Recent developments in the TRIPOLI-4 ® Monte-Carlo code for shielding and radiation protection applications

. TRIPOLI-4 ® is a 3D continuous-energy Monte-Carlo particle transport code developed by CEA (SERMA) and devoted to shielding, reactor physics, criticality-safety and nuclear instrumentation. In this paper, we present the recent developments in the TRIPOLI-4 ® for shielding and radiation protection applications. Some of these additional features are already available in the TRIPOLI-4 ® version 10 released in December 2015. Other features are in development.


Introduction
TRIPOLI-4 ® is a three-dimensional and continuousenergy Monte-Carlo particle transport code developed by the "Service d'Etudes des Réacteurs et de Mathématiques Appliquées" (SERMA), at the CEA Paris-Saclay center. It is devoted to shielding, reactor physics, criticality safety and nuclear instrumentation [1].
TRIPOLI-4 ® has been developed starting from the mid of 1990s in C++. A new version of the code is typically released every two years. The TRIPOLI-4 ® version 10 has been released in December 2015 with in particular a Monte-Carlo depletion feature.
In this paper, we present the recent developments in the TRIPOLI-4 ® for shielding and radiation protection applications. Some of these additional features are already available in the TRIPOLI-4 ® version 10 released in December 2015. Other features are in development.

Geometry
TRIPOLI-4 ® has its own geometry module allowing both surface-based and combinatorial representations. TRIPOLI-4 ® is also directly compatible with a geometry developed in the format of the ROOT software [2]. Thanks to its modularity, the code may be linked with any third party geometry with limited development effort.

Simulation modes
Three simulation modes are available in the TRIPOLI-4 ® code: • "Shielding" mode, fixed-source simulation typically used for radiation protection and shielding analysis. • "Fixed_Sources_Criticality" mode, fixed source simulation with treatment of fission events, typically used for subcritical fissile instrumentation problems. • "Criticality" mode, used to find the fundamental mode and the associated fundamental eigenvalue of the critical Boltzmann equation.

Tallies
A non-exhaustive list of the tallies available in the TRIPOLI-4 ® code includes: volume, surface and point fluxes, surface currents, mesh tallies, reaction rates, deposited energy, built-in KERMA response functions, dose equivalent rate, dpa, gamma spectroscopy and effective multiplication factor keff.

Variance reduction techniques
Standard variance reduction techniques are available in TRIPOLI-4 ® , such as implicit capture, particle splitting and Russian roulette. Moreover, TRIPOLI-4 ® has a special built-in variance reduction module, called INIPOND, based on the Exponential Transform Method, with an automatic pre-calculation of the importance map.

Doppler broadening of the elastic scattering kernel
For the Doppler broadening of the elastic scattering kernel, the algorithm "Sampling of the Velocity of the Target nucleus" (SVT) is by default used in the TRIPOLI-4 ® code. The "Doppler Broadening Rejection Correction" (DBRC) and the "Weight Correction Method" (WCM) have been implemented in TRIPOLI-4 ® (version 9) to overcome the SVT limitations that affect resonant nuclei (such as 238 U) typically in the epithermal region.

Reactor period calculation
The asymptotic time behavior of neutron transport can be used in reactor start-up analysis or kinetics studies of nuclear systems. In TRIPOLI-4 ® version 10, the asymptotic reactor period is calculated as the inverse of the dominant eigenvalue. The algorithm is based on a modified alpha-k power iteration scheme [3].

Kinetics parameters computing
Kinetics parameters are key to the study of nuclear reactor dynamics and to safety issues in the context of transient or accidental reactor behavior. The Iterated Fission Probability (IFP) method implemented in TRIPOLI-4 ® version 10 allows computing the adjointweighted kinetics parameters: the delayed neutron fraction, the mean generation time and the Rossi Alpha [4].

Deposited charge
It is possible to calculate the spectrum of the charge deposited in a given volume by charged particles (electrons and positrons) using the DEPOSITED_CHARGE response recently implemented in TRIPOLI-4 ® version 10. The charge deposition can be used for nuclear instrumentation in the interpretation of signal of sensors irradiated in nuclear reactors, such as Self-Powered Neutron Detectors (SPNDs).

3D core fuel-depletion calculation
TRIPOLI-4 ® has been recently extended so as to cover depletion calculations by coupling the code to the MENDEL depletion solver developed by SERMA [5]. This coupling allows solving the Boltzmann-Bateman system of equations governing the evolution of materials under neutron irradiation. At a given time step, TRIPOLI-4 ® computes first the reaction rates in each depleted medium. Then, the MENDEL depletion solver calculates the end-of-step nuclide concentration for each region. TRIPOLI-4 ® version 10 depletion capability is based on C++ interfaces (accessible via C++ interpreter of ROOT [4]) that wrap the methods of both TRIPOLI-4 ® and MENDEL. Controls rods insertion is adjusted during irradiation. We mention here an example recent shielding-V&V work that has been carried out on NAIADE 1 Water shielding benchmark [7]. For the nuclear decommissioning application, TRIPOLI-4 ® code capabilities on fission neutron deep penetration calculations were demonstrated. Both the shielding mode and the fixed-source subcriticality mode of the code were validated against the NAIADE 1 water shielding benchmark. The variance reduction options of TRIPOLI-4 ® code are helpful to perform these calculations.

Fig. 3
Recent example of shielding-V&V work: NAIADE 1 Water shielding benchmark [7] 3 New features of TRIPOLI-4 ® version 10 for shielding and radiation protection applications 3.1 Thick-Target Bremsstrahlung for electromagnetic shower simulation A simplified simulation mode for the electromagnetic shower, called Thick-Target Bremsstrahlung (TTB), has been implemented in TRIPOLI-4 ® version 10 to speed up coupled photon-electron-positron calculations. When this option is activated, secondary electrons and positrons produced by photon collisions are not transported, but part of their energy is converted into new bremsstrahlung photons. Fig. 4 shows a recent example of the use this feature for a benchmark of a sphere with a 20-MeV photon source in the center [8]. The simulation of the electromagnetic shower with TTB implicates a maximum difference of 30% in the deposited energy against a full coupled photon-electron-positron simulation, but the use of TTB speeds up calculations up 10 times. Fig. 4 Recent example of the use of the TTB feature. Here TTB vs full electromagnetic shower simulation: a maximum difference in deposited energy of 30% but acceleration up 10 times.

Analog neutron or photon transport with analog fission sampling
It is already possible with TRIPOLI-4 ® to perform a fully analog simulation (concerning both collisions and transport between collisions) for neutron and photon transport. TRIPOLI-4 ® version 10 enables analog fission simulation by sampling a full fission neutron multiplicity distribution using a coupling between TRIPOLI-4 ® and an external fission model providing fission sampling data (standard nuclear data libraries provide averaged neutron multiplicities only). It allows addressing time-dependent nuclear instrumentation applications needing detailed correlations between fission chains [9].

"Replicate" option upgrading
With TRIPOLI-4 ® , we can perform a two-step calculation using first a global geometry to store the properties (energy, position, direction, weight) of particles crossing a given surface. Then, we use stored particles as surface sources for simulation on a local geometry. The REPLICATE option activates the particle splitting at the second-step simulation. This technique of variance reduction allows for an improved exploration of the whole phase space, especially when only a limited number of particles has been stored. a) 1st step (global geometry) b) 2 nd step (local geometry) Fig. 6 Example of a two-step calculation in the case of the OSIRIS MTR reactor (CEA, Saclay). The blue rectangle (horizontal cross-section 30 cm x 30 cm) shows the boundary used for the storing of the particle characteristics. Inside the rectangle, we have two water boxes (horizontal cross-section 8 cm x 8 cm) with SPNDs monitors irradiated in the centers (about 3 mm of diameter) [8].
protection applications in development sampling TRIPOLI-4 ® Monte Carlo transport code and FIFRELIN fission model (developed by CEA, Cadarache center, SPRC) have been coupled by means of external files so that neutron transport can then take into account fission distributions (multiplicities and spectra) that are not averaged, as is the case when using evaluated nuclear data libraries. Spectral effects on responses in shielding configurations with fission sampling are then expected [9]. ® /Geant4 coupling The capability to simulate the transport of charged and/or high-energy hadrons (especially protons) is useful for, shielding, radiation protection and nuclear instrumentation applications. In the context of Monte-Carlo particle transport codes, solving these problems often requires the use of advanced variance-reduction techniques. TRIPOLI-4 ® is a reference Monte-Carlo particle transport code for the simulation of low-energy (< 20 MeV) neutrons and photons and offers a wide range of sophisticated variance-reduction schemes; however, it cannot be applied to the problems mentioned above because it lacks the capability to transport charged, highenergy hadrons. This limitation can be circumvented by coupling TRIPOLI-4 ® with the Geant4 particle transport toolkit (CERN) [10].

dose rate calculation
An activation scheme has been developed in TRIPOLI-4 ® for the shutdown dose rate calculations based on the Rigorous two-step approach (R2S). Two Monte Carlo transport calculations are used, the first for the neutrons to calculate the activation and second for photons emitted by activated materials. The production of the decay photons is performed by MENDEL inventory code (CEA) [14]. .

Fig. 10
Example of shutdown dose rate calculation using R2S TRIPOLI-4 ® in the case of a typical configuration of a port plug in ITER fusion facility [15]. a) ITER Equatorial Port Plug, b) Distribution of the total neutron flux calculated by TRIPOLI-4 ® , c) Shutdown dose rate at the rear face.

.4 Variance Reduction using the method of Adaptive Multilevel Splitting (AMS)
A new technique of variance reduction based on the method of Adaptive Multilevel Splitting (AMS) has been developed in the TRIPOLI-4 code [14]. The AMS algorithm is an iterative method to help simulate rare events. Each iteration includes the definition of a single splitting level alongside with the corresponding splitting process: • Classify simulated particle tracks and define a splitting level; • Remove the particles that have not reach the threshold; • Re-sample removed particles by splitting remaining ones.
These preliminary results show that the use of the Adaptive Multilevel Splitting algorithm in TRIPOLI-4 ® reduces significantly the variance. Furthermore, its connection to the TRIPOLI-4 ® importance map calculation module makes it quite simple to use [16].