Monte Carlo Particle Tracking Research Articles

A 3D unstructured mesh based particle tracking code for impurity transport simulation in fusion tokamaks

A fully 3D unstructured mesh based global impurity transport code, GITRm is presented in this paper. It is a high-performance Monte Carlo particle (neutral atom and ion) tracking code, based on the trace approximation, to simulate the erosion, ionization, migration, and redistribution of material from plasma-facing components in magnetically confined fusion devices. It is designed to target complex geometries including non-axisymmetric local features such as bumpers, probes, tile gaps etc., and uses strongly graded and anisotropic elements to accurately represent the plasma fields. GITRm is built on the PUMIPic infrastructure [1], executes using distributed meshes and is performant on GPU accelerated computer systems. Three example cases, including a weak scaling study with about 1.5 billion particles on up to 144 GPUs, are used to demonstrate the utility of GITRm.

Neutronics analysis of a source-driven subcritical system using G4-STORK

As a promising design of the next-generation reactors, source-driven subcritical systems (SC) are compelling for their safety and transmutation features. However, singular properties of SCs bring insuperable difficulties to their neutronics analysis with conventional numerical methods. Instead of applying oversimplified approximations, the limitations of deterministic approaches and quasi-static Monte Carlo approaches can be surmounted using G4-STORK (Geant4 STOchastic Reactor Kinetics), a time-dependent Monte Carlo particle tracking code for reactor physics applications. In this work, exploiting the exclusive features of G4-STORK, we demonstrate a novel analysis methodology by presenting a specialized neutronics analysis of an SC. A detailed inspection of neutron distributions, integral parameters, and source-induced kinetics are provided to reveal the singular behaviors neglected by oversimplifications.

GITR: An accelerated global scale particle tracking code for wall material erosion and redistribution in fusion relevant plasma–material interactions

The global impurity transport code (GITR — pronounced “guitar”) has been developed as a high-performance Monte Carlo particle (neutral atom and ion) tracking code to simulate the erosion, ionization, migration, and redistribution of plasma-facing components in magnetically confined fusion devices. The trace impurity assumption allows for a highly parallel computational model that enables increased scaling in the number of particles simulated as well as the domain size and geometric fidelity. Novel custom algorithms that query the 3D surface geometry has alleviated the need for traditional meshing needs. Presented here are the physics model, numerical schemes, algorithmic implementation, and example simulations. Program summaryProgram Title: GITRCPC Library link to program files:https://doi.org/10.17632/djpw9rpv5b.1Developer’s repository link:https://github.com/ORNL-Fusion/GITRLicensing provisions: GPLv2Programming language: C++Nature of problem: Net and gross erosion, kinetic redistribution, and deposition of material sputtered as a result of high energy particle flux in the plasma–material interaction.Solution method: Monte Carlo particle tracking through Lorentz force, background plasma collision operators, atomic physics processes, and interaction with material surfaces.

PCE point source apportionment using a GIS-based statistical technique combined with stochastic modelling

To meet the continuous growth of urbanised areas with the ever-increasing demand for safe water supplies, the implementation of new scientifically based methodologies can represent a key support for preventing groundwater quality deterioration.In this study, a new combined approach based on the application of the Weights of Evidence and the Null-Space Monte Carlo particle back-tracking methods was set up to assess tetrachloroethylene (PCE) contamination due to Point Sources in the densely urbanised north-eastern sector of the Milano FUA (Functional Urban Area). This combined approach offers the advantage of further enhancing the power of each individual technique by integrating both the advective transport mechanism, neglected by the Weights of Evidence, and the influence of specific factors, such as the land use variation, not considered by the Null-Space Monte Carlo particle tracking. To accurately test and explore the performance of this new approach, the analysis was carried out based on the simulation of synthetic PCE plumes using a groundwater numerical model already implemented in a previous study. The Weights of Evidence method revealed that the areas characterised by a groundwater depth lower than 17 m, a groundwater velocity higher than 2.6 × 10−6 m/s, a recharge higher than 0.26 m/y and a significant variation of the industrial activities extent are the most susceptible to groundwater pollution. The Null-Space Monte Carlo particle back-tracking has proved to be effective in delineating the potential source zones and contaminant travel path.The proposed approach can offer additional insights for the protection of groundwater resource. The end-product provides crucial information on the zones that require to be prioritised for investigations and can be easily understood by non-expert decision-makers constituting an advanced tool for enhancing groundwater protection strategies.

A mechanistic relative biological effectiveness model-based biological dose optimization for charged particle radiobiology studies

In charged particle therapy, the objective is to exploit both the physical and radiobiological advantages of charged particles to improve the therapeutic index. Use of the beam scanning technique provides the flexibility to implement biological dose optimized intensity-modulated ion therapy (IMIT). An easy-to-implement algorithm was developed in the current study to rapidly generate a uniform biological dose distribution, namely the product of physical dose and the relative biological effectiveness (RBE), within the target volume using scanned ion beams for charged particle radiobiological studies. Protons, helium ions and carbon ions were selected to demonstrate the feasibility and flexibility of our method. The general-purpose Monte Carlo simulation toolkit Geant4 was used for particle tracking and generation of physical and radiobiological data needed for later dose optimizations. The dose optimization algorithm was developed using the Python (version 3) programming language. A constant RBE-weighted dose (RWD) spread-out Bragg peak (SOBP) in a water phantom was selected as the desired target dose distribution to demonstrate the applicability of the optimization algorithm. The mechanistic repair-misrepair-fixation (RMF) model was incorporated into the Monte Carlo particle tracking to generate radiobiological parameters and was used to predict the RBE of cell survival in the iterative process of the biological dose optimization for the three selected ions. The post-optimization generated beam delivery strategy can be used in radiation biology experiments to obtain radiobiological data to further validate and improve the accuracy of the RBE model. This biological dose optimization algorithm developed for radiobiology studies could potentially be extended to implement biologically optimized IMIT plans for patients.

Null-space Monte Carlo particle tracking to assess groundwater PCE (Tetrachloroethene) diffuse pollution in north-eastern Milan functional urban area

The Lombardy Region in Italy is one of the most urbanized and industrialized areas in Europe. The presence of countless sources of groundwater pollution is therefore a matter of environmental concern. The sources of groundwater contamination can be classified into two different categories: 1) Point Sources (PS), which correspond to areas releasing plumes of high concentrations (i.e. hot-spots) and 2) Multiple-Point Sources (MPS) consisting in a series of unidentifiable small sources clustered within large areas, generating an anthropogenic diffuse contamination. The latter category frequently predominates in European Functional Urban Areas (FUA) and cannot be managed through standard remediation techniques, mainly because detecting the many different source areas releasing small contaminant mass in groundwater is unfeasible. A specific legislative action has been recently enacted at Regional level (DGR IX/3510-2012), in order to identify areas prone to anthropogenic diffuse pollution and their level of contamination. With a view to defining a management plan, it is necessary to find where MPS are most likely positioned. This paper describes a methodology devised to identify the areas with the highest likelihood to host potential MPS. A groundwater flow model was implemented for a pilot area located in the Milan FUA and through the PEST code, a Null-Space Monte Carlo method was applied in order to generate a suite of several hundred hydraulic conductivity field realizations, each maintaining the model in a calibrated state and each consistent with the modelers' expert-knowledge. Thereafter, the MODPATH code was applied to generate back-traced advective flowpaths for each of the models built using the conductivity field realizations. Maps were then created displaying the number of backtracked particles that crossed each model cell in each stochastic calibrated model. The result is considered to be representative of the FUAs areas with the highest likelihood to host MPS responsible for diffuse contamination.

Simulation of irradiation exposure of electronic devices due to heavy ion therapy with Monte Carlo Code MCNP6

During heavy ion irradiation therapy the patient has to be located exactly at the right position to make sure that the Bragg peak occurs in the tumour. The patient has to be moved in the range of millimetres to scan the ill tissue. For that reason a special table was developed which allows exact positioning. The electronic control can be located outside the surgery. But that has some disadvantage for the construction. To keep the system compact it would be much more comfortable to put the electronic control inside the surgery. As a lot of high energetic secondary particles are produced during the therapy causing a high dose in the room it is important to find positions with low dose rates. Therefore, investigations are needed where the electronic devices should be located to obtain a minimum of radiation, help to prevent the failure of sensitive devices. The dose rate was calculated for carbon ions with different initial energy and protons over the entire therapy room with Monte Carlo particle tracking using MCNP6. The types of secondary particles were identified and the dose rate for a thin silicon layer and an electronic mixture material was determined. In addition, the shielding effect of several selected material layers was calculated using MCNP6.

Tomographic reconstruction of the beam emissivity profile in the negative ion source NIO1

A versatile negative hydrogen ion source named NIO1 of a moderate size (130 mA total extracted H− current, 9 apertures, 60 kV total acceleration) has been developed and installed at Consorzio RFX. It will allow great experimental flexibility, very beneficial for studying several important issues related to beam extraction, optics and performance optimization, in view of SPIDER and MITICA, the two full-scale experiments for the ITER neutral beam injector under construction at RFX. The main target of emission tomography applied to an ion beam is the reconstruction of the emissivity profile, from which the ion density distribution can be obtained. The measurement of the beam density profile and of its uniformity throughout the pulse duration with a non-invasive diagnostic, such as tomography, would represent an effective method for monitoring the ion source operation and for malfunction detection. The application of this diagnostic to the NIO1 beam will represent the experimental verification of the possibility to reconstruct a multi-beamlet profile, in the interest of the next tomography systems for SPIDER and MITICA. In this paper, a feasibility study of the tomographic diagnostic for NIO1 is presented. A tomography code based on algebraic reconstruction techniques has been developed for this purpose and the transport of the nine H− beamlets is simulated with a Monte Carlo particle tracking code from the ion source to the tomography plane, where the beam emissivity profile to be reconstructed is calculated. The reference emissivity profile is reconstructed by the tomography code considering different possible layouts of the detection system, in order to find the best compromise between the quality of reconstructions and the complexity of the diagnostic. Results show that a tomography system based on six linear CCD cameras should be capable of reconstructing the NIO1 emissivity profile with an rms error lower than 10%. How instrumental noise in the integrated signals affects the reconstructed beam emissivity profiles is also studied. A simple low-pass filter is found effective if the noise level is less than 10%; otherwise a more sophisticated filtering technique must be considered.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons. The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE. When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 μm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.

Axial dispersion of granular material in inclined rotating cylinders with bulk flow: Geometric model for 50% fill

Monte Carlo particle tracking methods used to model particle motion in inclined rotating cylinders with bulk flow have been reported in the literature. This paper reports some analytic results for the mean squared deviation of axial position in the following special case: the particles are in the rolling mode; the bed surface is flat, with no axial variation of bed depth; the avalanche is instantaneous and of negligible thickness; collisional axial dispersion is ignored; fill=0.5. Fill=0.5 means that in every half-rotation of the cylinder every particle will have participated in one and only one avalanche; this simplification allows analytic results to be obtained. The calculations are carried out by relating the number densities of tracer particles in successive cycles of avalanching. In the case of well-mixed avalanches, the model is also developed using a random walk approach. The results confirm predictions obtained from discrete element modelling and Monte Carlo particle tracking simulations, which indicate that the mean squared deviation of axial position can oscillate with time for short enough times.

Weighted-delta-tracking for Monte Carlo particle transport

Monte Carlo particle transport (MCPT) codes are incredibly powerful and versatile tools to simulate particle behavior in a multitude of scenarios, such as core/criticality studies, radiation protection, shielding, medicine and fusion research to name just a small subset applications. However, MCPT codes can be very computationally expensive to run when the model geometry contains large attenuation depths and/or contains many components. This paper proposes a simple modification to the Woodcock tracking method used by some Monte Carlo particle transport codes. The Woodcock method utilizes the rejection method for sampling virtual collisions as a method to remove collision distance sampling at material boundaries. However, it suffers from poor computational efficiency when the sample acceptance rate is low. The proposed method removes rejection sampling from the Woodcock method in favor of a statistical weighting scheme, which improves the computational efficiency of a Monte Carlo particle tracking code. It is shown that the modified Woodcock method is less computationally expensive than standard ray-tracing and rejection-based Woodcock tracking methods and achieves a lower variance, given a specified accuracy.

G4-STORK: A Geant4-based Monte Carlo reactor kinetics simulation code

In this paper we introduce G4-STORK (Geant4 STOchastic Reactor Kinetics), a new, time-dependent, Monte Carlo particle tracking code for reactor physics applications. G4-STORK was built by adapting and expanding on the Geant4 Monte Carlo toolkit. The toolkit provides the fundamental physics models and particle tracking algorithms that track each particle in space and time. It is a framework for further development (e.g.for projects such as G4-STORK).G4-STORK derives reactor physics parameters (e.g.keff) from the continuous evolution of a population of neutrons in space and time in the given simulation geometry. In this paper we detail the major additions to the Geant4 toolkit that were necessary to create G4-STORK. These include a renormalization process that maintains a manageable number of neutrons in the simulation even in very sub- or supercritical systems, scoring processes (e.g.recording fission locations, total neutrons produced and lost, etc.) that allow G4-STORK to calculate the reactor physics parameters, and dynamic simulation geometries that can change over the course of simulation to illicit reactor kinetics responses (e.g.fuel temperature reactivity feedback).The additions are verified through simple simulations and code-to-code comparisons with established reactor physics codes such as DRAGON and MCNP. Additionally, G4-STORK was developed to run a single simulation in parallel over many processors using MPI (Message Passing Interface) pipes.

Magnetic field structure influence on primary electron cusp losses for micro-scale discharges

An experimental effort was used to examine the primary electron loss behavior for micro-scale (≲3 cm diameter) discharges. The experiment uses an electron flood gun source and an axially aligned arrangement of ring-cusps to guide the electrons to a downstream point cusp. Measurements of the electron current collected at the point cusp show an unexpectedly complex loss pattern with azimuthally periodic structures. Additionally, in contrast to conventional theory for cusp losses, the overall radii of the measured collection areas are over an order of magnitude larger than the electron gyroradius. Comparing these results to Monte Carlo particle tracking simulations and a simplified analytical analysis shows that azimuthal asymmetries of the magnetic field far upstream of the collection surface can substantially affect the electron loss structure and overall loss area.

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies.

Monte Carlo simulations of down-scattered neutron and knock-on deuteron spectra in deuterium-tritium capsule implosions

A Monte Carlo particle tracking (MCPT) code has been developed and coupled to hydrodynamic simulations to generate and track primary and scattered neutrons in addition to scattered charged particles by post-processing. This code uses one dimensional (1-D) deuterium-tritium implosion profiles, and the computed down-scattered neutron and knock-on deuteron spectra are analyzed for different areal densities. The mixing effects on the spectra of down-scattered neutron and knock-on deuteron are also investigated. The implementation of the numerical scheme is analyzed, and the particle splitting technique is adopted, which is proven to efficiently reduce computational effort.

Development of a randomized 3D cell model for Monte Carlo microdosimetry simulations

The objective of the current work was to develop an algorithm for growing a macroscopic tumor volume from individual randomized quasi-realistic cells. The major physical and chemical components of the cell need to be modeled. It is intended to import the tumor volume into GEANT4 (and potentially other Monte Carlo packages) to simulate ionization events within the cell regions. A MATLAB© code was developed to produce a tumor coordinate system consisting of individual ellipsoidal cells randomized in their spatial coordinates, sizes, and rotations. An eigenvalue method using a mathematical equation to represent individual cells was used to detect overlapping cells. GEANT4 code was then developed to import the coordinate system into GEANT4 and populate it with individual cells of varying sizes and composed of the membrane, cytoplasm, reticulum, nucleus, and nucleolus. Each region is composed of chemically realistic materials. The in-house developed MATLAB© code was able to grow semi-realistic cell distributions (~2 × 10(8) cells in 1 cm(3)) in under 36 h. The cell distribution can be used in any number of Monte Carlo particle tracking toolkits including GEANT4, which has been demonstrated in this work. Using the cell distribution and GEANT4, the authors were able to simulate ionization events in the individual cell components resulting from 80 keV gamma radiation (the code is applicable to other particles and a wide range of energies). This virtual microdosimetry tool will allow for a more complete picture of cell damage to be developed.

Mass transport subject to time-dependent flow with nonuniform sorption in porous media

We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particle trajectories, we derive the corresponding governing equations for the concentration of the mobile and immobile phases within a fractal mobile-immobile model approach. We show that this formulation is fairly general and can easily take into account nonconstant coefficients and in particular space-dependent sorption rates. The transport equations are solved numerically and a comparison with Monte Carlo particle-tracking simulations of spatial contaminant profiles and breakthrough curves is proposed, so as to illustrate the obtained results.

An efficiency study of the r-function method applied as solid modeler for Monte Carlo calculations

Unlike conventional methods the R-function theory can be efficiently applied both to deterministic and stochastic solution of neutron transport problems. This paper presents two procedures for Monte Carlo particle tracking based on R-function solid modeling. An extensive series of calculations is performed on three families of geometric models and timing comparison with the MCNP code is given. The presented results clearly confirm the potentials of the R-function approach.