Plane-parallel Beams Research Articles

Slipping instability of an inhomogeneous relativistic electron beam

The charged particle beams, such as electrons, ions, and plasma compression flow, have received considerable attention due to their applications in science and technology; therefore, studying the stability of these beams is of particular importance. Here, we examine theoretically the stability properties of a cold relativistic electron beam with a transverse velocity shear and non-uniform density profile. We consider a plane-parallel beam propagating along an external magnetic field and evaluate its macroscopic equilibrium state. We derive the dispersion relation of the slipping instability based on the linear electrodynamics of an inhomogeneous plasma and kinetic theory. In this model, the oscillation spectrum and the growth rate are derived by using the eikonal equation and the quasi-classical quantization rule. A linear velocity shear and a non-linear density gradient are assumed. Furthermore, we analyze numerically the dispersion relation of the slipping instability. The impacts of the inhomogeneity parameter and the relativistic factor on the properties of the slipping instability are discussed.

Reduction of recombination effects in large plane parallel beam monitors for FLASH radiotherapy with scanned ion beams

Purpose:Radiotherapy escalating dose rates above 50Gys−1, might offer a great potential in treating tumours while further sparing healthy tissue. However, these ultra-high intensities of FLASH-RT lead to new challenges with regard to dosimetry and beam monitoring. FLASH experiments at HIT (Heidelberg Ion Beam Therapy Center) and at GSI (GSI Helmholtz Centre for Heavy Ion Research) have shown a significant loss of signal in the beam monitoring system due to recombination effects. To enable accurate beam monitoring, this work investigates the recombination loss of different fill gases in the plane parallel ionisation chambers (ICs). Methods:Therefore, saturation curves at high intensities were measured for the currently used fill gases Ar/CO2 (80/20) and pure He and also for He/CO2 mixtures as alternative fill gases. Furthermore, breakdown voltages and ion mobilities were measured in ICs filled with He/CO2 mixtures. A numerical model for volume recombination in plane parallel ionisation chambers was developed and implemented in Python. This includes a novel simulation method of the space charge effect from the charge carriers in the detector volume and predicts a significant effect on the electric field for high intensity beams. Results:Even at high intensities the He/CO2 mixtures allow operation of the ICs at an electric field strength of 2 kVcm−1 or more which reduces recombination to negligible levels at intensities larger than 3 × 101012C-ions per second. Our measurements show that added fractions of CO2 to He decrease the ion mobility in the fill gas but significantly increase the breakdown voltage in the ICs compared to pure He.

Distance-dependency of the D2O-moderated 252Cf spectrum and influence on the calibration factors

The D2O-moderated 252Cf is a non-point neutron source used as a calibration facility for measuring devices. The Bonner spheres spectrometer (BSS) is one of the common instruments for neutron spectrometry. Due to having a non-point source, the neutron spectrum depends on distance. On the other hand, because of the detector and source size, there is a deviation in BSS reading from that expected according to the inverse square law. In the present study, the Monte Carlo simulations were applied to investigate the effect of beam divergence on the response of BSS. The average energy of neutrons reaching the surface of the BSS was dependent on distance, and its value increases with increasing distance. Subsequently, the response of the BSS under plane-parallel beams was also dependent on the distance. Thus, for 2″, 3″, and 5″ spheres, with increasing distance, the response decreased, and for larger spheres, it was the opposite. The calculated geometry correction factors for 12″, 15″ and 18″ spheres were less than one at all distances; however, for other spheres, at closer distances they were higher than one, and gradually reduced to below the one by increasing the distance.

Design of an optical system for a laser beam shaping system based on aspheric polymer lenses

Conversion of laser beam profiles is required in a wide variety of applications, such as producing a plane-parallel beam with a uniform intensity distribution. Traditional collimator systems are not capable of modifying the laser beam profile. High-quality uniformity of light can conveniently be achieved using high-order aspheric lens surfaces, which require expensive technology and equipment when they are manufactured from optical glass. A technique for using polymer optical materials for lens fabrication enables surfaces of any complexity to be obtained. In this paper, we describe the design of an aspheric-polymer-lens laser beam shaping system using ZEMAX software. We compare the quality parameters for systems using polymer optics and glass optics and provide recommendations for prudent selection of materials.

Sub-Doppler Spectroscopy of Excited Atoms in a Multilayer Gas Cell

The potential for spectroscopy in a multilayer cell with rarefied gas medium is theoretically investigated where said cell can be used as a compact analog of a large number of plane-parallel beams of atoms (or molecules) in an optically excited quantum level. In particular, this situation occurs for metastable and highly excited long-lived Rydberg states of atoms and molecules. Velocity selection of atoms (molecules) excited to said quantum level by broadband optical pumping was found to be efficient because of their characteristic transit and collisional relaxation in said cell. Sub-Doppler resonances at the optical transition frequencies from a given level were narrow as a result of the selection when the monochromatic probe light beam was absorbed.

Analysis of Plane-Parallel Electron Beam Propagation in Different Media by Numerical Simulation Methods

Simulation by the Monte Carlo method is widely used to calculate the character of ionizing radiation interaction with substance. A wide variety of programs based on the given method allows users to choose the most suitable package for solving computational problems. In turn, it is important to know exactly restrictions of numerical systems to avoid gross errors. Results of estimation of the feasibility of application of the program PCLab (Computer Laboratory, version 9.9) for numerical simulation of the electron energy distribution absorbed in beryllium, aluminum, gold, and water for industrial, research, and clinical beams are presented. The data obtained using programs ITS and Geant4 being the most popular software packages for solving the given problems and the program PCLab are presented in the graphic form. A comparison and an analysis of the results obtained demonstrate the feasibility of application of the program PCLab for simulation of the absorbed energy distribution and dose of electrons in various materials for energies in the range 1–20 MeV.

Narrowing of sub-Doppler saturated-absorption resonances in multilayer gas cells

We have studied theoretically nontrivial specific features of sub-Doppler resonances of saturated absorption in a multilayer gas cell with a rarefied gas medium, which is a compact analog of a large number of plane-parallel atomic beams. Spatially separated saturating and probing monochromatic laser beams that co- and counterpropagate (at the same frequency) in this cell have been considered. In this situation, the action of the light radiation of the saturating beam on the probing beam is determined by optically pumped atoms that fly between the beams under conditions that the longitudinal components of their velocities experience selection due to a specific geometry of the multilayer cell. Such a selection leads to a narrowing of the sub-Doppler resonance in the absorption of the probing beam and decreases the difference between the structures of this resonance for the cases of co- and counterpropagation of the saturating radiation. We have found that, in the considered multilayer cell, the effective width of the sub-Doppler resonance can be smaller (by a factor of about 1.5) than the extremely narrow characteristic width of the well-known Lamb dip in spectroscopy of saturated absorption in the standard gas cell. Results of this study can be used in atomic spectroscopy of ultrahigh resolution and for the laser-frequency stabilization.

Implementation of Boundary Conditions in Discrete Element Modeling of Rock Cutting under Pressure

The article presents an algorithm to implement the confining pressure at a sample’s boundary when modeling a process of rock cutting with a single cutter under pressure. The dynamic process of cutting is modeled using a discrete element method in which the cutter geometry is presented by rigid walls and the rock sample is approximated as a set of separated spherical particles interacting in accord with a given law. The algorithm unifies two approaches to identify boundary spheres and setting forces that act on them. In the areas with particles of big radii, the plane-parallel beam method (shining lamp) is employed, while in the area of cutting that is made of smaller elements, the boundary is identified using the α-shape algorithm.

Investigation of the effects of beam divergence on the response of neutron voluminous detectors

In the present study, the Monte Carlo calculations were carried out to evaluate the effect of beam divergence on the response of a spherical thermal-neutron counter at the center of a spherical moderating assembly. A model of 3He detector surrounded with 10 in. diameter polyethylene sphere was utilized to calculate the point isotropic and plane-parallel beams responses of twelve different energies, and obtain the geometry factor and its parameters (a 4 and a 5) based on general formulations. Furthermore, for 2, 3, 5, 8, 10 and 15 in. spheres exposed to three different radionuclide neutron sources with various energy spectra, the parameters of geometry factor were quantified, as a function of moderator radius and neutron energy. Obtained results based on this method were compared with the experimental data for one specific source. Finally, by these parameters the obtained values of the geometry factor based on two formulations were compared to each other.

Dependence of Monte Carlo microdosimetric computations on the simulation geometry of gold nanoparticles

Recently, interactions of x-rays with gold nanoparticles (GNPs) and the resulting dose enhancement have been studied using several Monte Carlo (MC) codes (Jones et al 2010 Med. Phys. 37 3809–16, Lechtman et al 2011 Phys. Med. Biol. 56 4631–47, McMahon et al 2011 Sci. Rep. 1 1–9, Leung et al 2011 Med. Phys. 38 624–31). These MC simulations were carried out in simplified geometries and provided encouraging preliminary data in support of GNP radiotherapy. As these studies showed, radiation transport computations of clinical beams to obtain dose enhancement from nanoparticles has several challenges, mostly arising from the requirement of high spatial resolution and from the approximations used at the interface between the macroscopic clinical beam transport and the nanoscopic electron transport originating in the nanoparticle or its vicinity. We investigate the impact of MC simulation geometry on the energy deposition due to the presence of GNPs, including the effects of particle clustering and morphology. Dose enhancement due to a single and multiple GNPs using various simulation geometries is computed using GEANT4 MC radiation transport code. Various approximations in the geometry and in the phase space transition from macro- to micro-beams incident on GNPs are analyzed. Simulations using GEANT4 are compared to a deterministic code CEPXS/ONEDANT for microscopic (nm–µm) geometry. Dependence on the following microscopic (µ) geometry parameters is investigated: µ-source-to-GNP distance (µSAD), µ-beam size (µS), and GNP size (µC). Because a micro-beam represents clinical beam properties at the microscopic scale, the effect of using different types of micro-beams is also investigated. In particular, a micro-beam with the phase space of a clinical beam versus a plane-parallel beam with an equivalent photon spectrum is characterized. Furthermore, the spatial anisotropy of energy deposition around a nanoparticle is analyzed. Finally, dependence of dose enhancement on the number of GNPs in a finite cluster of nanoparticles is determined. Simulations were performed for 100 nm GNPs irradiated in water phantom by various monoenergetic (11 keV–1 MeV) and spectral (50 kVp) sources. The dose enhancement ratio (DER) is very sensitive to the specific simulation geometry (µSAD, µS, µC parameters) and µ-source type. For a single GNP the spatial distribution of DER is found to be nearly isotropic with limited magnitude and relatively short range (∼100–200 nm for DER significantly greater than 1). For a cluster of GNPs both the magnitude and range are found much greater (∼1–2 µm). The relation between DER for a cluster of GNPs and a single GNP is strongly nonlinear. Relatively strong dependence of DER on the simulation micro-geometry cautions future studies and the interpretation of existing MC results obtained in different simulations geometries. The nonlinear relation between DER for a single and multiple GNPs suggests that parameters such as the number of adjacent nanoparticles per cell and the distances between the GNPs and the cellular target may be important in assessing the biological effectiveness associated with GNP.

Sci-Sat AM: Brachy - 02: Extracting Wair from the 1976 electron beam measurements of domen and lamperti.

The average energy expended by an energetic electron to create an ion pair in air, Wair is an important quantity in radiation dosimetry. The data obtained by Domen and Lamperti using electron beams in the energy range from 15 to 50 MeV can be used to extract a value for Wair if the electron stopping powers of graphite and air are assumed to be known. We use Monte Carlo techniques to reanalyze these data and obtain a new estimate for the value of Wair Using the EGSnrc Monte Carlo and its associated user codes, as well as the best availabl-e stopping power data for graphite, we calculate the perturbation effects due to the calorimeter and ionization chamber and the effect of extrapolating from scattered to plane-parallel beams. Without further adjustments, the extracted values of Wair show a significant trend as the mean electron energy decreases. We show that part of this trend can be attributed to an incorrect value of the density assigned to the graphite absorbers and part to the likelihood that the nominal energy assigned to the low-energy electron beams is not correct. Using all the data, we obtain a value for Wair of 33.84 eV per ion pair with a relative standard uncertainty of 0.4 %. This result serves to complement values obtained using 60 Co γ-rays, for which the value of the mean excitation of graphite contributes significantly to the uncertainty.

Geometry corrections for cylindrical neutron area survey meters

MCNP calculations have been performed to investigate the effects of beam divergence on the response of selected cylindrical neutron area survey meters irradiated by selected neutron sources. By comparing the results to calculations performed using plane-parallel beam irradiations, geometry correction factors have been calculated that can be applied to instrument calibrations. The results indicate that the effective centres of cylindrical detectors may not lie on the axis of symmetry, as previously assumed.

A phantom for effective dose measurement: organ dose distribution assessment based on a numerical approach

ICRP 60 has defined the personal dose equivalent Hp(10) as an estimator of the effective dose E. Personal dosimeters, worn on the trunk, allow the measurement of the quantity Hp(10). However, the characteristics of the instrumentation and the definition of Hp(10) itself can generate differences between the two quantities, depending on the energies and on the directional distribution of the incident radiation. The objective of this study is to evaluate the possibility of the measurement of the effective dose E using an instrumented anthropomorphic phantom at workplaces. In the first step of this study, calculations of the effective dose for standard configurations are made using the Monte Carlo code MCNPX. This paper presents the model of the numerical anthropomorphic phantom and the results for whole body irradiations by broad unidirectional or plane-parallel photon beams. The results agree with those calculated by Zankl et al., so confirming the good suitability of the code and the phantom used. Then, the dose distributions inside some organs are presented and the locations of future detectors for the instrumented phantom are discussed.

Comparison of dose calculation algorithms in phantoms with lung equivalent heterogeneities under conditions of lateral electronic disequilibrium

An extensive set of benchmark measurement of PDDs and beam profiles was performed in a heterogeneous layer phantom, including a lung equivalent heterogeneity, by means of several detectors and compared against the predicted dose values by different calculation algorithms in two treatment planning systems. PDDs were measured with TLDs, plane parallel and cylindrical ionization chambers and beam profiles with films. Additionally, Monte Carlo simulations by means of the PENELOPE code were performed. Four different field sizes (10 x 10, 5 x 5, 2 x 2, and 1 x 1 cm2) and two lung equivalent materials (CIRS, p(w)e=0.195 and St. Bartholomew Hospital, London, p(w)e=0.244-0.322) were studied. The performance of four correction-based algorithms and one based on convolution-superposition was analyzed. The correction-based algorithms were the Batho, the Modified Batho, and the Equivalent TAR implemented in the Cadplan (Varian) treatment planning system and the TMS Pencil Beam from the Helax-TMS (Nucletron) treatment planning system. The convolution-superposition algorithm was the Collapsed Cone implemented in the Helax-TMS. The only studied calculation methods that correlated successfully with the measured values with a 2% average inside all media were the Collapsed Cone and the Monte Carlo simulation. The biggest difference between the predicted and the delivered dose in the beam axis was found for the EqTAR algorithm inside the CIRS lung equivalent material in a 2 x 2 cm2 18 MV x-ray beam. In these conditions, average and maximum difference against the TLD measurements were 32% and 39%, respectively. In the water equivalent part of the phantom every algorithm correctly predicted the dose (within 2%) everywhere except very close to the interfaces where differences up to 24% were found for 2 x 2 cm2 18 MV photon beams. Consistent values were found between the reference detector (ionization chamber in water and TLD in lung) and Monte Carlo simulations, yielding minimal differences (0.4%+/-1.2%). The penumbra broadening effect in low density media was not predicted by any of the correction-based algorithms, and the only one that matched the experimental values and the Monte Carlo simulations within the estimated uncertainties was the Collapsed Cone Algorithm.

Optimization method for the design of beam shaping systems

A new geometrical optical method has been developed for the design of optical systems that perform intensity reshaping of spatially coherent input light, particularly that of plane parallel or spherical beams. The computation is based on the principle of automated optimization, making it available for the design of beam shapers of diverse structures (aspheric, diffractive, etc.), and especially for those where no analytic solution exists to calculate the necessary device geometry (e.g., in case of all-spherical systems). Novelty, and thus efficiency, of the method lies in its simplified definition of the error function, used for the evaluation of optical systems by optimization algorithms during the design process. Another advantage of the method is that it can be easily implemented in commercially available optical design programs commonly used by optical designers. The operation of the new method is shown for the particular case of Gaussian-to-uniform beam transforming systems, and a concrete design example is given for its application. Wave-optical calculations verify the accuracy of our computations and check the diffraction behavior of the geometrically designed device.

A theoretical evaluation of the assessment of effective dose using multiple personnel dosimeters.

The ability of a dose calculation algorithm, using the readings of multiple dosimeters, to accurately assess the effective dose under different photon irradiation conditions was assessed using computer simulation. The algorithm was that described in American National Standards Institute publication N13.41. Monte Carlo calculations with an anthropomorphic humanoid phantom were used to calculate the effective doses and also the expected readings of the multiple dosimeters. The irradiation geometries considered included a point source placed at several locations at a distance of 100 cm in front of the phantom, as well as an anterior-posterior plane parallel beam with a lead shield interposed between the phantom and the source. The point source energies considered were 0.05, 0.6, and 2 MeV, and the beam energy was varied between 0.03 and 10 MeV. Also considered were the estimates of effective dose based on the highest reading of the multiple dosimeters, a practice that is currently used in many work places. The results showed that use of the algorithm resulted in substantial improvements in the ability to accurately estimate effective dose. However, the results also showed that the improvements in accuracy were achievable only by using a calibration factor for the dosimetry that is different from the one obtained in current dosimetry calibration practices, and that without the use of this factor, the algorithm tended to underestimate the effective dose for nearly all the irradiation geometries considered. In addition, it appeared that this calibration factor is not constant but varies with irradiation conditions. There thus appears to be a problem of proper dosimetry calibration for use with the algorithm. This work considered only anterior posterior irradiations, and additional work is needed to assess the performance of the algorithm in other non-uniform irradiation geometries.

Optical method of determination of stress at a point

A method of determining stress at a point is suggested here. The effect of bending of a wave front that is due to variations of the refractive index is used to measure different aspects of stresses. A Fourier lens with a cross slit at its front focal plane is used to form interference fringes at planes near its back focal plane. The sample, illuminated by a plane-parallel coherent beam of light, is placed close to a cross slit, and the change in fringe pattern due to axial shift of the spectrum planes of the slits is measured to relate it to the state of stress.

Multiple-scattering effects on differential absorption for the transmission of a plane-parallel beam in a homogeneous medium

The transmission, including all scattering orders, of a plane-parallel beam in a homogeneous scattering medium containing aerosols (e.g., water cloud) mixed with an absorbing gas (e.g., ozone) is computed with a two-stream radiative transfer model. From differential transmission the concentration of the gas is deduced. The effect of multiple-scattering on the deduced concentration is shown for conservative scattering aerosols for which the multiple scattering by the aerosols is differentially absorbed by the gas and for nonconservative scattering aerosols for which the multiple scattering is differentially absorbed by the aerosols as well as differentially absorbed by the gas. The two-stream analytical model (with no dependence on the field of view) shows good qualitative agreement (especially for a small field of view) with a numerical radiative transfer model in which the trace gas concentration is computed for the different detector's field of view.

Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium

A two-stream radiative transfer model is used to derive expressions for the multiple-scattered transmitted flux (including single-scattering contributions) and the total effective average photon path length on transmission of a normally incident plane-parallel beam on a homogeneous layer characterized by the optical depth, the single-scattering albedo, and the asymmetry parameter of the scatterers. The results are simple analytical expressions that are useful for modifying the Beer-Lambert transmission law for a thick scattering medium in which the multiple-scattering contribution to the transmission is not negligible.

Angular Dependence Factors and Air Kerma to Dose Equivalent Conversion Coefficients for Cylindrical Phantoms Irradiated by Plane-Parallel Extended Monoenergetic Photon Beams

With the aid of the Monte Carlo method, conversion coefficients between the receptor-free air collision kerma and the collision kerma for 4-element ICRU tissue have been calculated at a depth of 0.007 g.cm −2 in circular cylinder phantoms irradiated by broad plane-parallel photon beams in a direction perpendicular to the cylinder main axis. The phantom material was ICRU tissue or PMMA; the phantom diameter 1.9 cm, 7.3 cm, or 30 cm; the phantom length 30 cm. The calculations were performed for monoenergetic photons in the energy range between 4 keV and 1.25 MeV. The conversion coefficients can be used in the field of extremity dosimetry to convert measured kerma or exposure values into personal dose equivalents: the results for the 7.3 cm diameter cylinder phantoms for the calibration of wrist or ankle dosemeters; those for the 1.9 cm diameter phantoms for the calibration of finger dosemeters. In addition to the conversion coefficients, their angular dependence factors in the middle plane of the phantoms perpendicular to the main axis were also studied. Such quantities for the ICRU tissue phantoms are necessary in the procedure for type testing extremity dosemeters on rod or pillar phantoms