FISSION REACTOR PHYSICS II
Recalls of Statistics. Probability theory, random data analysis.
The Boltzmann equation. The neutron transport equation. Fundamental physical assumptions for the derivation of the equation of neutron transport. Neutron angular density and angular flux. Neutron current. Transfer probabilities for scattering and fission. Derivation of the Boltzmann equation of neutron transport in Lagrangian and Eulerian form on the basis of neutron conservation. Integrodifferential formulation. General characteristics of the transport operator. Integration in the entire reactor. Linearity and Green’s functions. Integral formulation and its derivation by means of the characteristics method and on the basis of neutron conservation.
Solution methods. Integral formulation. Von Neumann method. Integrodifferential formulation. Analysis of nonstationary case by means of the alpha eigenvalue method. Effective multiplication factor eigenvalue method. Expansion of flux in Legendre polynomials for plane geometry. Pn approximation. P1 approximation. Derivation of the diffusion equation. Discrete ordinate method. Sn approximation. The Multigroup method. Numerical solutions and organization of modern computer codes (outline).
The adjoint transport equation. The adjoint to the transport operator. The adjoint function and neutron importance. Derivation of the adjoint transport equation for the neutron importance. Physical interpretations of the adjoint flux to certain kinds of adjoint source. Spectrum of the adjoint operator and criticality. Application of the perturbation theory. Perturbation of the effective multiplication factor. Application to a PWR core barrel oscillations. Derivation of the Point Kinetics equation.
Monte Carlo method. Application of the Monte Carlo method to the stochastic simulation of transport of neutrons and photons. Collision, transfer, and transport kernels. Von Neumann expansion. Iterated fission sources method.
Neutronic simulation of a TRIGA Reactor (*) (monographic topic in collaboration with the course 'Experimental Nuclear Reactor Kinetics') Monte Carlo approach to transport theory with application to the TRIGA reactor by Serpent code: 1) Determination of multiplication coefficient, kinetic parameters and neutron flux distribution, 2) Determination of group constants for defining a diffusive model for several energy groups.
Statistics of Neutron Fluctuations (*) (monographic topic). Probability generating functions. The convolution theorem. Fluctuations of the number of particles in a Markovian system of different types of particles: the branching model of Kolmogorov and Dmitriev. The ChapmanKolmogorov identity. The Kolmogorov equations. Application to the propagation of neutrons in multiplying system with a neutron source variable in time. The FokkerPlanck equation.
Neutron Noise (*) (monographic topic). Introduction to the analysis of random data and neutron noise. Stationary processes. Ergodic processes. Analysis in the time domain and frequency. Application to the determination of the directions and frequencies of oscillation of the corebarrel of PWR reactor. Estimate of the rate of rise of bubbles in a liquid twophase within a vertical channel.
(*) the monographic topics can be activated at the discretion of the professor in charge of the course
TRANSPORT OF RADIOACTIVE CONTAMINANTS
Recalls of Statistics (*). Probability theory, random data analysis.
Monte Carlo method (*). Outline of the application of the Monte Carlo method to the stochastic simulation of transport of neutrons and photons. Collision, transfer, and transport kernels. Von Neumann expansion.
Repositories of radioactive waste. Characteristics and types of radioactive waste. Concepts of deposit and barriers. Main processes of leakage of radionuclides from deposits. Transport in the nearfield and in the far field. Determination of the source term.
Transport of toxic and radioactive pollutants in aqueous solution in porous and fractured media. Basics concepts of hydrogeology. Porosity and water content. Hydraulic conductivity . Storage coefficient. Darcy law. Darcy velocity. Pore velocity. Models of water flow in saturated and unsaturated porous media. Flow field in a saturated porous medium: confined and unconfined aquifers. Main transport phenomena in hydrogeology. Derivation of the Advection Dispersion equation. Main physical and chemical parameters and their determination. Hydrodynamic dispersion. Reactive transport. Exchange processes between the phases. Isothermal linear equilibrium. Freundlich and Langmuir nonlinear Isotherms. Processes of decay, dissolution, degradation, adsorption, competition, colloidal transport. Dual porosity media. Two Region Model.
Stochastic approach. Probability generating functions. The convolution theorem. Fluctuations of the number of particles in a Markovian system of different types of particles: the branching model of Kolmogorov and Dmitriev. The ChapmanKolmogorov identity. The Kolmogorov equations. Probabilistic Kolmogorov equations and their application to the propagation of radionuclides in a porous media. Derivation of main rates by comparison with the advection dispersion deterministic model. Application of the Monte Carlo method to the stochastic simulation of the transport of contaminants in saturated and unsaturated media in presence of linear and nonlinear processes. .
Informatics laboratory. 1D model with Matlab. 3D Model with Groundwatervistas: MODFLOW, MODPATH, MT3D; compartment code AMBER and 3D code FEFLOW (outline).
Laboratory. Experimental techniques for the study and measurement of the dispersion of contaminants in porous media. Batch tests to study the phenomena of exchange between the phases and the determination of the equilibrium isotherms. Column tests of 1D transport. Determination of the effective porosity and coefficient of dispersivity Spectrophotometry. Liquid chromatography. Mass spectrometry.
The inverse problem (outline). Definition of the problem. Direct and indirect methods. Examples of methods for the solution of inverse problems for the determination of characteristic parameters of the models of flow and transport.
Transport of pollutants in the atmosphere (**) (monographic topic). Vertical movements and conditions of stability and instability of the atmosphere. Equation of diffusion of contaminants into the atmosphere. Decay and chemical reactions. The theory and assumptions underlying the simulation models of Gaussian type. Chemical and physical parameters. Source term.
(*) recalls for the students that attend only the 5CFU course Transport of Radioactive Contaminants
(**) the monographic topics can be activated at the discretion of the professor in charge of the course
At the end of the 10FU course a visit to the Joint Research Centre of Ispra is foreseen for all the students that attend any of the 5CFU versions of the course. The visit is comprehensive of the following seminars:
Seminar on Nuclear Safeguards and Security (outline). Illustration of issues related to nuclear safeguards.
Seminar on Decommissioning and Waste management (outline). Illustration of a decommissioning project.
