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[en] With recently published results of Kaper et al. as a basis, accurate extrapolated endpoints have been calculated for homogeneous pulsed slabs and spheres. The neutrons were assumed to be monoenergetic and to scatter isotropically. In contrast to P

_{3}calculations, the results indicate a zero slope at small bucklings of the curve describing the extrapolated endpoint as a function of buckling. (U.S.)Primary Subject

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Nuclear Science and Engineering; v. 57(1); p. 84-86

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[en] In an earlier paper the critical size of the spheres and infinite slabs was calculated with a method by Garlvik for monoenergetic neutrons scattering anisotropically. From the results and from the work by Sanchez on the critical size of infinite cylinders, accurate extrapolation lengths have been derived for various dimensions and for an average cosine of the scattering angle up to 0.3. For not too thin slabs there is good agreement with an approximation formula derived by Davison. However, the formula is not applicable to spheres or cylinders in the presence of anisotropic scattering. (author)

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Annals of Nuclear Energy (Oxford); ISSN 0306-4549; ; v. 6(1); p. 7-12

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[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)

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[en] Detailed calculations have been performed to establish the real time-eigen-values of one-speed neutrons. The systems studied are spheres and infinite slabs and cylinders. Vacuum boundary conditions and linearly anisotropic scattering are assumed. The eigenvalue curves in the three cases show great similarities, but the odd mode eigenvalues in slabs require a closer investigation. A comparison is made with eigenvalue curves obtained assuming periodic boundary conditions. The resemblances and differences are discussed. (author)

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[en] The complex time eigenvalues of the transport equation have been studied for one speed neutrons, scattered isotropically in a homogeneous sphere with vacuum boundary conditions. It is shown that the complex decay constants vary continuously with the radius of the sphere. Our earlier conjecture (Dahl and Sahni (1983-84)) regarding disjoint arcs is thus shown to be true. We also indicate that complex decay constants exist even for large assemblies, though with rapid oscillations in the corresponding eigenvectors. These modes cannot be predicted by the diffusion equation as this behaviour of the eigenvectors contradicts the assumption of 'slowly varying flux' needed to derive the diffusion approximation from the transport equation. For an infinite system, the existence of complex modes is related to the solution of a homogeneous equation. (author)

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[en] The time eigenvalue spectrum of the one-speed, isotropic scattering neutron transport equation has been studied for a homogeneous sphere with vacuum boundary conditions. There is a close relationship between the time eigenvalue problem and the critiality problem of the time independent equation for the same model. It is shown that this relation holds even when the time eigenvalues are complex. Using Carlvik's method to solve the criticality problem, it is shown that complex time eigenvalues do actually exist for this model problem. Thus the real eigenvalues found by van Norton do not form the complete spectrum

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 12(4); p. 341-368

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[en] The transport of monoenergetic neutrons in slabs and spheres with vacuum boundary conditions is studied. Isotropic scattering is assumed. The connection between the eigenvalues arising from the time-dependent and the stationary transport equation is established. Based on this, numerical values for the fundamental and higher order time eigenvalues are given. Finally, the more complicated case of anisotropic scattering is discussed

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Nuclear Science and Engineering; ISSN 0029-5639; ; v. 83(3); p. 374-379

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[en] The criticality eigenvalue problem has been studied for the one-speed neutron transport equation. Convex bodies of arbitrary shape and with vacuum boundary conditions have been considered. The cross sections may be space dependent, and the scattering is assumed to be anisotropic. Several new conditions have been derived which ensure that a point spectrum of eigenvalues exists and that all th eigenvalues are real. The most general such condition is that the even order coefficients in the development of the scattering function have a different sign than the odd order ones. As a consequence, for linearly anisotropic scattering the eignevalues are all real if the average cosine of the scattering angle is negative. Numerical results computed for homogeneous bodies in the form of spheres and infinite slabs and cylinders confirm the theoretical considerations. 14 refs., 1 fig., 3 tabs

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Claesson, Oe.; Dahl, E.B.; Pazsit, I.; Middleton, M.F.

Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Reactor Physics

Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Reactor Physics

AbstractAbstract

[en] Pilot measurements were performed to explore the possibilities of neutron radiation transmission measurements in the quantitative determination of the amount of extra water in porous concrete. The experiments were performed by using the 14 MeV neutron generator of the Department as a neutron source and plastic scintillation detectors. To expedite the interpretation and quantification of the results, a regular geometry was chosen for the sample with two rectangular concrete blocks above each other and a layer of water in between in a tray. The water content in the concrete was simulated by using different water heights in the tray between the concrete blocks. The measurements were compared with a simple first-flight analytical model of radiation attenuation as well as with more involved, advanced Monte-Carlo calculations with MCNP. With these latter calculations, a number of effects could be investigated separately, namely the contribution of multiply scattered neutrons (by simulating different energy cut-off in the detector), and the difference between having the water in the tray or distributed evenly in the concrete block. A noticeable difference was found between the measurements and the various calculations. The main trends are well understood in a qualitative way, but the quantitative differences require more experimental work and measurements

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1999; 11 p; 7 refs, 5 figs.

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