Dynamic Monte Carlo Code Research Articles

A pure dynamic Monte Carlo code for the neutronic analysis of nuclear reactors

Transient analysis is of great significance in the safety and economic assessment of nuclear systems. This kind of analysis is generally performed using simplified models such as the time-dependent diffusion theory or the point-kinetics approximation. Therefore, applying a more accurate approach seems necessary for situations exceeding the validity range of such models. Nowadays, with increasing computational power, special attention has been focused on the use of dynamic Monte Carlo methods due to their capabilities in simulating detailed geometries and physics. Hence, this paper attempts to develop a pure time-dependent Monte Carlo code called MC3-TD that is capable of modeling complex reactor core geometries considering neutrons and delayed neutron precursors as particles. Using this viewpoint during simulation, in addition to obtaining the spatial distribution of precursors, can also facilitate modeling their movements.Moreover, a new approach called the dynamic control method has been proposed for population control and its effectiveness has been compared to conventional methods. Several transient problems, including 2D and 3D geometries, have been used to assess the performance of MC3-TD and a highly satisfactory agreement has been found between the obtained results and reference data.

A time dependent Monte Carlo approach for nuclear reactor analysis in a 3-D arbitrary geometry

A highly reliable tool for transient simulation is vital in the safety analysis of a nuclear reactor. Despite this fact most tools still use diffusion theory and point-kinetics that involve many approximation such as discretization in space, energy, angle and time. However, Monte Carlo method inherently overcomes these restrictions and provides an appropriate foundation to accurately calculate the parameters of a reactor. In this paper fundamental parameters like multiplication factor (Keff) and mean generation time (tG) are calculated using Monte Carlo method and then employed in transient analysis for computing the neutron population, proportional to Keff, during a generation time considering precursors decay. Based on this approach, a dynamic Monte Carlo code named MCSP (Monte Carlo dynamic Simulation of Particles tracking) is developed for both the steady state and time-dependent simulation of particle tracking in an arbitrary 3D geometry. MCSP is able to use either continuous or multi-group energy cross section libraries. To speed up the simulation, the MCSP was empowered with parallel processing as well. Several test problems such as C5G7, LMW and TWIGL are examined to assess the performance of the method.

Implementation of a dynamic Monte Carlo method for transients analysis with thermal-hydraulic feedbacks using MCNPX code

Transient analysis which is vital in safety analysis requires a reliable calculation method. Most valid tools use diffusion theory with many approximations by now. However, the Monte Carlo method inherently overcomes these approximations and accurately calculates the parameters of a reactor. In this paper, a new time-dependent transport approach is described to simulate the nuclear reactor dynamic correctly using the MCNPX code. In this approach the fundamental parameters of a nuclear reactor like multiplication factor (Keff) and mean generation time (tG) are calculated using MCNPX code. They are then employed in the formulas to compute neutron population, proportional to Keff, during a generation time as well as precursors are decayed. Based on the approach, a dynamic Monte Carlo code namely DMCNP (Dynamical MCNPX code) is developed for a time-dependent simulation of particle tracking in an arbitrary geometry, considering the thermal-hydraulic feedbacks. The effects of temperature on cross section and density are applied at each time steps. Several test problems such as TWIGL, LMW, LRA and C5G7 are examined to assess the performance of the method.

Dynamic Monte Carlo simulations of radiatively accelerated GRB fireballs

We present a novel Dynamic Monte Carlo code (DynaMo code) which self-consistently simulates the Compton scattering driven dynamic evolution of a plasma. We use the DynaMo code to investigate the time-dependent expansion and acceleration of dissipationless GRB fireballs by varying their initial opacities and baryonic content. We study the opacity and energy density evolution of an initially optically thick, radiation-dominated fireball across its entire phase space - in particular during the $R_{\rm ph} < R_{\rm sat}$ regime. Our results reveal new phases of fireball evolution: a transition phase with a radial extent of several orders of magnitude - the fireball transitions from $\Gamma \propto R$ to $\Gamma \propto R^0$, a post-photopsheric acceleration phase - where fireballs accelerate beyond the photosphere, and a Thomson-dominated acceleration phase - characterized by slow acceleration of optically thick, matter-dominated fireballs due to Thomson scattering. We quantify the new phases by providing analytical expressions of Lorentz factor evolution, which will be useful for deriving jet parameters.

Thermal equilibrium and prehydration processes of electrons injected into liquid water calculated by dynamic Monte Carlo method

Abstract The thermalization length and spatial distribution of electrons in liquid water were simulated for initial electron energies ranging from 0.1 eV to 100 keV using a dynamic Monte Carlo code. The results showed that electrons were decelerated for thermalization over a longer time period than was previously predicted. This long thermalization time significantly contributed to the series of processes from initial ionization to hydration. We further studied the particular deceleration process of electrons at an incident energy of 1 eV, focusing on the temporal evolution of total track length, mean traveling distance, and energy distributions of decelerating electrons. The initial prehydration time and thermalization periods were estimated to be approximately 50 and 220 fs, respectively, indicating that the initial prehydration began before or contemporaneously with the thermal equilibrium. Based on these results, the prehydrated electrons were suggested to play an important role during multiple DNA damage induction.

FORMATION OF MASSIVE BLACK HOLES IN DENSE STAR CLUSTERS. II. INITIAL MASS FUNCTION AND PRIMORDIAL MASS SEGREGATION

A promising mechanism to form intermediate-mass black holes (IMBHs) is the runaway merger in dense star clusters, where main-sequence stars collide and form a very massive star (VMS), which then collapses to a black hole. In this paper we study the effects of primordial mass segregation and the importance of the stellar initial mass function (IMF) on the runaway growth of VMSs using a dynamical Monte Carlo code for N-body systems with N as high as 10^6 stars. Our code now includes an explicit treatment of all stellar collisions. We place special emphasis on the possibility of top-heavy IMFs, as observed in some very young massive clusters. We find that both primordial mass segregation and the shape of the IMF affect the rate of core collapse of star clusters and thus the time of the runaway. When we include primordial mass segregation we generally see a decrease in core collapse time (tcc). Moreover, primordial mass segregation increases the average mass in the core, thus reducing the central relaxation time, which also decreases tcc. The final mass of the VMS formed is always close to \sim 10^-3 of the total cluster mass, in agreement with the previous studies and is reminiscent of the observed correlation between the central black hole mass and the bulge mass of the galaxies. As the degree of primordial mass segregation is increased, the mass of the VMS increases at most by a factor of 3. Flatter IMFs generally increase the average mass in the whole cluster, which increases tcc. For the range of IMFs investigated in this paper, this increase in tcc is to some degree balanced by stellar collisions, which accelerate core collapse. Thus there is no significant change in tcc for the somewhat flatter global IMFs observed in very young massive clusters.

Molecular dynamics and dynamic Monte Carlo studies of mixed materials and their impact on plasma wall interactions

A molecular dynamics technique was used to study the sputtering characteristics of co-deposited carbon (C) and to investigate subsequent effects of introducing beryllium (Be) impurities. Amorphous C layers containing hydrogen (H) with atomic ratios of H/(C + H) < 0.3 together with a small amount of Be with ratios of Be/(C + H + Be) < 0.06 are produced on top of a tungsten (W). Noncumulative bombardment of the amorphous C layer without H ( i.e., H/(C + H) = 0) by H atoms, produces no atomic C sputtering at energies less than the threshold energy for physical sputtering, as calculated by a dynamic Monte Carlo code, EDDY. By examining the H uptake in the layer, it was observed that hydrocarbon sputtering occurs when the dominant emitted species are small radicals e.g. CH and at low H/(C + H) ratios (<0.1). When the ratio was increased, larger radicals (CH 2 and CH 3) were emitted. In the eV energy range, the larger molecules were the dominant emitted species, whilst C atoms were emitted even at very low energies. A small percentage of Be was implanted in the C layer, and was found to reduce sputtering of the large molecules, whereas the emission of the small molecules and the C atoms was slightly reduced or remained unchanged.

Calculation of deuterium retention, re-emission and reflection from a tungsten material under D + ions irradiation with ACAT-DIFFUSE code

We calculated, with a dynamic Monte Carlo code ACAT-DIFFUSE, fluxes of thermal D 2 re-emission, reflection and segregated self-sputtering of D from a D + implanted wrought tungsten material during a time sequence of l00 eV D + implantation, post-implanted isothermal out-gassing and thermal desorption spectroscopy. The obtained result was in good agreement with an existing experiment if two different trap sites with de-trapping energy of 0.85 eV and 2.2 eV and density fraction of 0.05 D/W and 0.01 D/W were assumed to exist. The re-emission, reflection and self-sputtering fluxes in the implantation period were shown to be almost comparable. The integrated deuterium flux released in the same period was estimated. The amount of deuterium retained at 300 K was nearly six times higher than that at 473 K, which reflects the result that mobile atoms and atoms trapped in 0.85 eV trap existed abundantly at 300 K but scarcely at 473 K.

Focused ion beam implantation of Ga in Si and Ge: fluence‐dependent retention and surface morphology

AbstractFocused ion beam implantation of 30‐keV Ga+ ions in single‐crystalline Si and Ge was investigated by SIMS, using Cs+ primary ions for sputtering. Nine different implantation fluences ranging from 1 × 1013 to 1 × 1017 Ga+‐ions/cm2 were used, with implanted areas of 40 × 40 µm2. The Ga concentration distributions of these implants were determined by SIMS depth profiling. Such 30‐keV Ga implantations were also simulated by a dynamic Monte‐Carlo code that takes into account the gradual change of the near‐surface composition due to the Ga incorporation. In both approaches, an essentially linear increase of the Ga peak concentrations with fluence is found up to ∼1 × 1016cm−2; for higher fluences, the Ga content approaches a saturation level which is reached at about (1–2) × 1017cm−2. The measured and simulated peak concentrations of the Ga distributions are in good agreement. The most probable ranges obtained from the experiments correspond closely with the respective values from the simulations. The surface morphology caused by Ga+ implantation was investigated by atomic force microscopy (AFM). The AFM data indicate that for low fluences (&lt;3 × 1015cm−2) the surface within the implanted areas is growing outward (i.e. is swelling). For increasingly higher fluences, sputter‐induced erosion of the surface becomes dominant and distinct craters are formed for fluences above ∼1 × 1016cm−2. At the boundary of the implanted region a wall‐like structure is found to form upon Ga implantation; its height is growing with increasing fluence, reaching a value of ∼15 nm at 1 × 1017 Ga+‐ions/cm2. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Comparison of carbon deposition on tungsten between molecular dynamics and dynamic Monte Carlo simulation

To investigate the low-temperature plasma wall interactions in fusion devices, e.g., ITER, we have developed a molecular dynamics (MD) simulation code. The calculated results are compared with the dynamic Monte Carlo (MC) simulation. The W surface is bombarded with C atoms at the temperature of 10 eV–1keV. During the plasma exposure with low temperature, a thick C layer is formed on the W surface. At high plasma temperature W surface is eroded and the W-C mixed layer is formed. These results are consistent with the calculated ones with the dynamic MC code, EDDY [K. Ohya, Phys. Scr. T124, (2006) 70.]. Inhomogeneous deposition of C is calculated, which indicates that atomic scale roughness is important for the development of C deposition and material mixing.

Focused ion beam implantation of Ga in nanocrystalline diamond: Fluence-dependent retention and sputtering

Focused ion beam implantation of 30-keV Ga+ ions in nanocrystalline diamond films was investigated by secondary-ion mass spectrometry (SIMS), using Cs+ primary ions for sputtering. Nine different implantation fluences ranging from 1×1013 to 1×1017 Ga+-ions/cm2 were used, with implanted areas of 40×40μm2. The Ga concentration distributions of these implants were determined by SIMS depth profiling. Such 30-keV Ga implants were also simulated by a dynamic Monte–Carlo code that takes into account the gradual change of the near-surface composition due to the Ga incorporation. In both approaches, an essentially linear increase of the Ga peak concentrations with fluence is found up to ∼1×1016cm−2; for higher fluences, the Ga content approaches a saturation level which is reached at about 2×1017cm−2. The measured and simulated peak concentrations of the Ga distributions are in good agreement. The most probable range obtained from the experiments corresponds closely with the respective value from the simulations; the peak width determined by SIMS is somewhat broader, possibly caused by the roughness of the films.

Computer simulation of neutron transmutation doping of isotopically engineered heterostructures

Neutron transmutation doping (NTD) of silicon-based isotopically engineered heterostructures is a powerful technique for the creation of the semiconductor devices with the desired spatial distribution of 31P impurities that is defined by the initial distribution of 30Si nuclei.Computer simulation allows to study dopant distribution changes during NTD process and post-irradiation annealing and to determine appropriate annealing regimes. The initial distribution of the radiation defects was obtained by the dynamic Monte Carlo code DYTRIRS_N, while the subsequent annealing stage was simulated by the rate equations (RE) method. Concentrations of intrinsic defects and depth profiles of phosphorus atoms were obtained.

Depth profiling of ZrO 2/SiO 2/Si stacks—a TOF-SIMS and computer simulation study

This study is dedicated to a better understanding of the processes occurring under ion bombardment of ultra-thin ZrO 2/SiO 2/Si gate dielectric stacks. Complex-shaped depth profiles were obtained by using TOF-SIMS with dual beam (500 eV for sputtering and 10 keV for analysis) Ar + ions. The SIMS intensities of all the elements depend critically on the amount of oxygen at any moment of the sputtering process. Increased intensity is observed at the surface and at the ZrO 2/SiO 2 interface. A long tail of the Zr signal is present in the Si substrate, even after the second (SiO 2/Si) interface, and a double bump structure in the 90 Zr and ZrO dimer is observed, which is more pronounced with increasing thickness of the interfacial SiO 2 layer. Computer simulations using the dynamic Monte Carlo code (TRIDYN) are performed in order to distinguish the ion-bombardment-induced effects from changes in the ionization degree. The original code is extended with simple models for the ionization mechanism and for the molecular yield during sputtering. Oxygen preferential sputtering at the surface and ballistic transport of Zr towards and through the interface are clearly demonstrated, but there is also evidence that due to recoil implantation oxygen gets piled-up near the ZrO 2/SiO 2 interface.

Depth profiling of ZrO2/SiO2/Si stacks?a TOF-SIMS and computer simulation study

This study is dedicated to a better understanding of the processes occurring under ion bombardment of ultra-thin ZrO 2 /SiO 2 /Si gate dielectric stacks. Complex-shaped depth profiles were obtained by using TOF-SIMS with dual beam (500 eV for sputtering and 10 keV for analysis) Ar + ions. The SIMS intensities of all the elements depend critically on the amount of oxygen at any moment of the sputtering process. Increased intensity is observed at the surface and at the ZrO 2 /SiO 2 interface. A long tail of the Zr signal is present in the Si substrate, even after the second (SiO 2 /Si) interface, and a double bump structure in the 90 Zr and ZrO dimer is observed, which is more pronounced with increasing thickness of the interfacial SiO 2 layer. Computer simulations using the dynamic Monte Carlo code (TRIDYN) are performed in order to distinguish the ion-bombardment-induced effects from changes in the ionization degree. The original code is extended with simple models for the ionization mechanism and for the molecular yield during sputtering. Oxygen preferential sputtering at the surface and ballistic transport of Zr towards and through the interface are clearly demonstrated, but there is also evidence that due to recoil implantation oxygen gets piled-up near the ZrO 2 /SiO 2 interface.

Dynamic Behavior of Carbon Deposited on Tungsten Surface due to Carbon Ion Bombardment and Its Influence on Ion–Solid Interactions

The fluence evolution of C deposited on a W surface due to C ion impact and its influence on ion–solid interactions such as physical sputtering and ion reflection are studied using a dynamic Monte Carlo code, EDDY. In particular, attention is focused on their impact energy dependence. In the code, the fluence evolution of surface composition changes due to collisional mixing resulting from the ion impact and also due to thermal activated diffusion of the deposited C resulting from the elevated surface temperature is simulated along with the particle emissions from the C-contaminated W surface. The physical sputtering of the deposited C is enhanced by the reflective scattering collision in the vicinity of the surface, which results from a difference between the C ion reflection from C and that from W. The energy dependence of the physical sputtering is dependent upon the fluence amount. As the energy increases, the physical sputtering is enhanced, and it is then suppressed above a certain impact energy which varies depending on the fluence amount. This results from the difference between a mixed layer of C and W formed at a low fluence and a C film formed on the W surface at a high fluence. In addition, its surface temperature dependence is strongly dependent upon the fluence amount. For a low fluence the physical sputtering is suppressed with increasing surface temperature, whereas it is enhanced for a high fluence. This is attributed to a remarkable growth of the mixed layer due to the diffusion of the deposited C.

Non-thermodynamic approach to including bombardment-induced post-cascade redistribution of point defects in dynamic Monte Carlo code

The redistribution of the elements as a result of atomic relocations produced by the ions and the recoils due to the ballistic and transport processes is investigated by making use of a dynamic Monte Carlo code. Phenomena, such as radiation-enhanced diffusion (RED) and bombardment-induced segregation (BIS) triggered by the ion bombardment may also contribute to the migration of atoms within the target. In order to include both RED and BIS in the code, we suggest an approach which is considered as an extension of the binary collision approximation, i.e. it takes place “simultaneously” with the cascade and acts as a correction to the particle redistribution for low energies. Both RED and BIS models are based on the common approach to treat the transport processes as a result of a random migration of point defects (vacancies and interstitials) according to a probability given by a pre-defined Gaussian. The models are tested and the influence of the diffusion and segregation is illustrated in the cases of 12 keV 121Sb + implantation at low fluence in SiO 2/Si substrate and of self-sputtering of Ga + ions during profiling of SiO 2/Si interfaces.

Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer

Using the dynamic Monte Carlo code, ACAT-DIFFUSE, the oxide sputtering and the SIMS depth profiling of a multilayered thin film sample was investigated. The ACAT-DIFFUSE code is based on the binary collision approximation, taking into account the generation of interstitial atoms and vacancies, annihilation of vacancies, diffusion and the relaxation of target materials according to the packing condition which include not only beam and target particles but also defects (interstitial atoms and vacancies). The observed shift of the delta layer peak to the surface in SIMS depth profiles can be reproduced by the ACAT-DIFFUSE simulation. It is found that this peak shift is mainly due to the relaxation or expansion caused by defects produced behind the delta layer, not due to preferential sputtering.

Segregation of gallium at SiO2/Si interfaces during sputtering with Ga+ ions: experimental and computer simulation study

The sputtering of SiO2/Si interfaces with gallium ions was studied both experimentally by using secondary neutral mass spectrometry (SNMS) and by computer simulations by means of a dynamic Monte Carlo code. Oscillations of the gallium signal (from implanted primary ions) at the interface between the SiO2 and Si layers were observed. By means of computer simulations, it was shown that cascade effects alone cannot explain the experimental depth profiles. A model that includes additional defect transport phenomena such as bombardment-induced segregation is proposed and incorporated in an existing dynamic Monte Carlo computer code. The simulations with the new code give rise to profiles that are comparable with the experimental ones, confirming the correctness of the chosen approach.

Mass Segregation in Globular Clusters

We present the results of a new study of mass segregation in two-component star clusters, based on a large number of numerical N-body simulations using our recently developed dynamical Monte Carlo code. Specifically, we follow the dynamical evolution of clusters containing stars with individual masses m_1 as well as a tracer population of objects with individual masses m_2=\mu m_1, using N=10^5 total stars. For heavy tracers, which could represent stellar remnants such as neutron stars or black holes in a globular cluster, we characterize in a variety of ways the tendency for these objects to concentrate in or near the cluster core. In agreement with simple theoretical arguments, we find that the characteristic time for this mass segregation process varies as 1/\mu. For models with very light tracers (\mu <~ 10^-2), which could represent free-floating planets or brown dwarfs, we find the expected depletion of light objects in the cluster core, but also sometimes a significant enhancement in the halo. Using these results we estimate the optical depth to gravitational microlensing by planetary mass objects or brown dwarfs in typical globular clusters. For some initial conditions, the optical depth in the halo due to very low-mass objects could be much greater than that of luminous stars. If we apply our results to M22, using the recent null detection of Sahu, Anderson, & King (2001), we find an upper limit of ~25% at the 63% confidence level for the current mass fraction of M22 in the form of very low-mass objects.

Simulation on SIMS depth profiling of delta-doped layer including relaxation caused by defects

Using the dynamic Monte Carlo (MC) code, ACAT-DIFFUSE, the SIMS depth profiling of a multilayered thin film (Ta 2O 5 (18 nm)/SiO 2 (0.5 nm)) sample was investigated. The ACAT-DIFFUSE code is based on the binary collision approximation, taking into account the generation of interstitial atoms and vacancies, annihilation of vacancies, diffusion of interstitial atoms and primary ions and the relaxation of target materials according to the packing condition which include not only beam and target particles but also defects (interstitial atoms and vacancies). The observed 1–3 nm shift of the delta layer peak to the surface in SIMS depth profiles can be reproduced by the ACAT-DIFFUSE simulation. It is found that this peak shift is mainly due to the relaxation or expansion caused by defects produced behind the delta layer, not due to the collision mixing which results mainly in broadening the observed delta layer peak. Therefore, as ion energy decreases or the angle of incidence becomes large, the peak shift becomes small, because the total amount of defects produced behind the delta layer is small before the delta layer is sputtered off.