[en] Critical calculations can constitute a good test for the comparisons of the performances of numerical methods to solve the neutron transport equation for multiplying systems. For some paradigmatic calculations, physically significant (collision and multiplication) eigenvalues can be compared with exact ones, when available. From such operations, a good insight into the capabilities of the numerical methods can be actually obtained. This work is devoted to present a selected set of comparisons of critical calculations in the one- and multi-energy-group cases. Results are obtained from iterative procedures applied to the integral form of the transport equation. The convergence rate enhancement that can be achieved by using spatially asymptotic guesses, in order to start the procedure, is also put into evidence in the multigroup cases. Higher order integration technique, referring to a Simpson-like integration rule, will be exploited and their performances highlighted

[en] The existence of certain reciprocity-like relations in neutron transport theory was shown earlier under some quite restrictive conditions. Here, these relations are shown to be valid in more general situations by using a different approach based on individual neutron trajectories. (author)

[en] Neutron spectra have been measured by the threshold foil activation technique for the White Sands Missile Range Fast Burst Reactor. The neutron spectra for free-field, free-field with the experimenters table in place, for the in-core irradiation port (Glory Hole) and with a one-half inch section of aluminum in place are reported. Neutron transport calculations are also performed for the above mentioned spectra and for six other geometrics reported elsewhere. The absolute values of the spectral parameters derived from calculations do not agree with the spectral parameters obtained by the foil activation method, but the same trends are observed. Transport calculation results are combined with the foil activation results to give ''best value'' spectral parameters. It was found that the free-field spectrum was moderately hard and the Glory Hole spectra to be softer by approximately 18 percent when compared to the free-field spectrum. The experimenters table and two sections of aluminum of differing thicknesses were found to have no major effect on the neutron spectrum when comparing spectral parameters. The neutron spectrum behind a section on plexiglas was found to be considerably harder than the free-field spectrum. The differences between the results of the neutron transport calculations and the foil activation method are discussed

No abstract available

[en] Conventional finite-element solutions of the even-parity transport equation for systems with voids treat the void as a region of low absorption. This treatment tends to give physically-unacceptable solutions to void problems as the void cross-section tends to zero. An explanation for the effect is proposed. Biased finite elements are used in two ways to obtain physically-acceptable solutions for the void regions. Two new methods are described and tested. The iterative method synthesizes finite-element solution using a sequence of problems with constant absorptions in the void regions. The sequence is terminated when the fluxes in the void regions become steady. The extrapolation method obtains a best approximation to the void solution by combining two or more independent biased trial functions in an optimum way. The extrapolation method is further subdivided into elementary and nodal or multiparameter extrapolation. The relevant theory of both the iteration and extrapolation methods is given. Several 2-D test problems using the above methods have been investigated. Results are compared with those obtained with other numerical methods and almost analytical results of the point kernel method for voids surrounded by purely absorbing media. (author)

[en] A simple projectional technique combined with an equally simple parametric representation of the transient part of the neutron total flux is proposed for an elementary straightforward calculation of the extrapolation distance in diffusing media. (author)

[en] An adaption is presented to an earlier method for the prediction of time-eigenvalues of the neutron transport equation. Instead of using the full-parity first-order equation, the algorithm uses the even-parity formalism in the most expensive part of the computations resulting in a more economic method

[en] In this work it is presented a generic method of analytical solution to the one-dimensional S_N, P_N, W_N, Ch_N, A_N and L D_N approximations of the linear transport equation. The main idea of this method consists in the application of the Laplace transform to solve the differential equation system related to the considered approximations and solution of the resultant algebraic system by Trzaska's algorithm. (author). 46 refs., 3 figs., 15 tabs

[en] In one-speed, time-independent, neutron transport theory, the Fsub(N) method is used for the FBIS (forward-backward-isotropic scattering) model to reinvestigate the behaviour of the critical size in plane and spherical geometries. For the FIS (forward-isotropic scattering) model the numerical results are compared with previously obtained variational results and it is shown that they are in agreement. For the BIS (backward-isotropic scattering) model exact results are obtained and compared with the first-order approximate results obtained using the method of elementary solutions. (author)

[en] The time dependence of a neutron population in a homogeneous sphere has been studied. The neutrons are of one speed and are assumed to be scattered with linear anisotropy. Vacuum boundary conditions are used. It is shown that the integral Boltzmann equation is simplified, when the decay constant is at the 'Corngold limit'. Using Carlvik's method it is possible to calculate the spectrum of sphere diameters corresponding to this decay constant. Detailed numerical results are given. (author)