Applied Reactor Physics

Contents 1 Introduction 2 Cross sections and nuclear data 2.1 Solid angles and spherical harmonics 2.2 Dealing with distributions 2.3 Dynamics of a scattering reaction 2.3.1 Collision of a neutron with a nucleus initially at rest 2.4 Definition of a cross section 2.5 Formation of a compound nucleus 2.5.1 The single level Breit-Wigner formulas 2.5.2 Low-energy variation of cross sections 2.6 Thermal agitation of nuclides and binding effects 2.6.1 Numerical convolution of cross sections 2.6.2 Convolution of Breit-Wigner cross sections 2.6.3 Convolution of a constant cross section 2.6.4 Convolution of the differential scattering cross section 2.6.5 Effects of molecular or metallic binding 2.7 Expansion of the differential cross sections 2.8 Calculation of the probability tables 2.9 Production of an isotopic cross-section library 2.9.1 Photo-atomic interaction data 2.9.2 Delayed neutron data 2.9.3 An overview of DRAGR Exercises 3 The transport equation 3.1 The particle flux 3.2 Derivation of the transport equation 3.2.1 The characteristic form of the transport equation 3.2.2 The integral form of the transport equation 3.2.3 Boundary and continuity conditions 3.3 Source density in reactor physics 3.3.1 The steady-state source density 3.3.2 The transient source density 3.4 The transport correction 3.5 Multigroup discretization 3.5.1 Multigroup steady-state transport equation 3.5.2 Multigroup transient transport equation 3.6 The first-order streaming operator 3.6.1 Cartesian coordinate system 3.6.2 Cylindrical coordinate system 3.6.3 Spherical coordinate system 3.7 The spherical harmonicsmethod 3.7.1 The Pn method in 1D slab geometry 3.7.2 The Pn method in 1D cylindrical geometry 3.7.3 The Pn method in 1D spherical geometry 3.7.4 The simplified Pn method in 2D Cartesian geometry 3.8 The collision probability method 3.8.1 The interface current method 3.8.2 Scattering-reduced matrices and power iteration 3.8.3 Slab geometry 3.8.4 Cylindrical 1D geometry 3.8.5 Spherical 1D geometry 3.8.6 Unstructured 2D finite geometry 3.9 The discrete ordinatesmethod 3.9.1 Quadrature sets in the method of discrete ordinates 3.9.2 The difference relations in 1D slab geometry 3.9.3 The difference relations in 1D cylindrical geometry 3.9.4 The difference relations in 1D spherical geometry 3.9.5 The difference relations in 2D Cartesian geometry 3.9.6 Synthetic acceleration 3.10 The method of characteristics 3.10.1 TheMOC integration strategy 3.10.2 Unstructured 2D finite geometry 3.10.3 The algebraic collapsing acceleration 3.11 The multigroupMonte Carlomethod 3.11.1 Mathematical background 3.11.2 Rejection techniques 3.11.3 The randomwalk of a neutron 3.11.4 Criticality calculations 3.11.5 Monte Carlo reaction estimators Exercises 4 Elements of lattice calculation 4.1 A historical overview 4.2 Neutron slowing-down and resonance self-shielding 4.2.1 Elastic slowing down 4.2.2 A review of resonance self-shielding approaches 4.2.3 The Livolant-Jeanpierre approximations 4.2.4 The physical probability tables 4.2.5 The statistical subgroup equations 4.2.6 The multigroup equivalence procedure 4.3 The neutron leakage model 4.3.1 The Bn leakage calculation 4.3.2 The homogeneous fundamental mode 4.3.3 The heterogeneous fundamental mode 4.3.4 Introduction of leakage rates in a lattice calculation 4.3.5 Introduction of leakage rates with collision probabilities 4.3.6 Full-core calculations in diffusion theory 4.3.7 Full-core calculations in transport theory 4.4 The SPH equivalence technique 4.4.1 Definition of themacro balance relations 4.4.2 Definition of the SPH factors 4.4.3 Iterative calculation of the SPH factors 4.5 Isotopic depletion 4.5.1 The power normalization 4.5.2 The saturation model 4.5.3 The integration factor method 4.5.4 Depletion of heavy isotopes 4.6 Creation of the reactor database 4.6.1 Selected information 4.6.2 Database information structure 4.7 A presentation of DRAGON 4.7.1 A DRAGON tutorial Exercises 5 Full-core calculations 5.1 The steady-state diffusion equation 5.1.1 The Fick law 5.1.2 Continuity and boundary conditions 5.1.3 The finite homogeneous reactor 5.1.4 The heterogeneous 1D slab reactor 5.2 Discretization of the neutron diffusion equation 5.2.1 Mesh-corner finite differences 5.2.2 Mesh-centered finite differences 5.2.3 A primal variational formulation 5.2.4 The Lagrangian finite-element method 5.2.5 The analytic nodal method in 2D Cartesian geometry 5.3 Generalized perturbation theory 5.3.1 Mathematical background 5.3.2 State variables and reactor characteristics 5.3.3 Computing the Jacobian using the implicit approach 5.3.4 Computing the Jacobian using the explicit approach 5.4 Space-time kinetics 5.4.1 Point-kinetics equations 5.4.2 The implicit temporal scheme 5.4.3 The space-time implicit scheme Exercises Answers to Problems A Tracking of 1D and 2D geometries B Special functions with Matlab C Numerical methods Bibliography Index