[en] Highlights: • Steady state noise techniques are widely known and applied to the monitoring of neutron reacting system. • This paper deals with the stochastic analysis of neutron chain systems which are changing in time due to an external parametric excitation. • Two cases are analyzed: 1) without reactivity feedback, and 2) a supercritical excursion with thermalhydraulic feedback. • Our goal is the analysis of usual noise techniques and how to calculate the variance of the power and energy released. - Abstract: Steady state noise techniques are widely known and applied to the monitoring of neutron reacting system. This paper deals with the stochastic analysis of neutron chain systems (nuclear reactors or fissile system) which are changing in time from subcritical states reaching other subcritical, critical or hypercritical states due to an external parametric excitation. Two cases are analyzed: 1) without reactivity feedback, that is from a subcritical state to one with almost zero power, and 2) a supercritical excursion with thermalhydraulic feedback. Our goal is to check in case 1 if the usual noise techniques can be used to monitoring the reactivity changes and in case 2 how to calculate the variance of the power and energy released.

[en] Highlights: • Monte Carlo analysis of the reactivity effects of the random dispersal of fuel kernels. • High Temperature Gas Cooled Reactors. Pebble bed design. • Calculations of the reactivity distributions with a simplified model. • Deterministic calculation of the average of the distribution. • Lattice cell positioning of the fuel kernels. - Abstract: Nuclear reactors are in general deterministic with respect to the distribution of materials, consequently the reactivity of their configurations are fixed (disregarding the fluctuations of the number of neutrons per fission). This is not the case of High Temperature Gas Cooled Reactors (HTGCR), where the fuel is constructed with a random distribution of fuel kernels with positions at random; additionally the pebble version of the HTGCR is build with the pebbles positions at random therefore having two degrees of randomness. In this study we analyze the fuel cell with one pebble at its center, an ensemble of fuel cells is constructed by the simulation for each pebble of the random dispersal of the several thousands fuel kernels per pebble. The objective is to calculate the width of the random dispersal of k_e_f_f; a simple model that simulates the effects of the random dispersal on the space averaged thermal cross sections was developed for this purpose. A limited set of calculations with the continuous energy Monte Carlo code MCNP gives a reactivity width compatible with the results of the simple model. Deterministic versions of the random dispersal are proposed to calculate the ensemble average k_e_f_f based on the positioning of the kernels according to cubic and hexagonal lattices.

[en] Highlights: • Radiation field inside an empty shell source. • Direct and inverse problem for this idealization. Analytical solution of the integral equation. • Zero collision flux when the shell source is filled with a material media. • Applications to medical physics and nondestructive assay. • Numerical algorithm and analytical results verified with Monte Carlo calculations of fluxes and doses. - Abstract: We present an integral equation that describes the uncollided particle flux for the case of an inward spherical shell source of radius R. This is a reasonable description, for example, of a point source that moves on a spherical surface located at distance R from the target of a radiation treatment. The additional assumption of conditions for radial symmetry allows the derivation of an integral equation that relates the scalar flux to the description of the beam source as function of the angle between the direction of the source particles and the normal to the sphere. Analytical and numerical solutions for this integral equation are successfully compared with, respectively, known analytical results and with Monte Carlo simulations. The integral equation can then be used for solutions of the inverse problem: given the flux obtain the source, i.e. the shape of the beam. A numerical algorithm was developed for this purpose as well as an analytical solutions based on the solution of the integral equation by the use of the Laplace transform. The optimal shape for the beam is then obtained based on the constraint that the source has to be positive and finite everywhere, allowing the design of appropriate collimators for the beams. Monte Carlo calculations as a function of the number of collisions show that the uncollided flux for the beam so determined behaves as expected and that penumbra effects due to multiple collisions are sufficiently small (∼20%) to consider the beam as a good first guess for an iterative procedure for the design, for example, of 3-D conformal radiotherapy treatment

[en] Highlights: • Coupled neutron kinetics with elastic equations. • Coupled neutron kinetics with thermal hydraulics transients. • Solve the system of coupled nonlinear first order differential equations. • Compute energy yield. • Compute thermodynamics conditions. - Abstract: A fatal critical accident in a compact, water moderated and highly enriched (90%) MTR facility is analyzed. A very detailed Monte Carlo model was used to define the initial conditions and the reactivity coefficients. The MCNP code was used to model all the heterogeneities of the facility. Once the reactivity parameters were calculated the kinetics equations were solved coupling them with the thermodynamics conditions of the core and the steady water. The power pulse was then calculated and compared with radiological data

[en] Procedures to produce light graphite foam (∼0.5 g/cm³) that exhibits heat conductivities similar to full density graphite have been developed at ORNL. The consequent substantial reduction in the thermal inertia might have a significant impact in standard designs of graphite system and it could make possible new concepts. We discuss two possible applications: (a) a modular, zero burnup reactivity swing, reactor and (b) the pebble bed accelerator-driven transmutator

[en] Under the auspices of the International Atomic Energy Agency, a series of well-documented benchmark experiments were performed at the Proteus facility of the Swiss Paul Scherrer Institute. Thirteen critical pebble bed reactor configurations were assembled, with ten of them deterministic with a precise location of the low-enriched fuel and moderator pebbles. Seven of these configurations were modeled with a very high spatial resolution with the Monte Carlo code MCNP with details that go from the fuel kernel (0.5 mm in diameter) to the walls surrounding the facility. The calculations of the k's of the configurations agree quite well with the experiments (within a fraction of a dollar). A sensitivity analysis is included to discuss the possibility of a small bias; also biases introduced by customary approximations of production codes were calculated. The experiments and the analysis of this paper might be very useful tools to check the calculational accuracy of procedures used in the emerging work related to pebble bed modular gas-cooled reactors

[en] The analysis of the fluctuations of signals coming from detectors in the vicinity of a subcritical assembly of fissile materials is commonly used for the control and safeguard of nuclear materials and might be used for the surveillance of an accelerator driven system. One of the stochastic techniques is the measurement of the probability distributions of counts in time intervals δt (gates); the departure of the ratio of the variance and the mean value with respect to 1 (the correlation) is directly related to the amount of fissile material and its subcriticality. The measurement of this correlation is affected by dead-time effects due to count losses because of the finite-time resolution of the detection system. We present a theory that allows (a) the calculation of the probability of losing n counts (P⁽ⁿ⁾) in gate δt, (b) the definition of experimental conditions under which P⁽²⁾ << P⁽¹⁾, and (c) a methodology to correct the measured correlation because of losing one count in any gate. The theory is applied to the analysis of experiments performed in a highly enriched subcritical assembly

[en] Important decisions related to the kind of reactors to be used for the disposition of the surplus weapons-grade plutonium are going to be based on calculations. Benchmarking computational methods in all aspects of the fuel cycle with measured data is then an obvious necessity. Analysis of public domain data reveals that the cycle-2 irradiation in the Quad Cities-1 boiling water reactor is the most recent U.S. destructive examination, involving the irradiation of five mixed-oxide (MOX) assemblies using 80 and 90% fissile Pu, quite close to weapons-grade Pu isotopic. Such measurements are rare, and they might be the only source of information to quantify differences in key neutronics parameters between high-fissile Pu systems and the well-characterized use of reactor-grade Pu. The pin neutronic performances for the UO₂ and MOX fuels are compared with assembly-level calculation in which ∼20% of the pins are MOX pins surrounded by UO₂ pins. For MOX rods, HELIOS models the chains for the isotopes of uranium and plutonium reasonably well when compared with measured data at ∼12,000 MWd/tonne. However, indications are that the amounts of heavier actinides are underpredicted. Measurements and calculations of the relative pin power distribution for the last few weeks of the irradiation and the burnup are fairly consistent. The critical effects of the contribution of the 0.296-eV resonance to the production of higher actinides and the destruction of ²³⁹Pu are discussed

[en] Highlights: ► Monte Carlo analysis of the propagation of fusion neutrons in a highly compact 90% U enriched system. ► MCNP model introduces all the heterogeneities of the system up to the local perturbation of the detector. ► The full analysis defines ideal experimental conditions in order to have an asymptotic complex wave vector. ► Even under non-ideal conditions Fourier transform of the detection rate is an observable to compare with MCNP calculations. ► The good results of this comparison emphasize the limitation of previous approximations to describe the experiment. - Abstract: Monte Carlo methods were used to calculate experimental observables related to the propagation of pulses of fusion neutrons in a compact and highly enriched (90%) subcritical system. These observables are the amplitude and phase of the Fourier transform of the detection rate of a ³He moving detector, they correspond to the propagation of neutron waves excited by a sinusoidal neutron source. The MCNP code was used to model in great details all the heterogeneities of the experimental set up allowing in particular to have a good model of the neutron leakage in the direction perpendicular to the propagation. The very good results of the comparison with the experimental results contrast with previous comparisons with diffusion and transport theory models. The Monte Carlo modeling allows a full analysis of neutron wave experiment in space, time and energy allowing to define asymptotic regions where global complex wave vector exists. We propose to use the extensive literature of neutron wave experiments for further benchmark of MCNP

[en] Within the context of the Fissile Materials Disposition Program of the U.S. Department of Energy we analyzed rod removal transient experiments performed at the Kurchatov Institute in a full-scale mockup of VVER reactors. The transients were started (via water inlet) in slightly (few cents) supercritical configurations with all the control rods withdrawn. After a few minutes, control rods banks or individual control rods were first inserted and later withdrawn (returning to the initial state). Available experimental data include the relative time profiles of nine in-core and ex-core detectors. Because of the mild nature of the transients (very low power and no more than 2 $ reactivities) we decided to use a quasi-static approach. The time-dependent flux is factorized into two terms: a function of phase space, given by the solution of the static equation with parametric excitation; and a function of time, given by the solution of the point kinetic equations with time-dependent kinetics parameters. Due to the nature of the experiment, cold conditions, control rods withdrawn and critical state with water level, the power distributions, measured and calculated, are quite unusual, with the inner part of the core heavily shielded. Measured power levels at the center of the reactor are almost 20 times smaller than similar regions at the periphery. Transport and diffusion calculations of the power distributions are in reasonable agreement, so the diffusion code BOLDVENTURE was used to calculate the kinetics parameters and the relative changes of the detector field of view. The numerical integration of the time-dependent part of the solution was made with the LSODE package using ENDF/B-V and VI delayed neutron data. Very good results were obtained for the nine time profiles. (author)