# Introduction

The MORET code is a simulation tool that solves the transport equation for neutrons using the Monte Carlo method. From its inception, the code has been constructed with the aim of providing a great flexibility to implement new components or methods without any difficulties. The result is a code that allows users to model complex three-dimensional geometrical configurations, use various evaluations and treatments for nuclear data to describe the materials, select the best adapted simulation method (from all methods available) related to their problem, define their own tallies and analyze the results.

# Geometry modelling

The description of the geometry should be as representative as possible of the industrial case. It relies on combinatorial geometry for which user have to create the set of volumes that will contain the configuration materials. Each volume is characterised by several properties: the mother volume, its shape, its position and the material it contains. Geometrical operators may be added to describe the combinatorial properties of the volumes, such as how they intersect one another, or how they may be positioned one another.

In addition to the capability of combining volumes, the code gives the user the possibility of defining the geometry as a composition of several regions. This modular geometry allows to model complex geometries by using basic building blocks, called "modules". These parts of the whole geometry can be embedded one in another using "holes".

Modelling of the Jules Horowitz Reactor

The modules make possible to describe only once the volumes of any structure that appears more than once in a geometry. Another way to define repeated structures is to use lattices. Two types are available using rectangular or triangular pitch and can be included in volumes of any shape. The definition of secondary mesh volumes allow users to describe alternative contents in the mesh volumes.

A geometry-plotting function helps the users to check their geometry modeling (in complement of several internal code checking to find input errors).

# Description of materials: two calculation routes

The MORET code allows two calculation routes for the treatment of the cross sections energy dependence.

Two calculation routes to treat the cross sections

## + Multi-group approach

The MORET multi-group calculations are possible with direct use of various macroscopic homogenized cross section sets. They result from preliminary calculations performed with several cell codes such as APOLLO2, DRAGON4 and the SCALE 5.1 package. Each of these codes or system relies on independently processed data libraries. Parsers forthese libraries are implemented into MORET in order to be able to get the information needed to make calculations.

## + Continuous energy calculations

Multi-group approach may sometimes give incorrect results, in particular for configurations with very steep neutron flux heterogeneities, and when the self-shielding models inherent to the multi-group treatment are not well adapted. The continuous energy approach is therefore essential in those cases. Continuous energy calculations are based on home-made nuclear data libraries with ACE format (these libraries are performed using the processing tool NJOY).

# Simulation and neutron tracking

The Monte Carlo simulation consists of simulating a certain number of individual neutrons by reproducing as accurately as possible their elementary behaviour as described by particle physics.

The calculation is an iterative process, following the neutrons from their birth until death (whatever the cause). For each cycle, the distribution of the neutron is defined on the basis of fissions generated in the previous cycle. Nevertheless the user must provide the distribution for the first cycle to initialize the iterative process. Two ways are available:

- in a volumic manner: neutrons are uniformly distributed in a volume,
- in a point wise manner: coordinates of starting neutrons are given.

## + Neutron tracking

When tracking a particle, the MORET code calculates the distance to the limit of the current volume, the distance to next collision, check if the neutron encounters a volume contained in the current one and takes the minimum as the distance traveled by the neutron. If the distance to the next collision is the lowest, then the neutron undergoes an interaction; else the neutron leaves the current volume, enters a new volume and undergoes a new transport calculation.

The MORET code can also perform the tracking with the Woodcock method. This tracking can be done on the whole geometry or in some parts of the geometry. This alternative tracking method may be used to treat complex geometries with a large number of volumes in order to reduce the computational time. It is particularly useful when volumes are significantly smaller than the mean free path or have complex shapes such as the pebble-bed reactor HTR-PROTEUS.

HTR-PROTEUS reactor

## + Source convergence

The source convergence is an important issue in Monte Carlo particle simulations. Weak neutronic coupling between the volumes containing the fissile material
may lead to erroneous results for the value of k_{eff}. Beyond the natural method, other sampling methods were designed to address two concerns:

- force neutrons to visit all fissile volumes to reduce the risk of weak coupling,
- accelerate the convergence to achieve more quickly a neutron distribution close to the reality and get the value of the reactivity of the system.

The MORET code embeds several techniques for tracking and sampling source neutrons among potential fission sites: stratified sampling, fission matrix method, importance sampling, oversampling, super-history powering and Wielandt method.

# Outputs

## + Define and use tallies

The code allows estimating various physical quantities for neutrons. Designed for criticality safety assessments, its aim is to estimate the effective multiplication
factor k_{eff} which can be seen as the mean number of neutrons produced in a generation per fission neutron. Based upon these simulations, the code is able to estimate
other physical quantities, such as:

- the neutron flux (the number of neutrons per cm² per second),
- the reaction rates (fission, absorption, diffusion) in the volumes,
- the neutron leakage of the whole geometry,
- the kinetic parameters of the system.

The code improves these output capabilities, allowing user to obtain any physical values using customized tallies described by the type of the response function to be calculated and others characteristics such as the selected volumes, the materials or isotopes, the energy group structure, etc.

## + Test the convergence

In the MORET 5 code, two main tools are available to help the user detect convergence issues:

- statistical tests to determine normality of samples,
- automated transient detection based on an indicator (k
_{eff}or Shannon entropy), a statistical test and a truncation method using a bridge constructed from the Student statistic.

The normality of k_{eff} sample is checked with two statistical tests:

- Chi-square test which is often used for its ease of implementation,
- Lilliefors method.