Reactor Physics Flashcards
Terms in the Integro-differential Radiation Transport Equation
Balance term – the rate of change of particle density with time.
Leakage/streaming term – describes particles moving out of the volume of interest
Interaction term – particles lost via interactions; a function of the total macroscopic cross-section and particle flux.
Scattering term – accounts for particles that are scattered down to the energy E and
into direction Ω of the phase space of interest.
External source term – particles that are entering the space by other means such as fission or delayed neutron emission
What methods can be used to solve the Boltzmann transport equation?
Deterministic or Stochastic methods
Outline deterministic methods for solving the BTE
Simplifies the equation by making parameters such as energy, angle and flux discrete. Groups between values have constant properties, such as cross section
Outline Stochastic methods for solving the BTE
Use probability distribution functions and random number generators to simulate a system. More particles are used to reduce statistical uncertainty. Methods include Monte Carlo simulations
Basic assumptions of neutron diffusion theory (4 assumptions)
Single (thermal) neutron energy
No change in neutron energy
Infinite medium
Interactions are purely scattering
Value of the mean scattering cosine
MSC = 2/3A
Transport mean path
TMP = Scattering mean free path / (1 - MSC)
Transport cross section is inverse of TMP
Additional assumptions for Fick’s law
Constant cross-sections Isotropic scattering Neutron flux varies slowly with position Neutron density is steady state (or varies very slowly) No fission source
Fick’s law
J = -D ∇ ϕ
J = Current density vector D = Diffusion coefficient (scattering cross-section/3) ϕ = Flux
What is the value of the diffusion coefficient, D, in terms of the scattering and transport cross sections?
D = 1/3 Es
What are the advantages and disadvantages of deterministic methods of solving the BTE?
Advantages:
Quick to run
Give solutions to the whole system
Disadvantages:
Assumptions are made about the system during discretisation
What are the advantages and disadvantages of stochastic methods of solving the BTE?
Advantages:
Allows the modelling of complex geometries and continuous energies in full
Disadvantages:
Takes a long time to run
Only models the input-specified regions of the system
In what regions would the assumptions of Fick’s law be unsuitable?
Close to boundaries Close to sinks/sources Within highly absorbing materials Close to a material interface In regions of highly varying flux
