Sample records for 566-group neutron transport

  1. Neutron transport

    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

  2. 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

  3. 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)

  4. 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)


    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.

  5. Coupled Neutron Transport for HZETRN

    Slaba, Tony C.; Blattnig, Steve R.


    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.

  6. 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)

  7. Neutron transport with periodic boundary conditions

    Angelescu, N.; Marinescu, N.; Protopopescu, V.


    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.

  8. 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

  9. ANEMONA: multiassembly neutron transport modeling

    Jevremovic, T.; Ito, T. E-mail:; Inaba, Y


    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.

  10. 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

  11. Neutron stars - cooling and transport

    Potekhin, A Y; Page, Dany


    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.

  12. 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)

  13. 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)

  14. 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 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 and 2,65 x 102, respectively. (author). 30 refs, 39 figs, 9 tabs

  15. 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)

  16. 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)

  17. 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.

  18. An Improved Neutron Transport Algorithm for HZETRN

    Slaba, Tony C.; Blattnig, Steve R.; Clowdsley, Martha S.; Walker, Steven A.; Badavi, Francis F.


    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.

  19. 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)

  20. 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

  1. 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)

  2. 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.

  3. Parallel Deterministic Neutron Transport with AMR

    Clouse, C


    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.

  4. 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

  5. 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)

  6. 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)

  7. 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

  8. 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)

  9. 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

  10. 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.


    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.

  11. 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.


    袁光伟; 沈智军; 闫伟


    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.

  13. 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

  14. Scattered Neutron Tomography Based on A Neutron Transport Inverse Problem

    William Charlton


    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.

  15. 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)


    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.

  16. 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

  17. Considerations in the design of an improved transportable neutron spectrometer

    Williams, A M; Brushwood, J M; Beeley, P A


    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.

  18. 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)


    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)

  19. 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.)

  20. 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

  1. 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)


    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.

  2. 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.

  3. 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

  4. Thermal and transport properties of the neutron star inner crust

    Page, Dany


    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.

  5. 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

  6. 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

  7. 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


    袁光伟; 沈智军; 沈隆钧; 周毓麟


    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.

  9. 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

  10. 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

  11. 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)


    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)

  12. Graphical User Interface for Simplified Neutron Transport Calculations

    Schwarz, Randolph; Carter, Leland L


    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.

  13. 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

  14. 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

  15. 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)


    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.

  16. Neutron shielding evaluation for a small fuel transport case

    Coeck, M; Vanhavere, F


    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).

  17. 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.

  18. 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)

  19. 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)

  20. 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


    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

  1. 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.)

  2. 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)

  3. 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)

  4. 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

  5. Neutron transport calculations using Quasi-Monte Carlo methods

    Moskowitz, B.S.


    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.

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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.

  12. 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)

  13. 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:; Tsagas, N.F. [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Xanthi (Greece)


    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.

  14. 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.

  15. 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)

  16. 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)

  17. 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

  18. 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

  19. Combining measurements and 3D neutron transport calculations. A powerful tool in detailed neutron dosimetry and damage analysis

    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

  20. 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)

  1. Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport

    Blattnig, S.R.; Slaba, T.C.; Heinbockel, J.H.


    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.

  2. 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)

  3. 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

  4. 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)

  5. Subroutines to Simulate Fission Neutrons for Monte Carlo Transport Codes

    Lestone, J P


    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.

  6. Gamma transport and diffusion calculation capability coupled with neutron transport simulation in KARMA 1.2

    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

  7. 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

  8. Birman-Schwinger principle and Nelkin conjecture theory of neutron transport

    Stepin, S A


    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

  9. 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)

  10. 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)

  11. 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)

  12. 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)

  13. 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)

  14. 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.)

  15. 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

  16. 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

  17. 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)

  18. 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.

  19. Subroutines to Simulate Fission Neutrons for Monte Carlo Transport Codes

    Lestone, J. P.


    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...

  20. Neutron and photon transport calculations in fusion system. 2

    Sato, Satoshi [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment


    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.)

  1. 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

  2. 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)

  3. 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

  4. 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)

  5. 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

  6. Experimental Transport Benchmarks for Physical Dosimetry to Support Development of Fast-Neutron Therapy with Neutron Capture Augmentation

    D. W. Nigg; J. K. Hartwell; J. R. Venhuizen; C. A. Wemple; R. Risler; G. E. Laramore; W. Sauerwein; G. Hudepohl; A. Lennox


    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].

  7. 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)

  8. Analytical formulation for solving the one-dimensional discrete ordinates of neutron transport with anisotropic scattering

    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)

  9. Angular neutron transport investigation in the HZETRN free-space ion and nucleon transport and shielding computer program

    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

  10. 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)


    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)

  11. Neutron production and time resolution of a new class moderator for pulsed neutron diffraction. Measurements and transport calculations

    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.)

  12. Transport calculation of thermal and cold neutrons using NMTC/JAERI-MCNP4A code system

    Iga, Kiminori [Kyushu Univ., Fukuoka (Japan); Takada, Hiroshi; Nagao, Tadashi


    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)

  13. 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)

  14. Diffusion/transport hybrid discrete method for Monte Carlo solution of the neutron transport equation

    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

  15. 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)

  16. Cosmic ray heliospheric transport study with neutron monitor data

    Ahluwalia, H. S.; Ygbuhay, R. C.; Modzelewska, R.; Dorman, L. I.; Alania, M. V.


    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

  17. 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)

  18. Neutron secondary-particle production cross sections and their incorporation into Monte-Carlo transport codes

    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

  19. Spin diffusive modes and thermal transport in neutron star crusts

    Sedrakian, Armen


    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.

  20. Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media


    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.

  1. 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)

  2. 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

  3. 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

  4. Discrete ordinates method for three-dimensional neutron transport equation based on unstructured-meshes


    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.

  5. 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)

  6. 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

  7. 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.

  8. 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


    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

  9. 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)

  10. Computational benchmarking of fast neutron transport throughout large water thicknesses; Benchmark theorique du transport de neutrons rapides a travers de larges epaisseurs d`eau

    Risch, P.; Dekens, O.; Ait Abderrahim, H. [SCK-CEN, Fuel Research Department, (Belgium); Wouters, R. de [Tractebel, Energy Engineering, (Belgium)


    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.

  11. Development of deterministic transport methods for low energy neutrons for shielding in space

    Ganapol, Barry


    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

  12. New approach to creation of geometrical module for nuclear reactor neutron transport computer simulation analysis

    Poveschenko, T.; Poveschenko, O. [RRC Kurchatov Inst., Kurchatov square, 1, 123182, Moscow (Russian Federation)


    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)

  13. New approach to creation of geometrical module for nuclear reactor neutron transport computer simulation analysis

    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)

  14. 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)


    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.

  15. 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


    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...

  16. 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)

  17. Computational Transport Modeling of High-Energy Neutrons Found in the Space Environment

    Cox, Brad; Theriot, Corey A.; Rohde, Larry H.; Wu, Honglu


    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

  18. New methods in linear transport theory. Part of a coordinated programme on methods in neutron transport theory

    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

  19. 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)

  20. 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)

  1. 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

  2. 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

  3. Evaluation of dominant time-eigenvalues of neutron transport equation by Meyer's sub-space iterations

    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.

  4. Flexible polyvinyl chloride neutron guides for transporting ultracold and very cold neutrons

    Arzumanov, S. S., E-mail:; 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)


    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.

  5. 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.

  6. 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)

  7. 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.)

  8. Arbitrary quadrature: its application in the solution of one-dimensional, planar neutron transport problems

    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)

  9. Description of a neutron field perturbed by a probe using coupled Monte Carlo and discrete ordinates radiation transport calculations

    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

  10. 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

  11. Monoenergetic time-dependent neutron transport in an infinite medium with time-varying cross sections

    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

  12. 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

  13. Improved treatment of anisotropic elastic neutron scattering with consistent transport approximations of energy-dependent order

    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.)

  14. On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions

    Song, Degong


    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...

  15. 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.)

  16. 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

  17. Guideline of Monte Carlo calculation. Neutron/gamma ray transport simulation by Monte Carlo method


    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.

  18. Analytical synthetic methods of solution of neutron transport equation with diffusion theory approaches energy multigroup

    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

  19. 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)

  20. 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)

  1. 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)

  2. 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

  3. 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)

  4. 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

  5. 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)

  6. 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.)

  7. Sensitive and transportable gadolinium-core plastic scintillator sphere for neutron detection and counting

    Dumazert, Jonathan; Coulon, Romain; Carrel, Frédérick; Corre, Gwenolé; Normand, Stéphane; Méchin, Laurence; Hamel, Matthieu


    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.

  8. Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

    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

  9. 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

  10. A three dimensional stochastic neutron transport code using new lattice model 'DIMOS' and analysis of neutron streaming problems

    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)

  11. 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

  12. 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


    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...

  13. 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)

  14. Spatially adaptive hp refinement approach for PN neutron transport equation using spectral element method

    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

  15. 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)

  16. Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

    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

  17. Radiative or neutron transport modeling using a lattice Boltzmann equation framework

    Bindra, H.; Patil, D. V.


    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.

  18. Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

    Saha Ray, S., E-mail:; Patra, A.


    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.

  19. Transport simulation and image reconstruction for fast-neutron detection of explosives and narcotics

    Micklich, B.J.; Fink, C.L.; Sagalovsky, L.


    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.

  20. The use of neutron generators for the detection of illicit materials in the sea transportation system

    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

  1. 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

  2. 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)

  3. 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

  4. 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)

  5. 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)

  6. 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

  7. 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)

  8. 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

  9. 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

  10. 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%.

  11. Secondary fusion coupled deuteron/triton transport simulation and thermal-to-fusion neutron convertor measurement

    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)

  12. Neutron transport in inhomogeneous solid cylinder with anisotropic scattering using a variational method

    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

  13. 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

  14. 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)

  15. Neutron transport by collision probability method in complicated geometries

    Constantin, Marin [Institute for Nuclear Research, Pitesti (Romania)


    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)

  16. Collocation method for the solution of the neutron transport equation with both symmetric and asymmetric scattering

    Morel, J.E.


    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.

  17. TDA, Time-Dependent 1-D Neutron Transport, Gamma Transport by ANISN Method in Slab, Spherical, Cylindrical Geometry

    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

  18. 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

  19. 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)

  20. 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)

  1. 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

  2. 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

  3. 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.))

  4. 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)

  5. Monte Carlo Neutrino Transport Through Remnant Disks from Neutron Star Mergers

    Richers, S; O'Connor, Evan; Fernandez, Rodrigo; Ott, Christian


    We present Sedonu, a new open source, steady-state, special relativistic Monte Carlo (MC) neutrino transport code, available at 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...

  6. Numerical evaluation of the light transport properties of alternative He-3 neutron detectors using ceramic scintillators

    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

  7. Numerical evaluation of the light transport properties of alternative He-3 neutron detectors using ceramic scintillators

    Ohzu, A., E-mail: [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)


    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.

  8. Improved method for solving the neutron transport problem by discretization of space and energy variables

    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

  9. 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.

  10. 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: [Laboratory of Nuclear Technology, School of Engineering, ' Democritus' University of Thrace, Vas. Sofias 12, Xanthi 67100 (Greece)


    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.

  11. 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.)

  12. 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

  13. Instrumentation development for magneto-transport and neutron scattering measurements at high pressure and low temperature

    Wang, Weiwei


    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,...

  14. Neutron, electron and photon transport in ICF tragets in direct and fast ignition

    A. Parvazian; A. Okhovat


    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...

  15. 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)

  16. Calculations in two-group neutron transport theory with isotropic-and linearly anisotropic scattering

    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

  17. Angular dependent rebalance acceleration arithmetic for neutron transport equation in unstructured mesh

    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)

  18. 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)

  19. 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

  20. Angular dependent coarse-mesh rebalance method for acceleration of the discrete ordinates neutron transport equation

    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

  1. 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

  2. A study on the criticality of modified neutron transport equation by using alternative scattering phase functions

    Kara, Ayahn [Sinop Univ. (Turkey). Dept. of Nuclear Energy Engineering; Anli, Fikret [Univ. Kahramanmaras (Turkey). Dept of Physics


    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.

  3. 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)

  4. 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)

  5. Integral experiments with 14 MeV-neutron source into multiplying assemblies and verification of neutron transport code

    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

  6. Neutron and gamma ray transport calculations in shielding system

    Masukawa, Fumihiro; Sakamoto, Hiroki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment


    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.)

  7. 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

  8. Numerical research on the anisotropic transport of thermal neutron in heterogeneous porous media with micron X-ray computed tomography

    Yong Wang; Wenzheng Yue; Mo Zhang


    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 ...

  9. 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)

  10. Modelling of neutron and photon transport in iron and concrete radiation shieldings by the Monte Carlo method - Version 2

    Žukauskaite, A; Plukiene, R; Plukis, A


    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.

  11. Development and application of neutron transport methods and uncertainty analysis for reactor core calculations. Final report

    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.

  12. 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)

  13. Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source

    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)

  14. FOCUS, Neutron Transport System for Complex Geometry Reactor Core and Shielding Problems by Monte-Carlo

    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

  15. Analysis of the neutrons dispersion in a semi-infinite medium based in transport theory and the Monte Carlo method

    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)

  16. Applicability of deterministic and Monte Carlo neutron transport models coupled with thermo-fluiddynamics

    Seubert, A.; Langenbuch, S.; Velkov, K.; Zwermann, W. [Gesellschaft fuer Anlagen- und Reaktorsicherheit mbH (GRS), Garching (Germany). Forschungsinstitute


    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.)

  17. A stochastic transport theory of neutron and photon coupled fields neutron and photon counting statistics in nuclear assemblies

    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

  18. 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)

  19. Transport equations and linear response of superfluid Fermi mixtures in neutron stars

    Gusakov, M E


    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.

  20. 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. AIRTRANS, Time-Dependent, Energy Dependent 3-D Neutron Transport, Gamma Transport in Air by Monte-Carlo

    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

  2. Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

    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)

  3. 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)

  4. 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

  5. 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.

  6. 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

  7. 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)

  8. 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)

  9. 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

  10. Extension of Applicability of integral neutron transport theory in reactor cell and core investigation

    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)