Neutron transport

B. Davison, Neutron Transport Theoty, Clarendon Egress, Oxford, UK, 1957, Chap. VI, Section 1. 

This is a technique developed during World War II for simulating stochastic physical processes, specifically, neutron transport in atomic bomb design. Its name comes from its resemblance to gambling. Each of the random variables in a relationship is represented by a distribution (Section 2.5). A random number generator picks a number from the distribution with a probability proportional to the pdf. After physical weighting the random numbers for each of the stochastic variables, the relationship is calculated to find the value of the independent variable (top event if a fault tree) for this particular combination of dependent variables (e.g.. components). 

J. Spanier, E.M. Gelbard Monte Carlo Principles and Neutron Transport Problems (Addison Wesley Publication Company 1969)... 

The discrete ordinates (DO) approximation is also a multiflux model. The discrete ordinates approximation was originally suggested by Chandrasekhar [19] for astrophysical applications, and a detailed derivation of the related equations was discussed by several researchers for application to neutron transport problems [33, 57-61], During the last two decades the method has been applied to various heat transfer problems [62-81]. 

E. E. Lewis and W. E. Miller, Jr., Computational Methods of Neutron Transport, Wiley, New York, 1984. 

Different perturbation theory expressions for reactivity are obtained from different formulations of the neutron transport equation. 

B. Davison, Neutron Transport Theory, Oxford Univ. Press, London and New York, 1957. 

P. C. E. Hemment, E. D. Pendlebury, M. J. Adams, B. A. Brett and D. Sams, "The Multigroup Neutron Transport Perturbation Program DUNDEE," UKAEA AWRE-O-40/66 (1966). 

Singular Eigenfunction Expansions in Neutron Transport Theory... 

Wigner by this time (1941) had worked out many of the most familiar results from neutron transport theory (Papers 3 and 4) for example, he showed that the distribution of monoenergetic neutrons around a point source diminished asymptotically as (l/r)e, where k was the solution of the transcendental equation... 

B. Davison, Neutron transport theory, Oxford, Clarendon Press, 1957, p. 98. 

EUR (1996b) Dosimetry and neutron transport methods for reactor pressure vessels, AMES Report N. 8, EUR 16470 EN, European Commission DG XI/ C/2. 

Safety-analysis capabilities are contained within the Nuclear Facility Operations and Nuclear Technology Programs organizations. These organizations produce Safety Analysis Reports for both reactor and nonreactor nuclear facilities, primarily in TA-V. Other organizations provide specialized safety-analysis support in the form of mechanistic accident-progression analysis, heat transfer, structural analysis, neutron transport, nuclear criticality safety, and other areas upon request. 

The effort to develop a neutron transport code based on an improved nodal method has been continued in order to treat the Hex-Z geometry of FBR cores more accurately. In order to reduce truncation error of the code, a new method to treat the radial leakage has been developed, in which the distribution of node boundary fluxes is obtained from local two-dimensional flux distribution. The local flux distribution is evaluated from average fluxes at surrounding nodes and node boundaries by second-order polynomials. An FBR core model with extremely large-sized assemblies was calculated by the new method and the results were compared with those of a reference Monte Carlo calculation. While the previous method overestimated the criticality by 0.3% dk for a control rod-insertion case, the new method agreed well with the Monte Carlo result. 

KEVROLEV, V.V., RECOL Continuous-Energy Monte-Carlo Code for Neutron Transport, Preprint RRC KI, IAE-5621/5 (1987). 

Dosimetry data are analyzed using the neutron transport code TRIPOLI in order to determine neutron fluences for energies over 1 MeV, parameter which indexes the aging results. The primary coolant temperatures are 286 °C for most 900 MWe units, 288 °C for 1300 MWe units and 293 °C for 1450 MWe units. The primary coolant temperature of Chooz-A increased from 257 to 265 °C due to a power uprate. 

J R Mossop, D A Thornton, and T A Lewis, Vahdation of neutron transport calculations on Magnox power plant. Reactor Dosimetry, ASTM STP1228, H Farrar, E P Lippincott, J G Williams and D W Vehar, eds, American Society for Testing and Materials, Philadelphia, PA, 1994,384-391. 

Introduction. In this paper we discuss time-dependent neutron transport in a medium. Our interest centers on problems in which the neutrons interact with the medium without affecting it, and in which the neutrons do not interact with each other. Equations describing such processes are not too difficult to write down [1]. In the classical formulation they are linear, although certain new approaches to the theory have produced non-linear versions [2 3 4]. In any event, the structure of these equations usually makes it impossible to find explicit solutions, and extremely difficult to determine rigorously what properties the solutions possess. From the mathematician s viewpoint, even the existence of the solution is often not obvious. 

B. Davison, Neutron transport theoryy Oxford University Press, London, Amen House, 1957. 

Invariant imbedding and neutron transport theory. II. Functional egua-... 

G. M. Wing, Solution of a time dependenty one dimensional neutron transport problemy J. Math. Mech. vol. 7 (1958) pp. 757-766. 

G. H. Pimbley, Solution of an initial value problem for the multi-velocity neutron transport equation with a slab geometry, J. Math. Mech. vol. 8 (1959) pp. 837-866. 

K. Jorgens, An asymptotic expansion in the theory of neutron transport. Comm. Pure Appl. Math. vol. 11 (1958) pp. 219-242. 

A discussion of applications of these concepts to neutron transport theory can be found in the papers [4 5 6 7 8 9]. For the interested reader we also call attention to the applications to radiative transfer theory [1 10 11], to wave propagation, [12 13 14], to random walk and multiple scattering [15 16], and to problems with moving boundaries [9]. 

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