Space asymptotic method for the study of neutron propagation

Space asymptotic theory is shown to be a suitable model for the study of pulsed experiments in neutron multiplying systems. After a short revisitation of the basic aspects of space asymptotic theory applied on the Laplace transformed one-group transport equation, the full solution is derived. It is shown how results are exact in representing localized pulse propagation in the first portion of the transient, until the boundary is reached by the neutron signal, since it propagates with a finite velocity. Approximate models are then derived starting from the exact formulation and the B_N method is used to account for anisotropy effects. Numerical results are presented for one-dimensional systems, discussing the physical phenomena and noting the distortions introduced by approximate models, which may then turn out to be inadequate for the simulation of realistic pulsed experiments situations.     

Numerical aspects in the study of neutron propagation

The study of the propagation of localized source pulses is an important problem in nuclear reactor physics and in the analysis of pulsed experiments. In a previous work the characterization of the transport operator has been performed and the physical distortions introduced by approximate models, such as spherical harmonics, have been evidenced by means of an analytical asymptotic approach. In this paper, the S_N and P_N−1 time-dependent models are numerically discretized in space and solved analytically in time, in order to evidence the error associated with discretization schemes.     

Monte Carlo Simulation of 2D Ising Spin Glass with Power Law Decaying Interactions

We study the distance dependent interaction coupling in 2D in order to show how a spin glass phase transition occurs when couplings between far away spins are permitted by considering the Edwards–Anderson Ising spin glass model. The interaction coupling is a quenched random variable whose probability of being non-zero decays with distance between two spin sites $(p(J_{ij})\propto r_{ij}^{-\rho })$ . We study the model by changing ρ in three different regimes (ρ>2D, $\frac{4}{3} D < \rho < 2D$ , $\rho <\frac{4}{3} D$ ). We obtain a phase transition temperature for ρ=2,3,4.     

Coupled dynamics in the physics of molten salt reactors

The present paper is devoted to the analysis of the coupled thermo-fluid and neutronic dynamics of fast fluid-fuel multiplying nuclear systems. A completely coupled model is needed since in some fast reactors designs, the velocity pattern could be very complicated and strongly affected by the neutron dynamics via the heat source from fission reactions. Furthermore, the neutron dynamics is strongly affected by the thermohydrodynamics via the motion of precursors and by feedback effects. The methods typical of solid fuel reactors of previous generations are not sufficient to handle these more highly coupled concepts. In the preset paper, we consider the coupling between neutronics and thermohydrodynamics with simple but realistic hypotheses assumed to model the evolution of all the variables involved in the calculation. The numerical scheme used represents the current state of the art in the solution of non-linear systems: the Newton–Krylov algorithm. Several calculations are presented to demonstrate the ability of the methods described here to study the behavior of molten salt reactors in both steady state and transient situations.     

Integral parameters in source-driven systems

Integral parameters can give useful information on the physical properties of a multiplying system. However, various theoretical problems are encountered when trying to introduce them in a consistent way for source-driven systems. Many questions also arise for their experimental estimation. After some general considerations, the paper presents comparisons of numerical results obtained in different approaches and by the application of inverse methods to localized neutron flux signal detections. Results presented refer to the Yalina Booster experimental facility, which constitutes an excellent challenging test for the models and methods, being a neutronically, spatially and spectrally decoupled system. Some considerations on the usefulness of such parameters for kinetic analyses and to qualify the system characteristics are also included in the paper, analyzing both highly and loosely coupled configurations.     

From transport to diffusion through a space asymptotic approach

The spatially asymptotic theory is a useful approach to the neutron transport model for nuclear reactor physics applications. For steady-state problems the transport equation is taken in an infinite medium and it is treated by the Fourier transform. A formal solution is thus obtained for any assumption on the order of anisotropy, leading to the _BN$B_N$ formulation. In the case of isotropic emissions the Green function of the problem can be given an explicit expression by the inverse Fourier transformation, leading to the solution that can also be obtained by Case method.