**4. Monte Carlo particle transport modeling of radiation effects in materials**

High-energy charged particles undergo a daunting number of interactions with target materials. Such interactions include:


The most commonly used approach to study radiation-induced effects in materials is the Monte Carlo (MC) particle transport method [102, 103]. In MC particle transport, the interactions of individual primary ions and their secondaries are sampled to build a history of charged particle passage and energy deposition in the target [104], with a large enough statistical sample of trajectories. The energy- and angle-dependent cross sections for different interactions are provided by theoretical models of the elementary interactions and/or experimental data, depending on the energy window. Codes, such as Geant4 [105], MCNP6 [106–108], FLUKA [109], PHITS [110], and HETC-HEDS [111], have been successfully applied to study the radiation at a hemispherical dome made of lunar regolith used to simulate a lunar habitat [112, 113] and the radiation environment around the Moon [114, 115].

Several relevant radiation-induced effects in materials are due to particles with an energy of a few MeV to a few tenths of MeV, as can be seen in **Table 2**. In this regime, below hadronic interactions causing fragmentation/spallation, atomic displacements are induced in the target by elastic nuclear interactions. Two concepts describe the slowing down of the impacting particles (and the induced secondaries), (i) the *electronic stopping power*, that is, the energy loss of the moving particle to the electronic degrees of freedom of the target (a concept valid in the whole energy range) and (ii) the *nuclear stopping power*, that is, the energy lost to elastic nuclear interactions causing atomic displacements (a concept only used for the regime below hadronic interactions). MC particle transport modeling is a very convenient approach to deal with the enormous amount of interactions that a highenergy particle can induce in a target. However, the approximations used for intermediate and low energies (few MeV and lower) may pose some challenges for the applicability of MC particle transport. At such energies, the atomic-scale structure and the electronic properties of the target system should be taken into account for a reliable description of the radiation-induced effects. In MC particle transport, however, the target materials are amorphous and the macroscopic interaction cross sections, as well as electronic and nuclear stopping power, are obtained by a simple stoichiometric averaging of the elemental cross sections and stopping power. The electronic stopping in MC particle transport simulations is calculated for a uniform electron gas with the same density as the target within the perturbative linear approach not appropriate at low energies [116]. Since the crystal structure of the target is ignored, the effects due to ion channeling (i.e., when the ion path is confined within the crystallographic planes), that have been shown to significantly influence the electronic stopping power [117, 118], are not taken into account.

A displacement cascade in MC particle transport simulations is generally modeled within the Binary Collision Approximation (BCA) [119] which assumes a series of independent two-body collisions. Between collisions, particles travel in a straight line. The BCA is valid when (i) the projectile energy is higher than 1 keV per nucleon, which, for PKAs, could be relevant energy, and (ii) the target material has low density, in which case the collisions between the incoming particle and the target atoms occur rarely. BCA allows reducing the computational complexity of the ion-matter interactions compared to a full many-body simulation (e.g., molecular dynamics, discussed in Section 5) and allows for reaching large dimensions with reduced computational needs. However, this method is valid for linear collisions only and describes only primary damage, that is, it does not account for the dynamic evolution of induced defects at later times (**Figure 2**).

One of the most popular tools in which the BCA is implemented is the Stopping and Range of Ions in Matter (SRIM) code [120]. Besides containing semiempirical data for the electronic stopping power of a variety of targets, SRIM can be applied to model the linear cascades and estimate the number of defects in any material and any ion energy up to 1 GeV. Nuclear stopping in very low-energy intervals uses the so-called ZBL (Ziegler-Biersack-Littmark) universal potential that combines classical Coulomb potential with a semiempirical screening function [120]. The electronic and nuclear degrees of freedom are completely separated in SRIM as well as in other MC particle transport tools used by the particle physics community and the space radiation effects community. Finally, it is important to remark that materials are static in MC particle transport methods—there is no dynamics induced in them by the impact of primaries and the generation and passage of secondaries. Thus, more accurate methods are needed to get access to the processes missing in MC particle transport calculations. Such methods are described in the next section.

*Modeling Radiation Damage in Materials Relevant for Exploration and Settlement on the Moon DOI: http://dx.doi.org/10.5772/intechopen.102808*
