MCTRAN

3D Monte Carlo particle transport code

INTRODUCTION

            MCTRAN is a Monte Carlo particle transport code which is specifically intended for reactor physics and shielding calculation. The code which is currently being developed at the I. R. Iran’s Advanced Nuclear Computing Center (ANCC), is capable of simulating arbitrary 3D geometry based on boundary-representation geometry (B-rep) with first or second-order surfaces, as well as macro bodies. The code also merits a multilevel lattice-universe based geometry model to simulate all conventional nuclear structures e.g. right or rotated rectangular or hexagonal cores.a

The first version of the code (MCTRAN 1.0) released at April 2015, is capable of performing criticality calculation using neutron multi-group anisotropic (Legendre expanded) cross sections.. This version utilizes an internal converter for taking into account anisotropy of scattering (described by Legendre polynomials) into a Monte Carlo algorithm. The code also contains a variety of estimators for scoring k-eigenvalue,flux and current quantities, as well as a coarse-fine mesh tally for fast scoring the volumetric parameters.  MCTRAN 1.0 is equipped by a graphical user interface which brings ease of application for the users.

The entire system has been verified using various benchmarks and reference data found in published reports, as well as, comparisons made mainly against the MCNP outputs. Excellent agreements found in almost all cases which bring a meaningful trust for the users. Yet, V&V is still going on for more certitude.

The next version of the code (MCTRAN 2.0) is supposed to be released in late 2023 by the ANCC. Future developments mainly contains shielding calculation capability, alpha eigenvalue search, continuous cross section support, coupled Neutron-Photon-Electron transport simulations, implementation of various variance reduction methods as well as parallel processing. It is supposed that the new features will promote MCTRAN as a powerful tool for both criticality and shielding analysis.

METHODOLOGY

The significance of the Monte Carlo simulations lies in its ability to create a model similar to the real system based on known probabilities of occurrence using random processes. This method is employed to evaluate the average or expected behavior of a system by simulating a large number of events responsible for its behavior and observing the outcomes. Thanks to MC's capabilities, transport of particles can be simulated over highly-detailed geometries along with continuous energy-angle physics, thus the particles can be
tracked in a continuous phase space. MCTRAN 1.0 as a typical MC code is composed of three independent components: physics modeling, geometry tracking and scoring tally sections.

• Physics:

Based upon known probability distribution, the physics kernel samples the distance between interactions, collision nuclide, energy loss and angular deflection in interactions and generation of secondary particles. In MCTRAN 1.0, multi-group anisotropic (Legendre expanded) cross sections are used to simulate neutron physics. The code internally converts Legendre polynomials of the angular distributions into some equiprobable cosine bins (based on nonlinear least-squares fitting) or discrete angles (based on conserving Legendre moments of the angular distributions).

In the code, the standard power method (the source iteration) is applied iteratively to obtain  the fundamental mode of source distribution and estimations of the k-eigenvalue, stochastically. In order to reduce the variance and to have a better distribution of fission sources, non-analog methods using the Russian roulette algorithm are employed for capture and fission events in addition to analog methods.

The flowchart of Monte Carlo criticality calculation based on fission source iteration method.

• Geometry:

The geometry module, also called ray-tracer, handles the transport of particles across the simulated cells and determines the material in which particles move. A cell is formed using Boolean operations (unions and/or intersections) on the regions defined by an arbitrary combination of surfaces. First and second-order surfaces as well as conventional closed surface (Macro Body) have been provided for the MCTRAN 1.0 code. It also benefits from a multilevel lattice-universe based geometry model to simulate repeated structures as found in a nuclear reactor core..

Ray-tracing begins by locating the particle position in the geometry. This is done by searching recursively from the zero level lattice (root lattice) to the universe (may be a higher level lattice) until the cell that contains the particle is found. When a particle enters a lattice, it is transported to a new level and lattice indices that contains the particle is found, according to its position, the (0,0,0) element of lattice, lattice coordinate and pitches. Then, the
position of particle is computed relative to the center point of founded universe and the collection cells of this universe are investigated until the cell that contains the particle position is found. The local position of particle, lattice indices, universe number, and the cell containing the particle are recorded in an array corresponding to the current level. Using this method, transport could be performed in lattice-universe model without reproduction of universes.

The physical track-length has been then computed and compared with the nearest directional distance to the surface within a cell. In the non-root level, this distance must be compared with the nearest directional distance to all surfaces bounding the cells in lower levels and frame of the universe.

• Tally:

The goal of a simulation is to estimate the quantities of interest. In criticality calculation, the value of particle multiplication factor, flux and power distributions are of interest. Various estimators such as collision, absorption and track-length estimators can be used for scoring these quantities. The MCTRAN 1.0 code benefits from these three estimators to estimate the multiplication factor, alongside with a covariance weighted average method for the mean value of this parameter. In addition to the cell volume and the surface area tally, the code has an efficient rectangular mesh tally for scoring volume flux and power distribution. The mesh tally provides user defined coarse meshes with equal fine meshes between them. Mesh tally scoring begins by finding the mesh that contains the particle position. First, the coarse mesh is found using the binary search of particle position in a coarse grid, and then the index of the fine mesh is computed directly. Finally, the tally scoring is done by dividing the track length over meshes along the particle's trajectory.

FEATURES

Followings are the major capabilities of MCTRAN 1.0:

• Simulating arbitrary 3D geometry using boundary-representation (B-rep) method;
• Rectangular and hexagonal lattice-universe geometry modeling;
• Criticality calculation using successive generation method;
• Supporting multi-group cross sections with anisotropy of scattering described by Legendre polynomials;
• Estimation of effective multiplication factor, flux and current;
• A dual coarse-fine mesh as a flexible tool to estimate the volumetric parameters, and
• User-friendly interface and graphical output display.

APPLICATIONS

• Criticality calculations with multigroup cross sections.
• Verification of deterministic transport codes.