Validation of Monte Carlo simulation of 6 MV photon beam produced by Varian Clinac 2100 linear accelerator using BEAMnrc code and DOSXYZnrc code

The Monte Carlo model for the photon-beam output from the Varian Clinac 2100 linear accelerator was validated to compare the calculated to measured PDD and beam dose profiles The Monte Carlo calculation method is considered to be the most accurate method for dose calculation in radiotherapy. The objective of this study is to build a Monte Carlo geometry of Varian Clinac 2100 linear accelerator as realistically as possible. The Monte Carlo codes used in this work were the BEAMnrc code to simulate the photons beam and the DOSXYZnrc code to examinate the absorbed dose in the water phantom. We have calculated percentage depth dose (PDD) and beam profiles of the 6 MV photon beam for the 6 × 6 cm², 10 × 10 cm² and 15 × 15 cm² field sizes. We have used the gamma index technique for the quantitative evaluation to compare the measured and calculated distributions. Good agreement was found between calculated PDD and beam profile compared to measured data. The comparison was evaluated using the gamma index method and the criterions were 3% for dose difference and 3 mm for distance to agreement. The gamma index acceptance rate was more than 97% of both distribution comparisons PDDs and dose profiles and our results were more developed and accurate. The Varian Clinac 2100 linear accelerator was accurately modeled using Monte Carlo codes: BEAMnrc and DOSXYZnrc codes package.     

Monte-Carlo simulations of Al2O3 dosimetry in uniform MV photon beams: Influence of field and detector size

This work was to evaluate the absorbed dose to different sizes Al₂O₃ dosimeter in uniform MV photon beams using Monte Carlo simulation. The absorbed dose ratio factor f_md of Al₂O₃ dosimeters was calculated. The incident beams included 4 MV–24 MV X-rays using Mohan's spectra with different field sizes. Results show that the maximum variation of f_md due to different dosimeter sizes is 5%. As the field diameter increases from 1 cm to 3 cm, the difference of f_md can be up to 8%. The results of this work show that the effect of dosimeter size and the field size can't be neglected when using Al₂O₃ dosimeter.     

Energy spectra in water for the 6 MV X-ray therapeutic beam generated by Clinac-2300 linac

There is a lack of extensive data comprising energy spectra of therapeutic beams used in teleradiotherapy, generated by medical linear accelerators. In particular there is a lack of the data for energy spectra in water. However, the spectra in water differ from those in air significantly because of strong photon scattering processes. The aim of this paper was the presentation of the wide range of detailed data for the 6 MV X-ray therapeutic beams from a medical linear accelerator Clinac-2300 by Varian. The presented data were derived by the use of Monte Carlo computer simulations (GEANT4 code). The performed investigations indicate that shapes of the spectra, total number of photon registered in a bin as well as mean energy of the considered beam depend on a depth in water, on a distance from the central-axis of the beam and on a radiation field size. However, shapes of the spectra as well as the beam mean energy does not depend on a bin size, independently of a depth in water and a radiation field whereas total number of photon registered in a bin is related to a bin size. Majority of the presented results were obtained for a cylindrical 1.41 cm³ bin with the radius of 1.5 cm. The obtained data are very useful for the accurate absorbed depth-dose determination particularly outside the reference conditions, for advanced treatment planning systems, for constructors of medical accelerators etc.     

Response of CaSO4:Dy phosphor based TLD badge system to high energy electron beams from medical linear accelerator and estimation of whole body dose and skin dose

Response of thermoluminescent dosimeter (TLD) badge based on CaSO₄:Dy phosphor to high energy electron beams from medical linear accelerators was simulated using FLUKA Monte Carlo code and experimentally verified. This study was carried out in order to determine the response of TL discs under different filter regions of the TLD badge and their ratios under different irradiation conditions in the energy range 6–20 MeV of high energy electron beams. It was found that the response of TL disc under metal filters of the TLD badge (D1) is always higher than the response of the TL discs under Polystyrene filter (D2) and open window (D3) and its response was found to decrease with increase in the energy of the electron beam. Estimation of whole body dose and skin dose including its error was carried out as an extension of the present study in case of accidental exposure of radiation worker to high energy electron beam.     

Characterization of miniature RAD-HARD silicon diodes as dosimeters for small fields of photon beams used in radiotherapy

The dosimetric response characterization and beam data acquisition performance of a miniature Float Zone (FZ) silicon diode for photon beams was investigated using Novalis TX linear accelerator (Varian Medical Systems^®). In all measurements the unbiased diode operated in a short-circuit mode, connected to the input of a Keithley 6517B electrometer using a water phantom. For photon beams of the 6 and 15 MV the results presented good repeatability (coefficient of variation ≤1.6%), measured through switching on/off the photon beams. Moreover, the diode showed a quite linear response, given by the charge versus absorbed dose, with charge sensitivities higher than 6.9 nC/Gy. The output factor, percentage depth dose profile (PDD) and transversal dose profile (TDP) were also measured in a water phantom. For small field sizes, the output factor values using the FZ diode were compared with measurements obtained with a SFD (Stereotactic Field Diode) commercial diode and the differences were 5.4%, 2.5% and 1.3% for the field sizes of 1 × 1, 2 × 2 and 3 × 3 cm². For larger field sizes (≥4 × 4 cm²), the maximum difference found was 0.7% in comparison with values obtained with a CC13 ionization chamber. Thus, the result demonstrates that the unshielded FZ diode has the potential to be used for measuring of, as it performed acceptably well for both small and large field sizes. The TDP experimental results obtained with the FZ diode for field sizes of: 1 × 1 cm², 2 × 2 cm² and 4 × 4 cm² are in agreement with experimental results acquired with several commercial detectors. Through the TDP study, the comparison of the field penumbra size confirmed the excellent spatial resolution of the miniature diode. However, the PDD study, requires further investigation.     

Effective radius of curvature of Hermite–Gaussian array beams

Analytical expressions for the effective radius of curvature, R, of Hermite–Gaussian (H–G) array beams propagating in free space for both coherent and incoherent combinations are derived. It is shown that for the two types of beam combination a minimum of the effective radius of curvature, R_min, appears as the propagation distance z increases. For the coherent combination, R is larger than that for the incoherent combination. The position z_min where the effective radius of curvature reaches its minimum is further away from the source plane for the coherent combination than that for the incoherent combination. For the two types of beam combination, R and z_min increase with increasing beam number, increasing beam separation distance, increasing waist width, and decreasing beam order and wavelength. In particular, the R of single H–G beams is always smaller than that of H–G array beams; the R of Gaussian array beams is always larger than that of H–G array beams.     

A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices

The measure of long-term memory is important for the study of economic and financial time series. This paper estimates the Hurst exponent from a Scaled Variance Ratio model for 17 commodity price series under the efficient market null H₀:H=0.5. The distribution about the estimates of H are obtained from 90%, 95% and 99% confidence intervals generated from 20,000 Monte Carlo replications of a geometric Brownian motion. The results show that the scaled variance ratio provides a very good and stable estimate of the Hurst exponent, but the estimates can be quite different from the measure obtained from rescaled range or R–S analysis. In general commodity prices are consistent with the underlying assumption of a geometric Brownian motion.     

Transmission of ∼10 keV electron beams through thin ceramic foils: Measurements and Monte Carlo simulations of electron energy distribution functions

Electron beams with particle energy of ~10 keV were sent through 300 nm thick ceramic (Si₃N₄ + SiO₂) foils and the resulting electron energy distribution functions were recorded using a retarding grid technique. The results are compared with Monte Carlo simulations performed with two publicly available packages, Geant4 and Casino v2.42. It is demonstrated that Geant4, unlike Casino, provides electron energy distribution functions very similar to the experimental distributions. Both simulation packages provide a quite precise average energy of transmitted electrons: we demonstrate that the maximum uncertainty of the calculated values of the average energy is 6% for Geant4 and 8% for Casino, taking into account all systematic uncertainties and the discrepancies in the experimental and simulated data.     

Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

The analytical expressions for the effective Rayleigh range z_R of Gaussian array beams in turbulence for both coherent and incoherent combinations are derived. It is shown that z_R of Gaussian array beams propagating through atmospheric turbulence depends on the strength of turbulence, the array beam parameters and the type of beam combination. For the coherent combination z_R decreases due to turbulence. However, for the incoherent combination there exists a maximum of z_R as the strength of turbulence varies. The z_R of coherently combined Gaussian array beams is larger than that of incoherently combined Gaussian array beams, but for the coherent combination case z_R is more sensitive to turbulence than that for the incoherent combination case. The larger the beam number is, the longer z_R is, and the more z_R is affected by turbulence. For the coherent combination z_R is not monotonic versus the relative beam separation distance, and the effect of turbulence on z_R is appreciable within a certain range of the relative beam separation distance.     

Photon beam softening coefficients evaluation for a 6 MeV photon beam for an aluminum slab: Monte Carlo study using BEAMnrc Code,DOSXYZnrc Code,and BEAMDP code

Determination and understanding the photon beam attenuation by the photon beam modifier and the radiation beam softening for clinical use is more important part of material study for the beam modifier enhancements and the linac improvements. A Monte Carlo model was used to simulate 6 MeV photon beams from a Varian Clinac 2100 accelerator with the flattening filter and the later was replaced by the aluminum slab with variable thickness. The Monte Carlo geometry was validated by a gamma index acceptance rate of 99% in PDD and 98% in dose profiles, the gamma criteria was 3% for dose difference and 3 mm for distance to agreement. The purpose was to investigate aluminum material attenuation and beam softening coefficients as a function of the inserted aluminum slab thickness and of off-axis distance. The attenuation and beam softening coefficients were not identical for the same off-axis distance and they varied as a function of aluminum slab thickness. The results of our study were shown that the beam softening coefficients were varied with thickness beam modifier material used for beam softening and the off-axis distance inside the irradiation field. Thereafter, the softening coefficient a ₁ have a maximum of 2.5 × 10^–1 cm^–1 for the aluminum slab thickness of 1 mm, 1.4 × 10^–1 cm^–1 for the aluminum slab thickness of 1.5 mm and 4.47 × 10^–2 cm^–1 for the aluminum slab thickness of 2 mm. The maximum of the second softening coefficient a ₂ was 1.02 × 10^–2 cm^–2 for the aluminum slab thickness of 1 mm, was 1.92 × 10^–2 cm^–2 for the aluminum slab thickness of 1.5 mm and was 1.93 × 10^–2 cm^–2 for the aluminum slab thickness of 2 mm. Our study can be a basic investigation of photon beam softening material that will be used in the future linac configuration and also in the photon beam modifiers.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

Axially magnetized electron–positron and electron plasma competition on the self focusing of intense laser beam

The spot-size evolution of circularly polarized intense laser beam propagating through the axially magnetized electron–positron (EP) and electron plasmas is discussed, in mildly relativistic and weakly non-linear (a² ? 1) regime. The non-linear current density source terms are obtained by making used of the perturbative technique. The variational principle approach method is applied to the solution of the non-linear Schrodinger wave equation. It is shown that the laser beam spot size decreases for the left and increases for the right handed polarized beams with increasing the external magnetic field, owing to the beam passages inside the electron plasma. Furthermore, it is revealed that the self focusing property strongly enhanced in the EP plasma in comparison to the electron plasma. Moreover, self focusing of linearly polarized laser beam is investigated for EP plasma by superposition of the right and left circularly polarized beams.     

Propagation properties of Lorentz beam in uniaxial crystals orthogonal to the optical axis

The properties of Lorentz beams propagating in uniaxial crystals orthogonal to the optical axis are studied. The diffraction field components and effective beam sizes of the Lorentz beams are derived in analytical forms. Numerical results show that, upon propagating in uniaxial crystals, a Lorentz beam loses its initial Lorentz type distribution. Also, after propagating for sufficient distances, the transverse components would finally convert into a specific four-petal profile with an axial shadow, which may find applications in the optical trapping of particles. It also shows that the Lorentz beam parameters w_0x, w_0y and the ratios of refractive indices have strong influences on the diffraction field components and on the effective beam sizes when propagating in uniaxial crystals.     

The positive charging effect of dielectric films irradiated by a focused electron beam

Space charge and surface potential profiles are investigated with numerical simulation for dielectric films of SiO₂ positively charged by a focused electron beam. By combining the Monte Carlo method and the finite difference method, the simulation is preformed with a newly developed comprehensive two-dimensional model including electron scattering, charge transport and trapping. Results show that the space charge is distributed positively, like a semi-ellipsoid, within a high-density region of electrons and holes, but negatively outside the region due to electron diffusion along the radial and beam incident directions. Simultaneously, peak positions of the positive and negative space charge densities shift outwards or downwards with electron beam irradiation. The surface potential, along the radial direction, has a nearly flat-top around the center, abruptly decreases to negative values outside the high-density region and finally increases to zero gradually. Influences of electron beam and film parameters on the surface potential profile in the equilibrium state are also shown and analyzed. Furthermore, the variation of secondary electron signal of a large-scale integration sample positively charged in scanning electron microscopic observation is simulated and validated by experiment.     

Evaluation of the dosimetric characteristics of a radiophotoluminescent glass dosimeter for high-energy photon and electron beams in the field of radiotherapy

We aimed to evaluate the suitability of a glass dosimeter (GD) for high-energy photon and electron beams in experimental and clinical use, especially for radiation therapy. We examined the expanded dosimetric characteristics of GDs including dose linearity up to 500 Gy, uniformity among GD lots and for individual GDs, the angular dependence, and energy dependence of 4 therapeutic x-ray qualities. In addition, we measured the dosimetric features (dose linearity, uniformity, angular dependence, and energy dependence) of the GD for electron beams of 10 different electron energy qualities. All measurements with the exception of dose linearity for photon beam were performed in a water phantom. For high-energy photon beams, dose linearity has a linear relationship for a dose ranging from 1 to 500 Gy with the coefficient of determination; R² of 0.998. The uniformity of each GD of dose measurements was within ±0.5% for four GD lots and within ±1.2% for 80 GDs. In terms of the effects of photon beam angle, lower absorbed doses of within 1.0% were observed between 60° and 105° than at 90°. The GD energy dependence of 4 photon beam energy qualities was within ±2.0%. On the other hand, the result of the dose linearity for high-energy electron beams showed well fitted regression line with the coefficient of determination; R² of 0.999 between 6 and 20 MeV. The uniformity of GDs exposed to the nominal electron energies 6, 9, 12, 16, and 20 MeV was ±1.2%. In terms of the angular dependence to electron beams, absorbed doses were within 2.0% between 60° and 105° than at 90°. In evaluation of the energy dependence of the GD at nominal electron energies between 5 and 20 MeV, we obtained responses between 1.1% and 3.5% lower than that for a cobalt-60 beam. Our results show that GDs can be used as a detector for determining doses when a high-energy photon beam is used, and that it also has considerable potential for dose measurement of high-energy electron beam.     

Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams

Illumination uniformity of a spherical capsule directly driven by laser beams has been assessed numerically. Laser facilities characterized by N _D  = 12, 20, 24, 32, 48 and 60 directions of irradiation with associated a single laser beam or a bundle of N _B laser beams have been considered. The laser beam intensity profile is assumed super-Gaussian and the calculations take into account beam imperfections as power imbalance and pointing errors. The optimum laser intensity profile, which minimizes the root-mean-square deviation of the capsule illumination, depends on the values of the beam imperfections. Assuming that the N _B beams are statistically independents is found that they provide a stochastic homogenization of the laser intensity associated to the whole bundle, reducing the errors associated to the whole bundle by the factor \hbox{1/N_B^1/21/N_{B}^{1{/}2}} 1 / N B 1 / 2 , which in turn improves the illumination uniformity of the capsule. Moreover, it is found that the uniformity of the irradiation is almost the same for all facilities and only depends on the total number of laser beams N _tot  = N _D  × N _B .     

Monte Carlo simulations of the production of neutrons at iThemba LABS

FLUKA Monte Carlo radiation transport code has been used to simulate neutron fluence spectrum at iThemba LABS neutron beam facility. Neutron beams with energy up to 200 MeV can be produced using different targets such as ⁷Li, ⁹Be and ¹²C bombarded with monoenergetic protons from the Separated-Sector Cyclotron. Simulated results at 66 MeV were compared with measured data. Different neutron emission angles with respect to the beam axis as well as the neutron background at different positions have been investigated.     

A linear stability analysis for nonlinear,grey, thermal radiative transfer problems

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens–Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ? 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.     

Theoretical study of the magnetic and magnetocaloric properties of the ZnFe3N antiperovskite

The antiperovskite ZnFe₃N is studied by using density functional theory calculations and Monte Carlo simulation. Based on the electronic and magnetic properties, it is found that ZnFe₃N behaves as a ferromagnetic metallic material. The exchange interactions and the magnetic anisotropy, defined as the Hamiltonian parameters of the studied system, are calculated and used in the Monte Carlo study. The second order transition at a Curie temperature T_c = 760K, reviled experimentally in a previous work, has been confirmed. The magnetic entropy change and the relative cooling power, under various applied magnetic fields are analyzed in order to evaluate the magnetocaloric effect of ZnFe₃N. The results suggest that ZnFe₃N is a good candidate for the magnetic refrigeration applications.     

Basic thermoluminescent and dosimetric properties of Al2O3:C irradiated by pulse intensive electron beam

The effect of deep traps filled by a pulse electron beam on the thermoluminescent (TL) properties in Al₂O₃:C dosimetric crystals is studied. When the deep traps are filled, the dosimetric peak at 170 °C acquires a double-peak structure not present in the initial samples. The effect of the population of the deep centers having various nature (electron or hole traps) and energy depth on the shape of the dosimetric TL peak structure is analyzed. An assumption is made that in the temperature ranges of 350–500 °C and 650–750 °C, electron traps are emptied, whereas at T = 500–650 °C hole traps are emptied. The possibility of using the TL associated with deep traps in high-dose dosimetry of pulse electron beams is shown.