Energy Spectrum Of Electron Beam Research Articles

Optimization of the regularization parameter in the Dual Annealing method used for the reconstruction of energy spectrum of electron beam generated by the AQURE mobile accelerator

IntroductionThe shape of the energy spectrum is an essential component of any electron beam Monte Carlo model. Due to specialized equipment and the long measurement time for the direct methods for determining the energy spectrum, attractive alternatives are backward spectrum reconstructions from the measured data. One such approach is solving the first-degree Fredholm integral equation with appropriate regularization. It makes it possible to calculate the depth distribution as the sum of the distributions from monoenergetic beams. This study aims to determine the optimal value of the regularization parameter for the problem of determining the spectrum of the electron beam produced by a mobile accelerator used during intraoperative radiotherapy. Material and methodsThe Geant4 package was used to generate the distributions of deep doses for monoenergetic beams for two models with different degrees of complexity, i.e. simple (theoretical) and full (for the mobile accelerator). The dose distributions for four different shapes of energy spectrum (for each model) were obtained similarly. They were established as the reference data for further calculations. The Dual Annealing optimization method was used to obtain the reconstructed spectrum. The multiple optimizations that differ by the regularization parameter (ranging from 0 to 1) were performed. For each reconstruction, similarity indicators of the energy spectrum and the dose distribution to the referenced data were calculated to determine the optimal regularization parameters. ResultsOptimal regularization parameters determined by similarity indicators for the spectrum and the dose distribution differ for geometry models considered in the study. The regularization parameter for the simple geometry ranged from 0.03 to 0.05, while for full geometry, they were from 0.05 to 0.06. The results for conventional linear accelerators found in the literature range from 0.5 to 1.1. ConclusionThe Dual Annealing optimization method can be effectively used to solve the Fredholm equation with Tikhonov regularization to reconstruct an electron beam's energy spectrum. The regularization parameter value depends on the beam-forming system. Its value for the mobile accelerator considered in the study ranges from 0.05 to 0.06, depending on the nominal beam energy value.

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

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

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.

Denoising application for electron spectrometer in laser-driven ion acceleration using a Simulation-supervised Learning based CDAE

Real experimental measurements in high-radiation environments often suffer from a high-flux of background noise which can limit the retrieval of the underlying signal. It is important to have an effective method to properly remove unwanted noise from measurement images. Machine learning methods using a multilayer neural network (deep learning) have been shown to be effective for extracting features from images. However, the efficacy of such methods is often restricted by a lack of high-quality training data. Here, we demonstrate the application for noise removal by performing simulations to generate virtual training data for a denoising deep-learning model. We first apply the model to simulations of an electron spectrometer measuring the energy spectra of electron beams accelerated from the interaction of an intense laser with a thin foil. By considering the chi-squared test and image test-indexes, namely the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM), we found our method to be highly effective. We then used the trained model to denoise real experimental measurements of the electron beam spectra from experiments performed at a state-of-the-art high-power laser facility. This application is offered as a new method for effectively removing noise from experimental data in high-flux radiation background environment.

Determination of the Pulsed Electron Beam Spectrum by Current and Voltage Oscillograms

The algorithm and results of calculating the integral and differential energy spectra of a pulsed electron beam (350–500 keV, 80 ns), generated by direct-action accelerators, are presented. The electron spectrum was calculated using the oscillograms of the accelerating voltage, electron current, total current of the diode, and the one-dimensional Child–Langmuir (1D CL) ratio. It was found that the discrepancy in the integrated electron beam energy spectrum, when measured using the total current in the diode and using the electron beam current, did not exceed 15% for 80%–95% of the electrons generated in a diode with graphite, carbon fabric, and multipoint cathodes. When calculating the electron spectrum using the 1D CL, the error was much higher.

Influence of the Kinetic Energy Spectrum of Pulsed Beam Electrons on the Effective Absorbed Dose Distribution Over the Target Depth

The analysis of the efficiency of the absorbed dose depth distribution as a function of the kinetic energy spectrum of a submicrosecond electron beam showed that the use of two operating modes of a submicrosecond electron accelerator, which differ in the amplitude of the accelerating voltage pulse (200 and 300 kV), under irradiation of various materials can provide different effects determined by different depth distributions of absorbed energy. For the constructed spectra of the beam electron kinetic energies, we used a model sample that takes into account the structure and penetration of the material, which determines the conditions for the electron beam absorbed energy distribution over the depth. Based on the experimental data, the absorbed dose in the structural parts of the object was estimated using the example of a wheat seed, and conclusions were drawn about the efficiency of using irradiation modes with different kinetic energy spectra of electrons in the beam.

Development of a neural network method for measuring the energy spectrum of a pulsed electron beam, based on Bremsstrahlung X-Ray

In the pulsed electron beam generators, such as plasma focus devices and linear induction accelerators whose electron pulse width is in the range of nanosecond and less, as well as in cases where there is no direct access to electron beam, like runaway electrons in Tokamaks, measurement of the electron energy spectrum is a technical challenge. In such cases, the indirect measurement of the electron spectrum by using the bremsstrahlung radiation spectrum associated with it, is an appropriate solution. The problem with this method is that the matrix equation between the two spectrums is an ill-conditioned equation, which results in errors of the measured X-ray spectrum to be propagated with a large coefficient in the estimated electron spectrum. In this study, a method based on the neural network and the MCNP code is presented and evaluated to recover the electron spectrum from the X-ray generated by collision of the electron beam with a target. Multilayer perceptron network showed good accuracy in electron spectrum recovery, so that for the X-ray spectrum with errors of 3% and 10%, the network estimated the electron spectrum with an average standard error of 8% and 11%, on all of the energy intervals.

Validation of a Lévy electron energy straggling model for an Elekta Synergy® linear accelerator

AimIn this study, an EGSnrc based Monte Carlo electron model was validated for an Elekta Synergy® 160-leaf Agility™ linear accelerator. A previously reported electron energy straggling model based on a Lévy distribution was tested against water tank measurements and a specially designed heterogeneous multi-layered phantom. This included PDD, beam profile, and relative output factor (ROF) comparison. All data passed a 2%/2 mm gamma criterion with the exception of some ROF data, which showed discrepancies of up to 2.7%. MethodsBEAMnrc was used to accurately model the linac that included the improved exit electron energy spectrum based on a Lévy distribution. The resulting BEAMnrc phase space files were used as sources in DOSXYZnrc for water tank dose distribution simulations consisting of 6 electron beam energies, 11 field sizes, and source-to-surface distances (SSDs) of 95 and 100 cm. Evaluation parameters included PDD, dose profiles, and relative output factors, as well as phantom PDD and dose profile measurements with EBT3 gafchromic film. ResultsThe improved exit electron beam energy spectrum caused simulated data to comply with measured data (PPD's and dose profiles) with a 100% pass rate using a 2%/2 mm criterion except for some relative output factors that deviated by 2.7% from measured ones in water. This was observed for both 95 and 100 cm SSD data. Good agreement was obtained between film and simulation data within 2% in more than 90% of PDD and profile measurements. ConclusionsThe Lévy based energy straggling model for electron beams allowed for accurate electron beam characterization in water tank and phantom measurements.

SOBRE LA POSIBILIDAD DE USAR EL MÉTODO DE REGULARIZACIÓN DE TIKHONOV PARA RECONSTRUIR EL ESPECTRO DE ENERGÍA DE UN HAZ CLÍNICO DE ELECTRONES

En radioterapia, el espectro de energía de electrones es la característica más importante para modelar la fuente de radiación cuando el propósito sea el cálculo exacto de la dosis. Usualmente, tres métodos son explorados la obtención del espectro: (i) simulación de la fuente vía Monte Carlo; (ii) medición directa vía un espectrómetro magnético y (iii) reconstrucción inversa. De entre ellos, reconstrucción inversa, a pesar de no ser el más exacto, es considerado el más apropiado por su simplicidad y rapidez. Reconstrucción inversa tiene por objeto extraer el espectro de energía a partir de la distribución de dosis en profundidad. Ya que reconstrucción inversa es un problema mal definido, el método de regularización de Tikhonov es usado para superar la mala definición del problema y con ello obtener el espectro. La idoneidad de la reconstrucción es evaluada usando el índice gamma. Los resultados muestran que la regularización de Tikhonov es capaz de reconstruir el espectro de energía de un haz de electrones dentro del criterio clínico de aceptación del índice gamma > 95 % para 1 %/1 mm.

Monte carlo calculation of the energy spectrum of a 6 MeV electron beam using penetration and energy loss of positrons and electrons code

Background:The limited bibliographic existence of research works on the use of Monte Carlo simulation to determine the energy spectra of electron beams compared to the information available regarding photon beams is a scientific task that should be resolved.Aims:In this work, Monte Carlo simulation was performed through the PENELOPE code of the Sinergy Elekta accelerator head to obtain the spectrum of a 6 MeV electron beam and its characteristic dosimetric parameters.Materials and Methods:The central-axis energy spectrum and the percentage depth dose curve of a 6 MeV electron beam of an Elekta Synergy linear accelerator were obtained by using Monte Carlo PENELOPE code v2014. For this, the linear accelerator head geometry, electron applicators, and water phantom were simplified. Subsequently, the interaction process between the electron beam and head components was simulated in a time of 86.4x104 s.Results:From this simulation, the energy spectrum at the linear accelerator exit window and the surface of the phantom was obtained, as well as the associated percentage depth dose curves. The validation of the Monte Carlo simulation was performed by comparing the simulated and the measured percentage depth dose curves via the gamma index criterion. Measured percentage depth- dose was determined by using a Markus electron ionization chamber, type T23343. Characteristic parameters of the beam related with the PDD curves such as the maximum dose depth (R100), 90% dose depth (R90), 90% dose depth or therapeutic range (R85), half dose depth (R50), practical range (Rp), maximum range (Rmax), surface dose (Ds), normalized dose gradient (G0) and photon contamination dose (Dx) were determined. Parameters related with the energy spectrum, namely, the most probable energy of electrons at the surface (Ep,0) and electron average energy (E– 0) were also determined.Conclusion:It was demonstrated that PENELOPE is an attractive and accurate tool for the obtaining of dosimetric parameters of a medical linear accelerator since it can reliably reproduce important clinical data such as the energy spectrum, depth dose, and dose profile.

Energy Spectra of Electron Beams and the Possibility of Double-Stage Energy Recuperation in a Double-Beam Terahertz Gyrotron

We study theoretically the possibilities of double-stage energy recuperation in a double-beam terahertz gyrotron. Numerical modeling, which was performed for a gyrotron producing radiation with a frequency of 0.78 THz and operating at the second cyclotron-frequency harmonic at the TE8.5 mode, demonstrates the possibility of spatial and energy separation of electron beams. This makes it possible to implement a double-stage recuperation scheme. The found energy spectra of electrons suggest an increase in the gyrotron efficiency by 3.5–4 times.

Accurate single-shot measurement technique for the spectral distribution of GeV electron beams from a laser wakefield accelerator

We present a technique, based on a dipole magnet spectrometer containing multiple scintillation screens, to accurately characterize the spectral distribution of a GeV electron beam generated by laser wakefield acceleration (LWFA). An optimization algorithm, along with a numerical code, was developed for trajectory tracking and reconstructing the electron beam angle, divergence, and energy spectrum with a single-shot measurement. The code was validated by comparing the results with the Monte-Carlo simulation of electron beam trajectories. We applied the method to analyze data obtained from laser wakefield acceleration experiments performed using a multi-Petawatt laser to accelerate electron beams to multi-GeV energy. Our technique offers a high degree of accuracy to faithfully characterize electron beams with the nonnegligible shot-to-shot beam pointing fluctuations, particularly in the state-of-the-art multi-GeV LWFA experiments performed to push the energy frontier.

Inverse reconstruction of energy spectra of clinical electron beams using the generalized simulated annealing method

In radiotherapy, the electron spectrum should be considered for accurate dose calculation. There are mainly three approaches to obtain the central axis electron energy spectrum, namely: (i) radiation source modeling; (ii) direct measurement and (iii) inverse reconstruction. To determine the electron spectra, it is proposed to use the inverse reconstruction approach. Inverse reconstruction consists in deriving the electron spectra from measured depth dose distributions. Since inverse reconstruction is a poorly conditioned problem the Tikhonov regularization is implemented to avoid the nonphysical oscillations inherent to this problem. Generalized simulated annealing method is used for minimizing the Tikhonov function in order to find the electron spectra. The effectiveness of the spectral reconstruction is verified by the gamma index criterion. Gamma Index defines the degree of agreement between two depth-dose distributions based on predefined tolerances in terms of distance-to-agreement (DTA) and difference dose (DD). Results show a good agreement between provided (measured in a water phantom) and reproduced (simulated from a reconstructed spectrum) depth dose curves within the gamma index tolerance level defined by >95% passing rate with 1% difference dose/1 mm distance to agreement. In addition, it is possible to evidence an acceptable agreement between provided and reproduced dose profiles according to >95% with 2%/2 mm for every beam, excepting the lowest energy beam. Therefore, it is concluded that generalized simulated annealing is able to reconstruct central-axis electron spectra incident on water phantom surface within restrictive limits of gamma index clinical acceptance.

Adaptive control of laser-wakefield accelerators driven by mid-IR laser pulses.

There has been growing interest both in studying high intensity ultrafast laser plasma interactions with adaptive control systems as well as using long wavelength driver beams. We demonstrate the coherent control of the dynamics of laser-wakefield acceleration driven by ultrashort (∼ 100 fs) mid-infrared (∼ 3.9 μm) laser pulses. The critical density at this wavelength is 7.3 × 1019 cm-3, which is achievable with an ordinary gas target system. Interactions between mid-infrared laser pulses and such near-critical-density plasma may be beneficial due to much higher absorption of laser energy. In addition, the normalized vector potential of the laser field a0 increases with longer laser wavelength, lowering the required peak laser intensity to drive non-linear laser-wakefield acceleration. Here, MeV level, collimated electron beams with non-thermal, peaked energy spectra are generated. Optimization of electron beam qualities are realized through adaptive control of the laser wavefront. A genetic algorithm controlling a deformable mirror improves the electron total charge, energy spectra, beam pointing and stability at various plasma density profiles. Particle-in-cell simulations reveal that the optimal wavefront causes an earlier injection on the density up-ramp and thus higher energy gain as well as less filamentation during the interaction, which leads to the improvement in electron beam collimation and energy spectra.

Comparison of measured electron energy spectra for six matched, radiotherapy accelerators

This study compares energy spectra of the multiple electron beams of individual radiotherapy machines, as well as the sets of spectra across multiple matched machines. Also, energy spectrum metrics are compared with central‐axis percent depth‐dose (PDD) metrics.MethodsA lightweight, permanent magnet spectrometer was used to measure energy spectra for seven electron beams (7–20 MeV) on six matched Elekta Infinity accelerators with the MLCi2 treatment head. PDD measurements in the distal falloff region provided R 50 and R 80–20 metrics in Plastic Water®, which correlated with energy spectrum metrics, peak mean energy (PME) and full‐width at half maximum (FWHM).ResultsVisual inspection of energy spectra and their metrics showed whether beams on single machines were properly tuned, i.e., FWHM is expected to increase and peak height decrease monotonically with increased PME. Also, PME spacings are expected to be approximately equal for 7–13 MeV beams (0.5‐cm R90 spacing) and for 13–16 MeV beams (1.0‐cm R90 spacing). Most machines failed these expectations, presumably due to tolerances for initial beam matching (0.05 cm in R 90; 0.10 cm in R 80–20) and ongoing quality assurance (0.2 cm in R 50). Also, comparison of energy spectra or metrics for a single beam energy (six machines) showed outlying spectra. These variations in energy spectra provided ample data spread for correlating PME and FWHM with PDD metrics. Least‐squares fits showed that R 50 and R 80–20 varied linearly and supralinearly with PME, respectively; however, both suggested a secondary dependence on FWHM. Hence, PME and FWHM could serve as surrogates for R 50 and R 80–20 for beam tuning by the accelerator engineer, possibly being more sensitive (e.g., 0.1 cm in R 80–20 corresponded to 2.0 MeV in FWHM).ConclusionsResults of this study suggest a lightweight, permanent magnet spectrometer could be a useful beam‐tuning instrument for the accelerator engineer to (a) match electron beams prior to beam commissioning, (b) tune electron beams for the duration of their clinical use, and (c) provide estimates of PDD metrics following machine maintenance. However, a real‐time version of the spectrometer is needed to be practical.

Modeling the influence of electron beam energy distribution on quality of radiation processing

The obtained values of most probable energy and practical range have been compared to values calculated according to the formula proposed by the internationally recognized documents. The presented results of the study are focused on the issue of the influence of electron beam energy spread on the depth dose distribution and practical range of electron beam in the irradiated material. The computational experiments have been performed using the Monte-Carlo simulation method for modeling the electron beam energy spectra and depth dose distributions of electrons in aluminum target. Obtained values of most probable energy Ep and practical range Rp have been compared to the values calculated according to formula proposed by the internationally recognized report. The value of a practical range of electrons Rp strongly depends on electron beam energy spread, even in case when value of most probable energy Ep of electrons in the beam is unchanged. Results of computer experiments show that in case of a large energy spread, and presence of asymmetry of electron energy distribution, the electrons energy can’t be determined properly by empirical formulas included to the international standards.

Signatures of quantum effects on radiation reaction in laser–electron-beam collisions

Two signatures of quantum effects on radiation reaction in the collision of a ${\sim}$GeV electron beam with a high intensity (${>}3\times 10^{20}~\text{W}~\text{cm}^{-2}$) laser pulse have been considered. We show that the decrease in the average energy of the electron beam may be used to measure the Gaunt factor $g$ for synchrotron emission. We derive an equation for the evolution of the variance in the energy of the electron beam in the quantum regime, i.e. quantum efficiency parameter $\unicode[STIX]{x1D702}\not \ll 1$. We show that the evolution of the variance may be used as a direct measure of the quantum stochasticity of the radiation reaction and determine the parameter regime where this is observable. For example, stochastic emission results in a 25 % increase in the standard deviation of the energy spectrum of a GeV electron beam, 1 fs after it collides with a laser pulse of intensity $10^{21}~\text{W}~\text{cm}^{-2}$. This effect should therefore be measurable using current high-intensity laser systems.

Variation of the beam parameters of runaway electrons in a gas discharge under the conditions of nonuniform preliminary ionization

Within the theoretical model of a high-pressure hybrid nanosecond discharge with runaway electrons, a strong dependence of the electron beam amplitude, duration, and energy spectrum on the conditions of the preliminary ionization of a gas in the discharge gap is demonstrated. The conditions with uniform and nonuniform distributions of initial electrons in a coaxial diode filled with sulfur hexafluoride at atmospheric pressure are simulated. It is shown that the amplitude and current pulse profile of the electron beam substantially change upon the variation of the initial distribution of the electrons in the discharge gap.

Development of a radiographic method for measuring the discrete spectrum of the electron beam from a plasma focus device

An indirect method is proposed for measuring the relative energy spectrum of the pulsed electron beam of a plasma focus device. The Bremsstrahlung x-ray, generated by the collision of electrons against the anode surface, was measured behind lead filters with various thicknesses using a radiographic film system. A matrix equation was considered in order to explain the relation between the x-ray dose and the spectral amplitudes of the electron beam. The electron spectrum of the device was measured at 0.6 mbar argon and 22 kV charging voltage, in four discrete energy intervals extending up to 500 keV. The results of the experiments show that most of the electrons are emitted in the 125–375 keV energy range and the spectral amplitude becomes negligible beyond 375 keV.

Permanent-magnet energy spectrometer for electron beams from radiotherapy accelerators.

The purpose of this work was to adapt a lightweight, permanent magnet electron energy spectrometer for the measurement of energy spectra of therapeutic electron beams. An irradiation geometry and measurement technique were developed for an approximately 0.54-T, permanent dipole magnet spectrometer to produce suitable latent images on computed radiography (CR) phosphor strips. Dual-pinhole electron collimators created a 0.318-cm diameter, approximately parallel beam incident on the spectrometer and an appropriate dose rate at the image plane (CR strip location). X-ray background in the latent image, reduced by a 7.62-cm thick lead block between the pinhole collimators, was removed using a fitting technique. Theoretical energy-dependent detector response functions (DRFs) were used in an iterative technique to transform CR strip net mean dose profiles into energy spectra on central axis at the entrance to the spectrometer. These spectra were transformed to spectra at 95-cm source to collimator distance (SCD) by correcting for the energy dependence of electron scatter. The spectrometer was calibrated by comparing peak mean positions in the net mean dose profiles, initially to peak mean energies determined from the practical range of central-axis percent depth-dose (%DD) curves, and then to peak mean energies that accounted for how the collimation modified the energy spectra (recalibration). The utility of the spectrometer was demonstrated by measuring the energy spectra for the seven electron beams (7-20 MeV) of an Elekta Infinity radiotherapy accelerator. Plots of DRF illustrated their dependence on energy and position in the imaging plane. Approximately 15 iterations solved for the energy spectra at the spectrometer entrance from the measured net mean dose profiles. Transforming those spectra into ones at 95-cm SCD increased the low energy tail of the spectra, while correspondingly decreasing the peaks and shifting them to slightly lower energies. Energy calibration plots of peak mean energy versus peak mean position of the net mean dose profiles for each of the seven electron beams followed the shape predicted by the Lorentz force law for a uniform z-component of the magnetic field, validating its being modeled as uniform (0.542 ± 0.027 T). Measured Elekta energy spectra and their peak mean energies correlated with the 0.5-cm (7-13 MeV) and the 1.0-cm (13-20 MeV) R90 spacings of the %DD curves. The full-width-half-maximum of the energy spectra decreased with decreasing peak mean energy with the exception of the 9-MeV beam, which was anomalously wide. Similarly, R80-20 decreased linearly with peak mean energy with the exception of the 9 MeV beam. Both were attributed to suboptimal tuning of the high power phase shifter for the recycled radiofrequency power reentering the traveling wave accelerator. The apparatus and analysis techniques of the authors demonstrated that an inexpensive, lightweight, permanent magnet electron energy spectrometer can be used for measuring the electron energy distributions of therapeutic electron beams (6-20 MeV). The primary goal of future work is to develop a real-time spectrometer by incorporating a real-time imager, which has potential applications such as beam matching, ongoing beam tune maintenance, and measuring spectra for input into Monte Carlo beam calculations.