
This chapter is intended to explain the system I'm studying (a bit of discussion on MYRRHA project), then we start describing what are the main objectives. 
Physical model employed to achieve the results are described. In particular the objective is to study the source term in fuel and LBE after irradiation in the ADS so it's necessary to couple transport equation with fixed source (conveyed by proton accelerator) and the Batemann equation that's a deterministic one and determines the concentration of all the nuclides present in a reference domain in which the materials undergo irradiation and decay.
The Batemann eq. (burn-up equation) consider both production and depletion deriving from particle interactions (with neutrons and protons) and phenomena of decay.
The tools used for those bu evaluations are Aleph (developed in SCK) and a built-in tool of Serpent. 
The neutronic analysis is performed with MCNP; it is the only code capable to deal with protons. We also take advantage of the strong coupling between the 2 main tools employed in the project since Aleph read directly MCNP spectra used to perform depletion and then is able to update the core structure with the new inventory of nuclides in each material that is used to compute new neutron fluxes. This iterative process goes on for the whole irradiation period. Then the decay of the tested materials happens without necessity of calling MCNP. 
For our case study the spectrum is kept constant for the whole irradiation period. Spectrum at BOC is used that is a good approximation if we consider BOC as the beginning of quasi equilibrium stage for the reactor.

The source term is evaluated for LBE and Fuel.
LBE is the coolant -reference concentration of each nuclide and reference paper from which is taken.
Idea to perform an analysis in different areas.

Fuel source term: burn up of fuel; considering quasi equilibrium condition in which keff remains constant.
We have a fixed power, loading and shuffling scheme and number of fuel assembly. It's all we need to evaluate Burn Up in each assembly (depending on the position in the core) and the flux. "In the external part more depleted, lower power production".
The idea is to start modeling the single assembly and the whole core taking advantage
of the hexagonal symmetry.

Uncertainty and sensitivity analysis is performed for all the results achieved.
For LBE source term the uncertainty is related to libraries used, different codes (verified no discrepancy between them) and the variance on the cross sections.
For the fuel uncertainty analysis we start looking at the uncertainty on nuclear data that are result in uncertainty in the inventory of radionuclide in the fuel assembly.
Those variances can be used as input for the uncertainty analysis in the study of the whole core. We end up with a confidence interval for the value of keff.

Uncertainty propagation is performed by means of statistical sampling and perturbation theory.

