Beam Spectrum Research Articles

On the response spectra of cracked beams under different types of moving force

On the response spectra of cracked beams under different types of moving force

Uncertainties in linac primary barrier transmission values

Primary barrier design for linac shielding depends very sensitively on tenth value layer (TVL) data. Inaccuracies can lead to large discrepancies between measured and calculated values of the barrier transmission. Values of the TVL for concrete quoted in several widely used standard references are substantially different than those calculated more recently. The older standard TVL data predict significantly lower radiation levels outside primary barriers than the more recently calculated values under some circumstances. The difference increases with increasing barrier thickness and energy, and it can be as large as a factor of 4 for 18 MV and concrete thickness of 200 cm. This may be due to significant differences in the beam spectra between the earlier and the more recent calculations. Measured instantaneous air kerma rates sometimes show large variations for the same energy and thickness. This may be due to confounding factors such as extra material on, or inside the barrier, variable field size at the barrier, density of concrete, and distal distance from the barrier surface. In some cases, the older TVL data significantly underestimate measured instantaneous air kerma rates, by up to a factor of 3, even when confounding factors are taken into account. This could lead to the necessity for expensive remediation. The more recent TVL values tend to overestimate the measured instantaneous dose rates. Reference TVL data should be computed in a manner that is mathematically consistent with their use in the calculation of air kerma rate outside barriers directly from the linac “dose” rate in MU/min.

Measurement of linear accelerator spectra, reconstructed from percentage depth dose curves by neural networks

Purpose Linear accelerator (linac) spectra, used to improve the accuracy of dose calculation and to produce a complete description of beam quality, among other aspects, are relevant in radiotherapy and linear accelerator physics.Methods In this work we apply neural networks in solving an ill-conditioned system of linear equations, to indirectly measure the linear accelerator spectra via the percentage depth dose curves. The photon beam spectra are related to radiation doses through a Fredholm integral equation. To address our problem we measured the percentage depth dose curve in water and solved a discretized Fredholm equation using artificial neural network. After analysing the typology of our physical problem we selected a MultiLayer Perceptron Neural Network and designed the most suitable neural network architecture.Results The reconstructed spectra were compared with spectra from three linacs, two of them obtained by us through simulations and the third produced by another author, achieving a concordance between 92 % and 96 %.Conclusions Therefore, the spectrum of any accelerator can be quickly and easily reconstructed from measured percent depth dose curves, applying a trained artificial neural network.

SCATTER RADIATION INTENSITIES IN HORIZONTAL AND VERTICAL PLANES ABOUT DIGITAL BREAST TOMOSYNTHESIS SYSTEM.

Digital breast tomosynthesis (DBT) is a main imaging modality for breast imaging. However, shielding calculations for DBT are commonly based on previous technology with softer beam spectra. In addition, shielding calculations often assume some patient attenuation is provided in locations to the posterior of the patient but without quantification of this attenuation. In this work, recent research in DBT shielding is validated by measuring scatter radiation in the vertical plane. It is also extended upon by measuring the scatter radiation in the horizontal plane and the effect of patient attenuation. These measurements are weighted by our local patient compressed breast thickness distribution to provide a simple scattering factor. Air kerma distributions are provided demonstrating the distribution of scatter radiation around the DBT system in the presence of patient body attenuation. The highest air kerma measured in any direction from a 4-view per patient screening tomosynthesis exam based on the local patient workload is 55μGy at 1m. This value can be used to conservatively treat the scatter radiation as an isotropic distribution for shielding assessments. This work is consistent with many recent publications, with the notable exception of the forward scattered peak which is smaller than previous studies. Under our locally encountered breast thickness distribution, the increased scatter radiation and consequent increased minimum shielding requirements is small in most cases. With 400 patients per week, the air kerma at 1m is 22mGy and, for a fully occupied public area 2m away, this requires a gypsum plasterboard thickness of 18.0mm which is 3.6mm more than previous data suggests. Although the increase is minimal, standard manufacturing thicknesses of shielding material may not be automatically assumed to be sufficient and careful consideration of the scatter radiation is warranted.

Spectral reconstruction of kilovoltage photon beams using generalized simulated annealing

To unfold the energy spectrum of two kilovoltage (kV) X-ray beams from transmission curves through a mathematical methodology based on Laplace transform and the generalized simulated annealing algorithm. Energy spectra of photon beams and transmission data were associated by means of a mathematical expression derived from the analytical solution of Laplace transform. Transmission data was calculated by relating the air kerma of the attenuated beams, passing through aluminium plates of different thickness, to that of the non-attenuated beam. Generalized simulated annealing function, developed in an early work, was employed to find the parameters of the expression and so determine the spectra. Validation of the methodology was done by the comparison of the half-value layers obtained from transmission curves and the spectra. The mean square percentage error between transmission data and fitting curve of each spectrum defined from the parameters found was lower than 1% indicating a good adjustment. The same error was observed when the first half-value layer (HVL) from the transmission curves and those of each reconstructed spectrum were compared. Calculation time of parameters was 5 sec for 80 kV and 14 sec for 120 kV. In no case, non-realistic solution of energy spectra was obtained. These results were better than an early work where least-squares were used. The reconstruction methodology based on generalized simulated annealing employed in this manuscript can efficiently derive the spectra of two X-ray beams with comparable accuracy to previous work. A limitation is that validation was not done by comparing data with the equipment’s spectra.

Topological charge of soft X-ray vortex beam determined by inline holography

A Laguerre–Gaussian (LG) vortex beam having a spiral wavefront can be characterized by its topological charge (TC). The TC gives the number of times that the beam phase passes through the interval [0, 2pi ] following a closed loop surrounding the propagation axis. Here, the TC spectra of soft X-ray vortex beams are acquired using the in-line holography technique, where interference between vortex waves produced from a fork grating and divergent waves from a Fresnel zone plate is observed as a holographic image. The analyses revealed the phase distributions and the TC for the LG vortex waves, which reflects topological number of the fork gratings, as well as for the Hermite–Gaussian (HG) mode waves generated from the other gratings. We also conducted a simulation of the present technique for pair annihilation of topological defects in a magnetic texture. These results may pave the way for development of probes capable of characterizing the topological numbers of magnetic defects.

Observation of the Rotational Doppler Effect With Structured Beams in Atomic Vapor

A vector beam with the spatial variation polarization has attracted keen interest and is progressively applied in quantum information, quantum communication, precision measurement, and so on. In this letter, the spectrum observation of the rotational Doppler effect based on the coherent interaction between atoms and structured light in an atomic vapor is realized. The geometric phase and polarization of the structured beam are generated and manipulated by using a flexible and efficacious combination optical elements, converting an initial linearly polarized Gaussian beam into a phase vortex beam or an asymmetric or symmetric vector beam. These three representative types of structured beam independently interact with atoms under a longitudinal magnetic field to explore the rotational Doppler shift associated with the topological charge. We find that the rotational Doppler broadening increases obviously with the topological charge of the asymmetric and symmetric vector beam. There is no rotational Doppler broadening observed from the spectrum of the phase vortex beam, although the topological charge, and spatial profile of the beam change. This study can be applied to estimate the rotational velocity of the atom-level or molecule-level objects, measure the intensity of magnetic fields and study the quantum coherence in atomic ensembles.

Determination and Verification of Parameters of Lévy Distribution Incident Energy Spectrum of High-energy Electron Beam

The incident electron energy spectrum was determined by an estimation formula based on the Lévy distribution in order to calculate the PDD and OAR that is consistent with the measurement. EGSnrc was used to calculate PDD and OAR at nominal energies of 4, 6, 9, 12, and 15 MeV. The parameters for determining the incident electron energy spectrum were adjusted to be a reasonable value in the error between the measured and the calculated values. Location and scaling parameters were determined to be 0.5 and 0.001, respectively. The calculated PDD based on the determination formula was in agreement with the measurement within 2 mm/2% at all depths. The OAR also was in agreement with the measurement within 2 mm/2%. In this study, the incident electron energy spectrum was estimated by determining the location and scaling parameters. This method is simpler and more accurate than previously reported, and can be applied to the calculation of dose distributions in Monte Carlo simulations.

Propagation properties of circularly symmetric Airy beam modulated by spectral asymmetric envelope

An asymmetric envelope function for modulating the spectrum of circular Airy beam is proposed in this work. The propagation properties of the modified circular Airy beam are investigated in both theory and experiment. The three parameters of the asymmetric hyperbolic secant function can be used to adjust the ratio of the high frequency components to the low frequency components in Fourier space, and thus tuning the propagation properties of this modified circular Airy beam. The results demonstrate that the focal position is affected mainly by the high frequency components. The maximum focal intensity will not be enhanced continuously by increasing the proportion of the high frequency components. It depends on the ratio of the high frequency components to the low frequency components when the center frequency is determined. Therefore, using an asymmetric envelope in Fourier space is much more reasonable than using the high pass filtering or symmetric Gaussian envelope. The FWHM decreases significantly with the increase of center frequency. When the parameters are chosen appropriately, the size of focal spot will be reduced significantly, the maximum focal intensity, especially the abruptly autofocusing property will be enhanced greatly and the focal position can remain almost the same as the focal position of the common circular Airy beam. The maximum focal intensity of the proposed beam is 3.4 times that of the common circular Airy beam and the abruptly autofocusing property of the proposed beam is much better than that of the beam using the symmetric Gaussian envelope. The phase-only encoding method in Fourier space is used to generate the proposed beam in experiment. The experimental results are in reasonable agreement with the simulation results. It indicates that the modified beam can be generated conveniently by using the same method as that used to generate the common circular Airy beam.

Assessing the Effect of Directional Bremsstrahlung Splitting on the Output Spectra and Parameters Using BEAMnrc Monte Carlo Simulation Package.

EGSnrc software package is one of the computational packages for Monte Carlo simulation in radiation therapy and has several subset codes. Directional bremsstrahlung splitting (DBS) is a technique that applies braking radiations in interactions in this software. This study aimed to evaluate the effect of this technique on the simulation time, uncertainty, particle number of phase-space data, and photon beam spectrum resulting from a medical linear accelerator (LINAC). The gantry of the accelerator, including the materials and geometries of different parts, was simulated using the BEAMnrc code (a subset code in the EGSnrc package). The phase-space data were recorded in different parts of the LINAC. The DBS values (1, 10, 100, and 1000) were changed, and their effects were evaluated on the simulation parameters and output spectra. Increasing the DBS value from 1 to 1000 resulted in an increase in the simulation time from 1.778 to 11.310 hours, and increasing the number of particles in the phase-space plane (5 590 732-180 328 382). When the DBS had been picked up from 1 to 100, the simulation uncertainty decreased by about 1.29%. In addition, the DBS increment value from 100 to 1000 leads to an increase in uncertainty and simulation time of about 0.71% and 315%, respectively. Although using the DBS technique reduces the simulation time or uncertainty, increasing the DBS from a specific value, equal to 100 in our study, increases simulation uncertainties and times. Therefore, we propose considering a specific DBS value as we obtained for the Monte Carlo simulation of photon beams produced by linear accelerators.

Comparison of the Natural Vibration Frequencies of Timoshenko and Bernoulli Periodic Beams.

This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions.

Photon beam dose enhancement in AuNP AC tumour through energy moderation of a 6 MeV electron beam: A Monte Carlo study

PurposeTo use Monte Carlo (MC) simulations (BEAMnrc and DOSXYZnrc) to investigate different moderators to slow down 6 MeV electrons before striking a tungsten bremsstrahlung target. The generated x-ray beam is then used to study the dose-effect when the beam traverses a gold-nanoparticle (AuNP) enriched tumour. Materials and methodsIn this study, the 6 MV linear accelerator model was without a beam flattening filter. The BEAMnrc code was used to simulate the 6 MeV electron beam traversing through water or carbon moderators of various thicknesses before striking a thin tungsten target to produce photon beams with effective energies less than the original 6 MV beam (without any moderation). For each beam, a phase-space (PHSP) file was scored to be used in subsequent DOSXYZnrc simulations. The DOSXYZnrc code was utilised to obtain percentage depth dose (PDD) and dose distributions in a 40 × 40 × 40 cm3 water phantom for each beam. All DOSXYZnrc simulations were repeated but with a tumour model near the surface of the water phantom. Dose enhancement effects (DEFs) were calculated in the tumour model as the ratio of the dose in the tumour with and without gold-nanoparticles (AuNPs) seeded into the tumour at a concentration of 7 mg/g. ResultsWater or carbon moderators slowed the primary 6 MeV electron beam down, resulting in lower energy photon beam spectra generated in the tungsten target. Significant dependence of DEFs on the mean energy of the resulting x-ray beams was shown as a function of moderator thickness. For beams moderated to kilovolt energies, the effect was more enhanced as anticipated. DEF values ranged between 1.01 and 1.075 for various moderator/bremsstrahlung x-ray target combinations. The highest DEF (1.075) was obtained for a moderator consisting of either 2.5 cm water or 1.4 cm carbon to slow the 6 MeV electrons down before hitting the tungsten target of 0.07 cm thickness. ConclusionsCarbon and water moderators can effectively slow electrons down before using them to generate low energy bremsstrahlung x-rays to enhance the dose in a tumour seeded with AuNPs. DEF's of up to 1.075 can be obtained whilst using beams of energy lower than 1 MV.

Effect of Collimator Elements on the Beam Spectrum and KERMA In Gamma Irradiator

In the development of low-medium energy photon calibration facilities we have simulated several types of gamma irradiator collimator materials with ISO 4037-1 design connected to the output beam spectrum and the resulting kerma. Four types of collimator material, namely Al, Fe, Pb, and WCu have been simulated with gamma radiation sources 241Am, 57Co, 137Cs, and 60Co. Simulations were carried out using the Monte Carlo method with the PHITS computer program. Based on the comparison of air kerma produced, collimators made from Al are suitable for gamma sources 241Am, Fe material for gamma sources 57Co, and Pb material for sources 137Cs and 60Co.

Orbital angular momentum spectrum of antenna vortex beam based on loop integration

Due to the divergence characteristics of vortex microwaves, it is difficult to determine orbital angular momentum (OAM) orders through far fields, while the spiral spectrum analysis method based on the area integral of antenna near fields is complicated. In this paper, combined with near-field approximation processing, a spiral spectrum analysis method based on loop integration is proposed. According to the Laguerre–Gaussian vortex beam model, the key parameter estimation formulas suitable for low-order OAM microwave beams are derived, including the position of the reliable observation plane and the size of the annulus area. On this basis, the radius of the integral loop used for the spiral spectrum calculation is provided. Since only field data on the loop are collected in this method, the calculation amount is reduced and the analysis efficiency of the spiral spectrum is greatly improved. Due to the combination of near-field and far-field considerations, this method can fully reflect the spiral spectrum characteristics of antenna vortex waves.

Simulation method for investigating the use of transition-edge sensors as spectroscopic electron detectors

Transition-edge sensors (TESs) are capable of highly accurate single particle energy measurement. TESs have been used for a wide range of photon detection applications, particularly in astronomy, but very little consideration has been given to their capabilities as electron calorimeters. Existing electron spectrometers require electron filtering optics to achieve energy discrimination, but this step discards the vast majority of electrons entering the instrument. TESs require no such energy filtering, meaning they could provide orders of magnitude improvement in measurement rate. To investigate the capabilities of TESs in electron spectroscopy, a simulation pipeline has been devised. The pipeline allows the results of a simulated experiment to be compared with the actual spectrum of the incident beam, thereby allowing measurement accuracy and efficiency to be studied. Using Fisher information, the energy resolution of the simulated detectors was also calculated, allowing the intrinsic limitations of the detector to be separated from the specific data analysis method used. The simulation platform has been used to compare the performance of TESs with existing x-ray photoelectron spectroscopy (XPS) analysers. TESs cannot match the energy resolution of XPS analysers for high-precision measurements but have comparable or better resolutions for high count rate applications. The measurement rate of a typical XPS analyser can be matched by an array of ten TESs with 120 response times and there is significant scope for improvement, without compromising energy resolution, by increasing array size.

Confocal Fluorescence Microscopy and Confocal Raman Microspectroscopy of X-ray Irradiated LiF Crystals

Radiation-induced color centers locally produced in lithium fluoride (LiF) are successfully used for radiation detectors. LiF detectors for extreme ultraviolet radiation, soft and hard X-rays, based on photoluminescence from aggregate electronic defects, are currently under development for imaging applications with laboratory radiation sources, as well as large-scale facilities. Among the peculiarities of LiF-based detectors, noteworthy ones are their very high intrinsic spatial resolution across a large field of view, wide dynamic range, and versatility. LiF crystals irradiated with a monochromatic 8 keV X-ray beam at KIT synchrotron light source (Karlsruhe, Germany) and with the broadband white beam spectrum of the synchrotron bending magnet have been investigated by optical spectroscopy, laser scanning confocal microscopy in fluorescence mode, and confocal Raman micro-spectroscopy. The 3D reconstruction of the distributions of the color centers induced by the X-rays has been performed with both confocal techniques. The combination of the LiF crystal capability to register volumetric X-ray mapping with the optical sectioning operations of the confocal techniques has allowed performing 3D reconstructions of the X-ray colored volumes and it could provide advanced tools for 3D X-ray detection.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters.

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l0 at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l0 with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l0; and (3) the OAM components of the generated beam could be tuned either by changing the value of l0, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Handling of beam spectra in training and application of proton RBE models

Published data from cell survival experiments are frequently used as training data for models of proton relative biological effectiveness (RBE). The publications rarely provide full information about the primary particle spectrum of the used beam, or its content of heavy secondary particles. The purpose of this paper is to assess to what extent heavy secondary particles may have been present in published cell survival experiments, and to investigate the impact of non-primary protons for RBE calculations in treatment planning. We used the Monte Carlo code Geant4 to calculate the occurrence of non-primary protons and heavier secondary particles for clinical protons beams in water for four incident energies in the [100, 250] MeV interval. We used the resulting spectra together with a conservative RBE parameterization and an RBE model to map both the rise of RBE at the beam entry surface due to heavy secondary particle buildup, and the difference in estimated RBE if non-primary protons are included or not in the beam quality metric. If included, non-primary protons cause a difference of 2% of the RBE in the plateau region of an spread out Bragg peak and 1% in the Bragg peak. Including non-primary protons specifically for RBE calculations will consequently have a negligible impact and can be ignored. A buildup distance in water of one millimeter was sufficient to reach an equilibrium state of RBE for the four incident energies selected. For the investigated experimental data, 83 out of the 86 data points were found to have been determined with at least that amount of buildup material. Hence, RBE model training data should be interpreted to include the contribution of heavy secondaries.

The Blow-Off Impulse Equivalence of Typical Missile Homogeneous Al-Alloy under Multienergy Composite Spectrum Electron Beam and Powerful Pulsed X-ray

The electron beam, one of the most effective approaches to simulate the irradiation effects of powerful pulsed X-ray in the laboratory, plays an important role in simulating the thermodynamic effects of powerful pulsed X-ray. This paper studies the thermodynamics equivalence between multienergy composite spectrum electron beam and blackbody spectrum X-ray, which is helpful to quickly determine the experimental parameters in the simulation experiment. The experimental data of electron beam are extrapolated by numerical calculation, to increase the range of energy flux. Through calculating the blow-off impulse of blackbody spectrum X-ray irradiation, we obtained the curve of X-ray blow-off impulse varying with energy flux, and then found two categories of equivalent relations—equal-energy flux and equal-impulse—by analyzing the calculation results of electron beam and X-ray blow-off impulse. Based on such relations, we could directly or indirectly obtain the results of blackbody spectrum X-ray irradiation blow-off impulse via electron beam experiment.

New nano-structure spectrometer by introducing gold nano-pillars for spectral reconstruction ability improvement

As a new proposed spectrometer, the filter-based spectrometer uses a group of filters with known transmittance to modulate the spectrum of an incident light beam. After employing a post-processing algorithm, the spectrum of the beam can be reconstructed. For such spectrometers, the transmittance curve characteristics of the filters have a crucial impact on the spectrum reconstruction results. To better capture the details of the spectrum curve of the incident light beam, we propose a new nano-structure spectrometer by introducing gold nano-pillars to the photonic crystal (PC) filters. Because of the surface plasmon resonance effect of the gold nano-pillars, narrow bands will be generated on the transmittance curve of the new filters, which can improve the spectral reconstruction capability of the filters. In this paper, we first briefly introduce the principle of the filter-based spectrometer. Then, the transmittance curves of the filters are simulated by multiple random Gaussian functions according to the waveform of the transmittance curve of practical filters. And the simulated transmittance curves are used to reconstruct the spectrum of a beam to study their anti-noise capability. Next, new filters are designed by introducing gold nano-pillars to the PC filters. And their transmittance curves are calculated by the finite-difference time-domain (FDTD) approach. Finally, the spectrum reconstruction results are compared with those of the PC filters. The simulation results show that the introduction of gold nano-pillars can significantly improve the spectrum reconstruction ability of the PC filters.