摘要:

We introduce a generalization of the neutron diffusion equation, the solution of which is an accurate approximation to the transport scalar Flux. In this generalization we utilize auxiliary transport calculations of the system of interest to compute an accurate, pointwise diffusion coefficient. We have specified a procedure to generate and improve this auxiliary information in a systematic way, leading to improvement in the calculated diffusion scalar flux. This improvement is shown to be contingent upon satisfying the condition of positive calculated-diffusion coefficients, and we present an algorithm that ensures this positivity. Our generalized diffusion theory is also shown to be compatible with conventional diffusion theory in the sense that the same methods and codes can be used to calculate a solution for both. The accuracy of the method compared to reference SNtransport calculations is demonstrated for a wide variety of examples.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26680

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

It is argued that variational synthesis with discontinuous trial functions requires variational principles applicable to equations involving operators acting between distinct Hilbert spaces. A description is given of a Roussopoulos-type variational principle generalized to cover this situation. This principle is suggested as the basis for a unified approach to the derivation of variational functionals. In addition to esthetics, this approach has the advantage that the mathematical details increase the understanding of the derived functional, particularly the sense in which a synthesized solution should be regarded as an approximation to the true solution. By way of illustration, the generalized Roussopoulos principle is applied to derive a class of first-order diffusion functionals which admit trial functions containing approximations at an interface. These“asymptotic”interface quantities are independent of the limiting approximations from either side and permit use of different trial spectra at and on either side of an interface. The class of functionals derived contains as special cases both the Lagrange multiplier method of Buslik and two functionals of Lambropoulos and Luco. Some numerical results for a simple two-group model confirm that the“multipliers”can closely approximate the appropriate quantity in the region near an interface.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26681

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

A multi-scale perturbation method for studying nonlinear oscillations and their stability in higher order systems is developed. The technique is applied to the two-temperature reactor model. Stability boundaries involving the various parameters are established and easily interpretable analytical expressions for nonlinear oscillations are presented. The method requires neither phase plane systems nor autonomous equations and thus provides an analytical tool for investigating higher order and space-dependent reactor models.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26682

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

Methods are investigated for calculating nuclear heating and dose due to the interaction of nuclear radiation with matter. A theoretical model is developed for calculating neutron fluence-to-kerma factors (kerma = kinetic energy released in materials) from basic nuclear data. No major simplifying assumptions are introduced, and the accuracy of the calculated fluence-to-kerma factors depends only on the availability and accuracy of the basic nuclear data. Based on this theoretical model, a computer program called MACK was written to calculate fluence-to-kerma factors from nuclear data in ENDF format.An algorithm for investigating the validity of the kerma factors by using an integral energy balance was also developed. The validity of the theoretical model and the correctness of the computation of the kerma factors obtained in the present work were verified through the use of this algorithm. Comparison of these kerma-factor results with previous work showed that they provide a considerable improvement in kerma-factor and nuclear-heating calculations. It is also shown that there is currently some inconsistency in preserving the energy between the basic neutron interaction data and the gamma-ray production data. It is suggested that the photon-production matrix be processed simultaneously with the neutron kerma factors to ensure consistency.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26683

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

The calculational methods developed for nuclear heating in an earlier paper are applied to fusion-reactor blankets and shields. The study shows that the nuclear heating in fusion-reactor blankets has been previously overestimated and is limited to≍16 MeV per DT neutron in the absence of beryllium or fissionable materials. Methods are also examined for increasing the energy multiplication in the blanket by maximizing the rates of exothermic reactions.A general study of the sensitivity of the neutron energy deposition to changes in basic nuclear data is carried out: this study shows the following:The (n, charged particles) reactions, in general, contribute≍30 to 50% to the neutron heating in typical fusion-reactor spectra. The data for these reactions, however, are not well known and in some cases are absent from the literature.Approximating the neutron heating due to the (n, n′, charged particles) reactions by that from the (n, n′) part only, amounts to ignoring 80 to 90% of the heating.For reference fusion-reactor spectra, a change in the average secondary neutron energy,n′l,of the7Li(n, n′α)t reaction results in a relative change in the neutron heating in7Li which is approximately one-third of that inn′, l.The relative change in the neutron heating by elastic scattering due to a change in the angular distribution is larger than the relative change in. Ignoring the anisotropy of scattering can result in severely overestimated kerma factors.The local energy deposition by radioactive decay is on the order of or less than 2% in most materials in typical spectra for controlled thermonuclear reactors.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26684

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

The results of experiments in which iodine, dissolved as I-in LiF-BeF2melts, was stripped as HI by sparging with HF-H2mixtures have indicated that it may be possible to use such treatment to remove iodine from the molten fluoride mixtures used in molten salt reactor (MSR) fuels. This is of particular significance to MSR technology because it indirectly provides the means for removing a significant fraction of135Xe, a decay daughter of135I.Data obtained from transpiration experiments indicated a linear decrease of the logarithm of the iodine concentration of the melt with the number of moles of HF passed, and a linear increase of the reciprocal of the apparent equilibrium quotient Q’app= PHI/ (PHF[I-]) with the partial pressure of HF in the sparge gas. The iodine removal mechanism is explained by a model which assumes that the rate-controlling step is the transport of I-from the bulk of the melt to the surface and that the rates of the other steps are rapid.The removal of iodine from a molten salt breeder reactor (MSBR) fuel was analyzed in terms of the redox potential required to remove the iodine efficiently while preventing undesirable reactions in the fuel or between the fuel and its environment.The relative abundances of different iodine species present in the off-gas during sparging of an MSBR fuel were estimated; as expected, the results indicated a strong dependence on the temperature and hydrogen partial pressure. Low hydrogen pressures and low temperatures favor the formation of molecular iodine. High temperatures and low hydrogen pressures favor the formation of atomic iodine, while HI is formed at high temperatures and relatively higher hydrogen pressures.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26685

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

AbstractA theory is described for solving the integral neutron transport equation by the transmission probability method. Detailed attention is given to the problem in rectangular x-y geometry. Within a mesh the neutron flux is assumed to be linearly dependent on the x and y coordinates. The angular dependence is given by a double P1approximation. At the mesh surfaces a term is considered that allows for an asymmetric flux distribution relative to the surface normal. The inner source is obtained from the equilibrium equation.Based on this method, the code COXY has been developed and applied to one- and two-dimensional rectangular cell calculations. The calculated results show good agreement with those of SNand collision probability codes.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26686

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

AbstractAnalytical expressions describing the measured auto- and cross-spectral densities of the zero-power noise at the Measuring and Research Reactor Braunschweig (FMRB) were derived from the two-point reactor kinetics equations. By means of this theory, the following properties of the two fission zones of the assembly were obtained from measurements: (a) the shutdown reactivities of the isolated cores, (b) the coupling reactivity, and (c) the power in the fission zones.The efficiencies of the detectors, needed to evaluate the properties mentioned, were obtained from these measurements also. Furthermore, the influence of the delayed neutrons-which were neglected when estimating the properties of the FMRB–on the coherence function is shown. This function was used to detect coupling effects in extended cores.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26687

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

AbstractA benchmark neutron propagation experiment in iron was used to compare experimental and calculated reaction rates to test ENDFIB iron cross sections. Excellent agreement was found between experiment and calculation when ENDF/B-I data and a more recent Oak Ridge National Laboratory evaluation were used.A background effect of the manganese impurity, stronger than earlier expected, is shown to play an important role in the assessment of the 25-keV s-wave scattering resonance minimum.The deficiencies in the high-energy (>30 keV) range of ENDFIB-III data, which are also indicated, seem to be overcome by the most recent evaluations.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26688

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor

摘要:

AbstractA program for the solution of the two-dimensional diffusion equation by the finite element method was developed and applied to realistic reactor calculations. Comparisons were made with well-known diffusion theory codes and with nodal programs. Results of these comparisons and first experiences with the finite element method and its success in our program FEM 2D are reported.

ISSN:0029-5639    

DOI:10.13182/NSE75-A26689

出版商:Taylor&Francis    

年代:1975

数据来源: Taylor