Beam Distribution Research Articles

Quantitative Assessment of Delivered Dose in Carbon Ion Spatially Fractionated Radiotherapy (C-SFRT) and Biological Response to C-SFRT.

Objective
Applying carbon ion beams, which have high linear energy transfer and low scatter within the human body, to Spatially Fractionated Radiation Therapy (SFRT) could benefit the treatment of deep-seated or radioresistant tumors. This study aims to simulate the dose distributions of spatially fractionated beams (SFB) to accurately determine the delivered dose and model the cell survival rate following SFB irradiation.
Approach
Dose distributions of carbon ion beams are calculated using the Triple Gaussian Model. The sensitive volume of the detector used in measurements was also considered. If the measurements and simulations show good agreement, the dose distribution and absolute dose delivered by SFB can be accurately estimated. Three types of dose distributions were delivered to human salivary gland cells (HSGc-C5): uniform dose distribution (UDD), and one-dimensional (1D) grid-like dose distributions (GDD) with 6 mm and 8 mm spacing. These provided high (Peak-to-Valley Dose Ratio, PVDR=4.0) and low (PVDR=1.64) dose differences between peak and valley doses, respectively. Linear-Quadratic (LQ) model parameters for HSGc-C5 were derived from the UDD and cell survival fractions (SF) were simulated for 1D GDD using these values.
Main results
Good agreement was observed between measurements and simulations when accounting for detector volume. However, the TPS results overestimated dose in steep gradient region, likely due to the 2.0 mm calculation grid size. LQ parameters for HSGc-C5 were α = 0.34 and β = 0.057. The 1D GDD with 6 mm spacing showed good agreement between simulations and experiments, but the 8.0 mm spacing resulted in lower experimental cell survival.
Significance
We successfully simulated grid-like dose distributions and conducted SF simulations. The results suggest potential cell-killing effects due to high-dose differences in SFB.&#xD.

Quantitative Assessment of Delivered Dose in Carbon Ion Spatially Fractionated Radiotherapy (C-SFRT) and Biological Response to C-SFRT

Abstract Objective
Applying carbon ion beams, which have high linear energy transfer and low scatter within the human body, to Spatially Fractionated Radiation Therapy (SFRT) could benefit the treatment of deep-seated or radioresistant tumors. This study aims to simulate the dose distributions of spatially fractionated beams (SFB) to accurately determine the delivered dose and model the cell survival rate following SFB irradiation.
Approach
Dose distributions of carbon ion beams are calculated using the Triple Gaussian Model. The sensitive volume of the detector used in measurements was also considered. If the measurements and simulations show good agreement, the dose distribution and absolute dose delivered by SFB can be accurately estimated. Three types of dose distributions were delivered to human salivary gland cells (HSGc-C5): uniform dose distribution (UDD), and one-dimensional (1D) grid-like dose distributions (GDD) with 6 mm and 8 mm spacing. These provided high (Peak-to-Valley Dose Ratio, PVDR=4.0) and low (PVDR=1.64) dose differences between peak and valley doses, respectively. Linear-Quadratic (LQ) model parameters for HSGc-C5 were derived from the UDD and cell survival fractions (SF) were simulated for 1D GDD using these values.
Main results
Good agreement was observed between measurements and simulations when accounting for detector volume. However, the TPS results overestimated dose in steep gradient region, likely due to the 2.0 mm calculation grid size. LQ parameters for HSGc-C5 were α = 0.34 and β = 0.057. The 1D GDD with 6 mm spacing showed good agreement between simulations and experiments, but the 8.0 mm spacing resulted in lower experimental cell survival.
Significance
We successfully simulated grid-like dose distributions and conducted SF simulations. The results suggest potential cell-killing effects due to high-dose differences in SFB.

Terahertz‐Wave Polarization Space‐Division Multiplexing Meta‐Devices based on Spin‐Decoupled Phase Control

AbstractThis study presents a generalized design strategy for novel terahertz‐wave polarization space‐division multiplexing meta‐devices, functioning as multi‐polarization generators, modulators, and analyzers. It introduces the spin‐decoupled phase control method by combining gradient phase design with circular polarization multiplexing techniques, enabling exceptional flexibility in controlling the polarization directions and spatial distributions of multiple output beams. The meta‐device M‐4D is significantly demonstrated as proof of concept, which converts an incident linearly polarized wave into four beams with distinct polarization angles. Additionally, the advanced meta‐devices M‐2B and M‐4B are designed to generate two‐vector and four‐vector Bessel beams with tunable spatial polarization distributions. These meta‐devices demonstrate dynamic multi‐polarization beam modulation, validated through simulations and experiments. The proposed method significantly expands the design methodology for multi‐beam polarization control using all‐dielectric metasurfaces and holds promising potential for applications in imaging, sensing, particle manipulation, communication, and information processing. Moreover, it holds potential for adaptation to other spectral ranges.

Modelling temperature distribution in three-side protected steel beams using evolutionary regression and gradient boosting to predict conductive heat flux

Modelling temperature distribution in three-side protected steel beams using evolutionary regression and gradient boosting to predict conductive heat flux

Second-order statistical characteristics of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase in a turbulent atmosphere

Abstract Based on the extended Huygens-Fresnel integral method, we have derived analytical formulae for the cross-spectral density matrix of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase (i.e., partially coherent radially polarized elliptical vortex (PCRPEV) beam) propagating through atmospheric turbulence, and have investigated the evolution laws of statistical characteristics such as the average intensity, degree of coherence (DOC), and degree of polarization (DOP) of the PCRPEV beam in turbulence. The results indicate that atmospheric turbulence causes the average intensity distribution of the PCRPEV beam to split and rotate during propagation, ultimately degenerating into a Gaussian-like distribution. Moreover, the PCRPEV beam with lower ellipticity, larger coherence length, and higher topological charge degenerates into a Gaussian-like beam at a slower rate in turbulence. Additionally, we also find that DOC distribution is related to topological charge, meaning that it can provide a new way to measure topological charge. In addition, we simulate the propagation of the PCRPEV beam through atmospheric turbulence using the complex screen and the multi-phase screens methods to verify the theoretical results. The research indicates that the simulation results are essentially consistent with the theoretical findings. These outcomes hold significant relevance for the advancement of free-space optical communication and remote sensing technologies.

Correction method for ionization chamber dosimetry in flattening filter free radiotherapy based on Monte Carlo simulation.

The clinical use of flattening filter free (FFF) radiotherapy has significantly increased in recent years due to its effective enhancement of dose rates and reduction of scatter dose. A proposal has been made to adjust the incident electron angle of the accelerator to expand the application of FFF beams in areas such as large planning target volumes (PTVs). However, the inherent softening characteristics and non-uniformity of lateral dose distribution in FFF beams inevitably lead to increased dosimetry errors, especially for ionization chambers widely used in clinical practice, which may result in serious accidents during FFF radiotherapy. This study constructs a comprehensive Monte Carlo model that encompasses not only conventional FFF beams but also incorporates FFF beams with varying incident electron angles, to investigate dosimetry errors and correction methods in FFF radiotherapy. We have innovatively introduced a FFF output correction factor ( ) to address dosimetry errors in various ionization chambers under different incident electron angle conditions in FFF beams. The primary variations in were analytically determined to result from changes in and the perturbation correction terms of the ionization chamber. Ionization chambers with smaller sensitive volumes typically exhibit reduced dosimetry errors. Our findings indicate that for ionization chambers with sensitive volumes ranging from 0.016 to 0.125cm3, the dosimetry error under various FFF beam conditions consistently remains below 1.15%. This study provides crucial guidance for selecting appropriate ionization chambers in FFF radiotherapy. A correlation was established between the absorbed dose to water in beams with a flattening filter (WFF) and those without (FFF), defined by the FFF output factor ( ). Using the proposed Monte Carlo model, the can be derived and applied to theoretically calculate the absorbed dose to water in FFF beams at varying incident electron angles, with a relative standard uncertainty of 0.2. This study provides a valuable reference for clinical dose measurements and crucial support for establishing dose calibration standards in FFF radiotherapy.

Preliminary Design and Thermal-Hydraulic Study of a 250-kW LBE Experimental Spallation Target for CiADS

The CiADS (China initiative Accelerator Driven System) project plans to build a 250-kW experimental target before construction of the 2.5-MW spallation target. In this paper, the effect of proton beam distribution on the performance of the 250-kW target is studied. Hence, a hollow beam distribution, formed by a Gaussian beam scanning around the center of the beam window, is proposed. Then, combined with the orthogonal test method and the CRITIC (Criteria Importance through Intercriteria Correlation) method, four key geometric parameters of the target flow channel are analyzed to simultaneously achieve optimization of the target performance from the viewpoints of both the maximum temperature and velocity under steady-state condition. Finally, transient analysis of the initiation of the Gaussian beam scanning is conducted; the calculation time was 15s. The results show that the temperature on the window rose gradually until reaching its maximum value corresponding to the steady-state analysis. Detailed analyses showed that the optimized target design is capable of meeting the thermal-hydraulic and mechanical requirements.

A method to determine the phase-space distribution of a pulsed molecular beam

Abstract We demonstrate a method to determine the longitudinal phase-space distribution of a cryogenic buffer gas cooled beam of barium-fluoride molecules based on a two-step laser excitation scheme. Temporal resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state $X^2\Sigma^+$ to the $A^2\Pi_{1/2}$ state around 860\;nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted $A^2\Pi_{1/2}$ to $D^2\Sigma^+$ transition around 797\;nm. Molecules in the $D$-state are detected background-free by recording the fluorescence from the $D-X$ transition at 413 nm. A temporal resolution of 11\;$\upmu$s and a velocity resolution of 6\;m/s is obtained. In order to calibrate the absolute velocity, we have determined the Doppler free transition frequencies for the $X-A$ and $X-D$ transitions with an absolute accuracy below 0.3\;MHz. The high resolution of the phase-space distributions allows us to observe a variation of the average velocity and velocity spread over the duration of the molecular beam pulse. Our method hence gives valuable insight into the dynamics in the source.

Оценка возможности верификации дозовых распределений протонов методом наведенной позитронной активности в тканях человека

A computational assessment was made of the possibility of verifying dose distributions during proton radiation therapy using PET imaging of positron activity in human tissues, which was formed as a result of proton irradiation. To compare the dose distribution of a particle energy-modulated proton beam with a diameter of 10 mm with an initial particle energy of 100 MeV, ensuring uniform irradiation of the target in a 13 mm zone (at the level of 90 % of the radiation dose) at the end of the particle path, with a map of induced activity from the radionuclides 11C, 13N and 15O, numerical calculations were performed in a Monte–Carlo code using the Geant4 simulation program. In the modeling process, a volume with dimensions of 50 × 50 × 100 mm was used, simulating soft tissues of the human body with a density of 1 g/cm3, consisting of hydrogen atoms (62 %), carbon (12 %), oxygen (24 %) and nitrogen (1.1 %). The cross sections for the formation of radionuclides 11C, 13N and 15O in the reactions 12C(p, pn)11C, 14N(p, α)11C, 16O(p, αpn)11C, 14N(p, pn)13N, 16O(p, α)13N, 16O(p, pn)15O have been calculated, which were used to calculate the distributions of positron activity in the irradiated volume. Taking into account the short half-lives of the radionuclides under consideration (primarily oxygen-15), calculations of isoactivities and depth distributions of accumulated radioactivities were performed for various time intervals after irradiation. The performed computational modeling of the distributions of activities of radionuclides 11C, 13N and 15O during the passage of a modulated proton beam, taking into account the decay of produced radionuclides after irradiation, shows that by recording for 15 minutes the induced activity of PET radionuclides 2 minutes after irradiation, it is possible to obtain data on the compliance of the planned and irradiation of tumors performed during proton therapy. However, small levels of generated activity (at a level of 2 Gy for finely fractionated irradiations) require a device with high efficiency in recording annihilation radiation and high spatial resolution at the level of 1.5–2.0 mm.

Characteristics of cylindrical Hall ion source with floating potential magnetic pole discharge

The discharge characteristics of a cylindrical Hall ion source (CHIS) with floating potential magnetic poles and grounded magnetic poles were investigated through experiments and simulations. The results revealed that the ion density distribution and ion energy were mainly affected by the discharge voltage and magnetic pole potential. The current utilization rate is 82%–93%, which is much more efficient than that of the conventional Hall ion source with grounded magnetic poles. As the gas supply increased, the floating potential of the magnetic pole increased. Under the same discharge current condition, the discharge voltage of a Hall ion source with floating magnetic poles is 300 V larger than that of grounded magnetic poles; meanwhile, this type of ion source has a higher mean ion energy and better uniformity of ion beam distribution. Ion acceleration in the CHIS with floating magnetic poles is expected to occur predominantly in the longitudinal direction and toward the CHIS outlet. The non-uniformity of the ion beam current density within a diameter of 40 mm along the radial directions approximately ±11.7% at a discharge voltage of 800 V, which is helpful for material surface cleaning, etching, sputtering, and ion beam-assisted deposition applications.

Design of cascaded diffractive optical elements generating different intensity distributions at several operating wavelengths

We consider the design of cascaded diffractive optical elements (DOEs) for generating specified intensity distributions for several incident beams with different wavelengths. For each incident beam with a given wavelength, the cascaded DOE forms a different specified intensity distribution. The problem of DOE design is formulated as the problem of minimizing a functional that depends on the functions of diffractive microrelief height of the cascaded DOE and represents the deviations of the intensity distributions generated at the operating wavelengths from the specified ones. Explicit expressions are obtained for the derivatives of the functional, and on this basis, a gradient method for calculating a cascaded DOE is formulated. The proposed gradient method is used for the calculation of cascaded DOEs focusing radiation of three different wavelengths into different areas. In particular, the calculation of a cascaded DOE generating a complex color image of parrots is considered. The presented numerical simulation results demonstrate high performance of the proposed method.

Propagation properties of two types of sinc Schell-model beams in oceanic turbulence

Abstract The evolution of two types of sinc Schell-model (SSM) beams, each considered with both circular and rectangular symmetries, is investigated during their propagation in oceanic turbulence. The expressions for the spectral intensity and spectral coherence of the transmitted optical field are derived using the extended Huygens-Fresnel principle. Based on these expressions, numerical simulations are carried out to explore how source and turbulence parameters influence the transmitted field. The results demonstrate that the spectral intensity distribution of the SSM1 beam evolves from an initial Gaussian profile into a circular or rectangular flat-topped shape during propagation, while the SSM2 beam develops into a ring-shaped or array-like pattern. As the dissipation rate of turbulent kinetic energy decreases, or the mean square temperature dissipation rate and the strength of temperature and salinity fluctuations increase, the energy of these beams disperses from its concentrated regions to the surrounding areas, causing the characteristic intensity distributions to become blurred. Additionally, the coherence of these beams exhibits oscillatory distributions, with the SSM2 beam showing stronger oscillations compared to the SSM1 beam and displaying greater sensitivity to changes in turbulence parameters. The intensity and coherence distributions are also affected by source parameters, which play a dominant role at shorter propagation distances. However, as the distance increases, turbulence parameters gradually become the primary influence. The results presented here may be applied to oceanic optical communication and remote sensing.

Fast and precise dose estimation for very high energy electron radiotherapy with graph neural networks

IntroductionExternal beam radiotherapy (RT) is one of the most common treatments against cancer, with photon-based RT and particle therapy being commonly employed modalities. Very high energy electrons (VHEE) have emerged as promising candidates for novel treatments, particularly in exploiting the FLASH effect, offering potential advantages over traditional modalities.MethodsThis paper introduces a Deep Learning model based on graph convolutional networks to determine dose distributions of therapeutic VHEE beams in patient tissues. The model emulates Monte Carlo (MC) simulated doses within a cylindrical volume around the beam, enabling high spatial resolution dose calculation along the beamline while managing memory constraints.ResultsTrained on diverse beam orientations and energies, the model exhibits strong generalization to unseen configurations, achieving high accuracy metrics, including a δ-index 3% passing rate of 99.8% and average relative error <1% in integrated dose profiles compared to MC simulations.DiscussionNotably, the model offers three to six orders of magnitude increased speed over full MC simulations and fast MC codes, generating dose distributions in milliseconds on a single GPU. This speed could enable direct integration into treatment planning optimization algorithms and leverage the model’s differentiability for exact gradient computation.

Research and application of chromatic effect in laser-driven proton therapy

Based on the rapid development of ultra high-power laser technology and due to the urgent need for miniaturized particle radiotherapy accelerator construction, compact laser accelerators have been studied as a research focus. The collection of the beam with large divergence angle and the selection of beam energy spread from initial generated beam are core issues in the design of laser accelerator. Chromatic effect is an effective method of energy selection while collecting beam. However, it is found that the nonlinear effect introduced by the actual edge field of a strong magnetic field and the special beam distribution produced by laser acceleration directly affect the energy selection. Based on the design of CLAPA-II, we analyze chromatic effect of energy selection by combining the 3-D strong magnetic field of particle collecting solenoid and the initial particle library of laser acceleration generated by PIC. We further propose a more compact laser-driven proton therapy design using the chromatic effect and energy reducer. And we research a broad-spectrum treatment planning system corresponding to it. It can effectively reduce proportion of low energy particles and complete energy selection after considering nonlinear effect of high 3-D magnetic field and special initial distribution. This can be applied in the design of gantry, which can be lighter than the traditional gantry. And for head, neck, and lung tumor models, dose delivery can be completed in 10 min and 20 min.

Influence of the RF-power on the etching yields and surface morphology in reactive ion beam etching of Si and photoresist

The change in ion energy distribution and composition of a reactive ion beam produced by an RF-excited ion beam source and operation with a mixture of CHF3 and O2 was investigated and correlated with the etching behavior. To this end, measurements were performed with an energy-selective mass spectrometer to determine ion energy distributions, current density measurements for the measurement of current density distributions of the ion beam, and tactile measurements to determine the etching rates of Si and photoresist. The morphology of the photoresist was measured with a scanning force microscope. In particular, alterations in the etching yield and surface morphology of the photoresist can be observed in response to changes in the applied RF-power. An increase in plasma density leads to an increase in fragmentation processes of the injected reactive gases, resulting in the formation of smaller fragments. These smaller fragments have a chemical impact on the substrate surface, which affects the etching performance. These effects can have significant consequences in the context of long-time reactive ion beam processing for patterning applications.

Numerical Analysis of Grouting Reinforcement Effects on Deep Foundation Pits Adjacent to Elevated Railways

To mitigate the impact of foundation pit construction on adjacent existing structures, grouting reinforcement techniques are often employed to enhance the deformation strength of the soil. This study focuses on the expansion project of the Dayun Comprehensive Hub in Shenzhen, conducting full-scale numerical simulations of the excavation of deep foundation pits adjacent to existing elevated railways and examining the effects of different grouting reinforcement schemes. The results indicate that the single-row and double-row grouting schemes increased the bearing capacity of the foundation piles by 23.7% and 31.9%, respectively, significantly enhancing the structural bearing performance. After reinforcement, the maximum deformation position of the elevated bridge foundation piles shifted upward, and the settlement distribution of the cap beam became more concentrated, indicating that grouting reinforcement effectively controlled the ground settlement and the deformation of the foundation piles. Furthermore, compared to controlling the deformation of the retaining structures, grouting reinforcement was more effective in controlling ground settlement and pile deformation, highlighting its advantages in complex environments. Although the double-row grouting scheme demonstrated superior technical performance, the single-row scheme remains the preferred option considering reinforcement efficiency and economic factors.

Change in coherence properties of ovally Gaussian Schell-model vortex beam in non-Kolmogorov turbulence along an uplink path

Analytical expressions are obtained for the cross-spectral density (CSD) matrix elements of an ovally Gaussian Schell-model vortex (OGSMV) beam propagating in non-Kolmogorov turbulence along uplink path based on the extended Huygens-Fresnel principle, and its coherence properties such as spectral degree of coherence (SDOC), phase distributions and coherence vortices are investigated in detail. Results indicate that the profile of the SDOC of OGSMV beam in turbulence gradually degrades into a Gaussian-like profile, and OGSMV beam with smaller ovality, larger topological charge number and initial coherence lengths will slow down this process. Interestingly, it is clearer to observe the coherence rings of the SDOC for OGSMV beam by reducing the initial auto-correlation lengths. Furthermore, one also finds that the number of elliptical edge dislocation for phase distribution of OGSMV beam is equal to topological charge number. They can provide two effectively ways for measuring topological charge number. Lastly, we used the phase screen simulation to verify our theoretical predictions. Theoretical outcomes are in good agreement with the simulations. Our results will be of important reference for optical communication.

Generation of the flat-top beam using convolutional neural networks and Gerchberg-Saxton algorithm

Abstract Laser technology has made rapid progress in recent years and has been widely used in various fields such as medicine, biology, military, and materials science. However, the limitations of traditional Gaussian intensity distribution of the laser beams in applications have prompted the emergence and development of flat-top beam shaping technology, which has received widespread attention. Here, we introduce a new method for generating flat-top beams that combines the traditional Gerchberg-Saxton algorithm with convolutional neural networks, using spatial light modulators to achieve flat-top beam shaping. A comparative analysis was conducted by comparing the root mean square error and diffraction efficiency of the generated flat-top beam with the results obtained using only the traditional Gerchberg-Saxton algorithm. Compared with the traditional Gerchberg-Saxton algorithm, the method proposed in this paper can generate a flat-top beam with smaller differences from the target light intensity and higher energy utilization, providing new possibilities for the application of laser technology.

Energy characteristics of the gridless ion sources beams

One of the most commonly used tools in ion-plasma technology is the End Hall ion source, which is used, in particular, for etching and other processes. The ability to operate on almost any gas, a highly divergent beam and the generated ions energy range up to several hundred electronvolts determine the wide possibilities of using End Hall ion sources in science and production. There are two main design schemes of such sources which are most actively used – with a floating and with an anode potential of the discharge chamber rear wall. The ion beam energy characteristics of the sources with a floating potential of the rear wall have been extensively studied by various research teams, but there is currently no comparable data available for sources with an anode potential, making it difficult to develop processes based on these ion sources. This study aims to investigate the energy characteristics of ions emitted from End Hall sources following these two design approaches. The ion beams were examined via a retarding potential analyzer. Measurements were conducted on argon at various discharge voltage and current settings for each source. One design included a floating potential of the discharge chamber rear wall, whereas the other design had an anode potential. The geometrical dimensions of the discharge chambers and the magnetic field intensities were identical for both configurations tested. Based on the ion beam retarding curves, corresponding ion energy distributions were determined. It was observed that for End Hall source with an anode potential of the discharge chamber rear wall an approximately continuous spectrum of ion energies was typical, whereas there was a clearly expressed peak in the energy distribution of the traditional configuration ion source beam. The mean ion energy in beam of the source with an anode potential of the discharge chamber rear wall was lower than that of the source with a floating potential, as confirmed by lower etch rates observed during control sputtering of stainless steel samples. These results can be used to develop technological procedures utilizing End Hall ion sources designed according to different configurations.

Propagation characteristics of a circular Airyprime Gaussian beam in a gradient refractive index medium

In this paper, the focusing characteristics of a circular Airyprime Gaussian beam (CAPGB) propagating in a gradient refractive index (GRIN) medium is studied for the first time, to the best of our knowledge, and some interesting features are observed. We find that the CAPGB exhibits periodic focus–defocus behavior and completes a period propagation process with two focal points within a half variation period L/2 of the GRIN medium. Meanwhile, the CAPGB has singularity at the positions of z=(2j+1)L/4 on the optical axis. The focal lengths of bifocal points, the distance between two focal points, the focal intensity, and the focusing ability can be manipulated by beam parameters and the GRIN factor. It is noteworthy that the number (one or two) of focal points in one focusing period, and the focusing period or frequency of the CAPGB in the GRIN medium could be controlled by the beam distribution factor and GRIN factor, respectively. Moreover, the focusing ability of the CAPGB is much higher than that of a circular Airy Gaussian beam in the GRIN medium.