Gas-cooled Reactors (HTGRs) and regulators, an effort has been made to verify the coupling scheme as well as the validity of application for this code package. At these initial stages a code to code comparison has been adopted as the qualification method of choice. This is done for both steady-state and transient benchmark problems, ranging from simplified to detailed models. As shown in the results section, all benchmarks have been successfully recalculated and generally show good to very good agreement with the 'reference' solutions. (authors)
Hill, T.R.; Reed, W.H.
1976-01-01
TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures. (auth)
TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures
Zwermann, W.; Aures, A.; Bernnat, W.; and others
2013-06-15
This report documents the status of the research and development goals reached within the reactor safety research project RS1503 ''Development and Application of Neutron Transport Methods and Uncertainty Analyses for Reactor Core Calculations'' as of the 1{sup st} quarter of 2013. The superordinate goal of the project is the development, validation, and application of neutron transport methods and uncertainty analyses for reactor core calculations. These calculation methods will mainly be applied to problems related to the core behaviour of light water reactors and innovative reactor concepts. The contributions of this project towards achieving this goal are the further development, validation, and application of deterministic and stochastic calculation programmes and of methods for uncertainty and sensitivity analyses, as well as the assessment of artificial neutral networks, for providing a complete nuclear calculation chain. This comprises processing nuclear basis data, creating multi-group data for diffusion and transport codes, obtaining reference solutions for stationary states with Monte Carlo codes, performing coupled 3D full core analyses in diffusion approximation and with other deterministic and also Monte Carlo transport codes, and implementing uncertainty and sensitivity analyses with the aim of propagating uncertainties through the whole calculation chain from fuel assembly, spectral and depletion calculations to coupled transient analyses. This calculation chain shall be applicable to light water reactors and also to innovative reactor concepts, and therefore has to be extensively validated with the help of benchmarks and critical experiments.
This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research
This research thesis addresses the resolution of the neutron transport equation inside reactor cells in non-structured grids and in general geometry by using the method of characteristics (MoC) and two acceleration methods developed during this research. The author introduces the MoC with a flat approximation of the neutron collision source within each computation area. This formulation leads to a linear approximation. The next part presents the mathematical framework for the use of the Lanczos iterative scheme. A new acceleration method is then introduced. The last part reports realistic cases with a high spatial and angular heterogeneity. Results obtained by using the Apollo2-TDT code are compared with those obtained with the Tripoli4 Monte-Carlo code
The neutron probe is a standard tool for measuring soil water content. This article provides an overview of the underlying theory, describes the methodology for its calibration and use, discusses example applications, and identifies the safety issues. Soil water makes land-based life possible by satisfying plant water requirements, serving as a medium for nutrient movement to plant roots and nutrient cycling, and controlling the fate and transport of contaminants in the soil environment. Therefore, a successful understanding of the dynamics of plant growth, nutrient cycling, and contaminant behavior in the soil requires knowledge of the soil water content as well as its spatial and temporal variability. After more than 50 years, neutron probes remain the most reliable tool available for field monitoring of soil water content. Neutron probes provide integrated measurements over relatively large volumes of soil and, with proper access, allow for repeated sampling of the subsurface at the same locations. The limitations of neutron probes include costly and time-consuming manual operation, lack of data automation, and costly regulatory requirements. As more non-radioactive systems for soil water monitoring are developed to provide automated profiling capabilities, neutron-probe usage will likely decrease. Until then, neutron probes will continue to be a standard for reliable measurements of field water contents in soils around the globe
TP2 is a FORTRAN-IV program for the calculation of the reactivity, effective delayed neutron fractions and mean generation time by the perturbation theory using the angular fluxes calculated by a two-dimensional Ssub(n) transport code. Group cross sections, delayed neutron fractions and spectra, isotope dependent prompt neutron spectrum, and direct and adjoint angular fluxes are read from disk files. This code can treat x-y, r-z and r-theta geometry in two dimensions, and the code structure is nearly the same as the TP1 code for the one-dimensional geometry. As in the TP1 code, there are two main options. One is for the exact perturbation calculation of the reactivity where the direct and adjoint angular fluxes are used for unperturbed and perturbed systems respectively. The other option is for the first order perturbation calculation of the probe reactivity in which usually unperturbed direct and adjoint angular fluxes are used. In both cases, reactivities for each reaction process are printed in the energy and space dependent form according to the input specification. The criticality factor calculated by the Ssub(n) transport code using an isotope independent fission spectrum can be corrected by the TP2 code by taking into account an isotope dependency of the prompt fission spectrum and delayed neutron spectrum. Numerical examples are presented to demonstrate the accuracy of the reactivity, the effect of the number of mesh points and the order of the Ssub(n) method. Comparisons with the diffusion method are given. (orig.)
Neutron-rich isotopes of heavy nuclei are until now poorly studied. In this work we investigate neutron-rich osmium isotopes produced in multi-nucleon transfer reactions. The reaction 136Xe+208Pb at energy near Coulomb barrier is used for production of osmium isotopes. The CORSAR-V setup is used to record the characteristics of osmium isotopes. The separation of the reaction products is based on their respective volatility. Experimental results are presented and discussed.
1 - Description of problem or function: TRIDENT solves the two- dimensional-multigroup-transport equations in rectangular (x-y) and cylindrical (r-z) geometries using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (K-eff and eigenvalue searches) problems subject to vacuum, reflective, white, or source boundary conditions are solved. General anisotropic scattering is allowed and anisotropic-distributed sources are permitted. 2 - Method of solution: The discrete-ordinates approximation is used for the neutron directional variables. An option is included to append a fictitious source to the discrete-ordinates equations that is defined such that spherical-harmonics solutions (in x-y geometry) or spherical-harmonics-like solutions (in r-z geometry) are obtained. This option is useful for cases in which ray-effect distortions are severe. A spatial-finite-element method is used in which the angular flux is expressed as a linear polynomial in each triangle that is discontinuous at triangle boundaries. Both inner (within-group) and outer iteration cycles are accelerated by either whole-system or fine-mesh re-balance. Provision is made for creation of standard interface output files for Sn constants, angle-integrated (scalar) fluxes, and angular fluxes. Standard interface input files for Sn constants, inhomogeneous sources, cross sections, and the scalar flux may be read. Subroutines DRED and DRIT perform information transfers between LCM and random disk. Data transfer between large and small core are performed by CRED and CRIT. Sequential binary operations are performed by SEEK, REED, and RITE. Flexible edit options as well as a dump and restart capability are provided. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXLEN can be accommodated. On CDC Machines MAXLEN can be about 40 000 words of Small Core Memory (SCM) and
Rubinson, Kenneth A; Faraone, Antonio
2016-05-14
X-ray and neutron scattering have been used to provide insight into the structures of ionic solutions for over a century, but the probes have covered distances shorter than 8 Å. For the non-hydrolyzing salt SrI2 in aqueous solution, a locally ordered lattice of ions exists that scatters slow neutrons coherently down to at least 0.1 mol L(-1) concentration, where the measured average distance between scatterers is over 18 Å. To investigate the motions of these scatterers, coherent quasielastic neutron scattering (CQENS) data on D2O solutions with SrI2 at 1, 0.8, 0.6, and 0.4 mol L(-1) concentrations was obtained to provide an experimental measure of the diffusive transport rate for the motion between pairs of ions relative to each other. Because CQENS measures the motion of one ion relative to another, the frame of reference is centered on an ion, which is unique among all diffusion measurement methods. We call the measured quantity the pairwise diffusive transport rate Dp. In addition to this ion centered frame of reference, the diffusive transport rate can be measured as a function of the momentum transfer q, where q = (4π/λ)sin θ with a scattering angle of 2θ. Since q is related to the interion distance (d = 2π/q), for the experimental range 0.2 Å(-1)≤q≤ 1.0 Å(-1), Dp is, then, measured over interion distances from 40 Å to ≈6 Å. We find the measured diffusional transport rates increase with increasing distance between scatterers over the entire range covered and interpret this behavior to be caused by dynamic coupling among the ions. Within the model of Fickian diffusion, at the longer interionic distances Dp is greater than the Nernst-Hartley value for an infinitely dilute solution. For these nm-distance diffusional transport rates to conform with the lower, macroscopically measured diffusion coefficients, we propose that local, coordinated counter motion of at least pairs of ions is part of the transport process. PMID:27096293
As part of a U.S.- Korea collaborative U.S. Department of Energy INERI project, a comprehensive high-fidelity reactor-core modeling capability is being developed for detailed analysis of existing and advanced PWR reactor designs. An essential element of the project has been the development of an interface between the computational fluid dynamics (CFD) module, STAR-CD, and the neutronics module, DeCART. Since the computational mesh for CFD and neutronics calculations are generally different, the capability to average and decompose data on these different meshes has been an important part of code coupling activities. An averaging process has been developed to extract neutronics zone temperatures in the fuel and coolant and to generate appropriate multi group cross sections and densities. Similar procedures have also been established to map the power distribution from the neutronics zones to the mesh structure used in the CFD module. Since MPI is used as the parallel model in STAR-CD and conflicts arise during initiation of a second level of MPI, the interface developed here is based on using TCP/IP protocol sockets to establish communication between the CFD and neutronics modules. Preliminary coupled calculations have been performed for PWR fuel assembly size problems and converged solutions have been achieved for a series of steady-state problems ranging from a single pin to a 1/8 model of a 17 x 17 PWR fuel assembly. (authors)
Tissue-equivalent proportional counters (TEPC) can potentially be used as a portable and personal dosemeter in mixed neutron and gamma-ray fields, but what hinders this use is their typically large physical size. To formulate compact TEPC designs, the use of a Monte Carlo transport code is necessary to predict the performance of compact designs in these fields. To perform this modelling, three candidate codes were assessed: MCNPX 2.7.E, FLUKA 2011.2 and PHITS 2.24. In each code, benchmark simulations were performed involving the irradiation of a 5-in. TEPC with monoenergetic neutron fields and a 4-in. wall-less TEPC with monoenergetic gamma-ray fields. The frequency and dose mean lineal energies and dose distributions calculated from each code were compared with experimentally determined data. For the neutron benchmark simulations, PHITS produces data closest to the experimental values and for the gamma-ray benchmark simulations, FLUKA yields data closest to the experimentally determined quantities. (authors)
We introduce a new coupled neutronics/thermal hydraulics code system for analyzing transients of nuclear power plants and research reactors, based on a neutron transport theory approach. For the neutron kinetics, we have developed the code DORT-TD, a time-dependent extension of the well-known discrete ordinates code DORT. DORT-TD uses a fully implicit time integration scheme and is coupled via a general interface to the thermal hydraulics system code ATHLET, a generally applicable code for the analyses of LWR accident scenarios. Feedback is accounted for by interpolating multigroup cross sections from precalculated libraries, which are generated in advance for user-specified, discrete sets of thermal hydraulic parameters, e.g., fuel and coolant temperature. The coupled code system is applied to the high-flux research reactor FRM-II (Germany). Several design basis accidents are considered, namely the unintended control rod withdrawal, the loss of offsite power, and the loss of the secondary heat sink as well as a hypothetical transient with large reactivity insertion
Charles Simon; Alain Pautrat; Christophe Goupil; Joseph Scola; Patrice Mathieu; Annie Brûlet; Antoine Ruyter; M J Higgins; Shobo Bhattacharya; D Plessis
2006-01-01
The existence of a peak effect in transport properties (a maximum of the critical current as function of magnetic field) is a well-known but still intriguing feature of Type II superconductors such as NbSe2 and Bi-2212. Using a model of pinning by surface irregularities in anisotropic superconductors, we have developed a calculation of the critical current which allows estimating quantitatively the critical current in both the high critical current phase and the low critical current phase. The only adjustable parameter of this model is the angle of the vortices at the surface. The agreement between the measurements and the model is really very impressive. In this framework, the anomalous dynamical properties close to the peak effect is due to coexistence of two different vortex states with different critical currents. Recent neutron diffraction data in NbSe2 crystals in the presence of transport current support this point of view.
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
Basso Barichello, Liliane; Dias da Cunha, Rudnei [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst. de Matematica; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2015-05-15
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
Transport is one of the major causes of environmental damage in Austria. Energy consumption, pollutants emissions, noise emissions, use of surfaces, sealing of surfaces, dissection of ecosystems and impact on landscape are the most significant environmental impacts caused by it. An overview of the transport development of passengers and freight in Austria is presented. Especially the energy consumption growth, carbon dioxide and nitrogen oxide emissions by type of transport, and the emissions development (HC, particle and carbon monoxide) of goods and passengers transport are analyzed covering the years 1980 - 1999. The health cost resulting from transport-related air pollution in Austria is given and measures to be taken for an effective control of the transport sector are mentioned. Figs. 8, Table 1. (nevyjel)
here explores the inverse problem of optical tomography applied to heterogeneous domains. The neutral particle transport equation was used as the forward model for how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newtons method served as the basis of the inverse problem. Optical tomography aims at reconstructing the material properties using (a) illuminating sources and (b) detector readings. However, accurate simulations for radiation transport require that the particle (gamma and/or neutron) energy be appropriate discretize in the multigroup approximation. This, in turns, yields optical tomography problems where the number of unknowns grows (1) about quadratically with respect to the number of energy groups, G, (notably to reconstruct the scattering matrix) and (2) linearly with respect to the number of unknown material regions. As pointed out, a promising approach could rely on algorithms to appropriately select a material type per material zone rather than G2 values. This approach, though promising, still requires further investigation: (a) when switching from cross-section values unknowns to material type indices (discrete integer unknowns), integer programming techniques are needed since derivative information is no longer available; and (b) the issue of selecting the initial material zoning remains. The work reported here proposes an approach to solve the latter item, whereby a material zoning is proposed using one-group or few-groups transport approximations. The capabilities and limitations of the presented method were explored; they are briefly summarized next and later described in fuller details in the Appendices. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the
FOREWORD: Neutron metrology Neutron metrology
Thomas, David J.; Nolte, Ralf; Gressier, Vincent
2011-12-01
industry, from the initial fuel enrichment and fabrication processes right through to storage or reprocessing, and neutron metrology is clearly important in this area. Neutron fields do, however, occur in other areas, for example where neutron sources are used in oil well logging and moisture measurements. They also occur around high energy accelerators, including photon linear accelerators used for cancer therapy, and are expected to be a more serious problem around the new hadron radiation therapy facilities. Roughly 50% of the cosmic ray doses experienced by fliers at the flight altitudes of commercial aircraft are due to neutrons. Current research on fusion presents neutron metrology with a whole new range of challenges because of the very high fluences expected. One of the most significant features of neutron fields is the very wide range of possible neutron energies. In the nuclear industry, for example, neutrons occur with energies from those of thermal neutrons at a few meV to the upper end of the fission spectrum at perhaps 10 MeV. For cosmic ray dosimetry the energy range extends into the GeV region. This enormous range sets a challenge for designing measuring devices and a parallel challenge of developing measurement standards for characterizing these devices. One of the major considerations when deciding on topics for this special issue was agreeing on what not to include. Modelling, i.e. the use of radiation transport codes, is now a very important aspect of neutron measurements. These calculations are vital for shielding and for instrument design; nevertheless, the topic has only been included here where it has a direct bearing on metrology and the development of standards. Neutron spectrometry is an increasingly important technique for unravelling some of the problems of dose equivalent measurements and for plasma diagnostics in fusion research. However, this topic is at least one step removed from primary metrology and so it was felt that it should not be
Basic neutronics. Neutrons migration
This article presents the basic neutronics necessary for the understanding of the operation of the different types of nuclear reactors: 1 - introduction to neutronics: principle of fission chain reactions, fast neutron reactors and thermal neutron reactors, capture, neutron status, variations with the reactor lattices; 2 - Boltzmann equation: neutrons population, neutrons migration, characterization of neutrons population and reactions, integral form of the Boltzmann equation, integral-differential form, equivalence between the two forms; 3 - reactor kinetics: fast neutrons and delayed neutrons, kinetic equations in punctual model, Nordheim equation, reactivity jumps, reactivity ramp; 4 - diffusion equation: local neutron status, Fick's law, diffusion equation, initial, boundary and interface conditions, nuclei in infinite and homogenous medium, some examples of solutions, developments in Eigenmodes; 5 - one-group theory: equation of the 'one-group - diffusion' theory, critical condition of the naked and homogenous reactor, critical condition of a reactor with reflectors, generalizations; 6 - neutrons moderation: different moderation mechanisms, elastic shock laws, moderation equation, some examples of solutions; 7 - resonance absorption of neutrons: advantage of the discontinuous moderation character, advantage of an heterogenous disposition, classical formula of the anti-trap factor in homogenous and heterogenous situation; 8 - neutrons thermalization: notions of thermalization mechanisms, thermalization equation, Maxwell spectrum, real spectrum, classical formula of the thermal utilisation factor, classical formula of the reproduction factor, moderation optimum. (J.S.)
The Monte Carlo stochastic simulation technique has traditionally been the only well-recognized method for computing three-dimensional radiation dose distributions in connection with boron neutron capture therapy (BNCT) research. A deterministic approach to this problem would offer some advantages over the Monte Carlo method. This paper describes an application of a deterministic method to analytically simulate BNCT treatment of a canine head phantom using the epithermal neutron beam at the Brookhaven medical research reactor (BMRR). Calculations were performed with the TORT code from Oak Ridge National Laboratory (ORNL), an implementation of the discrete ordinates, or Sn method. Calculations were from first principles and used no empirical correction factors. The phantom surface was modeled by flat facets of approximately 1 cm2. The phantom interior was homogeneous. Energy-dependent neutron and photon scalar fluxes were calculated on a 32x16x22 mesh structure with 96 discrete directions in angular phase space. The calculation took 670 min on an Apollo DN10000 workstation. The results were subsequently integrated over energy to obtain full three-dimensional dose distributions. Isodose contours and depth-dose curves were plotted for several separate dose components of interest. Phantom measurements were made by measuring neutron activation (and therefore neutron flux) as a function of depth in copper--gold alloy wires that were inserted through catheters placed in holes drilled in the phantom. Measurements agreed with calculations to within about 15%. The calculations took about an order of magnitude longer than comparable Monte Carlo calculations but provided various conveniences, as well as a useful check
Ding, M.; Hartl, M.; Wang, Y.; Hjelm, R.
2013-12-01
In nuclear waste management, clays are canonical materials in the construction of engineered barriers. They are also naturally occurring reactive minerals which play an important role in retention and colloidal facilitated reactive transport in subsurface systems. Knowledge of total and accessible porosity in clays is crucial in determining fluids transport behavior in clays. It will provide fundamental insight on the performance efficiency of specific clays as a barrier material and their role in regulating radionuclide transport in subsurface environments. The aim of the present work is to experimentally investigate the change in pore characteristics of clays as function of moisture content, and to determine their pore character in relation to their water retention capacity. Recent developments in small-angle neutron scattering (SANS) techniques allow quantitative measurement of pore morphology and size distribution of various materials in their pristine state under various sample environments (exposure to solution, high temperature, and so on). Furthermore, due to dramatic different neutron scattering properties of hydrogen and deuterium, one can readily use contrast variation, which is the isotopic labeling with various ratios of H and D (e.g. mixture of H2O/D2O) to highlight or suppress features of the sample. This is particularly useful in the study of complex pore system such as clays. In this study, we have characterized the pore structures for a number of clays including clay minerals and field samples which are relevant to high-level waste systems under various sample environments (e.g., humidity, temperature and pressure) using SANS. Our results suggest that different clays show unique pore features under various sample environments. To distinguish between accessible/non-accessible pores and the nature of pore filling (e.g. the quantity of H2O adsorbed by clays, and the distribution of H2O in relation to pore character) to water, clays were exposed for
Lucero, Catherine L.; Bentz, Dale P.; Hussey, Daniel S.; Jacobson, David L.; Weiss, W. Jason
Air entrainment is commonly added to concrete to help in reducing the potential for freeze thaw damage. It is hypothesized that the entrained air voids remain unsaturated or partially saturated long after the smaller pores fill with water. Small gel and capillary pores in the cement matrix fill quickly on exposure to water, but larger pores (entrapped and entrained air voids) require longer times or other methods to achieve saturation. As such, it is important to quantitatively determine the water content and degree of saturation in air entrained cementitious materials. In order to further investigate properties of cement-based mortar, a model based on Beer's Law has been developed to interpret neutron radiographs. This model is a powerful tool for analyzing images acquired from neutron radiography. A mortar with a known volume of aggregate, water to cement ratio and degree of hydration can be imaged and the degree of saturation can be estimated.
Calculation of physically-realistic radiation dose distribution for Boron Neutron Capture Therapy (BNCT) is a complex, three-dimensional problem. The Monte Carlo stochastic simulation technique has traditionally been the primary method for performing such calculations. A three-dimensional deterministic approach to the problem would offer some complementary advantages. Recently-completed work at the Idaho National Engineering Laboratory (INEL) has established that the three-dimensional discrete-ordinates (Sn) formulation offers such an approach. The method has been validated in detail against measurements taken in a canine-head Medical Research Reactor (BMRR) located at Brookhaven National Laboratory (BNL) in Upton, NY. In addition, three-dimensional deterministic calculations of all relevant BNCT dose components have been completed for the three-dimensional phantom in the proposed INEL Power Burst Facility (PBF) epithermal-neutron beam
Spectra of linear energy transport of neutrons from 0.2 to 200 MeV obtained by SSTD
Brabcová, Kateřina; Spurný, František; Jadrníčková, Iva
Bratislava: Slovak Society of Nuclear Medicine and Radiation Hygiene, 2008, s. 84-86. ISBN 978-80-89384-01-3. [Days of Radiation Protection /30./. Liptovský Ján, Low Tatras (SK), 10.11.2008-14.11.2008] Grant ostatní: Evropské společenství(XE) ILSRA - 2004 - 248 Institutional research plan: CEZ:AV0Z10480505 Keywords : neutrons * track detectors * linear energy transfer Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders
Although vanadium has a suspected physiological role in man, the existing data available on its metabolism at molecular level are very limited and inadequate for modern toxicological and nutritional evaluations. To study its metabolic patterns in the human body it is necessary to determine the association with different biochemical components. The paper describes the identification of V-binding components in human blood by means of fractionation of human serum proteins and neutron activation analysis of the protein fractions of different molecular weight. Since information on the chemical form of V in blood is not well known, preliminary radiotracer experiments were performed by injecting 48V into rats and successively fractionating the 48V plasma proteins by gel filtration, ion-exchange chromatography and poliacrylamide gel electrophoresis. The results indicated that V in rat blood was mainly present in the serum as a V-transferrin biocomplex. It seemed reasonable to assume that a similar biocomplex could also be present in the blood of human subjects. To confirm on man the results obtained by 48V experiments on rats, human plasma proteins were isolated and separated by gel filtration on Sephadex resin and the V content in the elution fractions was determined by neutron activation followed by a rapid radiochemical separation of the induced 52V and gamma-ray spectrometry using a Ge(Li) detector. The results show that V in human plasma was effectively associated with transferrin protein, the iron transport system of the blood. A brief discussion of the results and of the determination of metal-binding components in the human body by combining biochemical techniques and neutron activation analysis is also given (author)
This paper presents a synthesis of the latest advances in the Verification and Validation (V and V) process of the new French (CEA) deterministic neutron transport code APOLLO3® developed within the framework of a common CEA, AREVA and EDF project. It focuses more precisely on the generic V and V of the main transport flux solvers of the code (namely IDT, Minaret, Pastis, TDT and Minos,) through 1D to 3D international benchmarks (ZPR-1D, Stepanek, C5G7, Takeda). Precise criteria have been defined to assess the quality of each solver by comparison with TRIPOLI4® multigroup Monte-Carlo calculations that have been performed for each configuration. We show that pure transport flux solvers (IDT, Minaret, Pastis and TDT-MOC) based on Sn , Pn and characteristics methods meet the keff target precision criteria (100 pcm) whereas SPn solver (Minos) give satisfactory results within reasonable computation time. The complementary of the APOLLO3® flux solvers set is globally highlighted. (author)
A method was derived to calculate from integral transport theory the neutron flux density close to boundaries between plate lattice regions of fast zero power reactors. Leakage parallel to the plate planes is treated by a momentum method. Linearly anisotropic scattering and the space dependence of effective cross sections in the resonance region are taken into account by suitable approximations. The method was applied to evaluate reaction rate measurements in the vicinity of the core-blanket-boundary of a SNEAK-assembly mocking up parts of the reactor SNR 300. Using the cross section set KFKINR agreement with the experiment was achieved for the space dependence of the 239Pu fission rate and the 238U capture rate. Further improvements of the nuclear data of 238U are required for solving discrepancies found in the outer blanket regions and in a U-metal blanket. (Orig.)
ANISN-JR, a one-dimensional discrete ordinates code for neutron and gamma-ray transport calculations
The ANISN code available from RSIC is designed to solve the one-dimensional Boltzmann equation for deep penetration problems taking into consideration the anisotropic scattering by Legendre expansion of the scattering cross sections. To extend its applicability for shielding analyses, the code has been modified by adding options of calculating the reaction rates distributions from detector response, generating the volume-flux weighted cross sections in arbitrary regions or zones and plotting the neutron or gamma-ray spectra and the reaction rates distributions. The formats of input data necessary in the options are described in detail. (auth.)
V Wagner; A Krása; M Majerla; F Křížek; O Svoboda; A Kugler; J Adam; V M Tsoupko-Sitnikov; M I Krivopustov; I V Zhuk; W Westmeier
2007-02-01
The set-up `energy plus transmutation', consisting of a thick lead target and a natural uranium blanket, was irradiated by relativistic proton beams with the energy from 0.7 GeV up to 2 GeV. Neutron field was measured in different places of this set-up using different activation detectors. The possibilities of using the obtained data for benchmark studies are analyzed in this paper. Uncertainties of experimental data are shown and discussed. The experimental data are compared with results of simulation with MCNPX code.
Hoffman, A. J.; Lee, J. C. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI, 48109-2104 (United States)
2013-07-01
A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependence of the angular flux time derivative. The accuracy of this method is assessed through implementation in the neutron transport code DeCART. The method is employed with variable-order local source representation to model a TWIGL transient. The results demonstrate that this method is accurate and more efficient than the discretized method. (authors)
A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependence of the angular flux time derivative. The accuracy of this method is assessed through implementation in the neutron transport code DeCART. The method is employed with variable-order local source representation to model a TWIGL transient. The results demonstrate that this method is accurate and more efficient than the discretized method. (authors)
Spent nuclear fuels (SNF) involve fissile materials, fission products, and transuranium, so that they are highly radioactive and have a possibility to be critical state. Therefore, criticality safety for the transport cask loading spent fuel assemblies should be guaranteed through reliable evaluation procedure. According to the 10CFR71 and IAEA TS-R-1, the regulatory requirement for subcriticality is prescribed as follows: the keff, including all biases and uncertainties at a 95% confidence level, do not exceed 0.95. However, because there are uncertainties of modeling and possibility of design modification, the subcriticality limit is established that the maximum value of keff at a 95% confidence level do not exceed 0.935. The objective of this study is to evaluate the criticality for the transport cask that is designed for transportation of 18, 21, and 24 fuel cells with the inserted-type neutron absorber and to determine the minimum gap size between the adjacent fuel cells for each cask to meet the regulatory requirements. Prior to criticality calculation, cavity (internal region of cask, exclusive of shields and the outermost structural material) inner radius must be determined with loading capacities and gap sizes between two fuel cells. Various errors, manufacturing tolerance included, has to be taken into account in the calculation process. For this reason, in this study, it is considered a margin of 2mm. As fuel cell type of the exclusive transport cask for CE-type 16x16 spent fuel assemblies is not yet definitely decided, the cavity inner radius must be determined as the maximum value out of calculation results for the two - overlapped and inserted - types
Experimental evaluation proved that no chloride induced stress corrosion cracking will occur on the metal cask which utilizes propylene glycol aqueous solution as neutron shield. Crevice corrosion, precursor of cracking, occurs at about 0.4V vs. 0.1M-KCl silver silver-chloride reference electrode in aqueous solution with chloride concentration of more than 5 times higher than limit value. On the other hand, the electrochemical potential (ECP) of cask material was 0.08V in air saturated aqueous solution. Since ECP is much smaller than the crevice corrosion potential below which no crevice corrosion is expected, the possibility is very small for chloride induced stress corrosion cracking to occur on the cask. (author)
The principle of the curved neutron guide is to transport neutrons far away from the reactor core with as minimum particle loss as possible. After a series of total reflection,the neutron beam is no longer visible from the reactor core and consequently, gamma radiations and fast neutrons emitted from the core are scattered by the walls of the guide and absorbed by the biological shielding set around the guide. The curved neutron guide provides a high-quality beam of slow neutrons. The first chapter deals with the theoretical concept of curved guide, we have determined the parameters for the setting of such a guide in the EL3 reactor at Saclay (France). The different tolerances on the state the surface, on the alignment of the different parts of the guide, on the waving of the guide wall have been assessed. The second chapter presents the technical solution chosen that complies to all the required specifications. The curved neutron guide has been designed for neutrons with wavelength of 4 Angstroms, it is 29 m long, has a bending radius of 835 m and is composed of 87 rectangular components made of glass plates on which a 1500 angstrom thick layer of nickel has been deposited. Each component is set with a fixed angle of (4±0.25)*10-4 radians from the previous component in order to form the bending radius. The last chapter is dedicated to the neutron flux measurement made at the end of the neutron guide