P3-approximation for gaseous media and vacuum
International Nuclear Information System (INIS)
Raevskaya, V.E.
1986-01-01
The problems connected with calculation of neutron field in a fuel assembly (FA) of a gas cooled reactor are discussed. The problem of P 3 -approximation applicability for the description of neutron fields in closed vacuum and gas volumes is considered. Under the assumption of the field azimuthal symmetry derived are the formulas for determination of the field in cylindrical vacuum layer of multizone FA as well as the solution for the cluster central zone, where the rods with vacuum between them are placed. Because of the finiteness of voids surrounded by medium it is possible to use the condition of neutron flux density continuity as the boundary conditions for the interface with vacuum. For representation of boundary conditions for rod surfaces and the cluster central zone with vacuum the addition theorems for the field in vacuum between the roads are derived. The formulas for mean neutron fluxes in vacuum cylindrical layer and in vacuum between rods are derived. The numerical calculations performed according to various programs confirmed the validity of the derived formulas
Solution of the kinetic equation in the P3-approximation in a plane geometry
International Nuclear Information System (INIS)
Vlasov, Yu.A.
1975-01-01
A method and a program are described for solving single-velocity kinetic equations of neutron transfer for the plane geometry in the finite-difference approximation. A difference high-accuracy scheme and a matrix factorization method are used for the differential-difference equation systems. The program is written in the ALGOL-60 language and is adapted for M-20, M-220, M-222 and BESM-4 computers
Neutron disadvantage factors in heavy water and light water reactors
International Nuclear Information System (INIS)
Pop-Jordanov, J.
1966-01-01
A number od heavy water and light water reactor cells are analyzed in this paper by applying analytical methods of neutron thermalization. Calculations done according to the one-group Amouyal-Benoist method are included in addition. Computer codes for ZUSE Z-23 computer were written by applying both methods. The obtained results of disadvantage factors are then compared to results obtained by one-group P 3 approximation and by multigroup K7-THERMOS code [sr
International Nuclear Information System (INIS)
Zmijarevic, I.
1980-01-01
Space-energy distribution of resonance neutrons in reactor lattice cell was determined by solving the Boltzmann equation by spherical harmonics method applying P-3 approximation. Computer code SPLET used for these calculations is described. Resonance absorption and calculation of resonance integrals are described as well. Effective resonance integral values for U-238 resonance at 6.7 Ev are calculated for heavy water reactor cell with metal, oxide and carbide fuel elements
Description of the RZV and RZF programs
International Nuclear Information System (INIS)
Raevskaya, V.E.; Torlin, B.Z.
1980-01-01
An instruction for running the P3B and P3F programs intended for an implementation of a one-group calculation of the neutron field in a polycell with multizone ring blocks in the P 3 approximation. The program is written in the FORTRAN language for the BESM-6 computer. Time for the calculation of one variant constitutes about 20 s for a simple cell and for double lattices for uniform blocks and 40 s - for double lattices from 30-zone blocks. 4 minutes is the maximum time required for the calculation of the 8x8 polycell consisting from 20 nonequivalent 30-zone blocks of 20 kinds
International Nuclear Information System (INIS)
Milosevic, M.
1979-01-01
One-dimensional variational method for cylindrical configuration was applied for calculating group constants, together with effects of elastic slowing down, anisotropic elastic scattering, inelastic scattering, heterogeneous resonance absorption with the aim to include the presence of a number of different isotopes and effects of neutron leakage from the reactor core. Neutron flux shape P 3 and adjoint function are proposed in order to enable calculation of smaller size reactors and inclusion of heterogeneity effects by cell calculations. Microscopic multigroup constants were prepared based on the UKNDL data library. Analytical-numerical approach was applied for solving the equations of the P 3 approximation to obtain neutron flux moments and adjoint functions
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de
Abstract of programs for nuclear reactor calculation and kinetic equations solution
International Nuclear Information System (INIS)
Marakazov, A.A.
1977-01-01
The collection includes about 50 annotations of programmes,developed in the Kurchatov Atomic Energy Institute in 1971-1976. The programmes are intended for calculating the neutron flux, for solving systems of multigroup equations in P 3 approximation, for calculating the reactor cell, for analysing the system stability, breeding ratio etc. The programme annotations are compiled according to the following diagram: 1.Programme title. 2.Computer type. 3.Physical problem. 4.Solution method. 5.Calculation limitations. 6.Characteristic computer time. 7.Programme characteristic features. 8.Bound programmes. 9.Programme state. 10.Literature allusions in the programme. 11.Required memory resourses. 12.Programming language. 13.Operation system. 14.Names of authors and place of programme adjusting
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)
Model Comparison for Electron Thermal Transport
Moses, Gregory; Chenhall, Jeffrey; Cao, Duc; Delettrez, Jacques
2015-11-01
Four electron thermal transport models are compared for their ability to accurately and efficiently model non-local behavior in ICF simulations. Goncharov's transport model has accurately predicted shock timing in implosion simulations but is computationally slow and limited to 1D. The iSNB (implicit Schurtz Nicolai Busquet electron thermal transport method of Cao et al. uses multigroup diffusion to speed up the calculation. Chenhall has expanded upon the iSNB diffusion model to a higher order simplified P3 approximation and a Monte Carlo transport model, to bridge the gap between the iSNB and Goncharov models while maintaining computational efficiency. Comparisons of the above models for several test problems will be presented. This work was supported by Sandia National Laboratory - Albuquerque and the University of Rochester Laboratory for Laser Energetics.
Massively parallel performance of neutron transport response matrix algorithms
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1993-01-01
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 P 3 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.)
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
Analytical modeling of light transport in scattering materials with strong absorption.
Meretska, M L; Uppu, R; Vissenberg, G; Lagendijk, A; Ijzerman, W L; Vos, W L
2017-10-02
We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In particular, we study the transport of light in the visible wavelength range between 420 and 700 nm through silicone plates filled with YAG:Ce 3+ phosphor particles, that even re-emit absorbed light at different wavelengths. We measure the total transmission, the total reflection, and the ballistic transmission of light through these plates. We obtain average single particle properties namely the scattering cross-section σ s , the absorption cross-section σ a , and the anisotropy factor µ using an analytical approach, namely the P3 approximation to the radiative transfer equation. We verify the extracted transport parameters using Monte-Carlo simulations of the light transport. Our approach fully describes the light propagation in phosphor diffuser plates that are used in white LEDs and that reveal a strong absorption (L/l a > 1) up to L/l a = 4, where L is the slab thickness, l a is the absorption mean free path. In contrast, the widely used diffusion theory fails to describe this parameter range. Our approach is a suitable analytical tool for industry, since it provides a fast yet accurate determination of key transport parameters, and since it introduces predictive power into the design process of white light emitting diodes.
International Nuclear Information System (INIS)
Cambi, G.; Cepraga, D.G.; Boeriu, S.; Maganzani, I.
1995-01-01
The radioactive inventory, the decay heat and the contact dose rate of permanent components such as the vacuum vessel of two experimental fusion tokamaks, the compact IGNITOR-ULT and the ITER-EDA fusion machines, are evaluated by using the ENEA-Bologna integrated methodology. The vacuum vessel material considered is the INCONEL 625. The neutron flux is calculated using the VITAMIN-C 171-group library, based on EFF-2 data and the 1-D transport code XSDRNPM in the S 8 -P 3 approximation. The ANITA-2 code, using updated cross sections and decay data libraries based on EAF-3 and IRDF90 evaluation files is used for activation calculations. The fusion neutron source has been normalised to a neutron first wall load of 2 MW/m 2 and 1 MW/m 2 for IGNITOR-ULT and ITER, respectively. The material irradiation have been described by multistep time histories, resulting in the designed total fluence. Variations in the composition of INCONEL 625 have been assessed and their impact on the activation characteristics are discussed, also from the point of view of waste disposal. (orig.)
Conception of thermonuclear reactor with a shielding layer of the first wall
International Nuclear Information System (INIS)
Marin, S.V.
1979-01-01
Considered is the way of the shielding of the first wall of a thermonuclear reactor by the layer of ISSEC (Internal spectral shifter and Energy Converter). It is a constructive non-power element placed between a plasma and the first wall, and intended for the softening of the spectrum and intensity reduction of particle fluxes falling on the first wall. Results of neutron-physical calculations of the UWMAK-type reactor blanket (in the S 4 -P 3 approximation) are presented. While comparing five materials (C, Mo, Nb, V,W) by the rate of radiation damage formation, gas production, radioactivity level and energy output in the blanket with the 316 stainless steel first wall, it is obvious that the conception of ISSEC permits to prolong the service period of the first wall. Construction elements should be then in the same irradiation conditions as those in fast reactors. Molybdenum has been taken as the best ISSEC material. It reduces the number of displaced atoms of the first wall by 20% and decreases helium production by about 100%, increases energy output in the blanket by 15-18%. However, graphite is advantageous, while comparing it to molybdenum in values of residual energy output, radioactivity level, costs and manufacture simplicity. One problem stays unsolved, which is connected with chemical sputtering of graphite at the formation of C 2 H 2 in the high temperature range. So it is hard to prefer any material now
International Nuclear Information System (INIS)
Matausek, M. V.
1966-06-01
A combination of multigroup method and P 3 approximation of spherical harmonics method was chosen for calculating space-energy distribution of thermal neutron flux in elementary reactor cell. Application of these methods reduced solution of complicated transport equation to the problem of solving an inhomogeneous system of six ordinary firs-order differential equations. A procedure is proposed which avoids numerical solution and enables analytical solution when applying certain approximations. Based on this approach, computer codes were written for ZUSE-Z-23 computer: SIGMA code for calculating group constants for a given material; MULTI code which uses results of SIGMA code as input and calculates spatial ana energy distribution of thermal neutron flux in a reactor cell. Calculations of thermal neutron spectra for a number of reactor cells were compared to results available from literature. Agreement was satisfactory in all the cases, which proved the correctness of the applied method. Some possibilities for improving the precision and acceleration of the calculation process were found during calculation. (author)
General solution of the multigroup spherical harmonics equations in R-Z geometry
International Nuclear Information System (INIS)
Matausek, M.
1983-01-01
In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)
International Nuclear Information System (INIS)
Boufraqech, A.
1991-01-01
Two methods for determining the diffusion parameters of thermal neutrons for non-moderator and non-multiplicator media have been developped: The first one, which is a pulsed method, is based on thermal neutrons relaxation coefficients measurement in a moderator, with and without the medium of interest that plays the role of reflector. For the experimental results interpretation using the diffusion theory, a corrective factor which takes into account the neutron cooling by diffusion has been introduced. Its dependence on the empirically obtained relaxation coefficients is in a good agreement with the calculations made in P3L2 approximation. The difference between linear extrapolation lengths of the moderator and the reflector has been taken into account, by developping the scalar fluxes in Bessel function series which automatically satisfy the boundary conditions at the extra-polated surfaces of the two media. The obtained results for Iron are in a good agreement with those in the literature. The second method is time independent, based on the 'flux albedo' measurements interpretation (Concept introduced by Amaldi and Fermi) by P3 approximation in the one group trans-port theory. The independent sources are introduced in the Marshak boundary conditions. An angular albedo matrix has been used to deal with multiple reflections and to take into account the distortion of the current vector when entring a medium, after being reflected by this latter. The results obtained by this method are slightly different from those given in the literature. The analysis of the possible sources causing this discrepancy, particulary the radial distribution of flux in cylindrical geometry and the flux depression at medium-black body interface, has shown that the origin of this discrepancy is the neutron heating by diffusion. 47 figs., 20 tabs., 39 refs. (author)
Depth of origin and angular spectrum of sputtered atoms
International Nuclear Information System (INIS)
Vicanek, M.; Jimenez Rodriguez, J.J.; Sigmund, P.
1989-01-01
A theoretical analysis is presented of the depth of origin of atoms sputtered from a random target. The physical model aims at high energy sputtering under linear cascade conditions and assumes a dilute source of recoil atoms. The initial distribution of the recoils is assumed isotropic, and their energy distribution is E -2 like without an upper or lower cutoff. The scattering medium is either infinite or bounded by a plane surface. Atoms scatter according to the m=0 power cross section. Electronic stopping is ignored. The sputtered flux, differential in depth of origin, ejection energy and ejection angle has been evaluated by Monte Carlo simulation and by five distinct methods of solution of the linear Boltzmann equation reaching from continuous slowing down neglecting angular scattering to the P 3 approximation and a Gram-Charlier expansion going over spatial moments. The continuous slowing down approximation used in previous work leads to results that are identical to those found from a scheme that only ignores angular scattering but allows for energy loss straggling. Moreover, these predictions match more closely with the Monte Carlo results than any of the approximate analytical schemes that take account of angular scattering. The results confirm the common assertion that the depth of origin of sputtered atoms is determined mainly by the stopping of low energy recoil atoms. The effect of angular scattering turns out to be astonishingly small. The distributions in depth of origin, energy, and angle do not depend significantly on whether the scattering medium is a halfspace or an infinite medium with a reference plane. The angular spectrum comes out only very slightly over cosine from the model as it stands, in agreement with previous experience, but comments are made on essential features that are not incorporated in the physical model but might influence the angular spectrum. (orig./WL)
Autofluorescence and diffuse reflectance patterns in cervical spectroscopy
Marin, Nena Maribel
Fluorescence and diffuse reflectance spectroscopy are two new optical technologies, which have shown promise to aid in the real time, non-invasive identification of cancers and precancers. Spectral patterns carry a fingerprint of scattering, absorption and fluorescence properties in tissue. Scattering, absorption and fluorescence in tissue are directly affected by biological features that are diagnostically significant, such as nuclear size, micro-vessel density, volume fraction of collagen fibers, tissue oxygenation and cell metabolism. Thus, analysis of spectral patterns can unlock a wealth of information directly related with the onset and progression of disease. Data from a Phase II clinical trial to assess the technical efficacy of fluorescence and diffuse reflectance spectroscopy acquired from 850 women at three clinical locations with two research grade optical devices is calibrated and analyzed. Tools to process and standardize spectra so that data from multiple spectrometers can be combined and analyzed are presented. Methodologies for calibration and quality assurance of optical systems are established to simplify design issues and ensure validity of data for future clinical trials. Empirically based algorithms, using multivariate statistical approaches are applied to spectra and evaluated as a clinical diagnostic tool. Physically based algorithms, using mathematical models of light propagation in tissue are presented. The presented mathematical model combines a diffusion theory in P3 approximation reflectance model and a 2-layer fluorescence model using exponential attenuation and diffusion theory. The resulting adjoint fluorescence and reflectance model extracts twelve optical properties characterizing fluorescence efficiency of cervical epithelium and stroma fluorophores, stromal hemoglobin and collagen absorption, oxygen saturation, and stromal scattering strength and shape. Validations with Monte Carlo simulations show that adjoint model extracted
Energy Technology Data Exchange (ETDEWEB)
Takac, S M; Krcevinac, S B [Institute of nuclear sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1966-07-15
introduced if measurements are to be made. The thermal neutron distribution in the fuel rod was experimentally determined in two ways: - by the conventional method using tube technique with uranium spacers, so that the perturbing effect could be reduced to a possible minimum, and - by the newly developed cell perturbation method, where the perturbing effect on the thermal neutron distribution was investigated in various geometrical configurations, to the unperturbed distribution can be determined by extrapolation of the obtained results. The results obtained by both methods were compared with the existing experimental data on equivalent systems, and with the following theoretical results: - P-3 approximation, - the analytical method (12), - the numerical method (11) (author)
International Nuclear Information System (INIS)
Takac, S.M.; Krcevinac, S.B.
1966-07-01
introduced if measurements are to be made. The thermal neutron distribution in the fuel rod was experimentally determined in two ways: - by the conventional method using tube technique with uranium spacers, so that the perturbing effect could be reduced to a possible minimum, and - by the newly developed cell perturbation method, where the perturbing effect on the thermal neutron distribution was investigated in various geometrical configurations, to the unperturbed distribution can be determined by extrapolation of the obtained results. The results obtained by both methods were compared with the existing experimental data on equivalent systems, and with the following theoretical results: - P-3 approximation, - the analytical method (12), - the numerical method (11) (author)
Investigation of tritium and 233U breeding in a fission-fusion hybrid reactor fuelling with ThO2
International Nuclear Information System (INIS)
Yildiz, K.; Sahin, S.; Sahin, H. M.; Acir, A.; Yalcin, S.; Altinok, T.; Bayrak, M.; Alkan, M.; Durukan, O.
2007-01-01
In the world, thorium reserves are three times more than natural Uranium reserves. It is planned in the near future that nuclear reactors will use thorium as a fuel. Thorium is not a fissile isotope because it doesn't make fission with thermal neutrons so it could be converted to 2 33U isotope which has very high quality fission cross-section with thermal neutrons. 2 33U isotope can be used in present LWRs as an enrichment fuel. In the fusion reactors, tritium is the most important fossil fuel. Because tritium is not natural isotope, it has to be produced in the reactor. The purpose of this work is to investigate the tritium and 2 33U breeding in a fission-fusion hybrid reactor fuelling with ThO 2 for Δt=10 days during a reactor operation period in five years. The neutronic analysis is performed on an experimental hybrid blanket geometry. In the center of the hybrid blanket, there is a line neutron source in a cylindrical cavity, which simulates the fusion plasma chamber where high energy neutrons (14.1 MeV) are produced. The conventional fusion reaction delivers the external neutron source for blankets following, 2 D + 3 T →? 4 He (3.5 MeV) + n (14.1 MeV). (1) The fuel zone made up of natural-ThO 2 fuel and it is cooled with different coolants. In this work, five different moderator materials, which are Li 2 BeF 4 , LiF-NaF-BeF 2 , Li 2 0Sn 8 0, natural Lithium and Li 1 7Pb 8 3, are used as coolants. The radial reflector, called tritium breeding zones, is made of different Lithium compounds and graphite in sandwich structure. In the work, eight different Lithium compounds were used as tritium breeders in the tritium breeding zones, which are Li 3 N, Li 2 O, Li 2 O 2 , Li 2 TiO 3 , Li 4 SiO 3 , Li 2 ZrO 3 , LiBr and LiH. Neutron transport calculations are conducted in spherical geometry with the help of SCALE4.4A SYSTEM by solving the Boltzmann transport equation with code CSAS and XSDRNPM, under consideration of unresolved and resolved resonances, in S 8 -P 3
Fissile fuel breeding and minor actinide transmutation in the life engine
International Nuclear Information System (INIS)
Sahin, Suemer; Khan, Mohammad Javed; Ahmed, Rizwan
2011-01-01
zone (50 cm), containing MA as fissionable fuel. A 3rd ODS layer (2 cm) separates the molten salt zone on the right side from the graphite reflector (30 cm). Calculations have been conducted for a fusion driver power of 500 MW th in S 8 -P 3 approximation using 238-neutron groups. Minor actinides (MA) out of the nuclear waste of LWRs are used as fissile carbide fuel in TRISO particles with volume fractions of 0, 2, 3, 4 and 5% have been dispersed homogenously in the Flibe coolant. For these cases, tritium breeding at startup is calculated as TBR = 1.134, 1.286, 1.387, 1.52 and 1.67, respectively. In the course of plant operation, TBR and fissile neutron multiplication factor decrease gradually. For a self-sustained reactor, TBR > 1.05 can be kept for all cases over 8 years. Higher fissionable fuel content in the molten salt leads also to higher blanket energy multiplication, namely M = 3.3, 4.6, 6.15 and 8.1 with 2, 3, 4 and 5% TRISO volume fraction at start up, respectively. For all investigated cases, fissile burn up exceeds 400 000 MW D/MT. Major damage mechanisms have been calculated as DPA = 50 and He = 176 appm per year. This implies a replacement of the first wall every 3 years.
ZZ DLC-11 RITTS, 121-Group Coupled Cross-Section for ANISN, DOT, MORSE
International Nuclear Information System (INIS)
1970-01-01
neutron-to-gamma-ray group transfer cross sections were generated, using POPOP-4, with account being taken for neutron capture, inelastic scattering, and other neutron reactions. The 100-group neutron kerma factors were generated by DLC-10/ AVKER and the 21-group gamma-ray kerma factors by MUG. The DLC-11 cross sections represent a P3 approximation to elastic (or Compton) scattering angular distributions. The 100 neutron groups cover an energy range from 14.92 MeV to thermal. For gamma-rays, 21 energy groups cover the range from 14.0 to 0.01 MeV. The group structures are given in ref. 2